{ "cells": [ { "cell_type": "markdown", "id": "624aa68f", "metadata": {}, "source": [ "Tutorial: geometrically non-linear benchmarks with pyfe3d.solver\n", "===\n", "\n", "Two benchmarks of Sze, K. Y., Liu, X. H. and Lo, S. H., Popular benchmark\n", "problems for geometric nonlinear analysis of shells, *Finite Elements in\n", "Analysis and Design*, 40(11), 1551-1569, 2004,\n", "[doi:10.1016/j.finel.2003.11.001](https://doi.org/10.1016/j.finel.2003.11.001),\n", "solved with the non-linear static analyses of `pyfe3d.solver.Analysis`:\n", "\n", "- cantilever under an end moment (Section 3.2, Fig. 3, Table 3), with the\n", " Newton-Raphson method;\n", "- hinged cylindrical roof under a central point load (Section 3.8, Fig. 9,\n", " Tables 9a and 9d), whose snap-through, and snap-back for the thinner roof,\n", " are traced with the arc-length methods.\n", "\n", "Sze et al. (2004) computed their reference values with ABAQUS's S4R element,\n", "a finite-strain shell element with an updated Lagrangian formulation (their\n", "Table 1). The elements of pyfe3d use the von Karman strains, valid for small\n", "strains and moderate rotations, in a total Lagrangian formulation whose\n", "element coordinate systems are not updated. The convergence of every\n", "increment is checked with Crisfield's criterion, the default of `Analysis`\n", "(`convergence='crisfield'`, `relTOL=1e-9`).\n", "\n", "The models are those of `tests/test_nonlinear_benchmarks_sze2004.py`, whose\n", "`Model` class, from `tests/test_solver_nonlinear_static.py`, provides the\n", "callables `calc_fext`, `calc_fint`, `calc_kC` and `calc_kG` of `Analysis` for\n", "a list of pyfe3d elements. A further section measures the sensitivity of\n", "the roof to the transverse hourglass stiffness of `Quad4R`, and a last one\n", "traces the snap-through of Williams' toggle frame with `BeamC` elements. The\n", "cells below run in about five minutes." ] }, { "cell_type": "code", "execution_count": 1, "id": "f0ac9864", "metadata": { "execution": { "iopub.execute_input": "2026-10-25T10:35:29.539923Z", "iopub.status.busy": "2026-10-25T10:35:29.539820Z", "iopub.status.idle": "2026-10-25T10:35:30.135071Z", "shell.execute_reply": "2026-10-25T10:35:30.134264Z" } }, "outputs": [], "source": [ "import os\n", "import sys\n", "sys.path.insert(0, os.path.join('..', '..', 'tests'))\n", "\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "from test_nonlinear_benchmarks_sze2004 import (\n", " CANTILEVER, TABLE_3A_EXACT, TABLE_9A, TABLE_9D, ROOF, elastica_tip,\n", " von_karman_tip, cantilever_end_moment, run_cantilever_end_moment,\n", " hinged_roof, run_hinged_roof, compare_with_table_9a, limit_points,\n", " linear_roof_WC, ritz_roof_WC)" ] }, { "cell_type": "markdown", "id": "d592ac7b", "metadata": {}, "source": [ "Cantilever under an end moment\n", "---\n", "\n", "Fig. 3a of Sze et al. (2004): $L = 12$, width $b = 1$, thickness $h = 0.1$,\n", "$E = 1.2 \\times 10^6$, $\\nu = 0$, $M_o = E I/L = 25/3$ and\n", "$M_{max} = 2 \\pi M_o$. Under the end moment $M$ the cantilever bends into a\n", "circular arc of radius $E I/M$ and the exact tip deflections are\n", "\n", "$$\n", "\\frac{U}{L} = \\frac{M_o}{M} \\sin\\frac{M}{M_o} - 1, \\qquad\n", "\\frac{W}{L} = \\frac{M_o}{M} \\left(1 - \\cos\\frac{M}{M_o}\\right)\n", "$$\n", "\n", "such that at $M_{max}$ the cantilever is a full circle and the tip is back at\n", "the root. The text of Section 3.2 gives $M_{max} = \\pi M_o$; Fig. 3a and the\n", "exact values of Table 3a, e.g. $-U = 12$, $W = 0$ at $M/M_{max} = 1$,\n", "correspond to $M_{max} = 2 \\pi M_o$, used here.\n", "\n", "With the von Karman axial strain $\\epsilon_{xx} = u_{,x} + w_{,x}^2/2$ the\n", "free end gives a null axial force, the bending equation is that of the linear\n", "theory and\n", "\n", "$$\n", "\\frac{W}{L} = \\frac{\\varphi}{2}, \\qquad \\frac{U}{L} = -\\frac{\\varphi^2}{6},\n", "\\qquad \\varphi = \\frac{M L}{E I}\n", "$$\n", "\n", "the first terms of the expansion of the exact solution in the tip rotation\n", "$\\varphi$. The von Karman cantilever never rolls up into a circle.\n", "\n", "The cantilever is modelled with a strip of $16 \\times 1$ `Quad4R` elements,\n", "as the $16 \\times 1$ S4R mesh of Table 3a, and loaded in 20 equal increments\n", "of the Newton-Raphson method, `initialInc = maxInc = 0.05`." ] }, { "cell_type": "code", "execution_count": 2, "id": "bf9bda86", "metadata": { "execution": { "iopub.execute_input": "2026-10-25T10:35:30.137536Z", "iopub.status.busy": "2026-10-25T10:35:30.137325Z", "iopub.status.idle": "2026-10-25T10:35:30.201208Z", "shell.execute_reply": "2026-10-25T10:35:30.200636Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Newton-Raphson, 16x1 Quad4R: 20 increments\n", "\n", " | -U_tip | W_tip \n", " M/Mmax | Table 3a v. Karm. Quad4R | Table 3a v. Karm. Quad4R\n", " 0.05 | 0.196 0.197 0.197 | 1.870 1.885 1.885\n", " 0.10 | 0.774 0.790 0.789 | 3.648 3.770 3.770\n", " 0.15 | 1.699 1.777 1.775 | 5.248 5.655 5.655\n", " 0.20 | 2.918 3.158 3.155 | 6.598 7.540 7.540\n", " 0.25 | 4.361 4.935 4.930 | 7.639 9.425 9.425\n", " 0.30 | 5.945 7.106 7.099 | 8.333 11.310 11.310\n", " 0.35 | 7.585 9.672 9.663 | 8.664 13.195 13.195\n", " 0.40 | 9.194 12.633 12.621 | 8.637 15.080 15.080\n", " 0.45 | 10.688 15.989 15.973 | 8.281 16.965 16.965\n", " 0.50 | 12.000 19.739 19.720 | 7.639 18.850 18.850\n", " 0.55 | 13.073 23.884 23.861 | 6.775 20.735 20.735\n", " 0.60 | 13.871 28.424 28.397 | 5.758 22.619 22.619\n", " 0.65 | 14.377 33.359 33.327 | 4.665 24.504 24.504\n", " 0.70 | 14.595 38.689 38.651 | 3.571 26.389 26.389\n", " 0.75 | 14.546 44.413 44.370 | 2.546 28.274 28.274\n", " 0.80 | 14.270 50.532 50.483 | 1.650 30.159 30.159\n", " 0.85 | 13.818 57.046 56.991 | 0.926 32.044 32.044\n", " 0.90 | 13.247 63.955 63.893 | 0.405 33.929 33.929\n", " 0.95 | 12.621 71.259 71.189 | 0.098 35.814 35.814\n", " 1.00 | 12.000 78.957 78.880 | 0.000 37.699 37.699\n", "\n", "check: Quad4R against the von Karman solution, max relative difference W 1.1e-10, U 9.8e-04\n", "check: Quad4R against Table 3a (exact) at M/Mmax = 0.05: W +0.80 %, -U +0.61 %\n" ] } ], "source": [ "L = CANTILEVER['L']\n", "m, U, W = run_cantilever_end_moment('Quad4R', 16, inc=0.05)\n", "U_vk, W_vk = von_karman_tip(m)\n", "print('Newton-Raphson, 16x1 Quad4R: %d increments' % len(m))\n", "print()\n", "print('%7s | %8s %8s %8s | %8s %8s %8s'\n", " % ('', '-U_tip', '', '', 'W_tip', '', ''))\n", "print('%7s | %8s %8s %8s | %8s %8s %8s'\n", " % ('M/Mmax', 'Table 3a', 'v. Karm.', 'Quad4R', 'Table 3a', 'v. Karm.',\n", " 'Quad4R'))\n", "for (mr, Ur, Wr), mi, Ui, Wi, Uv, Wv in zip(TABLE_3A_EXACT, m, U, W, U_vk,\n", " W_vk):\n", " assert np.isclose(mr, mi)\n", " print('%7.2f | %8.3f %8.3f %8.3f | %8.3f %8.3f %8.3f'\n", " % (mr, Ur, L*Uv, L*Ui, Wr, L*Wv, L*Wi))\n", "print()\n", "print('check: Quad4R against the von Karman solution, max relative '\n", " 'difference W %.1e, U %.1e' % (np.abs(W/W_vk - 1).max(),\n", " np.abs(U/U_vk - 1).max()))\n", "print('check: Quad4R against Table 3a (exact) at M/Mmax = 0.05: '\n", " 'W %+.2f %%, -U %+.2f %%'\n", " % (100*(L*W[0]/TABLE_3A_EXACT[0, 2] - 1),\n", " 100*(L*U[0]/TABLE_3A_EXACT[0, 1] - 1)))" ] }, { "cell_type": "markdown", "id": "ff927691", "metadata": {}, "source": [ "The `Quad4R` strip reproduces the von Karman solution: the deflection exactly,\n", "the axial displacement within 0.1 %, converging with the mesh. It agrees with\n", "the exact values of Table 3a only for small tip rotations, within 1 % at\n", "$M = 0.05 M_{max}$ (tip rotation of 0.31 rad), and departs from them beyond.\n", "The same analysis with 16 `BeamC` elements is plotted below." ] }, { "cell_type": "code", "execution_count": 3, "id": "3a6cf2c7", "metadata": { "execution": { "iopub.execute_input": "2026-10-25T10:35:30.203439Z", "iopub.status.busy": "2026-10-25T10:35:30.203248Z", "iopub.status.idle": "2026-10-25T10:35:30.525930Z", "shell.execute_reply": "2026-10-25T10:35:30.525314Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "mb, Ub, Wb = run_cantilever_end_moment('BeamC', 16, inc=0.05)\n", "mm = np.linspace(0, 1, 201)\n", "Ue, We = elastica_tip(mm)\n", "Uv, Wv = von_karman_tip(mm)\n", "fig, axes = plt.subplots(1, 2, figsize=(10, 4), sharey=True)\n", "for ax, label, exact, vk, quad, beam, table in [\n", " (axes[0], '-U/L', Ue, Uv, U, Ub, TABLE_3A_EXACT[:, 1]/L),\n", " (axes[1], 'W/L', We, Wv, W, Wb, TABLE_3A_EXACT[:, 2]/L)]:\n", " ax.plot(exact, mm, 'k-', lw=1.5, label='exact')\n", " ax.plot(table, TABLE_3A_EXACT[:, 0], 'ko', mfc='none',\n", " label='Table 3a, Sze et al. (2004)')\n", " ax.plot(vk, mm, 'C0--', lw=1.5, label='von Karman')\n", " ax.plot(quad, m, 'C0s', ms=5, label='16x1 Quad4R')\n", " ax.plot(beam, mb, 'C1^-', ms=5, label='16 BeamC')\n", " ax.set_xlabel(label)\n", " ax.set_xlim(0, 1.6)\n", " ax.grid(True, alpha=0.3)\n", "axes[0].set_ylabel('M/Mmax')\n", "axes[1].legend(loc='upper right', fontsize=8)\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "9a55d0c2", "metadata": {}, "source": [ "The deformed cantilever at $M = 0.1 M_{max}$, $0.2 M_{max}$ and\n", "$0.35 M_{max}$, the last one the first configuration of Fig. 3c of Sze et al.\n", "(2004): the exact circular arcs and the edge $y = 0$ of the `Quad4R` strip,\n", "both without amplification." ] }, { "cell_type": "code", "execution_count": 4, "id": "089674a2", "metadata": { "execution": { "iopub.execute_input": "2026-10-25T10:35:30.528222Z", "iopub.status.busy": "2026-10-25T10:35:30.527923Z", "iopub.status.idle": "2026-10-25T10:35:30.677319Z", "shell.execute_reply": "2026-10-25T10:35:30.676767Z" } }, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "model, bu, tip_deflections, Mmax = cantilever_end_moment('Quad4R', 16)\n", "an = model.analysis(bu, NL_method='NR', initialInc=0.05, maxInc=0.05)\n", "increments, cs = an.static(NLgeom=True, silent=True)\n", "x = model.x.reshape(-1, 3)\n", "edge = np.isclose(x[:, 1], 0.)\n", "s = np.linspace(0, L, 200)\n", "fig, ax = plt.subplots(figsize=(8, 5))\n", "for k, (frac, color) in enumerate([(0.1, 'C0'), (0.2, 'C1'), (0.35, 'C2')]):\n", " i = int(np.argmin(np.abs(np.array(increments) - frac)))\n", " u = cs[i].reshape(-1, 6)\n", " radius = L/(2*np.pi*frac)\n", " ax.plot(radius*np.sin(s/radius), radius*(1 - np.cos(s/radius)), '-',\n", " color=color, lw=1.5, label='exact, M = %.2f Mmax' % frac)\n", " ax.plot(x[edge, 0] + u[edge, 0], x[edge, 2] + u[edge, 2], 'o--',\n", " color=color, ms=4, label='16x1 Quad4R, M = %.2f Mmax' % frac)\n", "ax.plot([0, L], [0, 0], 'k:', lw=1, label='undeformed')\n", "ax.set_aspect('equal')\n", "ax.set_xlabel('X')\n", "ax.set_ylabel('Z')\n", "ax.grid(True, alpha=0.3)\n", "ax.legend(fontsize=8, loc='center left', bbox_to_anchor=(1.02, 0.5))\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "90ed4ce3", "metadata": {}, "source": [ "The beam elements `BeamC` and `BeamLR` interpolate the axial displacement\n", "linearly and integrate the von Karman axial strain with Gauss points along\n", "the element, where $w_{,x}^2$ is not constant: the axial strain cannot vanish\n", "in the element and the cantilever is too stiff (membrane locking). The\n", "stiffening grows with the moment and decreases with the number of elements;\n", "at $M = 0.05 M_{max}$:" ] }, { "cell_type": "code", "execution_count": 5, "id": "c708dfca", "metadata": { "execution": { "iopub.execute_input": "2026-10-25T10:35:30.679927Z", "iopub.status.busy": "2026-10-25T10:35:30.679736Z", "iopub.status.idle": "2026-10-25T10:35:30.969776Z", "shell.execute_reply": "2026-10-25T10:35:30.969041Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "element elements W_tip von Karman error %\n", "BeamC 16 1.0636 1.8850 -43.57\n", "BeamC 64 1.6477 1.8850 -12.59\n", "BeamC 256 1.8621 1.8850 -1.21\n", "BeamLR 16 1.0637 1.8850 -43.57\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "BeamLR 64 1.6477 1.8850 -12.59\n", "BeamLR 256 1.8621 1.8850 -1.21\n", "Table 3a (exact) at M/Mmax = 0.05: W_tip 1.870\n" ] } ], "source": [ "print('%-7s %9s %10s %12s %10s' % ('element', 'elements', 'W_tip',\n", " 'von Karman', 'error %'))\n", "for name in ['BeamC', 'BeamLR']:\n", " for n in [16, 64, 256]:\n", " mi, Ui, Wi = run_cantilever_end_moment(name, n, inc=0.25, m_max=0.05)\n", " Wv = von_karman_tip(mi[-1])[1]\n", " print('%-7s %9d %10.4f %12.4f %10.2f'\n", " % (name, n, L*Wi[-1], L*Wv, 100*(Wi[-1]/Wv - 1)))\n", "print('Table 3a (exact) at M/Mmax = 0.05: W_tip %.3f' % TABLE_3A_EXACT[0, 2])" ] }, { "cell_type": "markdown", "id": "9a738562", "metadata": {}, "source": [ "Hinged cylindrical roof, 12.7 thick\n", "---\n", "\n", "Fig. 9a of Sze et al. (2004): cylindrical roof of radius $R = 2540$, length\n", "$2L$ with $L = 254$ along the axis, opening $2\\theta$ with\n", "$\\theta = 0.1$ rad, thickness $h = 12.7$, $E = 3102.75$, $\\nu = 0.3$,\n", "central point load $P$ with $P_{max} = 3000$. The straight edges are hinged,\n", "with all the translations restrained, the curved edges are free. One quarter\n", "is modelled, with symmetry conditions on the planes through the centre C, as\n", "in Sze et al. (2004), who used $16 \\times 16$ S4R elements and Riks' method\n", "(Table 9a).\n", "\n", "Here one quarter is meshed with $16 \\times 16$ flat `Quad4R` elements and the\n", "path is traced with Crisfield's arc-length method up to $1.2 P_{max}$, with\n", "the arc-length increment of `initialInc = maxInc = 0.05`. The load factor\n", "decreases past the limit points, where the tangent stiffness matrix is\n", "singular, which the Newton-Raphson method cannot pass." ] }, { "cell_type": "code", "execution_count": 6, "id": "62e4018b", "metadata": { "execution": { "iopub.execute_input": "2026-10-25T10:35:30.971942Z", "iopub.status.busy": "2026-10-25T10:35:30.971751Z", "iopub.status.idle": "2026-10-25T10:35:59.730646Z", "shell.execute_reply": "2026-10-25T10:35:59.729952Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Crisfield's arc-length method: 84 increments, P/Pmax 1.200 at -W_C 29.800\n", "Riks' arc-length method: 84 increments, P/Pmax 1.200 at -W_C 29.800\n", "Newton-Raphson: 20 increments, stops at P/Pmax 0.7459, -W_C 10.033\n", "\n", " -W_C Table 9a pyfe3d diff diff %\n", " 0.693 0.0877 0.0941 +0.0064 +7.33\n", " 1.638 0.1980 0.2126 +0.0146 +7.39\n", " 3.087 0.3473 0.3718 +0.0245 +7.06\n", " 4.477 0.4686 0.4991 +0.0305 +6.50\n", " 5.802 0.5647 0.5971 +0.0324 +5.74\n", " 7.057 0.6381 0.6686 +0.0305 +4.78\n", " 8.237 0.6908 0.7158 +0.0250 +3.62\n", " 9.339 0.7246 0.7407 +0.0161 +2.22\n", " 10.358 0.7412 0.7449 +0.0037 +0.50\n", " 11.293 0.7421 0.7315 -0.0106 -1.43\n", " 12.141 0.7286 0.7027 -0.0259 -3.56\n", " 12.903 0.7023 0.6618 -0.0405 -5.76\n", " 13.583 0.6649 0.6132 -0.0517 -7.78\n", " 14.188 0.6182 0.5600 -0.0582 -9.42\n", " 14.728 0.5643 0.5064 -0.0579 -10.27\n", " 15.217 0.5055 0.4545 -0.0510 -10.10\n", " 15.676 0.4442 0.4050 -0.0392 -8.83\n", " 16.125 0.3830 0.3580 -0.0250 -6.53\n", " 16.590 0.3245 0.3129 -0.0116 -3.56\n", " 17.094 0.2717 0.2701 -0.0016 -0.60\n", " 17.657 0.2272 0.2313 +0.0041 +1.78\n", " 18.299 0.1940 0.1991 +0.0051 +2.63\n", " 19.028 0.1750 0.1776 +0.0026 +1.50\n", " 19.852 0.1729 0.1719 -0.0010 -0.56\n", " 20.771 0.1905 0.1857 -0.0048 -2.51\n", " 21.780 0.2303 0.2235 -0.0068 -2.95\n", " 22.875 0.2950 0.2879 -0.0071 -2.41\n", " 24.049 0.3871 0.3827 -0.0044 -1.13\n", " 24.663 0.4443 0.4426 -0.0017 -0.39\n", " 25.293 0.5093 0.5105 +0.0012 +0.24\n", " 25.940 0.5826 0.5879 +0.0053 +0.92\n", " 26.601 0.6644 0.6741 +0.0097 +1.46\n", " 27.276 0.7551 0.7704 +0.0153 +2.03\n", " 27.964 0.8549 0.8766 +0.0217 +2.54\n", " 28.663 0.9643 0.9928 +0.0285 +2.96\n", " 29.374 1.0835 1.1199 +0.0364 +3.36\n", "\n", " Table 9a pyfe3d\n", "upper limit point 0.7421 at 11.29 0.7459 at 10.16 +0.51 %\n", "lower limit point 0.1729 at 19.85 0.1713 at 19.74 -0.92 %\n", "\n", "check: Riks' and Crisfield's methods, max difference of P/Pmax at the deflections of Table 9a 1.3e-09\n" ] } ], "source": [ "P16, W16 = run_hinged_roof(n=16, NL_method='arc_length_crisfield')\n", "P_riks, W_riks = run_hinged_roof(n=16, NL_method='arc_length_riks')\n", "P_nr, W_nr = run_hinged_roof(n=16, NL_method='NR', load_factor=1.)\n", "print(\"Crisfield's arc-length method: %d increments, P/Pmax %.3f at -W_C %.3f\"\n", " % (len(P16) - 1, P16[-1], W16[-1]))\n", "print(\"Riks' arc-length method: %d increments, P/Pmax %.3f at -W_C %.3f\"\n", " % (len(P_riks) - 1, P_riks[-1], W_riks[-1]))\n", "print('Newton-Raphson: %d increments, stops at P/Pmax %.4f, -W_C %.3f'\n", " % (len(P_nr) - 1, P_nr[-1], W_nr[-1]))\n", "\n", "P_calc = compare_with_table_9a(P16, W16)\n", "P_riks_calc = compare_with_table_9a(P_riks, W_riks)\n", "print()\n", "print('%8s %10s %10s %10s %10s' % ('-W_C', 'Table 9a', 'pyfe3d', 'diff',\n", " 'diff %'))\n", "for (Pr, Wr), Pc in zip(TABLE_9A, P_calc):\n", " print('%8.3f %10.4f %10.4f %+10.4f %+10.2f'\n", " % (Wr, Pr, Pc, Pc - Pr, 100*(Pc - Pr)/Pr))\n", "print()\n", "(Pa, Wa), (Pb, Wb) = limit_points(P16, W16, 15.)\n", "(Pa_r, Wa_r), (Pb_r, Wb_r) = limit_points(TABLE_9A[:, 0], TABLE_9A[:, 1], 15.)\n", "print('%-18s %16s %16s' % ('', 'Table 9a', 'pyfe3d'))\n", "print('%-18s %7.4f at %5.2f %7.4f at %5.2f %+6.2f %%'\n", " % ('upper limit point', Pa_r, Wa_r, Pa, Wa, 100*(Pa/Pa_r - 1)))\n", "print('%-18s %7.4f at %5.2f %7.4f at %5.2f %+6.2f %%'\n", " % ('lower limit point', Pb_r, Wb_r, Pb, Wb, 100*(Pb/Pb_r - 1)))\n", "print()\n", "print(\"check: Riks' and Crisfield's methods, max difference of P/Pmax at the \"\n", " \"deflections of Table 9a %.1e\" % np.abs(P_riks_calc - P_calc).max())" ] }, { "cell_type": "markdown", "id": "d4b684dd", "metadata": {}, "source": [ "The pyfe3d values are interpolated linearly along the computed path at the\n", "deflections of Table 9a, and the limit points of Table 9a are its largest and\n", "smallest tabulated loads (the table samples the path, the limit points may\n", "lie between its points). Both arc-length methods trace the same path, and\n", "the Newton-Raphson method stops at the upper limit point.\n", "\n", "The limit loads agree within about 1 % with Table 9a. Along the path the\n", "differences are larger: pyfe3d is about 7 % stiffer at the start of the path\n", "and the descending branch lies below the reference values by up to about\n", "0.06 $P_{max}$. Most of the stiffening at the start of the path comes from\n", "the transverse hourglass stiffness of `Quad4R`, see the\n", "[last section](#Sensitivity-to-the-transverse-hourglass-stiffness-of-Quad4R).\n", "The mesh convergence of the pyfe3d path is shown below, comparing\n", "$8 \\times 8$, $16 \\times 16$ and $32 \\times 32$ meshes, the last one with a\n", "larger arc-length increment." ] }, { "cell_type": "code", "execution_count": 7, "id": "37d61b41", "metadata": { "execution": { "iopub.execute_input": "2026-10-25T10:35:59.732607Z", "iopub.status.busy": "2026-10-25T10:35:59.732465Z", "iopub.status.idle": "2026-10-25T10:36:32.131117Z", "shell.execute_reply": "2026-10-25T10:36:32.130411Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " 8x8 Quad4R: limit loads 0.7467, 0.1753; P/Pmax at -W_C = 0.693: 0.0957 (Table 9a 0.0877)\n", "16x16 Quad4R: limit loads 0.7459, 0.1713; P/Pmax at -W_C = 0.693: 0.0941 (Table 9a 0.0877)\n", "32x32 Quad4R: limit loads 0.7446, 0.1704; P/Pmax at -W_C = 0.693: 0.0931 (Table 9a 0.0877)\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "P8, W8 = run_hinged_roof(n=8)\n", "P32, W32 = run_hinged_roof(n=32, initialInc=0.1, maxInc=0.1)\n", "for n, (P, W) in [(8, (P8, W8)), (16, (P16, W16)), (32, (P32, W32))]:\n", " (Pa, Wa), (Pb, Wb) = limit_points(P, W, 15.)\n", " Pc = compare_with_table_9a(P, W)\n", " print('%2dx%-2d Quad4R: limit loads %.4f, %.4f; P/Pmax at -W_C = %.3f: '\n", " '%.4f (Table 9a %.4f)' % (n, n, Pa, Pb, TABLE_9A[0, 1], Pc[0],\n", " TABLE_9A[0, 0]))\n", "\n", "fig, ax = plt.subplots(figsize=(7, 5))\n", "ax.plot(W8, P8, 'C1:', lw=1.5, label='8x8 Quad4R, Crisfield')\n", "ax.plot(W16, P16, 'C0-', lw=1.5, label='16x16 Quad4R, Crisfield')\n", "ax.plot(W32, P32, 'C2--', lw=1.5, label='32x32 Quad4R, Crisfield')\n", "ax.plot(W_riks, P_riks, 'C0x', ms=5, label='16x16 Quad4R, Riks')\n", "ax.plot(W_nr, P_nr, 'C3s', ms=5, mfc='none', label='16x16 Quad4R, Newton-Raphson')\n", "ax.plot(TABLE_9A[:, 1], TABLE_9A[:, 0], 'ko', mfc='none',\n", " label='Table 9a, Sze et al. (2004)')\n", "ax.set_xlabel('-W_C')\n", "ax.set_ylabel('P/Pmax')\n", "ax.set_xlim(0, 31)\n", "ax.grid(True, alpha=0.3)\n", "ax.legend(fontsize=8, loc='upper left')\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "daed24c8", "metadata": {}, "source": [ "Hinged cylindrical roof, 6.35 thick\n", "---\n", "\n", "The same roof with half the thickness, $h = 6.35$, Table 9d of Sze et al.\n", "(2004), computed with $24 \\times 24$ S4R elements on one quarter. Past the\n", "upper limit point the load becomes negative and the path turns back in the\n", "deflection (snap-back) twice before stiffening. One quarter with\n", "$24 \\times 24$ `Quad4R` elements, Crisfield's arc-length method up to\n", "$1.1 P_{max}$ with `initialInc = maxInc = 0.02`." ] }, { "cell_type": "code", "execution_count": 8, "id": "c6d401c4", "metadata": { "execution": { "iopub.execute_input": "2026-10-25T10:36:32.133292Z", "iopub.status.busy": "2026-10-25T10:36:32.133065Z", "iopub.status.idle": "2026-10-25T10:37:27.305531Z", "shell.execute_reply": "2026-10-25T10:37:27.304927Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Crisfield's arc-length method: 117 increments, P/Pmax 1.100 at -W_C 38.648\n", "turning points of -W_C (snap-back): P/Pmax -0.0139 at -W_C 17.186, P/Pmax -0.1336 at -W_C 14.850\n", "\n", " Table 9d pyfe3d\n", "upper limit point 0.1953 at 12.89 0.1944 at 12.02 -0.47 %\n", "lower limit point -0.1288 at 15.78 -0.1436 at 16.24 +11.53 %\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "P, W = run_hinged_roof(n=24, h=6.35, load_factor=1.1, initialInc=0.02,\n", " maxInc=0.02)\n", "print(\"Crisfield's arc-length method: %d increments, P/Pmax %.3f at -W_C %.3f\"\n", " % (len(P) - 1, P[-1], W[-1]))\n", "dW = np.diff(W)\n", "turns = np.flatnonzero(np.sign(dW[1:]) != np.sign(dW[:-1])) + 1\n", "print('turning points of -W_C (snap-back): %s' % ', '.join(\n", " 'P/Pmax %.4f at -W_C %.3f' % (P[i], W[i]) for i in turns))\n", "(Pa, Wa), _ = limit_points(P, W, 13.5)\n", "(Pa_r, Wa_r), _ = limit_points(TABLE_9D[:, 0], TABLE_9D[:, 1], 13.5)\n", "i_min, i_min_r = np.argmin(P), np.argmin(TABLE_9D[:, 0])\n", "print()\n", "print('%-18s %16s %16s' % ('', 'Table 9d', 'pyfe3d'))\n", "print('%-18s %7.4f at %5.2f %7.4f at %5.2f %+6.2f %%'\n", " % ('upper limit point', Pa_r, Wa_r, Pa, Wa, 100*(Pa/Pa_r - 1)))\n", "print('%-18s %7.4f at %5.2f %7.4f at %5.2f %+6.2f %%'\n", " % ('lower limit point', TABLE_9D[i_min_r, 0], TABLE_9D[i_min_r, 1],\n", " P[i_min], W[i_min], 100*(P[i_min]/TABLE_9D[i_min_r, 0] - 1)))\n", "\n", "fig, ax = plt.subplots(figsize=(7, 5))\n", "ax.plot(W, P, 'C0-', lw=1.5, label='24x24 Quad4R, Crisfield')\n", "ax.plot(TABLE_9D[:, 1], TABLE_9D[:, 0], 'ko', mfc='none',\n", " label='Table 9d, Sze et al. (2004)')\n", "ax.axhline(0, color='k', lw=0.5)\n", "ax.set_xlabel('-W_C')\n", "ax.set_ylabel('P/Pmax')\n", "ax.grid(True, alpha=0.3)\n", "ax.legend(fontsize=8, loc='upper left')\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "4b281752", "metadata": {}, "source": [ "The upper limit load agrees with the largest load of Table 9d within 0.5 %;\n", "the lower limit load of pyfe3d, negative, is lower than the smallest load of\n", "Table 9d, by about 0.015 $P_{max}$." ] }, { "cell_type": "markdown", "id": "f7a96dee", "metadata": {}, "source": [ "Sensitivity to the transverse hourglass stiffness of Quad4R\n", "---\n", "\n", "`Quad4R` integrates its stiffness with one point at the centroid and\n", "controls the hourglass modes with the artificial stiffnesses of Brockman,\n", "R. A., Dynamics of the bilinear Mindlin plate element, *International\n", "Journal for Numerical Methods in Engineering*, 24(12), 2343-2356, 1987,\n", "[doi:10.1002/nme.1620241208](https://doi.org/10.1002/nme.1620241208), see\n", "the Notes of `pyfe3d.quad4r`. The transverse one keeps Brockman's factor\n", "$1/(1 + 1/A)$, $A$ being the element area,\n", "\n", "$$\n", "E^{(h)}_w = \\frac{0.05 \\, f_w (E_{1eq} + E_{2eq}) h^3}{1 + 1/A}\n", "= \\frac{0.1 \\, f_w E h^3}{1 + 1/A} \\quad \\text{(isotropic)}\n", "$$\n", "\n", "with $f_w$ = `hgfactor_w`, `1` by default. The elements of the quarter of the\n", "roof have areas from 16 ($64 \\times 64$) to 1008 ($8 \\times 8$) in the unit\n", "of length of the model, so that the default $E^{(h)}_w$ is 0.94 to 1.0 times\n", "$0.1 E h^3$. The hourglass operator cannot distinguish the spurious pattern\n", "$w = x y$ from a twist curvature, and this stiffness also stiffens the\n", "twist, by the ratio $3 E^{(h)}_w/(E h^3)$, about 30 % here. As documented in\n", "`pyfe3d.quad4r`, the amount of hourglass stiffness that is acceptable\n", "depends on the problem. The default follows the references documented\n", "there and is used in all the comparisons with Sze et al. (2004) above. The\n", "values of `hgfactor_w` below measure the sensitivity of this problem only:\n", "none of them is a recommendation, and new default values would require\n", "more studies.\n", "\n", "Two references without hourglass control are used:\n", "\n", "- `Tria3DSG`, with the same meshes split into two triangles per\n", " quadrilateral;\n", "- the linear shallow-shell (Donnell-Marguerre) Kirchhoff solution of\n", " `ritz_roof_WC`, a Ritz method with the Legendre-based functions of\n", " Castro, S. G. P. and Donadon, M. V., *Composite Structures*, 160,\n", " 232-247, 2017,\n", " [doi:10.1016/j.compstruct.2016.10.026](https://doi.org/10.1016/j.compstruct.2016.10.026),\n", " `m` functions per direction for each of $u$, $v$ and $w$. It has no\n", " transverse shear deformation, so the finite elements are compared with it\n", " with their transverse shear stiffnesses $A_{44}$, $A_{45}$ and $A_{55}$\n", " multiplied by 100 (`shear_factor=100.` of `hinged_roof`).\n", "\n", "The linear deflection $-W_C$ of the 12.7 thick roof under $P_{max}$:" ] }, { "cell_type": "code", "execution_count": 9, "id": "69dc60e2", "metadata": { "execution": { "iopub.execute_input": "2026-10-25T10:37:27.307356Z", "iopub.status.busy": "2026-10-25T10:37:27.307218Z", "iopub.status.idle": "2026-10-25T10:37:51.373250Z", "shell.execute_reply": "2026-10-25T10:37:51.371644Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "shallow-shell Kirchhoff Ritz solution: -W_C 7.4798 (m = 20), 7.4801 (m = 30)\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\n", "linear -W_C under P_max, h = 12.7, transverse shear stiffness x1\n", " 16x16 32x32 64x64 64x64 vs Tria3DSG\n", "Tria3DSG 7.5480 7.6295 7.6733 +0.00 %\n", "Quad4R, hgfactor_w = 1 7.0949 7.1372 7.1668 -6.60 %\n", "Quad4R, hgfactor_w = 0.1 7.5543 7.6061 7.6255 -0.62 %\n", "Quad4R, hgfactor_w = 0.03 7.6170 7.6698 7.6882 +0.19 %\n", "Quad4R, hgfactor_w = 0.01 7.6494 7.7026 7.7206 +0.62 %\n", "Quad4R, hgfactor_w = 0.002 7.6825 7.7378 7.7557 +1.07 %\n", "Quad4R, hgfactor_w = 0.0002 7.7031 7.7816 7.8003 +1.65 %\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\n", "linear -W_C under P_max, h = 12.7, transverse shear stiffness x100\n", " 16x16 32x32 64x64 64x64 vs Ritz\n", "Tria3DSG 7.3996 7.4626 7.4795 -0.01 %\n", "Quad4R, hgfactor_w = 1 6.9602 7.0050 7.0348 -5.95 %\n", "Quad4R, hgfactor_w = 0.1 7.3562 7.4083 7.4272 -0.71 %\n", "Quad4R, hgfactor_w = 0.03 7.3940 7.4469 7.4646 -0.21 %\n", "Quad4R, hgfactor_w = 0.01 7.4050 7.4583 7.4756 -0.06 %\n", "Quad4R, hgfactor_w = 0.002 7.4095 7.4630 7.4802 +0.00 %\n", "Quad4R, hgfactor_w = 0.0002 7.4105 7.4641 7.4815 +0.02 %\n" ] } ], "source": [ "HGFACTORS = [1., 0.1, 0.03, 0.01, 0.002, 0.0002]\n", "MESHES = [16, 32, 64]\n", "W_ritz = {m: ritz_roof_WC(m) for m in (20, 30)}\n", "print('shallow-shell Kirchhoff Ritz solution: -W_C %.4f (m = 20), %.4f '\n", " '(m = 30)' % (W_ritz[20], W_ritz[30]))\n", "rows = [('Tria3DSG', dict(element='Tria3DSG'))] + [\n", " ('Quad4R, hgfactor_w = %g' % hg, dict(hgfactor_w=hg)) for hg in HGFACTORS]\n", "for shear_factor, ref_name in [(1., 'Tria3DSG'), (100., 'Ritz')]:\n", " W_lin = {name: [linear_roof_WC(n, shear_factor=shear_factor, **kw)\n", " for n in MESHES] for name, kw in rows}\n", " ref = (W_lin['Tria3DSG'][-1] if ref_name == 'Tria3DSG'\n", " else W_ritz[30])\n", " print()\n", " print('linear -W_C under P_max, h = 12.7, transverse shear stiffness '\n", " 'x%g' % shear_factor)\n", " print('%-28s' % '' + ''.join('%9s' % ('%dx%d' % (n, n)) for n in MESHES)\n", " + ' 64x64 vs %s' % ref_name)\n", " for name, _ in rows:\n", " Wn = W_lin[name]\n", " print('%-28s' % name + ''.join('%9.4f' % Wi for Wi in Wn)\n", " + ' %+8.2f %%' % (100*(Wn[-1]/ref - 1)))" ] }, { "cell_type": "markdown", "id": "eba5c12f", "metadata": {}, "source": [ "With the actual transverse shear stiffness the default `Quad4R` meshes are\n", "6.0 to 6.6 % stiffer than the `Tria3DSG` meshes of the same size, and\n", "decreasing `hgfactor_w` increases $-W_C$ monotonically. From\n", "`hgfactor_w = 0.03` down the `Quad4R` meshes are more flexible than\n", "`Tria3DSG`, whose deflection still grows with the mesh, by 1.1 % and 0.6 %\n", "for each refinement, so that this comparison has no converged reference.\n", "\n", "With the transverse shear stiffnesses multiplied by 100 the comparison has\n", "one: the Ritz solution converges to $-W_C = 7.480$ and the $64 \\times 64$\n", "`Tria3DSG` mesh agrees with it within 0.01 %. The default `Quad4R` mesh is\n", "6.0 % stiffer, and the deflection approaches the Ritz solution\n", "monotonically as `hgfactor_w` decreases, within 0.7 % with 0.1 and 0.06 %\n", "with 0.01.\n", "\n", "The limit loads of the non-linear paths, with $16 \\times 16$ meshes, the\n", "arc-length increments of `test_hinged_roof_thick` (0.05) for both\n", "thicknesses and the load at the first point of Tables 9a and 9d,\n", "interpolated along the rising part of the path:" ] }, { "cell_type": "code", "execution_count": 10, "id": "a5c46fe5", "metadata": { "execution": { "iopub.execute_input": "2026-10-25T10:37:51.375799Z", "iopub.status.busy": "2026-10-25T10:37:51.375573Z", "iopub.status.idle": "2026-10-25T10:40:08.597765Z", "shell.execute_reply": "2026-10-25T10:40:08.596883Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "h = 12.7, 16x16, P/Pmax: upper and lower limit loads, load at the first point of Table 9a\n", " upper lower first\n", "Table 9a 0.7421 0.1729 0.0877\n", "Quad4R, hgfactor_w = 1 0.7459 0.1713 0.0941\n", "Quad4R, hgfactor_w = 0.1 0.7427 0.1684 0.0884\n", "Quad4R, hgfactor_w = 0.03 0.7422 0.1682 0.0877\n", "Quad4R, hgfactor_w = 0.01 0.7420 0.1681 0.0873\n", "Quad4R, hgfactor_w = 0.002 0.7413 0.1681 0.0869\n", "Quad4R, hgfactor_w = 0.0002 0.7379 0.1690 0.0867\n", "Tria3DSG 0.7420 0.1679 0.0884\n", "\n", "h = 6.35, 16x16, P/Pmax: upper and lower limit loads, load at the first point of Table 9d\n", " upper lower first\n", "Table 9d 0.1953 -0.1288 0.0517\n", "Quad4R, hgfactor_w = 1 0.1944 -0.1435 0.0558\n", "Quad4R, hgfactor_w = 0.1 0.1954 -0.1299 0.0526\n", "Quad4R, hgfactor_w = 0.03 0.1954 -0.1286 0.0523\n", "Quad4R, hgfactor_w = 0.01 0.1954 -0.1282 0.0521\n", "Quad4R, hgfactor_w = 0.002 0.1953 -0.1274 0.0520\n", "Quad4R, hgfactor_w = 0.0002 0.1952 -0.1243 0.0520\n", "Tria3DSG 0.1956 -0.1287 0.0524\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cases = [('Quad4R, hgfactor_w = %g' % hg, dict(hgfactor_w=hg))\n", " for hg in HGFACTORS] + [('Tria3DSG', dict(element='Tria3DSG'))]\n", "paths_thick, paths_thin = {}, {}\n", "for name, kw in cases:\n", " if kw.get('hgfactor_w') == 1.:\n", " # NOTE the path of the 12.7 thick roof with the default, see above\n", " paths_thick[name] = (P16, W16)\n", " else:\n", " paths_thick[name] = run_hinged_roof(n=16, **kw)\n", " paths_thin[name] = run_hinged_roof(n=16, h=6.35, load_factor=1.1, **kw)\n", "\n", "\n", "def first_point(P, W, table):\n", " # NOTE -W_C increases monotonically up to the upper limit point\n", " rising = W < 10.\n", " return np.interp(table[0, 1], W[rising], P[rising])\n", "\n", "\n", "(Pa_r, _), (Pb_r, _) = limit_points(TABLE_9A[:, 0], TABLE_9A[:, 1], 15.)\n", "print('h = 12.7, 16x16, P/Pmax: upper and lower limit loads, load at the '\n", " 'first point of Table 9a')\n", "print('%-28s %9s %9s %9s' % ('', 'upper', 'lower', 'first'))\n", "print('%-28s %9.4f %9.4f %9.4f' % ('Table 9a', Pa_r, Pb_r, TABLE_9A[0, 0]))\n", "for name, (P_, W_) in paths_thick.items():\n", " (Pa, _), (Pb, _) = limit_points(P_, W_, 15.)\n", " print('%-28s %9.4f %9.4f %9.4f' % (name, Pa, Pb,\n", " first_point(P_, W_, TABLE_9A)))\n", "(Pa_r, _), _ = limit_points(TABLE_9D[:, 0], TABLE_9D[:, 1], 13.5)\n", "print()\n", "print('h = 6.35, 16x16, P/Pmax: upper and lower limit loads, load at the '\n", " 'first point of Table 9d')\n", "print('%-28s %9s %9s %9s' % ('', 'upper', 'lower', 'first'))\n", "print('%-28s %9.4f %9.4f %9.4f' % ('Table 9d', Pa_r, TABLE_9D[:, 0].min(),\n", " TABLE_9D[0, 0]))\n", "for name, (P_, W_) in paths_thin.items():\n", " (Pa, _), _ = limit_points(P_, W_, 13.5)\n", " print('%-28s %9.4f %9.4f %9.4f' % (name, Pa, P_.min(),\n", " first_point(P_, W_, TABLE_9D)))\n", "\n", "fig, ax = plt.subplots(figsize=(7, 5))\n", "for (name, (P_, W_)), style in zip(paths_thin.items(),\n", " ['C0-', 'C1-', 'C2-', 'C3-', 'C4-', 'C5-',\n", " 'k--']):\n", " ax.plot(W_, P_, style, lw=1., label='16x16 ' + name)\n", "ax.plot(TABLE_9D[:, 1], TABLE_9D[:, 0], 'ko', mfc='none',\n", " label='Table 9d, Sze et al. (2004)')\n", "ax.axhline(0, color='k', lw=0.5)\n", "ax.set_xlabel('-W_C')\n", "ax.set_ylabel('P/Pmax')\n", "ax.set_xlim(10, 25)\n", "ax.set_ylim(-0.2, 0.3)\n", "ax.grid(True, alpha=0.3)\n", "ax.legend(fontsize=8, loc='upper right')\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "1ad5fff4", "metadata": {}, "source": [ "For both thicknesses the default makes the start of the path stiffer, by\n", "7 % ($h = 12.7$) and 8 % ($h = 6.35$) at the first point of the tables,\n", "whereas the reduced values of `hgfactor_w` and `Tria3DSG` are within 1.8 %\n", "of it. The upper limit loads agree within 0.6 % with the tables for all\n", "the values of `hgfactor_w`. The lower limit loads behave\n", "differently: for $h = 12.7$ the default is the closest to Table 9a (-0.9 %),\n", "the reduced values and `Tria3DSG` being 2.3 to 2.9 % below it; for\n", "$h = 6.35$ the default is 0.015 $P_{max}$ below Table 9d, while the values\n", "of `hgfactor_w` from 0.1 to 0.002 and `Tria3DSG` are within 0.0014\n", "$P_{max}$, and 0.0002 is 0.0045 $P_{max}$ above it.\n", "\n", "The smaller values of `hgfactor_w` leave the hourglass pattern of $w$ with\n", "little stiffness, and the path then depends more on the mesh and on the\n", "increments: with the $24 \\times 24$ mesh and the arc-length increment of\n", "0.02 used above for Table 9d, `hgfactor_w = 0.002` gives another path after\n", "the upper limit point:" ] }, { "cell_type": "code", "execution_count": 11, "id": "d8598efa", "metadata": { "execution": { "iopub.execute_input": "2026-10-25T10:40:08.599524Z", "iopub.status.busy": "2026-10-25T10:40:08.599366Z", "iopub.status.idle": "2026-10-25T10:41:05.973358Z", "shell.execute_reply": "2026-10-25T10:41:05.972576Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "24x24 Quad4R, hgfactor_w = 0.002: upper and lower limit loads 0.1948, -0.1112; Table 9d: 0.1953, -0.1288\n", "hgfactor_w = 1, above turning points of -W_C: P/Pmax -0.0139 at -W_C 17.186, P/Pmax -0.1336 at -W_C 14.850\n", "hgfactor_w = 0.002 turning points of -W_C: P/Pmax 0.0478 at -W_C 16.778, P/Pmax -0.0343 at -W_C 13.970\n", "Table 9d turning points of -W_C: P/Pmax 0.0083 at -W_C 17.008, P/Pmax -0.1142 at -W_C 14.451\n" ] } ], "source": [ "P24_002, W24_002 = run_hinged_roof(n=24, h=6.35, load_factor=1.1,\n", " initialInc=0.02, maxInc=0.02,\n", " hgfactor_w=0.002)\n", "(Pa, _), _ = limit_points(P24_002, W24_002, 13.5)\n", "print('24x24 Quad4R, hgfactor_w = 0.002: upper and lower limit loads %.4f, '\n", " '%.4f; Table 9d: %.4f, %.4f' % (Pa, P24_002.min(), Pa_r,\n", " TABLE_9D[:, 0].min()))\n", "for name, (P_, W_) in [('hgfactor_w = 1, above', (P, W)),\n", " ('hgfactor_w = 0.002', (P24_002, W24_002)),\n", " ('Table 9d', (TABLE_9D[:, 0], TABLE_9D[:, 1]))]:\n", " dW = np.diff(W_)\n", " turns = np.flatnonzero(np.sign(dW[1:]) != np.sign(dW[:-1])) + 1\n", " print('%-22s turning points of -W_C: %s' % (name, ', '.join(\n", " 'P/Pmax %.4f at -W_C %.3f' % (P_[i], W_[i]) for i in turns)))" ] }, { "cell_type": "markdown", "id": "2cc228ea", "metadata": {}, "source": [ "This path turns back in $-W_C$ for the first time at 0.0478 $P_{max}$,\n", "against 0.0083 $P_{max}$ in Table 9d and -0.0139 $P_{max}$ with the default,\n", "and its lower limit load is 0.018 $P_{max}$ above the\n", "smallest load of Table 9d, whereas with the $16 \\times 16$ mesh and the\n", "increment of 0.05 the same `hgfactor_w` was within 0.0014 $P_{max}$.\n", "\n", "The sensitivity is therefore not a single trend: reducing `hgfactor_w`\n", "removes the excess stiffness of the linear response and of the start of the\n", "non-linear path, and, in the Kirchhoff limit, converges to the independent\n", "solution, but it does not improve every result of the non-linear paths and\n", "it makes them depend more on the mesh and on the increments. The\n", "assertions of the linear trend are in `test_hinged_roof_hourglass_sensitivity`." ] }, { "cell_type": "markdown", "id": "92f8ae95", "metadata": {}, "source": [ "Williams' toggle frame\n", "---\n", "\n", "The toggle frame of Williams, F. W., An approach to the non-linear behaviour\n", "of the members of a rigid jointed plane framework with finite deflections,\n", "*The Quarterly Journal of Mechanics and Applied Mathematics*, 17(4),\n", "451-469, 1964,\n", "[doi:10.1093/qjmam/17.4.451](https://doi.org/10.1093/qjmam/17.4.451), as\n", "reproduced in Fig. 7 of Karamanlidis, D., Honecker, A. and Knothe, K., Large\n", "deflection finite element analysis of pre- and postcritical response of thin\n", "elastic frames, in: Wunderlich, W., Stein, E. and Bathe, K.-J. (eds.),\n", "*Nonlinear Finite Element Analysis in Structural Mechanics*, Springer,\n", "Berlin, Heidelberg, 217-235, 1981,\n", "[doi:10.1007/978-3-642-81589-8_12](https://doi.org/10.1007/978-3-642-81589-8_12)\n", "(p. 228); the paper of Williams was not consulted. Fig. 7 gives: two\n", "straight members of horizontal length 12.943 rising by 0.386 to the apex,\n", "both ends clamped, a central load $P$ at the apex, $E = 10.3 \\times 10^6$,\n", "a rectangular cross-section 0.753 wide and 0.243 deep, in the plane of the\n", "frame; it states no units. The reference is the load-deflection curve of\n", "the \"present analysis\" of Fig. 7, the mixed-hybrid beam elements of\n", "Karamanlidis et al., which agrees with the points of Wood and Zienkiewicz\n", "plotted in the same figure, $w$ being the deflection of the apex.\n", "\n", "The curve below was digitised from a scan of the printed figure, at the\n", "square markers of the curve, after fitting the grid lines, whose positions\n", "the fit reproduces within 0.23 in $P$ and 0.0013 in $w$. The line is about\n", "0.3 thick in $P$ and the common origin of the curves is read at\n", "$w = 0.005$, $P = 0.3$: the readings are uncertain by about $\\pm 0.3$ in\n", "$P$ and $\\pm 0.005$ in $w$, and the deflections of the limit points, on flat\n", "parts of the curve, by about $\\pm 0.02$. The limit loads read from the line\n", "are $P = 34.4$ at $w \\approx 0.24$ and $P = 32.2$ at $w \\approx 0.40$.\n", "\n", "Each member is modelled with `BeamC` elements in the $XZ$ plane, with the\n", "out-of-plane displacement and the rotations about $X$ and $Z$ restrained;\n", "Fig. 7 gives no Poisson's ratio, $\\nu = 0.3$ is used for the transverse\n", "shear modulus (with $\\nu = 0$ or $0.5$ the limit loads of 16 elements per\n", "member change by less than 0.01). The reference load is $P = 70$, reached at\n", "the load factor 1.0 after the snap-through, with arc-length increments of\n", "`initialInc = maxInc = 0.02`." ] }, { "cell_type": "code", "execution_count": 12, "id": "665f624c", "metadata": { "execution": { "iopub.execute_input": "2026-10-25T10:41:05.975051Z", "iopub.status.busy": "2026-10-25T10:41:05.974882Z", "iopub.status.idle": "2026-10-25T10:41:07.928135Z", "shell.execute_reply": "2026-10-25T10:41:07.927582Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "arc_length_riks 16 BeamC/member: 129 increments, P 70.00 at w 0.6516; upper limit 33.957 at w 0.236, lower limit 31.717 at w 0.389\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "arc_length_crisfield 16 BeamC/member: 129 increments, P 70.00 at w 0.6516; upper limit 33.957 at w 0.236, lower limit 31.717 at w 0.389\n", "Fig. 7, read: upper limit 34.4 at w ~0.24, lower limit 32.2 at w ~0.40\n", "check: Riks' and Crisfield's methods, max difference of P 7.6e-08\n" ] }, { "data": { "image/png": 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YOnQoV1555XmPsayvV/zvY8eOERwczLBhw9i2bRsWi4UjR47w7rvvus75448/qF27No0bNz7z2LtpvOei6OfoVD1kX3jhBZYtW8bXX39N06ZNMQyDH374gbS0NNc2wEVsNpvr5/nEcRUf73fffUfdunVJSkoq85xTOdnP+Vm/Bi4i5fGzUPR4wzBK/Y6pyop+vyoe5U+xda9KFd+gMRw+lk+dhIk4lk/B7CjAETIOgsZABRy/u2JaYRLZxYsXc+jQIe6//34A0tPTAfD19S1xnq+vLzt37jzpdWJjY5kwYUKp4/v37yc/P991u6CgAIfDgc1mw2azndEYzYYJy/IY7A4HjqAxmJOmYVkxCXu/Z3Cc4TVOpXjPtxPHNW3aNJYtW4bZbMZms9GwYcMyx110rOjvzMxMDMOgRo0a2Gw2cnJyePrpp9mwYQO5ubn07t2bmTNn4u3tzcyZM1mwYAE2m811u0ePHgD4+Pjw0ksvsWTJEg4ePMjs2bP54Ycf+PbbbykoKGDu3LlceeWVfPzxx9SqVYtnn33WtXuS1Wpl5MiRrjF99tln3HTTTdhsNq699lq6d+/OmjVrSE1NdW3T+8Ybb7B3714mTpzI7bffDsC6desYN24c2dnZOBwOnnnmGcLCwkhNTaV379489NBDfP311xw7dowPPviAd999l9WrV1OtWjXi4uJo0qQJDoeDQ4cOERYWxl9//UXdunWZM2cOzZs3B2DGjBnExcVhs9lo3Lgxb7zxBs2aNePFF1/kr7/+4siRI/z555988cUXXHbZZWV+H48cOcLUqVP56aefaNy4set5BwcHA85Evnfv3owcOZL/+7//Y+jQoWRlZXHkyBEmT57M6tWrefLJJ7Hb7dhsNh599FHatGlDZGQk2dnZdO7cmcmTJzN37ly6devGiBEjKCgo4IUXXiAxMZH8/Hzatm3LG2+8Qb169VwJls1mIysri4cffpjff/+dZs2acemll5YYY1VhGAZ2ux3gvHf2stlsOBwODh48iLe3d3kMr9JzOBxkZWVhGIY2DSlniq17Vbb4vnnkBsYZr2B1FGCYvclodx9kZHh6WGXKyspyy3UrTCL7v//9jxtuuIEmTZqUOH7ifzKGYZzyP56oqChGjx7tup2dnU2zZs1o2LBhqS1qc3Jy8PLywsvrDMMQ+gyG2YwlMQbzyhmY7PkYIeMwB0eWe41G8XFlZ2ezf/9+vvjiC+Lj4wEYNWqUK8E78XGHDh3iqquuwm63s23bNp5++mn8/f0BGDt2LMHBwa4Z0oceeoi33nqLp556ivvuu8/1MfNPP/3EQw89xMaNG13XrlevHmvWrGHhwoXceuutLFiwgJdffplXXnmFKVOm8Mknn/Drr7/Su3fvU8b0iy++4L333nNtD7pnzx4SExNJT0+ndevWjB49mlWrVrFmzRpuueUW7rrrLg4dOsTIkSNZunQpfn5+HDhwgO7du9OvXz+8vLw4ePAgffv2JSYmhqlTp3L99deTkJDAO++8w4gRI3jrrbeIiYnBbDazcuVKfv31V9q2bcuUKVN44okn+PLLL5k7dy5//PEHycnJWCwWPvroI5566inXVn/Lly/n559/plGjRqf83m3duhUfHx86dux40u/twYMHueKKK4iOjgacH/GbTCa8vLyYOnUqERERDB8+nIKCAg4fPkz9+vWZMGECX375JQsXLgScW/6azWa8vLyYMmUKderUYc2aNQC89NJLvPTSS7z66quYzWbXeTExMdStW5fNmzdz4MABunXrxm233Xbmr4GLTHkknl5eXpjNZho0aKAtags5HA5MJhMNGzasFMlAZaLYuldliu/RfBuNNj6P1WTDYfbG7Cig0ZYPoN/Tnh5amXx8fNxy3Qrxv9fOnTv5/vvvXUkaQOPGjQHnzKyfn5/reEZGRqlZ2uKsVitWq7XU8aL/zIvfLt4p4YyFjIWkaZjs+WDxwRQy9swfexaKj8tms5Gfn09ubi4//fQTu3btonfv3gQEBBAQEFDqcfXq1WP9+vWAs67ymmuuoUePHgwZMoQlS5awevVqZsyYAThLAaxWKyaTifXr1zNx4kQOHjyIl5cXmzdvpqCgwPXDd8cdd2AymejWrRtms5lBgwZhs9no1q0bixYtKtV9oizp6elkZ2fTtm1b17HbbrsNi8XCZZddxqWXXsott9yCyWSie/fupKWlkZeXR3JyMn/99Rc33nij63GGYbBt2zZatGhBrVq1GDx4MADdunWjadOmdOnSBYDu3buzbNky17iuvvpq2rVrB8AjjzziSiaXLFnCunXr6N69O+Dct9pisbgeN3jw4FP+7J34vTtZDEwmE9WqVWP48OGuc4o/JjQ0lIkTJ/LHH38QHBxMcHBwiesVv27R8SVLlpCdnc1nn30GOEt1Lr/88lLXT0xM5PXXX3f9og4LCzv718BFoPgb4vN97kXxO/F3TFWnmLiPYutelSW+f8S9wEgW8D/vO7k/6k1Imoo5YSKYTCVLICsId8WzQiSyc+bMoVGjRgwaNMh1zN/fn8aNG7Ns2TJXQpKfn8/y5cuZPHmyp4bqrIktTGKx5ztvu/kHpkGDBtSqVYu7774bgObNm9O3b1/WrVtXKpE90SWXXMKAAQP49ttvGTJkCIZhsHjxYlq1alXivPz8fG699VYSExPp1q0b2dnZ1K1bl/z8fFciWzTbZLFYSrxZsFgsro+mu3Xrxttvv33S8SxZsoQhQ4aUOFZ8FstisZT4OuBM5A3DoGPHjqxYsaLUNVNTU0uN58RrnslH54Zh8Oyzz/Kvf/2rzPtr1ap12msAdOjQgby8PDZv3kyHDh3KPKdmzZonTaBGjRrFkCFD+P7773nuuecICAjgzTffPO3YZ8+eTf/+/U97noiIVG4Oh8H6nf/wfwXhXDrwGSzmYsmrw+7ZwV1gHn+74XA4mDNnDvfdd1+JjzdNJhOjRo0iJiaGRYsWkZKSwv3330+NGjUYPny4ZwZbtCIwdDw8t9/5d/EVg25055138s033wDOutc1a9ac9KPr4vLy8li5cqVrBnTIkCFMmjSpRA3tH3/8QW5uLgUFBa6FSK+//vo5j/PQoUO89NJLrhrEo0ePMmnSJMBZC33LLbec9XX79OnD9u3b+eGHH1zH1q9fX6Lu+UytXLmSbdu2AfDuu+/Sv39/TCYTQ4YMYfbs2fzzzz+As466aNFcWaKiosrsBlCrVi3GjBnDQw89xN69e13Hv/rqK1avXn3a8W3dupVWrVrx0EMPMXbs2DN6zJAhQ5gxYwZHjx4FnDEvq+fyNddcw5w5cwDnbP2iRYtOe20REakgCltu/bAlg+icIXzgPYw7j80/3nIrOBJCz3/xeWXi8RnZ77//nl27dpU5CxYZGcmxY8cYMWIEmZmZ9OzZk++++47atWt7YKQ43+WEjj/+rqec3/2MHDmSJUuWkJ6ezrXXXkutWrX4448/AIiJieGBBx5g9uzZgDOJ6tq1a5nXOXToEJ07dwaciWxoaCiPPfYYADNnzmTs2LF07twZs9mMt7c3kydPpnXr1rz44ov06NGD5s2bl5o1PVM1atRg+fLlPPPMM7Ru3ZpatWphMpkYPnw42dnZbNu2zfXR/dmoX78+X3zxBU8//TRPPfUUBQUFNG/enMWLF5/1tYKDg4mOjmbz5s3UrVuXDz/8EIB77rmHgwcPEhISgslkwmaz8eCDD7o+ETjRhg0b6NatW5n3vfjiizRs2JCBAwdit9sxmUx06dKFSZMmuRL8k3n99ddJSEjAx8cHs9nMtGnTTvucnnnmGSZMmEDPnj1dM71jx44t1aniueee41//+hcdOnSgRYsWDBgw4LTXFhGRCqKw5dY/tXcBNzCr6ff4JL3tzE2qKJNxkX/WWPQReWZmZqnFXjt27MDf318LNM5RUVeCokVbpzN//nx+/PHHk/Y0rUwcDge9e/cmOTnZbXU/ZxtfOXPlGVv9LinN4XCQkZFBo0aNKnydYWWj2LpXZYjvvi9exPfn6eQbXviYbCUn2CqwQ4cOUb9+fbKysqhTp065XbdifpfkonTHHXdcFEksOIvWV69eXWF/0YmIyMVp0tEh5BUlsRafSpHEupP+FxYRERGpBNKzcmm+cVZhy61ii86rMCWyIiIiIpXA9oXP8ZTXQhbUugfz8xd20XlF5fHFXiIiIiJyakfybKTs+Yc1BeEE3vCs82AVbblVnBJZERERkQrus1/2MDk3jJYNajCqfbHNeap4jawS2bNkt9tJSkoiLS0NPz8/goKCXI37RURERMpNQiyYLTiCnua9H3cA8Irfd1iW/1Tl+sWejGpkz0J8fDytW7cmNDSU4cOHExoaSuvWrUtsrXs+WrZsSbt27ejcuTOdO3fm0Ucf5fPPP+fpp89v3+Tvv//edc3OnTvTpEmTk/agPZHJZOLw4cOAs4F+7969iYiIqFQ7RL3//vuEh4cDsG7dOu66664yz0tNTeXSSy8FYO/evYSGhpbbGGbOnElGRsZZP2758uVcddVVZ3SuYRj07duXnTt3AvDee+8RGBiIl5dXqW4R+/btIywsjI4dO9KuXTtmzpzpui83N5f777+fwMBAAgICGDJkCAcOHACcMQoJCaFu3bql+gGnp6fTs2fPM9pFrSwtW7YkJSUFgBtvvJE///zztI/597//TVJSEuDcbGPNmjWu+071vT4X0dHRjBkzptyuJyJyWoV9Y//67AVSDx7l6WpL6PLHbOdxAZTInrH4+HjCw8MJDAwkOTmZnJwckpOTCQwMJDw8vNyS2bi4ONavX8/69et56623GDJkCFOnTj2va1577bWua65fv56uXbue9X/we/fuJTg4mEGDBjF9+vSz6r15ug0ALqTu3bvzySefnPa8Jk2akJCQUG5f91wT2bOxcOFC2rZtS4sWLQDndsGffvppmTvhjR49msDAQDZs2MC6det47733WLt2LQD//e9/OXz4MBs2bCAlJQVfX1+mTHEuJKhTpw4vv/wyc+fOLXXNxo0b07NnTz7++OPzfi5fffUVl19++WnPe/fddwkKCgJKJ7Jn+r0WEamwgiMhdDytN73KVuu9jGRBpekbe6EokT0DdrudiIgIBg8ezOLFi+nVqxe1atWiV69eLF68mMGDBzNmzBi3JGzFZxMBxo8fT+vWrenZsydPP/30We+StXfvXn744QfuueeeM37Mn3/+Sb9+/RgxYgTPPussMLfZbFx//fX06tWLgIAA7rrrLtf2qO+//z7XX3899957L927d2fNmjXMmDGDq666ii5dutCjR48S266aTCZiY2Pp0aMHrVq14vvvvycqKoouXbpw5ZVXurZaTU9PJzQ0lG7dunHllVfy5JNPumaGo6OjGT58ODfddBMdOnSgf//+rq1mi0tMTCwRszfeeIPWrVsTFBTEu+++6zpefHb22LFj3H777XTo0IFOnToxcODAMuOUnp7OsGHD6NGjBx07duT5558HnLt87d27l/DwcDp37sz69etLPfbuu++me/fudOzYkcGDB59T0vvf//63xBuUTp060b59+zJ73f72228MGjQIcG6pGxwczEcffeS6/+jRoxQUFGCz2Th8+DBNmzYF4JJLLuHqq6+mZs2aZY5h+PDhvPPOO2c03qSkJAIDA+nRowePP/54iVn+4rOzmzdvpmfPngQEBDB8+HB69erF0qVLAQgJCWHp0qV89dVXfP7550yaNInOnTvz7rvvlvhe79+/n4EDBxIYGEjHjh1L7CQ4bdo0evToQdeuXbnxxhvZvXs3AFlZWYSHh9OhQweuu+461y57IiIX0s8tHyLP8MJqsmGob2xpxkUuKyvLAIzMzMwSx48dO2Zs3rzZOHbs2GmvkZCQYABGcnJymfevWrXKAIyEhITzGmuLFi2Mtm3bGp06dTI6depkxMfHG3PmzDFuvfVWwzAM4/PPPzc6duxoHD582LDb7cYtt9xidOvW7ay+RkxMjBEWFnbG5wNGgwYNjLfeeqvEcYfDYezfv9/Iz8837Ha78eijjxpTp041DMMw5syZY9SsWdPYtm2b6/yMjAzXv5OTk40rr7yyxNeYNWuWYRiG8emnnxo1atQwli5dahiGYUyePNm48847DcNwfs9ycnIMwzAMm81mDBo0yFi4cKFhGIbxwgsvGK1atTIOHjxoGIZh3H777UZMTIxrPEUxTEhIcMXst99+M/z8/Iz09HTDMAzjscceMxo0aGAYhmHs2LHD9e/4+HhjwIABrvEWfY0TDRw40Fi+fLlhGIZRUFBgXHfddUZ8fLxhGM7v7caNG08a5/3797v+HRsba4wcOdJwOBzGsmXLzuh7nJ+fb1SrVs04cuRIqfvuu+8+4/XXXy9x7P777zf+85//GHa73di3b5/Rpk0b46abbjIMwxnn22+/3ahbt65xySWXGDfccINht9tLPL54HE8cR/Xq1Y3Dhw+fcry5ublGkyZNXK+ZBQsWGIArRsXj1bVrV+Ojjz4yDMMw1q1bZ5jNZuOLL74wDMMwgoODXf8+8XkWH+OMGTOMhx56yHXfgQMHjPz8fOPjjz82HnroIcNmsxmGYRgffvihMWTIEMMwDGP06NHGAw88YBiG8/vTrFkzIyIiotRzOZvfJVWF3W430tLSSv3cyPlTbN2rIsZ30cwnDeOFOkZBdAPDeKGOYSRO9vSQzklmZqYBGFlZWeV6Xc3InoG0tDQAAgICyry/6HjReeejeGnBLbfcUuK+hIQEhg0bRs2aNTGbzdx3331nff05c+bw4IMPntVjBg0axHvvvUdWVpbrmGEYvPLKK1x11VV06tSJL7/8ssRM49VXX02bNm1ct3/99VeCg4MJCAjg0UcfZfPmzeTn57vuv/322wHo2rUrZrPZNVvYrVs3/vrrL8C5deDYsWPp1KkTXbp0Yd26dSW+5g033MAll1wCQO/evU9bY5mYmMigQYPw9XWu/nz44YfLPK9Tp05s2bKFESNGsGDBAry9vUudc+TIEX744QeefPJJOnfuTPfu3fnjjz/YsmXLKcdQ5JNPPqF79+4EBgby7rvvljlreyoHDhzAx8eHGjVqnNH506dPJzs7m65du3LvvffSv39/1/P6/vvvMZlMpKenk5aWRr169XjxxRfP6Lre3t7Uq1fvtK+FrVu3UqNGDUJCQgAYNmwYdevWLXVednY2KSkprvKIbt260bFjxzMaS3G9evXim2++ISIigs8//9w1o7xkyRK+//57unXrRufOnZkyZYqrxjghIcH1Wrn00ksJCws7668rInI+Dn71EkMz32eGLZzUx1LVN7YMSmTPgJ+fH4Dro84TFR0vOs9dDMM4r33hV6xYwdGjR7nuuuvO6nGzZs2ie/fuXHvttWRmZgIwd+5cVqxYwQ8//MCGDRsYM2YMubm5rsfUqlXL9e/8/HxuvfVWZsyYQUpKCitWrMAwjBKJbNEe9RaLBavV6jpusVhci4dmzJjBwYMHWb16NRs2bGD48OElvmbxfe6LP+5kjDNcsNaqVSs2b97M9ddfz8qVKwkICHDFoYjD4cBkMrF27VrXG5E//viDqKjTryr98ccfmTVrFl9//TUbN25kxowZJZ7XmahRo8ZZPeaSSy7hvffeY/369XzzzTcAdOjQAYC33nqLW265hWrVquHj48Ndd911VvXCubm5VK9e/ZTnnGnsi37mz+fnHpxvbNavX0/Pnj357LPP6NGjB3a7HcMwePbZZ13fs40bN7reRJzpGEVE3OXnHQeYXhDOliseo3WjWq6a2arcN/ZESmTPQFBQEC1btiQmJgaHw1HiPofDQWxsLP7+/q5FJ+4SGhrKwoULOXr0KA6Ho0RN45l47733uP/++0u1C7vmmmtKLJI5kclk4o033qB3795ce+21/PPPP2RmZtKgQQNq165NTk4O77///kkfn5ubS0FBAc2aNQPg9ddfP6txF8nMzKRx48ZUq1aNffv2sXDhwnO6TpHQ0FC++uorVz3q//73vzLP27NnDyaTiSFDhjBt2jQMw3DVURapXbs2QUFBTJo0yXVs79697NmzB3Aukio+o33i86pTpw6XXHIJ+fn5/Pe//z3r51K3bl38/Pxcs9enc/DgQQoKCgD45ZdfWLx4MSNGjACcifu3336LYRgYhsHSpUtP+mnEifbt24eXlxdNmjQBICoqqlTHBIB27dpx7NgxVqxYATg/iSgrPnXr1qVDhw7MmzcPcM7sb9y4scyvfaoY79ixg1q1ajFs2DBef/11tm3bxuHDh7npppuYPXu2q566oKCAX3/9FXC+LubMmQM4O3YsWrTojGIgInJeEmJh+RTSso4xcu91vG4PI7rel87jUJjMqvVWESWyZ8BisTB9+nSWLl3K0KFDS3QtGDp0KEuXLmXatGlu7yc7ZMgQrrvuOjp16kRoaCiXX3656+PYvXv30rlz55M+Nicnh88++6zEIhdwLmT77bffXIt5TuW1114jKCiIa6+9liFDhnD48GE6duzIrbfeesokvk6dOrz44ov06NGDfv36lZhxPRtPPvkkq1atonPnzvzrX//i2muvPafrFOnYsSPjxo2jT58+XH311a7k60QbN26kT58+dOzYka5du3LPPfeU+fH2J598wu+//05gYCCBgYHceuutHDx40DX2Bx54oMzFXjfccAOtW7emXbt2XHfddaf8Pnbu3Jm9e/eWed+tt97K119/7br98ccf07RpUxYuXMhzzz1H06ZNXUnamjVraN++Pe3bt+fRRx/l008/dX2iEB0dTVZWFldeeSUBAQEcOHCAl156CYC8vDyaNm3KbbfdxoYNG2jatGmJWedvvvmGW265xTWDumHDBho3blxqrFarlXnz5jFy5Eh69OjBmjVraN68eZnP68MPP+SVV16hW7duvPHGG3Tq1KnMMoR77rmHuXPnuhZ7FZeYmOgqH+jbty9Tpkyhbt263HPPPdx9992EhITQqVMnOnfu7Jp9fu6558jMzKRDhw7cddddDBgwoOxviohIeSpsubXt0+cosBtMvvRrmvwyQy23TsJkXOSfn2VnZ1O3bl0yMzOpV6+e63hubi47duzA39+/xEfSpxIfH09ERASpqamuY/7+/kybNu2C1c/l5ORQu3ZtHA4H//73v2nSpAkvv/zyOV/vl19+Yfbs2aX+4z8ThmFgs9nw8vI6749+pbSzje/OnTsJDw9n9erVZXYquBCCgoJ45513aNeuHQ6Hg969e5OcnHxe4zly5Ag1atTAZDKxefNmQkJC2Lp1K/Xr1z/na5bnz+65/C652DkcDjIyMmjUqJHHfhYvVoqte1WU+OZ+H0u1Hye5uhVcDC23Dh06RP369cnKyqJOnTrldl3t7HUWwsLCuPnmmz26s9e9995Lamoqx44do2vXrkRGnt8PdteuXc8piZWKp0WLFowdO5a9e/ee0Qx7edu3bx+PPfYY7dq1A8BsNpdos3auVq5cydNPP+2qWX3nnXfOK4kVEano3jWH85AxzdVyy1TJk1h3UiJ7liwWi2ultSeoTk9OpXjP4QvN19e3zM0XztfAgQNP2rtXRORik1tgx5I0FavJht3sjcWe7+xSoGS2TPpcQkRERKSC2LLgOR4zFvCO150Y4zPUcus0qvyM7EVeIiwibqbfISJSXmx2B7+mHuD/CsJpMGAsXhbz8ZlYtdwqU5VNZIvqWvPz80/b81JE5GSK+iFfyFp5Ebk4fZ2SzoTDN1O/hjcrr2p2/A6VFZxUlU1kvby8qFGjBvv378fb21urP8+Buha4l+LrPuUVW4fDwf79+6lRowZeXlX216mInI+EWDBbMPo9zVvLnTtSzm76f9RY+bP6xZ6BKvub12Qy4efnx44dO1xbUsrZMQwDh8OB2WxWouUGiq/7lGdszWYzzZs31/dIRM5NYd/YnQeOsGlvD0b7LKb3rk/h8vGeHlmlUGUTWQAfHx/atGlTYqtUOXMOh4ODBw/SoEEDzWi7geLrPuUZWx8fH31/ROTcFZYNtEyYyFbrxdM39kKp0oksOGdT1MT83DgcDry9valWrZr+I3cDxdd9FFsRqUh+bvkQAcZk9Y09B/oNLiIiIuJBO+NfwGqyYTN5YyrqGytnRImsiIiIiIekfT6BsKwPeMV2G38/vlN9Y89SlS8tEBEREfGUtX8dYHtBOH93epwWDWqqb+xZUiIrIiIi4gGb9mbxZPr1mEzwfWjr43eoRvaMKZEVERERuZAKe8fO2n0NAIM7NuHyzbOds7DqHXtWVCMrIiIiciEV9o5t/ftsAF6os9RZF2vWDoFnSzOyIiIiIhdScCRfbkgj4uB7POm9BO+1Beode440IysiIiJyAf25/zCP772WPMMLbwrA4qMk9hwpkRURERG5gN5I+IPHzfHOXbwsPqDesedMiayIiIjIBbLz4BGabZhFhHccaV1Hw3P71Tv2PKhGVkREROQCmZ3wJ37Y+azufdw65AXnQfWOPWdKZEVERETcqbDd1p6Oj/PZL3uwOcJZ2Wqt83hRuy3VyJ4TJbIiIiIibmQ3TCTNmcB3luUcPnY1r3bZw2W/fuwsKZDzokRWRERExE3i4+OJiPgvqalHga+Ar3jmaxPeo+8mTLOw502LvURERETcID4+nvDwcAIDA7kv9iMOPFOf5AdrEOjrTfgLHxMfH+/pIVZ6SmRFREREypndbiciIoLBgwfz+ntz6XQ4kQZWOz2a12Dx7VYG927HmDFjsNu1wOt8KJEVERERKWdJSUmkpqYybtw4fl/wPE95LSSuzr2Yn9+Puf+zRLXbyY4dO0hKSvL0UCs1JbIiIiIi5SwtLQ2AGr4t2ZqWyfSCcC4Pf9F5Z3AkAeHPlDhPzo0SWREREZHylBCL375EAF766FtesYVzecNadPnzLdcpKfWuBcDPz88TI7xoKJEVERERKU9mC0H/zKN5o3p8+dFsRpo/Y+ih98FsAcDhcBAbG4u/vz9BQUGeHWslp0RWREREpDwFR2K55lleCckj9481JH32EcmN7ian62MkJyczdOhQli5dyrRp07BYLJ4ebaWmRFZERESknG24/GEGtatO3LDqbMxw0GfkbOrUqUOfPn1ISUkhLi6OsLAwTw+z0vN4Ivv3339z991306BBA2rUqEHnzp35+eefXfcbhkF0dDRNmjShevXqhISEsGnTJg+OWEREROTUti98HqvJxpAONfjjiZokvPIwc+fOJSEhge3btyuJLSceTWQzMzPp27cv3t7efP3112zevJnp06dTr1491zlTpkxhxowZzJo1i7Vr19K4cWMGDBhATk6O5wYuIiIichJ/L4nm1qwPeMV2G38/vhPLNc8Scmg+dzbZTUhIiMoJypFHt6idPHkyzZo1Y86cOa5jLVu2dP3bMAxmzpzJ+PHjXe9cPvjgA3x9fZk7dy6PPPLIhR6yiIiIyCklb9/PzoJwDnR7khYNakLRVrQObX5Q3jyayH7++edcd9113HbbbSxfvpzLLruMESNG8NBDDwGwY8cO0tPTGThwoOsxVquV4OBgVq1aVWYim5eXR15enut2dnY24Fwh6HA43PyMqhaHw4FhGIqrmyi+7qPYupfi6z6KrXuVR3xX/XmQMQduxMdi4v9CLj9+raAxRV+kHEZa+bjrZ9ajiexff/3Fm2++yejRoxk3bhxr1qzhySefxGq1cu+995Keng6Ar69vicf5+vqyc+fOMq8ZGxvLhAkTSh3fv38/+fn55f8kqjCHw0FWVhaGYWA2e7zc+qKj+LqPYuteiq/7KLbuda7xrbX2dQyzmcNdRzD5q60AvO73DfVXriTjqifcNdxKJSsryy3X9Wgi63A46N69OzExMQB06dKFTZs28eabb3Lvvfe6zjOZTCUeZxhGqWNFoqKiGD16tOt2dnY2zZo1o2HDhiVqb+X8ORwOTCYTDRs21C9UN1B83UexdS/F130UW/c65/jWroM5MYaMY7AxrRdP+SziugMLcQSMo0ajRu4bcCXi4+Pjlut6NJH18/OjQ4cOJY61b9+ezz77DIDGjRsDkJ6eXmLni4yMjFKztEWsVitWq7XUcbPZrBe9G5hMJsXWjRRf91Fs3UvxdR/F1r3OKb4hY3EAlyfGsNU6G6vJBqHjMRfVxorbfl49+iro27cvW7duLXFs27ZttGjRAgB/f38aN27MsmXLXPfn5+ezfPly+vTpc0HHKiIiInIyi2rfRZ7hhdVkw7D4HF/gJW7l0UT2qaee4qeffiImJoY//viDuXPn8vbbbzNy5EjA+a5o1KhRxMTEsGjRIlJSUrj//vupUaMGw4cP9+TQRURERADILbBz8KuXsJps2E3emOz5sHyKp4dVJXi0tOCqq65i0aJFREVF8eKLL+Lv78/MmTO56667XOdERkZy7NgxRowYQWZmJj179uS7776jdu3aHhy5iIiIiNPGueN52D6fty13cO8zs7Gsmg4JE513ambWrTyayAIMHjyYwYMHn/R+k8lEdHQ00dHRF25QIiIiImfg0NF81u3Yz4qCcFrc9BzVvC3qG3sBeTyRFREREal0EmLBbOGNw4N5JzeMdo1r81XOJ5DggNAozcReIFryKCIiInK2zBZImEjNn2YA8Gaz7zEnxjiPywWjGVkRERGRsxUcyVcb0xh14D1GWhbjvbEAQsdrJvYC04ysiIiIyFlK+TuLEXuuJc/wwpsCUMstj1AiKyIiInKWJn29hScs8c7NDyw+oJZbHqFEVkREROQsrNi2ny473ibCO46sXk/Dc/udZQUJE5XMXmCqkRURERE5Q3aHQezXW7jO5CCxyUOEXP+s8w613PIIJbIiIiIip1PYbmtxreH8npbNnmp3sMb/F+fx0CjnOaqRveBUWiAiIiJyOoXttg5+9RIA/2uZQPWVk9Ruy8M0IysiIiJyOsGRrN5xkIdT3+L+anH4pNrUbqsC0IysiIiIyGnsy87lgb9CyTO88MGmdlsVhBJZERERkdOY/M0WHrQvxGqyYajdVoWhRFZERETkFNbvPsRlv71OhHccaV1HY1K7rQpDNbIiIiIiJyrsUuAIeprozzcRYnKwvUZX2tT2cd6vdlsVghJZERERkRMVdinYkpbF+t19uMbHizZHfwHzDcfPUY2sxymRFRERETlRcCT5NgcdkmLZan3LuRWtuhRUOKqRFRERESnDa7ZbyDO8ji/wUhJb4SiRFRERETnB7n+O4vXjVKwmGw6zNyZ1KaiQlMiKiIiInODXj8cxyrKQhXXuVZeCCkw1siIiIiLFJP95kL8ysphBOIOGx2AymdSloIJSIisiIiKSEAsmM7Yr7uWlL39niy2c//n/QNvfZ0HjKOc5qpGtcFRaICIiImK2YE6M4e+vp7ElPYenqy3hmrR3nW24pMLSjKyIiIhIcCRH8230XDmZrdb3saJ2W5WBZmRFREREgBezB6vdViWjRFZERESqvJ93/kPDX14tbLflo3ZblYQSWREREanSbHYHm+Y9S4R3HEvr3wvP7lO7rUpCNbIiIiJSpb2/KpXDh4/xhtftXDNkrPOg2m1VCkpkRUREpOpJiAWzhb2dnmDGsm0ctYXzefuVNE15E1q85DxHNbIVnkoLREREpOoxWyBhIus+iOJovp1JDb6m4/Y3MMxKjSoTzciKiIhI1RMcyV/7DzMk5VWus36E9YgNR8g4jrS7j5qeHpucMb3tEBERkSrnWL6de/8McbXbwuID/Z729LDkLCmRFRERkSrn1WVbCNw4jfiUYyTsAntBHqyY6ulhyVlSaYGIiIhUKbPe+4Spox/ln6zDvAXAMVo2rs/0rRMYcO9huGGCh0coZ0ozsiIiInLxS4iF5VP47LPPeOLf9+DXqD7zHutCzpcvkJycTOBVVxO+MJfPf9zs6ZHKWVAiKyIiIhc/swX7/73Mfx57kOqXX8W/bx/IHY3+pFbNGvTq1YvFixczaNAgxs1dh92u3rGVhRJZERERufgFR/J9ndv5e38W3/TbwijLQufuXYW9Ys1mM8888wy7du0iKSnJw4OVM6VEVkRERKqEV3e1AqCrr4Fh8Sm14UFAQAAAaWlpF3xscm6UyIqIiMhFL3FrBi3+cc60bthvxmTPh+VTSpyTkpICgJ+f3wUfn5wbJbIiIiJyUTucZ2P7wueZ1epHGjeow6R9/XAER0HCRFcy63A4mDRpEs2bNycoKMjDI5YzpURWRERELj6FXQoApn27lSO5efzq1ZFXRw5i6dKlDH1lFcmN7ibn8FGSk5MZOnQoX375Jc8//zwWi8XDg5czpT6yIiIicvExWyBhIn8fOsoHP13F42Yz3R0b6d5/CF6dwomIiKDPF18UnjwBf39/Pv30U66++mqPDlvOjhJZERERufgER2JzOLhseSxbfAq3oS3sUhAG3HzzzSQlJZGWloafnx9BQUGYTCYyMjI8PXI5C0pkRURE5KI0PW8oo4ypWE02DIsPpmJdCiwWCyEhISXOdzgcF3iEcr5UIysiIiIXnfW7D+H9ozOJdZi9y+xSIJWfElkRERG5qOQW2Pn14yhGe8Xx5aX/wvz8AWdZQbEuBXJxUGmBiIiIVH4Jsc4FXsGRzPx+O9WO5LLGO4D+VzRw3l9UVuDQ9rMXE4/OyEZHR2MymUr8ady4set+wzCIjo6mSZMmVK9enZCQEDZt2uTBEYuIiEiFVNilYO/nE3h7xZ/YDTM9jBSqW32OnxMcCaFRnhujlDuPz8heeeWVfP/9967bxXu3TZkyhRkzZvD+++9zxRVX8PLLLzNgwAC2bt1K7dq1PTFcERERqYiCIymwO2iyIpbfT+hSIBcvj9fIenl50bhxY9efhg0bAs7Z2JkzZzJ+/HjCwsIICAjggw8+4OjRo8ydO9fDoxYREZGKZtLRIeQZXq4uBUpiL34en5Hdvn07TZo0wWq10rNnT2JiYmjVqhU7duwgPT2dgQMHus61Wq0EBwezatUqHnnkkTKvl5eXR15enut2dnY24GypobYa5cvhcGAYhuLqJoqv+yi27qX4uo9ie3LJfx6kRvJ0rN7OLgVmez6OxMnQ7+kzvobi6z7uiqlHE9mePXvy4YcfcsUVV7Bv3z5efvll+vTpw6ZNm0hPTwfA19e3xGN8fX3ZuXPnSa8ZGxvLhAkTSh3fv38/+fn55fsEqjiHw0FWVhaGYWA2e3xy/6Kj+LqPYuteiq/7KLZlO5xnJ2XeBCK84/jqknvpOmw8NX9+g9qJMeQcOcyRbiPP6DqKr/tkZWW55boeTWRvuOEG178DAwPp3bs3l19+OR988AG9evUCwGQylXiMYRiljhUXFRXF6NGjXbezs7Np1qwZDRs2pF69euX7BKo4h8OByWSiYcOGesG7geLrPoqteym+7qPYHmdKnIRhtkC/p5mycAPN8wv42SeQa9r74t2oEdwwAUfNWtRy2KnZqNEZXVPxdR8fH5/Tn3QOPF5aUFzNmjUJDAxk+/btDB06FID09HT8/Pxc52RkZJSapS3OarVitVpLHTebzfqhdAOTyaTYupHi6z6KrXspvu6j2BayeGFKmMi2jMPE/9qLJ73MdHNsBJ8hUBSbkLEAnHz6qzTF1z3cFc8K9V3Ky8vj999/x8/PD39/fxo3bsyyZctc9+fn57N8+XL69OnjwVGKiIiIxwVHcrjPWK7Y/Bpbrfcy2itOXQqqII8msmPGjGH58uXs2LGD1atXEx4eTnZ2Nvfddx8mk4lRo0YRExPDokWLSElJ4f7776dGjRoMHz7ck8MWERERD3M4DB7bfY26FFRxHi0t2LNnD3feeScHDhygYcOG9OrVi59++okWLVoAEBkZybFjxxgxYgSZmZn07NmT7777Tj1kRUREqrj3Vu6g819vF3Yp8MFsz3duP6tktkrxaCI7f/78U95vMpmIjo4mOjr6wgxIREREKryUv7M4/F0MEd5x/NZ6JJ3ujnEmsQkTnScoma0yKtRiLxEREZEyJcSC2cKx3hH8Z/6v3GTY+b1aFzpeVst5f1Hy6rB7boxywSmRFRERkYrPbIGEifz4+z7+3N+fajV8aJ/7K5hvPH6OZmKrHCWyIiIiUvEFR7J9Xw4DNr/GVuv7WB02dSmQitV+S0RERKQsu/85yq2br3Z1KUBdCgQlsiIiIlLB5dscPD7vV+4r+PR4q62iLgVSpSmRFRERkQpt2ndb6bf3PSK848jq9TSm5/Y7ywoSJiqZreJUIysiIiIVS2GHAoIj+WHLPt5e8RdzvTdxsGFPGlz/rPMcdSkQlMiKiIhIRVPYoSAnt4DRq6/iCUs8fSy/Q8D4kuepRrbKUyIrIiIiFUtwJDaHQe3lMaw2vLB627AFR+GlxFVOoBpZERERqXAmHh7s6lBgmH3wCn3G00OSCkiJrIiIiFQoX/y2l1o/zcBqsuEwe2NyqEOBlE2JrIiIiHhWQqwrUd2+L4cdn71AhHccO2t3w/z8AXUokJNSjayIiIh4hN1uJykpibSEjfjtWkKPPBuPbuzDS8ZGAJp2vc55ojoUyEkokRUREZELLj4+noiICFJTU13HWi55lkkDatKng5kjfcdSM3Ts8QdooZeUQaUFIiIickHFx8cTHh5OYGAgycnJ5OTk8PQbC7mykRd3LjxM3BaDmgPGeXqYUgkokRUREZELxm63ExERweDBg1m8eDG9evVi3d9Habz3az6/oxqDrvAm8tvD2H+Y5OmhSiWgRFZEREQumKSkJFJTUxk3bhxms5kdB46QMm88o73i+N7330TNSWTHIYOkD1/S4i45LSWyIiIicsGkpaUBEJC5jMN5Nh7+cB02m40N3h3p37YBgYGBzvOa36zFXXJaWuwlIiIiF4yfnx8AKZ9NYt+2A2zPGEi1Gj50LNgAXjeRkpLiPK//wxAS4sGRSmWgRFZEREQumKCgIFq2bMmYdRZWXDaHG6wf4+OwQeh4HEFjiB06FH9/f4KCgjw9VKkEVFogIiIiF4zFYmHYyHGs/O0vhszP5ec9ueTYvEj2CWLo0KEsXbqUadOmYbFYPD1UqQQ0IysiIiIXzM87M1l0qCn3hYWy/IcE+rxXAByFiX3w9/cnLi6OsLAwTw9TKgklsiIiIuI+CbFgtkBwJHsyj/LIR+uYY3qRvoGbKRgxkZWW3qT98DZ+u5YQdO/DWPoriZUzp0RWRERE3MdsgYSJ5Nkc/HtjH+48Np++3puxtQjC+5ooQsC5qGv5FHUpkLOmRFZERETcJzgSu8PAujyGJYYXVm8b2b0jqXPd+FLniZwtLfYSERERtzEMg2czbyTP8MJqsuEw+5ROYkXOkRJZERERcZs3l//JpT/PLExivTE78rVjl5QbJbIiIiJSfhJiXYnqkvV/c2xZLBHecaTVvwrz8wcgdDwkTFQyK+VCNbIiIiJSfgoXd+365whj1vXkA/MmAPw6D3TeX1QLq4VdUg6UyIqIiEj5CY4kIyeX5uumk+JVWBcbMg5z8cVcWtgl5USlBSIiIlJudh08yqDf+rgWdxkWH8whYz09LLlIKZEVERGRc1esJnZ/Th73vLeambnPuZJYk12Lu8R9VFogIiIi566wJjbXZue+lKuJyR5HX8tm8ppdjfXBL51JbMJE57kqKZBypkRWREREzl1wJAV2B9VWxLLI8MJqsXGsaV+qP/il635Ai7vELVRaICIiIucs3+bgkV3XlNjwoPq/vyp5UnAkhEZ5ZoByUVMiKyIiIufEZncwasGvXLn9LVcSqw0P5EJSaYGIiIicmYRYZ01scCQOh0Fk3Abu2vI4fb03syNwFP63TlBNrFxQSmRFRETkzBQu7DIMg2czb+SyDa/T13szBxv2ciaxoJpYuaCUyIqIiMiZCY7EMAxMiTG8YEzB6m3j93ZP0P6Ol0udJ3IhqEZWREREzohhGLyYM9i1sMtu9i6dxIpcQEpkRURE5LQMw+DFpZup9dMMZxJr8sbiKNDCLvEoJbIiIiJStsJduwzDYMIXziQ2wjuOfZdcheWFAxA63rmwS8mseIhqZEVERKRshYu7ErZk8P6OUOZ6bwLAt9NA5/1a2CUepkRWREREsNvtJCUlkZaWhp+fH0FBQRD0NP+3KZ2Bae+w1ToHq8nmnIUtvphLC7vEg5TIioiIVHHx8fFERESQmprqOtayZUvaDx3JZus1bLV+4ExiLT5KXKVCUY2siIhIFRYfH094eDiBftVIfmMEOTk5JCb9iKNeM76Z+TSP/Dn6eBJr165dUrFUmEQ2NjYWk8nEqFGjXMcMwyA6OpomTZpQvXp1QkJC2LRpk+cGKSIichGx2+1EREQwePBgFk+8j14ZH+OzZhbvbPHi8RtaM/gKL975fjv2flHw3H4t7pIKp0KUFqxdu5a3336bjh07ljg+ZcoUZsyYwfvvv88VV1zByy+/zIABA9i6dSu1a9f20GhFREQuDklJSaSmpjJv3jzMvXpxzGZQfUUs/zOmYvWx0XlIVwZOW0OSuRchoMVdUuF4fEb28OHD3HXXXbzzzjvUr1/fddwwDGbOnMn48eMJCwsjICCADz74gKNHjzJ37lwPjlhEROTikJaWBkBAQAB7Mo8yaENv12YHDrMPvZ7/vsR5gDOZDY3yxHBFSvH4jOzIkSMZNGgQ1157LS+/fHx3kB07dpCens7AgQNdx6xWK8HBwaxatYpHHnmkzOvl5eWRl5fnup2dnQ2Aw+HA4XC46VlUTQ6HA8MwFFc3UXzdR7F1L8XXfcoztqbESfjuSwXgi4SfmLkRZhx7DqvFmcSaHfls+HAsAL6+vlXi+6mfXfdxV0w9msjOnz+fX375hbVr15a6Lz09HXC+eIrz9fVl586dJ71mbGwsEyZMKHV8//795Ofnn+eIpTiHw0FWVhaGYWA2e3xy/6Kj+LqPYuteiq/7lGdsax47RvA/87msYV0eiXiWL4dBX6/fyfHtwZFbPqL62llMHjOZlr71aNu2LRkZGeX0LCou/ey6T1ZWlluu67FEdvfu3fznP//hu+++o1q1aic9z2QylbhtGEapY8VFRUUxevRo1+3s7GyaNWtGw4YNqVev3nmPW45zOByYTCYaNmyoF7wbKL7uo9i6l+LrPuUa2xsmsDXHwWuhrxD+6WqmLvSCW6+i4/A4/kxJYdLbv/HldjsLX7gRPz+/8nkCFZx+dt3Hx8fHLdf1WCL7888/k5GRQbdu3VzH7HY7K1asYNasWWzduhVwzswWfwFlZGSUmqUtzmq1YrVaSx03m836oXQDk8mk2LqR4us+iq17Kb7uUx6xNQyD13/4gxnr+7C13VvEDYOI7/LoF5sMsfUA8Pf3Jy4ujrCwsHIaeeWgn133cFc8PZbIXnPNNWzcuLHEsQceeIB27doxduxYWrVqRePGjVm2bBldunQBID8/n+XLlzN58mRPDFlERKRySoh1bjcbHEmezU7UZxu5bMPrzPXehNVk45aAmtzc1oukS+4kzTfEtbOXxWLx9MhFTsljiWzt2rUJCAgocaxmzZo0aNDAdXzUqFHExMTQpk0b2rRpQ0xMDDVq1GD48OGeGLKIiEjlZLZAwkSO5du5768Qeu56lwjvOOd9oeMxBUdiWT6FkISJ0OVyCL7Ts+MVOUMe71pwKpGRkRw7dowRI0aQmZlJz549+e6779RDVkRE5GwER3LgcB6XrpzER8Y0rN42Mhv1pP6V1x7vDasesVIJVahENjExscRtk8lEdHQ00dHRHhmPiIhIpVSslADgm5R0tq3exQiT2dUjtv6I70o/riiZFakkKlQiKyIiIuWgsJTAYRi8WnALjsTJrlICw+KD2Z7v3GZWiatUckpkRURELjaFi7qsiTGMMKZg9bYBYA8ehyV0rDOJTZjoOlekslIiKyIicpH5PS2bEb/25pui7WYxYw6NwqJ6WLnIKJEVERGpzE6oh124bjd7l0xgIikltpstRTOxchFQIisiIlKZFdbDFtgdjP/nBnx/fc1VD3us7zNUHxClUgK5aCmRFRERqcyKWmutiOUlYypWbxt76najSZfrqB4y1nUOoFICueic1X5hR48eZeTIkVx22WU0atSI4cOHc+DAAXeNTURERE5Qa+3rsGIq4Nxq9qOfdvLJTzuxGcdbazV96gfMRUlskeBICI3ywIhF3OesEtkXXniB999/n0GDBnHnnXeybNkyHnvsMXeNTURERE5gmM2YE2M4uiyWhz/6mYwvXuQ/loV4mRzO1lqOwtZaIlXAWZUWxMfH87///Y877rgDgLvuuou+fftit9u1H7OIiMgFcKTbSA7kmvBfOYlZhbt0AThCxjlnYVUPK1XIWSWyu3fvJigoyHW7R48eeHl5sXfvXpo1a1bugxMREamK7HY7SUlJpH3/Fn6X1iXoidlYLBaO5Nn45dOJbMs4zGMWZ2stAzOm0CjMaq0lVdBZJbJ2ux0fH5+SF/DywmazleugREREqqr4+HgiIiJITU11HWs5eSGPPP8Klx5M5t+2edQ1dXAmsRYfTHa11pKq66wSWcMwuP/++7Fara5jubm5PProo9SsWdN1LD4+vvxGKCIiUkXEx8cTHh7O4MGDmTdvHgEBAfw6J5Kps95h3Ij7iRtWnbUdutDXkgKh4zEFR6qUQKq0s0pk77vvvlLH7r777nIbjIiISFVl/34iESOnM3jwYBYvXozZbOavz55n2yEbC26vze0LchjzXR6rh12No8EQlRKIcJaJ7Jw5c9w1DhERkSotKWUXqemZzLu+GQePFLD6/WcYfPA90uwdqG6xM7ZfDa5+N5u12/Zy/djYkg/WTKxUUWfVfktERETcI803BICAPR9Rd3oTBh98j5X2DvS1bCY/KIqOM/YAkLXuM1cfWZGqTomsiIiIJyTEluj3ethcC4D1+wx8sFGAF627D4TQ8fhc8wwpKSkA1O1+KyaVEYgA2qJWRETEM8wWSJjIkXwb0YcG0Wh9PC3rmZjyYy4976iDt8mGb72aEByJw+EgNjYWf39/Ot07CcPPD5Onxy9SASiRFRER8YDcPhFsTP2Hq1ZO5mVjOlarjcsHViN8YS63/tqXqOubEfDNy6Rs2knsN7tZunQpn376qTYgEilGiayIiIi7JcQ6Z2CDI3E4DL7YsJeMpS9xJDePjsU2NggbEU3c7a2JiIigzxdfFD54Nv7+/sTFxTF06FAyMjI8+lREKhIlsiIiIu5WWEaw65+jPP73tQSnzSHCO4613gFYjZIbG4SFhXHzzTc7d/ZKS8PPz4+goCAsFgsOh8PDT0SkYlEiKyLHt8M84T9NETkHxWZfi/x96BhZPh3p8NsrLDRex+ptY3fdq7gqa22ZGxtYgiMJCQnx0BMQqTyUyIpUcWVuh9myJdOnTycsLMxtX1fJs1y0CmdfATZc/jB/LHyesKwPmF8QTmuvza6tZZt1vgbMA48nvNrYQOSsqf2WSAVit9tJTExk3rx5JCYmYre79z+0ou0wAwMDSU5OJicnh+TkZAIDAwkPD3fbdtPx8fG0bt2a0NBQhg8fTmhoKK1bt9b21lIhnfJ1eUILrSLZjXtBwkTavnM5YVkf8IrtNgIuq4uPyQZFZQQnzNoCztuhUW5+RiIXDyWyIhXEicndNddcQ+/evd2W3NntdiIiIlzbYfbq1YtatWrRq1cvFi9ezODBgxkzZky5J9OeSp5FzsVp33QVzb4un4JhGOz47AVImMg7u5uSZzgXcdlM3tzftyXXZfwPQsfDc/udfxc+TkTOnRJZkQqgrORu5cqVtG/fnmHDhrkluUtKSiI1NZVx48ZhNpf8VWA2m4mKimLHjh0kJSWV29f0VPIsci7KfNM161ECm1Q//qYrOBJ7y36QMBHbhEvx3ziT6QXhWMwmZwmB2Qcvo4D6+35yJq/FywhCx6uMQOQ8qUZWxMNOTO6KkspevXoxZ84cHnnkEcaMGcPNN99cdg1pGQtLeH+w8+/7l570WFpaGgAB66Oh1zfHr7VrFTTvQ0D3x53nzX8KUi875bXKPFbsWkUflSa9PoLU1FTmzZt30uS5T58+JCUllftCl+I1ub6+vrRt27Zcry8Xl5O+LgP8WXztJwylHaMjIvDNTKbv7hXYDDPeJhv5hhfdWtQnZO87pRdx+fcr+UVOLCsQkbOmRFbEw4pmRstK7ur8/AbPXN+Mq5cuPZ7cnZgwFn20uWOF89jyKZDqnEU9/F0MaZ2eoNbqGfgVHts8fzwbL3+EIynOx6esS8Lrg2dY2+IhBq//P5plrWXnwaNMXd8SAL/cbZD6F79+HMWWKx6j45//5crCa/0V9zz7u/6HVpvfoGHhMUfiZMwhY51J7I4Vx5/M8imkJX0EQEBAwPHjxZ5P0fG0H94GI7ncagXLWtDWrFkzZsyYQXh4eLl8Dbm4uF6XT99Y4nVpGAZHmvQhql0SfVYdpSBpNiubdaSvZTN2kzc+FBDis6X07Cto9lXEDZTIiniYa2b0n29g+YoSszTe6evouCf5+HnFktQdnz3Pmub/pvmfB+kNkJpEQXQDvLHxujGMfJuDiFWTab5yOlaTjekFzoQtYsssLv/9LbwsBUTWrcWDK+qz8bLZBP71DlaTjZX2DvTOWkvq/CT865lY6zeMnwvMRPwxmw7b3y55rZRXuWzjGyWPJcaQnzgFH2z86tWRLjtWUBB9Kd4UYPJtB/zKlzOfoOXwabTZMptLCp8Py6eQ4hMEgN+uJbAr53iQypjdZfkUZ2JwmmS36OPhwYMHM2/ePAICAtiwYQMTJkxg2LBhxMXFubU7g1ROrtflno9geQuyejzFX589T5c/ZvN2QTj3NbQCR/k7B+6ybMYWPA6v0LGafRW5wJTIinhCsXIAPz8/AFKSv6eXZSMAjqCnyfp2IvX//olvjrUF1tHw20ehJcywhWMYELHxVZpsOJ5EPu61GKvJRp7hxfS8oQCuY/l48e2l91LT6sWTGUuwmgooMPnQ4/5n+Pa1SG6e78W4q+20863G23VGMmnOv/hqWwELhtViTddR5NsdFGxdgpUCCvBmbYt/k29z8GTG8ev/l3Dy7Y4S47jl8DNstd6L1VRAnuHF2FrR1K97F5989DEL8pdQ3Wx31RM++cPLTJyfi389E02v7AE7VrDt0+c40ms0Hf76EevuH4/H72TJwgnJ7XmXbZwHtRerZE4o0Sl6XSYXtGdAwkSq/zCZLoWvNYvZxPb0PAAuqw3493MmsaDZV5ELTImsyIVwYh1rsXKAq+6Ip1mjesR8uppp/+rLFQkTsf0wmfomG1Pzb+WFLzfRsp6Z0OYGeYY3r9nCqOFj4QkWu1ZE97q8AdZdNhxmb6yOAn7p9wvVvb2wrnS2+vGx5/Nd19XOr51RABYfvO35fHOLg/gGdxMx42P6vFcAHAXuwb+eibg7ahPW1sRtjb51Pm7L8cfNb1s4i5px/PrbBm6kwO7Ae4VzgYvVkc+vzV/HmmHDbvLGSgHvtVrO5HufZ+nrkdy+IIcxfavzat3rKTiwk+/X5PLVtgLm3VaLaw+O4QlLPBGbXyNv02ysJhur7FfSZ8cK16zzrrrdab5jBXsWR+MV+gyNfn0Vc2JMieTW9fHw3U1Klm2smEqdnGyeeeYZrr766nKvyfVUb96qwi1vEor1ft3c5lEcW7+gZT0To5akse4OC9XNzjdsoe0a0fmPNxi6pQX+/rkE3fswrChswXViKYGIuJ0SWZHyVtbiq8J6UcMw+LvTE+SkZdMeIDUJr1g/ZobkEf6pje/fPcbXQQZdfQv4aR9MWb2F3D/XMP226uDlg9VRwOZrfqO6twVTojOJ9LLn03fXfyF0PObChSWXFP6H7KrTK7Zj0InHwoCbP4shydyLtAWj8Tu2laDgUCwPLD3l48o65l14zBQcCR/cRP0dK8C/H5b7voDlU7gmYSLXdOtH/LDqRHyXR/CcHGAYAJvrmfj09lqEtzPT+LIEPq05koJtx2d3hxeMZ6v5XtftfvtGO5Pd9a+Q9+vrmE02frEE0nXHCv7vvxHs6DCSnEWvAhBg33g80Xh/MObUJIyrnnRLTW5ZpQwpKSnExMQQHh6uUobzVC5vEk54jRqGwf6cXHLrdKN5wkQu/2EyHUw2gvuH8mH8D9y+wIux/WrS8dIC8rauYGhCU5YmbyEuLg5L/zCwmDUDK+IhJsMwDE8Pwp2ys7OpW7cumZmZ1KtXz9PDuag4HA4yMjJo1KhRqUVKF4NznvUpSvQKk7zsbydSJ3kK22p05Yqjv7h6SxYvB8jHi4H7I9m6IIb0g9muS7W8tDrT+0PYiOiTJ5HvD3bWzRZfXHImXQXKOlZWLWp5XuuDm5wLwELHY786gqTXR5CW9BF+tU0E3fsclv7PlCwb2LECLD5gzyev2dVYd/+I3eyNxVHAMt8H+cD7dt7bcyM+OJPbtnkfOpNb7zjyDC+Sd+YS+sFRnrhvMK+1XEEBXnhjA+DnFg+xvs61/Dv8BhLuq0FIaH+474tTP8fT1OXa7XZat25NYGBgiVIGcL5ehg4dSkpKCtu3b3dbmUFFKGlw1++G4m8Sxo0bV+JNwtKlS0/+JuHEN5eFP2PZjXvxRouZNPrlVR4smFfiNVmANzuvfIwNcdOJWFGN1PRM1+X8/S5h2qx3PPKG5GL/vetpiq/7HDp0iPr165OVlUWdOnXK7bpKZOWcXcwv+DOe9Slj9rXgh0kc3vID9TNWk48XPjiT1tftYYX1ojYK8OLHJg8QuvcdjKJdfvz7Yf9zOUmX3Emabwi++xII/mc+plbBmO8/vwSrwjjTVmHFEl4KZ3cpnN2lcHa3eLJbFMNdHUexqumDhH/dFS+jgFyHhbqv+2C5tAUH79xOdbOdPMOLWbahPOW1kCHzc9mcYeOjkT3p67WZz+s/wKY2jzAo8yM6bn8DAEfIOGcXhuJfs3jCWyz2iYmJhIaGkpycTK9evUo9/eTkZPr06UNCQkK5txeDilPS4I7fDWf8JuHtB7F4e5f8GSv8+TnW9xm+vfRevH+cxqCD7wG43li+ar+NlpfW5ObM94+/JlsGOV+XV0ccf3OwL5GggOZYrh1fLs/rbF3Mv3crAsXXfdyVyKq0QOQEp/1oeMLdhD33ofPkwrq6/D8SWdTxLayrpjM0833eKwjnca+fXR+DJzX5Fx9XW4x1t3OPdW97PqFl9Jm0XB5MyH3/BcDhuJ0jX/tSq3r1kgMsnvAVqSw1eWUl2mU9n+Z9nElE0fNq3qfk38GRzlnowmS3KIbNEybSPOcXMJz1vNXIZ97ogYS/8DG3L7Awtl8NOl5agFfBEYbEHa/Jvcv2LE8Y8URkzuG61R+dtAvDX7W60WrHCv6Kex5Hv0hafXk75p0/OhNuTtKbF1zJrqs3b+F55cnTJQ3u7tNbZpu6wjdG5uDI4z2Iv19KSLXNABztPZp9X7yI/44V/ObVkU4rJ3GDMc31/X3C2zn7ajd781hQa3ySYsvs/WqxWIq98bizXJ+XiJwfzcjKObsY37medtYnKICUzVvY/lkMh3o8xZ4lE+hUOHNXvGSgVjUvHrHPx2H2xuwoOP4x+anKAU6YVb0Y41uuyprdPXEmtzAZif+9oPTHw/VMTL2+Fre2NfFPjzH81uoR+i3ogMVwdma4rnYce/45xkavu11vSE4sXbCanGUKn9a+l1/9H6L5mkmMmDyP5Adr0OXO57BeU7JUIvmKccdnZFOnOQdSDjPrni5puBB9euc9ewfDJy4gJyeHWrVqOQ8W+37ndH2MOnXqMDesOr379qZl9jryDS98TKU/EbGZvEnv9DhN17/iKl0pmn0t8fNUAT/p0O8F91J83cddM7L6LokUU2Lb1uWTS+yDbjabGXNHMDsOGSR9+BK1pjah0/Y3mF4Q7kpq7CZv7undgkfs852Lr54/4Eyqij4WL/pP8v6lpbenDI6sUP9hVnihUaVnopv3Kd2IvmUQYTf05489+0lISGDuc3eScF8NUmKv4ZZPDkHoeC5ZM43Q1Q9iKZzJ9aaAH7qvYcuADVhNNhxmH6wmGx+2TuSP9iMowOt4q7OCcIblfEj0b6E87LOU+nVr8eCKBniviCE/ugEkTGRbja44/lrOuMfv47JmLeiW+6PzjUxq0vGfsaKEd9eq488nIdaZrCXEHj+2fErJ23hmu+EibtleOSG2xGsPwM+2E4CUD51trnL/LxZ2rODv+ldBwkR+HXUZACuqhxCSMZq8wiQ2Hy/2dXmSrzsnO994WJxbxjZd/4rzZ+W5/c6/U8uIjV6TIhWeSgtEinF9NBwQAD+vgISJGIbB2hYPkfn1y/TZ+wkAu3JMhBTWuva7oiHWHc7/IC32fBodWHNmu/pUlnKAyuQUpQsWcH48bCTjMHUio919VINSZQrFZ3LNUKIbRL+EifTz3wI4S0Ss9nzu6NEM+2/Otmc2sw9tho1mzbvPMmS+F+OvttOmoZXgPwdxyeo/+X37dubdVovaP03ldWMY9Wp4c0/CRGyJU/AyCjjYsBcNdqzg8Hcx1Lg2CnMZu6OV1T83bf5TwAk7phWbTXR1ZyjnkoZz6tN7JnXSxdrT5d/9OdnfTiTIZxNNL6lGzKtv8+m+eVQzOXsQv54Wxu8+9zDtxxxa1jPzR5cxvFNjKdZ9zjZwPo58phx5tuxPRIqo96tIpaVEVgRc/7n6+fUAICUlhU4Fdv6p153LEmPoZEzBarLxxN5gYCnNaxsYZh+8HflctePN0q2ptKtPxRUaBQ4HZGQcP3ZiTW5w5PEEsvixMupyLyvqIlHYCm31XV7ENzuxN+/THGt0GfOH1WJYe/PxTSvyYJh1AVacG0Z02/0kT1iaErFqMvkrp+NjsrHRpxOBO1Zgm3ApXkYB+y/tScMdKzjw5UuYgiOpv26mcxthnLOVvUa8UernMCUlBQC/316Dxqnn35Gi8FjSloPH61aXTz7epSJ4rHMmuONB+i7dUbJPb/HkPDgSI3EypsKk8s+Fz5Po9wAtt+zjGnDG+6WGXGqyMd1+G3n9GrN0cQzD5ucQ0bc6C1vcwmOZH3D7ohyWbrcRd1t1wi59pdT3yBWL4p+IFCX6RfQaFamUlMiKgGsGKKhfFE2aNWfUQ3exKmw/82238bjXemeLLMOLLb9vw7+es1WUqf8zmtm5WJzrIrQiLYOOJ0cn9ub94W38di0hKLgzlp1JUDiT+3O/Xzh0pADrJmfNppUCYhp8xWsFw3k873j/3JuyxzprOwuT3av2/MdZp7t2GnlrZmI22djccjiX1l9AzKtvE7dvPj4mGzvrdKfFjhX89lEUo/73My0aVCfIZxPH/qzP0atGU3v1K/gU2x7Y9UbsLI6lbS8ACmeCP3POoBbYDdI6HsVY8SqBDmcC/XP8q+yt3opWm9+g184VbKnehXYJE8lPmOzq6gEQselVmqaU3q0u3/Dix8v+xceXfcZhH2cP4pA5OcBNrMbZDisu7h3CGvxROmnVJyIiFzUt9pJzVmmL4sv4aNOROJnMlP+jwYHVLNjs4M6Fh2nfphm3XtOdp+t9z8YDZiatOOKc9Zlwz/GuBeC2BSGVNr6VQLnF9lzbiZ1qo4kTWortv7QnDQ+sxmbyxssoYGHte3nHHM7SrLAS/XOPbl3FgcUxDL7Ci4i+1bmn7v+4+Z8P2fnTNyzdZiNuWHV8r+hEX8vmEgsTTSYY7RXnahX3rvedWMwmHsib6+q7+2G1uwC4N/cT13nv+Qzn9z//Ztp7X7DiwToENYWV9g4lrv/Ejn7M+nApCffVoHeLaq6vWXzhVdH4L63lQ7LtDrxxJva/t3mYwG1vlGhPV2YP4jadCJr44/HShQq4QKs86feCeym+7qM+sudIiaz7VNoXfLENC3L7RLDt0+foWLhoq2gGaOHvDiISvdidccj1MH+/S5gWdOz45gRuVmnjWwlc8Ni6uX/uvm4RHM238eun04j4Lo/UQw7XJf3rmZk20Mrg9tUJsX5KYu4wfIolkECppPJMjxkOO6Z3bqFjIzMLbq9N+/yPXOfkGhYuW9iOYxmp/DMil2pmOzaTNzN6/sg1GR/Q7a/ZOMw+mB35FPSLwttidj63oi4CUHaSf5IevlWFfi+4l+LrPuojK1JegiPJtzvwSZiIOWEyHQs/2rR6m7EWLuK5rX0+Ydf1ISm7KWm+Icd3SPpxusoG5Oy5uX+ub+Hsrv+IaG6ee8Jspc8mLN5WsOezqslM2HF8odqWazdgcxhYVzkXRlkd+azqsw67w8C63obD7FzElthjDSbAuqGwg4Mjnx97r8UErN5pJXzhMW5fkMNHt8aQn1/AzwfMTFqRQ+b2n4ibcDfV7EtcNcSR+552jb9oEZ33yXarK6LyABE5Cc3IyjmrNO9ci82GHc238VHyThyJk3nIsRAvk4N8vNjY6mG6/TW79AxQ8e4DF1iliW8lVKljW96zu3BmJQ+nOBZ/sDURj9xN6oFjri/f0rce04PzCGvvffqZ1cq8W90FVql/disBxdd9NCMrcq4KF3KtS/2HR3Zdw/Dc+UR4x4EJ7GZvfBwFdHNsPLOWWSKeVp6zu2V1ZjiHY2HAzXXGk/T9UtK8WuDb/2Hatm1Lk+8eBpPp9K+ryrxbnYh4lGZk5ZxVyHeuJ8xWORwGvy94ltxtCXQzNpXYjckePA5L6NgKMftalgoZ34uEYuteiq/7KLbupfi6j2ZkRc5EUSN1IKnJA+z47AXuzf2E6QXhBHpvxWqyYZjMmEKisGj2VUREpFLz6NuNN998k44dO1KnTh3q1KlD7969+frrr133G4ZBdHQ0TZo0oXr16oSEhLBp0yYPjlgqArvdTmJiIvPmzSMxMRG7vWRT8396jIGEifT4uB335n7CLIYR1KYhPjh33zIZjtIX1VaUIiIilY5HE9mmTZsyadIk1q1bx7p16+jfvz8333yzK1mdMmUKM2bMYNasWaxdu5bGjRszYMAAcnJyPDls8aD4+Hhat25NaGgow4cPJzQ0lNZNGxIfH8+RPBuTv9nCh8k7sRlmrCZnP8oH+7aiR+qbJfdVT5hYai93ERERqVw8msjedNNN3HjjjVxxxRVcccUVTJw4kVq1avHTTz9hGAYzZ85k/PjxhIWFERAQwAcffMDRo0eZO3euJ4ctHhIfH094eDiBgYEkJyeTk5ND8hsjCKyTQ3j4rXT518t4JU1llMXZjcAw++BlFFD975WlF3KFjlcpgYiISCVXYWpk7XY7Cxcu5MiRI/Tu3ZsdO3aQnp7OwIEDXedYrVaCg4NZtWoVjzzySJnXycvLIy8vz3U7OzsbcBZwOxxlfKQs58zhcGAYxgWJq91uJyIigkGDBhEfH+8qwvcbNpm7j5rgnf+y8auXGPVETcCEIzjKuY/7iqmYE2NwtAyC4uMMGlP0JNw+9nN1IeNb1Si27qX4uo9i616Kr/u4K6YeT2Q3btxI7969yc3NpVatWixatIgOHTqwatUqAHx9fUuc7+vry86dO096vdjYWCZMmFDq+P79+8nPzy/fwVdxDoeDrKwsDMNw++rOVatWkZqayruPh3DgwAFsDoNP12dgSX4dw7Azpm91gufksGKXg+63PcWR9vdDRga0u4+aRw5jysnmcEaGW8dY3i5kfKsaxda9FF/3UWzdS/F1n6ysLLdc1+OJbNu2bVm/fj2HDh3is88+47777mP58uWu+00mU4nzDcModay4qKgoRo8e7bqdnZ1Ns2bNaNiwodpvlTOHw4HJZKJhw4Zuf8EfO+ZstN7z4GccXduSx1KvISR9Dv/xjmOjTydaFr7fSc9xULNmLWo2anT8wTc439jUcOsIy9+FjG9Vo9i6l+LrPoqteym+7uPj4+OW63o8kfXx8aF169YAdO/enbVr1/Lqq68yduxYANLT0/Hz83Odn5GRUWqWtjir1YrVai113Gw264fSDUwm0wWJ7WWXXQbAfPPN/PvnGcQZr2H1tpF+SQ8C/1lDcrN7gNn4Bd2DOTGmZBP2SuxCxbcqUmzdS/F1H8XWvRRf93BXPCvcd8kwDPLy8vD396dx48YsW7bMdV9+fj7Lly+nT58+HhyhXBAJsSW6CjRt35WG9Wsz89PlHHNYnP1gLT40DuyPIziK2G924+/vT9ATs7WQS0REpIrw6IzsuHHjuOGGG2jWrBk5OTnMnz+fxMREvvnmG0wmE6NGjSImJoY2bdrQpk0bYmJiqFGjBsOHD/fksOVCKNzYwDAMPq52B5lfvcxbA2yEf7qb2xd48Uy/mgRemkfK73uI/WY3S5cuJS4uDovFclHMxIqIiMjpeTSR3bdvH/fccw9paWnUrVuXjh078s033zBgwAAAIiMjOXbsGCNGjCAzM5OePXvy3XffUbt2bU8OWy6E4EiO5tupkRjDMGMKVrONlE5XEcdaIlZUo++7mYUnzsbf7xLi4uIICwvz6JBFRETkwvJoIvu///3vlPebTCaio6OJjo6+MAMSz0mIdc7CFs6mrtnxD7/+lMqDhRsb2E3eXNnrOgL6DuLmuREkJSWRlpaG375EggKaY7lWSayIiEhV4/HFXiKAq5TAYRi8YQ+jIGESo73iwAQOsw8WRz5YvCA4EgsQEhJS+MA7PThoERER8SQlslIxBEdyJN9GzcQYHjamYPWyAZAfFIXPNc84F34lTHSdKyIiIqJEViqE9bsP8di6niQaXlhNNhyYMYdG4VN8W1lQNwIRERFxUSIrF94J9bAL1u4i7fMXmU4KVosNw+yD2VHGLmyaiRUREZFilMjKhVdYD2tzOHgucxCX/jyTCO84APKCnsF6TZRKCUREROS0lMjKhVdUD7s8lmhjKlZvG3vqdqNJl+uwhox1nQOolEBEREROSomsXHBb03N48Jde/F9RPazZm6ZP/VD6RM3EioiIyClUuC1q5SJUbLvZhK0Z3PrmKiYfHu/cZtbsg9lRUGI7WhEREZEzoRlZcb/CmthfdmXy4Oar+cjrZfpaNlPQPAjvfy1VPayIiIicEyWy4naOoKdZsTWDkD9n87vP286dulr2w/v+L5wnqB5WREREzoESWXGrPJudpxdu4PO/QtlqneMsJ7D4YClKYotoJlZERETOkmpkpXwVq4fNyS3gX++vpUXKLOb5vIzVZAOLDyZ7vmpiRURE5LxpRlbKV2E97OE8G7f/HsQ1Ge+7esQSOt4586qaWBERESkHSmSlfAVHknUsn7qrJrPImI7V28Zhv97Uatf/eNKqmlgREREpB0pkpVz9tf8wd/3am8TCHrGG2Ydaj3xT+kTNxIqIiMh5Uo2snJdaa1+HFVMB+D0tm2H/TWba0Wddi7pMDtXDioiIiHtoRlbOid1uZ/ny5aQmbaZVxne0zjzKHRv6Mtv2An0tm8lvfjU+//pS9bAiIiLiNkpk5azFx8cTERFBamqq61jLJS8xaUBN+nYwU9A8CJ9/LXXeoXpYERERcROVFshZiY+PJzw8nMDAQFauXMmSpPX4/2sGVzby4s6Fh/lsq+Hcrau44EgIjfLMgEVEROSipURWzpjdbidi5L8Z3LsdixcvxqdJW575bi8fNfmUz++oxuC2Pjz9zWHsP0zy9FBFRESkClAiK2csKSmJ1PRMxrXfSfrSl7h/zlreMV6kr2Uzjpb9iJqTyI5DBkkfvqQFXiIiIuJ2qpGVM5aWlgbApQP+Q5NfZvAzXlgtNmwtgvB6YCkBOTnO85rfrJpYERERcTvNyMoZ8/PzA+D6Zb7kufrEemO+73MAUlJSnOf1f1g1sSIiIuJ2SmTljDVr3xWfeo2xrpiONwWFfWILYMVUHA4HsbGx+Pv7ExQU5OmhioiISBWgRFZOLiHWVeu699Ax7p2zjheurcPv23dz03eXsar/YvZe+QirP3qRoUEBLF26lGnTpmGxWDw8cBEREakKVCMrJ2e2QMJEjuTbuPu3PoTlfELElem0btiVsV//w9VXX+061d8vnbi4OMLCwjw4YBEREalKlMjKyQVHkmdzUDMplq8NL6zeNrJ7RzLsuvHcWriz19atW2nbti3BwcGaiRUREZELSomsnFS+zcGDO0L5nzG1cGGXD3WuGw+AxWIhJCSEDh060KhRI8xmVamIiIjIhaXsQ8rkcBg8HfcbXXa8jdVkw2H2weTIV39YERERqTCUyMpxxRZ3TfpmC803ziLCO47MRj0xP78fQsdDwkQlsyIiIlIhqLRAjitc3PXzzkze3nw1c703AVD/ymud9wdHOv/WZgciIiJSASiRleOCI9m+L4dum19jq9VZUkDo+OMJbOE5IiIiIhWBSgvE5bfdh7hpY5/ju3ZZfJS4ioiISIWlRFYA+PvQMf794ToecsS5kliTXYu7REREpOJSIluVFS7uyskt4MH313LH0XlEeMdha94X03Na3CUiIiIVm2pkq7LCxV3LftnDln3X8XK13wHwujzEeb8Wd4mIiEgFpkS2KguOJHFrBmF732Gw9RN80OIuERERqTxUWlCFffbzHu7/K5Q8wwsfkw20uEtEREQqESWyVdT63YeIWrSRJyzxzjZbFh/Q4i4RERGpRFRaUFUkxDprYoMjycjO5ZGP1jHH9CJ9vTbjCBmHOWSsM4lNmOg8XzOzIiIiUsEpka0qChd22RwOHvk9iGFH5tHXezO2FkF4hYx1nqPFXSIiIlKJKJGtKgqTVK+Eicw3pmL1tpHZ82nq3/BsmeeJiIiIVHSqka1CPq1xp2vXLofZu3QSKyIiIlKJKJGtIlL+ziLt8wlYTTbsJm/MjgIt7BIREZFKTaUFF6uEWOyGiSRzL/5M3c2WpIVMuiyR362daTt2OSRN1cIuERERqdQ8OiMbGxvLVVddRe3atWnUqBFDhw5l69atJc4xDIPo6GiaNGlC9erVCQkJYdOmTR4aceUR/+PvtL51HKGhofz7gXuZ9t4XtH79ML/lNsNsNjmT19DxWtglIiIilZZHE9nly5czcuRIfvrpJ5YtW4bNZmPgwIEcOXLEdc6UKVOYMWMGs2bNYu3atTRu3JgBAwaQk5PjwZFXbPHx8YS/8DGBHdqR/GANDjxTn+QHa3DFFVcw/KV5xMfHO08MjoTQKM8OVkREROQcmQzDMDw9iCL79++nUaNGLF++nH79+mEYBk2aNGHUqFGMHetsEZWXl4evry+TJ0/mkUceOe01s7OzqVu3LpmZmdSrV8/Nz8Dz7HY7rVu3JjAwkGdm/I9uH7Vz1sWavTE9m8HQoUNJSUlh+/btWCyW8/paDoeDjIwMGjVqhNmscuvypvi6j2LrXoqv+yi27qX4us+hQ4eoX78+WVlZ1KlTp9yuW6G+S1lZWQBccsklAOzYsYP09HQGDhzoOsdqtRIcHMyqVas8MsaKLikpidTUVEaOGsPGec9iNdmwmbyxOAowJ00jKiqKHTt2kJSU5OmhioiIiJyXCrPYyzAMRo8ezdVXX01AQAAA6enpAPj6+pY419fXl507d5Z5nby8PPLy8ly3s7OzAee7LIfD4Y6hVyh///03APvXzOUR+3zm+Awn/KlXqbn6FcwJE+nQI8J13vnGw+FwYBhGlYirJyi+7qPYupfi6z6KrXspvu7jrphWmET28ccfZ8OGDfz444+l7jOZTCVuG4ZR6liR2NhYJkyYUOr4/v37yc/PL5/BVkC11r6OYTZTvXoXANZt3c3lza6k/+W1OZL1D0fa3UfNI4dZt+lPAKpXr05GRsZ5fU2Hw0FWVhaGYegjGDdQfN1HsXUvxdd9FFv3Unzdp+hT9/JWIRLZJ554gs8//5wVK1bQtGlT1/HGjRsDzplZPz8/1/GMjIxSs7RFoqKiGD16tOt2dnY2zZo1o2HDhhd1jay9Ri1WfvQyf9e/DkvN+nz340ZmDD8EvjdDo0YAOK57gZlv3YK/vz833XRTudTImkwmGjZsqBe8Gyi+7qPYupfi6z6KrXspvu7j4+Pjlut6NJE1DIMnnniCRYsWkZiYiL+/f4n7/f39ady4McuWLaNLF+dMY35+PsuXL2fy5MllXtNqtWK1WksdN5vNF+0PZXx8PBERb5OaehRYBMDvf2TSc8FlvHZ9PwKOHCElJYXY2Fi+/PJL4uLi8Pb2LpevbTKZLurYepri6z6KrXspvu6j2LqX4use7oqnRxPZkSNHMnfuXJYsWULt2rVdNbF169alevXqmEwmRo0aRUxMDG3atKFNmzbExMRQo0YNhg8f7smhVxjx8fGEh4czePBgevwrmtlHn2L7/jye+DqfdVv/pk+fPq5z/f39iYuLIywszHMDFhERESknHk1k33zzTQBCQkJKHJ8zZw73338/AJGRkRw7dowRI0aQmZlJz549+e6776hdu/YFHm3FY7fbiYiIYPDgwdz/whvsiI+mgdVO/eY1WP1vCzcvu4x1Ow4xbdo0LrvsMoKCgs67nEBERESkovB4acHpmEwmoqOjiY6Odv+AKpmiVlsz35rD7s9fJMI7juTmj9L7X5Nh+RTG7ZlAn+SjXHbZZaXeLIiIiIhUdioAqawSYkn74W0A5my2YbPb2ODdiZ4t6zrvD44kIPwZANLS0jw1ShERERG3USJbWZkt+O1aAsDqX37DYvGiY8FvmC3HJ9lT6l0LUKLjg4iIiMjFokK035JzEBxJm8wjtFzyEleuiWJkq2oQ+iwERwLOFiKxsbH4+/sTFBTk4cGKiIiIlD/NyFZSuQV27vurP5MG1OSrbQUMXZBHsk8QOTk5JCcnM3ToUJYuXcq0adO0wEtEREQuSpqRraSmf7eVGw5+yO0dzHjdUZsx3xxWqy0RERGpUpTIVkJrdvxD9eTpjPaO48+A/3Br9IsM/WESSR++RFrzm/Hr/7BabYmIiMhFT4lsZZEQC2YLR3qNZszC3wjDwfaaXWnToDoAlv7PEGIxg8MOarUlIiIiVYAS2crCbIGEiaz6fR+7/ulPzVpW2hz5Bcw3HD+ncKGXiIiISFWgRLayCI5k58EjDNgwk63W97HabBA6XsmriIiIVFnqWlBJHMmzcdf2YPIML6wmG1h8lMSKiIhIlaZEtpKY+u1Wbsn+BKvJhmHxAXs+LJ/i6WGJiIiIeIwS2Upgbeo/1F49gwjvOFIDR2F6br+zrCBhopJZERERqbJUI1tRFXYpyO0Twdi4DQwxFXYpuKSa8/6isgKH3XNjFBEREfEgJbIVVWGXgjXb9/PXgRCq1fBRlwIRERGRYpTIVlTBkezLzqXfz9PZan0Pq0NdCkRERESKU41sBWWzO3gwNVRdCkREREROQolsBfX+qlRC099XlwIRERGRk1AiWwHtyTzK0WWxRHjHsaHNSHUpEBERESmDamQrisIuBUa/p3l+ySY6OmxsrNaJQL9azvvVpUBERESkBCWyFUVhl4Jt6Tn8sKUXHb0tBOb/BpbBx89RjayIiIiIixLZiiI4klybnbZJk9hqne1c4KUuBSIiIiInpRrZCmTSkSGuLgWGuhSIiIiInJIS2Qpi094s6qyZgdVkw2H2waQuBSIiIiKnpES2AnA4DH77ZByjveJY2uABzM+rS4GIiIjI6ahG1lMKuxQQHMnCn3eTkXWUn8xXEtKmgfN+dSkQEREROSUlsp5S2KXgWL6dScnduNsw08u8CaoPPX6OamRFRERETkqJrKcUJqnVEybyk+GF1duGPXgcFiWvIiIiImdENbIe9Furh11dChxmHyyhYz09JBEREZFKQ4mshzgcBpvmj8dqsmEzeWN2qEuBiIiIyNlQIushWxY8y/AjH/O6YxgHn9qjLgUiIiIiZ0k1sh5wOM/Gj9sz+LognBoDnsG3TjV1KRARERE5S5qRvVASYl2zra//sJ2Yo0OpV8Obh+zzj58THAmhUR4aoIiIiEjlohnZC6Ww3dY/R/J4b2U3nrDE82BBHHiN9/TIRERERColJbIXSmHpwCUJE0nxcnYqIHS8esWKiIiInCOVFlxAK/wecLXbMsw+SmJFREREzoMS2QvEZnew47PnXe22TGq3JSIiInJelMheIJvmPct9eXN5w3Q7R55OU7stERERkfOkGtkLIDu3gJ/+zOD7gnAa3BhF3RrearclIiIicp40I+suxdptvZHwB7HHbuGSmj7ckzfv+DlqtyUiIiJyzjQj6y6F7bYOHc1nzo/OdlsP5MeBRe22RERERMqDEll3KSwdqJcwkY2F7baMkHGY1KlAREREpFyotMCNfvV/yNVuy2H2wRQy1tNDEhEREbloKJF1E8Mw2Pbpc652W2a12xIREREpV0pky5ndbicxMZFXR92Kb8ocXim4lYz/7Fa7LREREZFyphrZchQfH09ERASpqamuY/V9v6NFt68JC1O7LREREZHypES2nMTHxxMeHs7g3u144NlFvLvJRrWcv7li01uEh4cTFxd3PJkVERERkfPm0dKCFStWcNNNN9GkSRNMJhOLFy8ucb9hGERHR9OkSROqV69OSEgImzZt8sxgT8FutxMREcHg3u1YfO0eGv39NWaf6swLSufzAX8zuHc7xowZg92u2VgRERGR8uLRRPbIkSN06tSJWbNmlXn/lClTmDFjBrNmzWLt2rU0btyYAQMGkJOTc4FHempJSUmkpqYybvp7rPV/jEcd89lW7V66/TUbc/9niZr2P3bs2EFSUpKnhyoiIiJy0fBoacENN9zADTfcUOZ9hmEwc+ZMxo8fT1hYGAAffPABvr6+zJ07l0ceeeRCDvWU0tLSAGjWqi3Xf9Ofdca7WE02sPhAcCQBhYl30XkiIiIicv4qbNeCHTt2kJ6ezsCBA13HrFYrwcHBrFq1yoMjK83Pzw+A2Lnfcn/Bp87NDyw+YHe23EpJSSlxnoiIiIicvwq72Cs9PR0AX1/fEsd9fX3ZuXPnSR+Xl5dHXl6e63Z2djYADocDh8PhhpFC3759ada8Bctnj+W1OzPZ3uE/XB4+AWPFVPjhZWK+b4q/vz99+/Z12xg8weFwYBjGRfWcKhLF130UW/dSfN1HsXUvxdd93BXTCpvIFjGZTCVuG4ZR6lhxsbGxTJgwodTx/fv3k5+fX+7jK9Lt1hEseWUs3T9twYQpPTD99RdbDl/J7G8a883a33nnnXc5ePCg276+JzgcDrKysjAMA7O5wk7uV1qKr/sotu6l+LqPYuteiq/7ZGVlueW6FTaRbdy4MeCcmS3+kXxGRkapWdrioqKiGD16tOt2dnY2zZo1o2HDhtSrV69cx2hKnIRhtrC34+Nsqh7ApUPHsX/VbIYMGeI6x9/fn08/Xeiq872YOBwOTCYTDRs21AveDRRf91Fs3UvxdR/F1r0UX/fx8fFxy3UrbCLr7+9P48aNWbZsGV26dAEgPz+f5cuXM3ny5JM+zmq1YrVaSx03m83l/0Np8cKUMJHff99Hvv0aXu+bRXignaRLHibNNwQ/Pz+CgoKwWCzl+3UrEJPJ5J7YCqD4upNi616Kr/sotu6l+LqHu+Lp0UT28OHD/PHHH67bO3bsYP369VxyySU0b96cUaNGERMTQ5s2bWjTpg0xMTHUqFGD4cOHe3DUxQRHknk0nwGrp7LV+gHWwza45llCgrXxgYiIiIi7eTSRXbduHaGhoa7bRSUB9913H++//z6RkZEcO3aMESNGkJmZSc+ePfnuu++oXbu2p4ZcSnTWIKYYr5RotyUiIiIi7ufRRDYkJATDME56v8lkIjo6mujo6As3qLOwNT2HFimzsHrZcJh9MBe221IyKyIiIuJ+KgA5D1sWPMtorzi+uOQBzM/vh9DxkDDRmcyKiIiIiFtV2MVeFd363YfYsT+bGYQz5I6XnAeLZmIdds8NTERERKSK0Izs2UiIdc22Tv9uKzNt4bT3q0vrTbOOnxMcCaFRHhqgiIiISNWhGdmzYbZAwkR2Zx4laftVjPJexA37F4J5vKdHJiIiIlLlKJE9G8GRGIZBs8QYtlq9nJ0KQsdrcZeIiIiIB6i04CwlN32QPMOZxBpqtyUiIiLiMUpkz9KeJdFYTTZsJm9MRe22REREROSCUyJ7FvYsiWZYzkfMtN9Gxn92q92WiIiIiAepRvYsrPlzPwsKwjnQ7T80qVdd7bZEREREPEiJ7OkkxILZwq/+DzE640YsZhO/1FgCCUudbbZUIysiIiLiESotOJ3Cllup8dEAvHHZ99T9aarzuIiIiIh4jGZkTyc4kn3Zudzy83RutH6Mdb9abomIiIhUBJqRPQPPH7rR1XILtdwSERERqRCUyJ7GlvRsrtjyprNvrNkH1HJLREREpEJQInsa2xc+T4R3HF9c8gCm5/er5ZaIiIhIBaEa2VP4IyOHP/dlMd0I58bbXnQeVMstERERkQpBiewpvJHwJ4ts4Qzo4EuEX53jd6hGVkRERMTjVFpwooRYWD6F1ANHWLL+bwBerv+V87iIiIiIVBhKZE9U2Dd264LncBgww/dbfH+err6xIiIiIhWMSgtOFBxJdm4B1yVPYav1A6xZ6hsrIiIiUhFpRrYMM/NvUd9YERERkQpOiewJDh3Np97aV7CabDjM3uobKyIiIlJBKZE9wZYFz/Gk+VM+rHYXpufUN1ZERESkolKNbDG5BXZ+23WQlQXhtB46HpPJpL6xIiIiIhWUZmQL220BxP28h9hjt1CnujeD//ng+DnBkRAa5aEBioiIiEhZNCNb2G7LYRi8s7YHT1jiecgWB5bxnh6ZiIiIiJyCEtnC0gFzwkS+M7ywetvI7xeFjzoViIiIiFRoKi0AjH5PU4Cz3ZbN5I1P/2c8PSQREREROQ0lssDuxRPwxka+4YWXUaAOBSIiIiKVgEoLlk+h+W+vML0gnENXPcVL9b9yttsCbYQgIiIiUoFV+UR2f/ZRPiwI5w1HGAlB/tBA7bZEREREKoMqn8jGHB3KIvvfDOroR4sGNZ0HNRMrIiIiUuFVzRrZwt6xezKP8vlvewF4vvZS53ERERERqRSqZiJb2Dt2+8LnsTsMpjb6Bt+fpzuPi4iIiEilUDVLC4IjyS2wE/rjJLZa52DNtkHoeJUUiIiIiFQiVXNGFnjfexh5hrN3rGHxURIrIiIiUslUyUTWZndgXjEFq8mG3eyNyZ6v3rEiIiIilUyVTGT/jHuBh+3zedN8OwVR+5xlBQkTlcyKiIiIVCJVskZ2/a6DLC0IxxQyhmreluNlBeodKyIiIlJpVLlEdv3uQ4w9OAhvi4mVvZofv0M1siIiIiKVStUpLVj5KgBzVu4A4LUmy2i07hVPjkhEREREzkOVmZE1/zidHC9vvtzQmScs8dywPw7M4z09LBERERE5R1UmkXVcHUG95Mls8na23FLfWBEREZHKrcqUFuT2eJx8nEmsw+ytJFZERESkkqsyiexfi2OwOApYlmqw4LejJM58BLtdXQpEREREKquqk8h+PZuGrxkM/CCH4fHHCH3qbVo3bUh8fLynhyYiIiIi56BSJLKzZ8/G39+fatWq0a1bN5KSks76GvcsyqWg0ZV8n5hETk4OyW+MINDfl/DwcCWzIiIiIpVQhU9kFyxYwKhRoxg/fjy//vorQUFB3HDDDezateusrlOtVTdGT3mHa4KvplatWvQa8QaLf9zE4MGDGTNmjMoMRERERCqZCp/IzpgxgwcffJB///vftG/fnpkzZ9KsWTPefPPNs7pOnatuYZR1CSTEuo6ZzWaioqLYsWPHOc3yioiIiIjnVOhENj8/n59//pmBAweWOD5w4EBWrVp1Vtea2P4v6q+eCmZLieMBAQEApKWlnd9gRUREROSCqtB9ZA8cOIDdbsfX17fEcV9fX9LT08t8TF5eHnl5ea7bWVlZADT6fS6H7nkGOj0Mhw657l+zZg0AtWrV4lCx43J6DoeD7OxsfHx8MJsr9HuiSknxdR/F1r0UX/dRbN1L8XWfohzLMIxyvW6FTmSLmEymErcNwyh1rEhsbCwTJkwodfzmBbmwIBqILvNxQ4YMOc9RioiIiMipHDx4kLp165bb9Sp0InvppZdisVhKzb5mZGSUmqUtEhUVxejRo123Dx06RIsWLdi1a1e5Bk4gOzubZs2asXv3burUqePp4Vx0FF/3UWzdS/F1H8XWvRRf98nKyqJ58+Zccskl5XrdCp3I+vj40K1bN5YtW8Ytt9ziOr5s2TJuvvnmMh/z/+3dfUhd9R8H8Pe16zNcXXswmWBzbT7MSLuSmuG1NPsjqA2koUwUHEwk8oEtbixQ99+ibRG5yqEVW9poS1o02fzDe/FhK5ZXyVndarY50jbXhLsKS/38/mhKpqud6z3n3m+/9wvuH56dy3nfN1+On8nXY2hoKEJDQ5ccj4qK4qLUicViYbc6Yr/6Ybf6Yr/6Ybf6Yr/68fWWjYAeZAGgrq4OpaWlyMjIQHZ2Npqbm3HlyhVUVlb6OxoRERER+VHAD7Lbt2/HjRs3sG/fPoyPjyM1NRWnT59GfHy8v6MRERERkR8F/CALAFVVVaiqqvLqvaGhoaivr192uwGtDLvVF/vVD7vVF/vVD7vVF/vVj17dmsTXz0EgIiIiIjIAH5JGREREREriIEtERERESuIgS0RERERK+k8MsocPH8aGDRsQFhYGq9WKnp6efzzf6XTCarUiLCwMCQkJeOuttwxKqh4t3Y6Pj6OkpASJiYkICgpCTU2NcUEVpaXfjz76CE8++STWrl0Li8WC7OxsnDlzxsC0atHSbW9vL3JycrB69WqEh4cjKSkJhw4dMjCterTed+f19fXBbDYjLS1N34AK09Ktw+GAyWRa8vr6668NTKwOret2enoae/fuRXx8PEJDQ7Fx40a0trYalFY9WvotLy9fdu1u2bJF20VFcR988IEEBwfLkSNHZGRkRKqrqyUyMlIuX7687PmXLl2SiIgIqa6ulpGRETly5IgEBwfLiRMnDE4e+LR2Ozo6Ki+88IK89957kpaWJtXV1cYGVozWfqurq2X//v3y+eefi9vtlpdeekmCg4NlYGDA4OSBT2u3AwMD0tbWJsPDwzI6OipHjx6ViIgIefvttw1Orgat/c6bmpqShIQEKSwslIceesiYsIrR2m13d7cAkG+++UbGx8cXXjMzMwYnD3zerNtnnnlGMjMzpaurS0ZHR+Wzzz6Tvr4+A1OrQ2u/U1NTi9bs2NiY3HvvvVJfX6/pusoPso888ohUVlYuOpaUlCR2u33Z81988UVJSkpadGzXrl2SlZWlW0ZVae32r2w2GwfZf7GSfuelpKRIY2Ojr6Mpzxfdbtu2TXbs2OHraP8J3va7fft2efnll6W+vp6D7B1o7XZ+kL1586YB6dSmtdvOzk6JioqSGzduGBFPeSu973Z0dIjJZJIffvhB03WV3lrw+++/44svvkBhYeGi44WFhejv71/2PefOnVty/lNPPYULFy7gjz/+0C2rarzplu6eL/qdm5uDx+Px+d+tVp0vunW5XOjv74fNZtMjotK87fedd97B999/j/r6er0jKmslazc9PR2xsbHIz89Hd3e3njGV5E23p06dQkZGBl555RWsX78emzdvxu7du/Hbb78ZEVkpvrjvtrS0oKCgQPMfvFLiDyLcyeTkJGZnZxETE7PoeExMDCYmJpZ9z8TExLLnz8zMYHJyErGxsbrlVYk33dLd80W/Bw4cwC+//ILnnntOj4jKWkm3cXFxuH79OmZmZtDQ0ICdO3fqGVVJ3vT77bffwm63o6enB2az0t92dOVNt7GxsWhubobVasX09DSOHj2K/Px8OBwO5ObmGhFbCd50e+nSJfT29iIsLAwdHR2YnJxEVVUVfv75Z+6T/ZuVfk8bHx9HZ2cn2traNF/7P3FHMZlMi74WkSXH/u385Y6T9m5JG2/7bW9vR0NDAz7++GOsW7dOr3hK86bbnp4e3Lp1C+fPn4fdbscDDzyA4uJiPWMq6277nZ2dRUlJCRobG7F582aj4ilNy9pNTExEYmLiwtfZ2dkYGxvDq6++ykF2GVq6nZubg8lkwvvvv4+oqCgAwMGDB1FUVISmpiaEh4frnlc13n5Pe/fddxEdHY2tW7dqvqbSg+yaNWtwzz33LJn2r127tuR/BfPuu+++Zc83m81YvXq1bllV4023dPdW0u/x48dRUVGBDz/8EAUFBXrGVNJKut2wYQMA4MEHH8RPP/2EhoYGDrJ/o7Vfj8eDCxcuwOVy4fnnnwfw54AgIjCbzTh79iyeeOIJQ7IHOl/dd7OysnDs2DFfx1OaN93GxsZi/fr1C0MsACQnJ0NEcPXqVWzatEnXzCpZydoVEbS2tqK0tBQhISGar630HtmQkBBYrVZ0dXUtOt7V1YVHH3102fdkZ2cvOf/s2bPIyMhAcHCwbllV4023dPe87be9vR3l5eVoa2vD008/rXdMJflq7YoIpqenfR1PeVr7tVgs+PLLLzE4OLjwqqysRGJiIgYHB5GZmWlU9IDnq7Xrcrm4Te5vvOk2JycHP/74I27durVwzO12IygoCHFxcbrmVc1K1q7T6cR3332HiooK7y6u6VfDAtD84x5aWlpkZGREampqJDIycuG33ux2u5SWli6cP//4rdraWhkZGZGWlhY+fusOtHYrIuJyucTlconVapWSkhJxuVxy8eJFf8QPeFr7bWtrE7PZLE1NTYseWTI1NeWvjxCwtHb7xhtvyKlTp8Ttdovb7ZbW1laxWCyyd+9ef32EgObNveGv+NSCO9Pa7aFDh6Sjo0PcbrcMDw+L3W4XAHLy5El/fYSApbVbj8cjcXFxUlRUJBcvXhSn0ymbNm2SnTt3+usjBDRv7ws7duyQzMxMr6+r/CArItLU1CTx8fESEhIiDz/8sDidzoV/KysrE5vNtuh8h8Mh6enpEhISIvfff7+8+eabBidWh9ZuASx5xcfHGxtaIVr6tdlsy/ZbVlZmfHAFaOn29ddfly1btkhERIRYLBZJT0+Xw4cPy+zsrB+Sq0HrveGvOMj+My3d7t+/XzZu3ChhYWGyatUqeeyxx+TTTz/1Q2o1aF23X331lRQUFEh4eLjExcVJXV2d/PrrrwanVofWfqempiQ8PFyam5u9vqZJ5PZvOhERERERKUTpPbJERERE9P+LgywRERERKYmDLBEREREpiYMsERERESmJgywRERERKYmDLBEREREpiYMsERERESmJgywRERERKYmDLBEREREpiYMsERERESmJgywRERERKYmDLBFRgPnkk08QHR2Nubk5AMDg4CBMJhP27NmzcM6uXbtQXFzsr4hERAGBgywRUYDJzc2Fx+OBy+UCADidTqxZswZOp3PhHIfDAZvN5q+IREQBgYMsEVGAiYqKQlpaGhwOB4A/h9ba2loMDQ3B4/FgYmICbrcbeXl5fs1JRORvHGSJiAJQXl4eHA4HRAQ9PT149tlnkZqait7eXnR3dyMmJgZJSUn+jklE5FdmfwcgIqKl8vLy0NLSgqGhIQQFBSElJQU2mw1OpxM3b97ktgIiIvAnskREAWl+n+xrr70Gm80Gk8kEm80Gh8PB/bFERLdxkCUiCkDz+2SPHTu2sBc2NzcXAwMD3B9LRHQbB1kiogD1+OOPY3Z2dmFoXbVqFVJSUrB27VokJyf7NxwRUQAwiYj4OwQRERERkVb8iSwRERERKYmDLBEREREpiYMsERERESmJgywRERERKYmDLBEREREpiYMsERERESmJgywRERERKYmDLBEREREpiYMsERERESmJgywRERERKYmDLBEREREpiYMsERERESnpf3H7SOuDCK/jAAAAAElFTkSuQmCC", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from pyfe3d import BeamC, BeamCData, BeamCProbe, DOF\n", "from pyfe3d.beamprop import BeamProp\n", "from test_solver_nonlinear_static import Model\n", "\n", "# NOTE w and P of the curve \"present analysis\" of Fig. 7 of Karamanlidis et\n", "# al. (1981), digitised at its markers, and its end point\n", "FIG7_W_P = np.array([\n", " [0.005, 0.3], [0.033, 10.5], [0.067, 19.0], [0.073, 20.1],\n", " [0.099, 25.1], [0.135, 29.8], [0.165, 32.4], [0.198, 34.0],\n", " [0.232, 34.4], [0.265, 34.2], [0.297, 33.5], [0.330, 33.0],\n", " [0.364, 32.4], [0.398, 32.2], [0.429, 32.8], [0.461, 34.1],\n", " [0.494, 36.3], [0.527, 40.4], [0.561, 45.8], [0.596, 52.5],\n", " [0.627, 61.7], [0.659, 72.2]])\n", "# NOTE limit loads read from the line of Fig. 7\n", "FIG7_UPPER, FIG7_LOWER = 34.4, 32.2\n", "\n", "\n", "def toggle_frame(n_member, P_ref=70., span=12.943, rise=0.386, E=10.3e6,\n", " b=0.753, t=0.243, nu=0.3):\n", " \"\"\"Williams' toggle frame with n_member BeamC elements per member\"\"\"\n", " prop = BeamProp()\n", " prop.A = b*t\n", " prop.E = E\n", " prop.G = E/2/(1 + nu)\n", " prop.Iyy = b*t**3/12 # bending in the XZ plane\n", " prop.Izz = t*b**3/12\n", " prop.J = b*t**3/3\n", " num_nodes = 2*n_member + 1\n", " xs = np.linspace(0, 2*span, num_nodes)\n", " zs = rise*(1 - np.abs(xs - span)/span)\n", " x = np.vstack((xs, 0*xs, zs)).T.flatten()\n", " data, probe = BeamCData(), BeamCProbe()\n", " elements = []\n", " for k in range(num_nodes - 1):\n", " elem = BeamC(probe)\n", " elem.n1, elem.n2 = k, k + 1\n", " elem.c1, elem.c2 = DOF*k, DOF*(k + 1)\n", " elem.init_k_KC0 = k*data.KC0_SPARSE_SIZE\n", " elem.init_k_KCNL = k*data.KCNL_SPARSE_SIZE\n", " elem.init_k_KG = k*data.KG_SPARSE_SIZE\n", " elem.update_rotation_matrix(0., 1., 0., x)\n", " elem.update_probe_xe(x)\n", " elements.append(elem)\n", " N = DOF*num_nodes\n", " bk = np.zeros(N, dtype=bool)\n", " # NOTE planar frame: v, rx and rz restrained; both ends clamped\n", " bk[1::DOF] = bk[3::DOF] = bk[5::DOF] = True\n", " bk[:DOF] = bk[-DOF:] = True\n", " fext = np.zeros(N)\n", " apex = DOF*n_member + 2\n", " fext[apex] = -P_ref\n", " return Model(elements, data, prop, x, N, fext), ~bk, apex\n", "\n", "\n", "def run_toggle_frame(n_member, NL_method, P_ref=70., inc=0.02):\n", " model, bu, apex = toggle_frame(n_member, P_ref=P_ref)\n", " an = model.analysis(bu, NL_method=NL_method, initialInc=inc,\n", " maxInc=inc, maxArcLength=1e6)\n", " increments, cs = an.static(NLgeom=True, silent=True)\n", " P = P_ref*np.r_[0., increments]\n", " w = -np.r_[0., [c[apex] for c in cs]]\n", " return P, w\n", "\n", "\n", "def toggle_limit_points(P, w):\n", " \"\"\"First local maximum of P and the next local minimum\"\"\"\n", " dP = np.diff(P)\n", " i = int(np.flatnonzero(dP < 0)[0])\n", " j = i + int(np.flatnonzero(dP[i:] > 0)[0])\n", " return (P[i], w[i]), (P[j], w[j])\n", "\n", "\n", "paths = {}\n", "for method in ['arc_length_riks', 'arc_length_crisfield']:\n", " P, w = run_toggle_frame(16, method)\n", " paths[method] = P, w\n", " (Pa, wa), (Pb, wb) = toggle_limit_points(P, w)\n", " print('%-21s 16 BeamC/member: %d increments, P %.2f at w %.4f; upper '\n", " 'limit %.3f at w %.3f, lower limit %.3f at w %.3f'\n", " % (method, len(P) - 1, P[-1], w[-1], Pa, wa, Pb, wb))\n", "print('Fig. 7, read: upper limit %.1f at w ~0.24, lower limit %.1f at w '\n", " '~0.40' % (FIG7_UPPER, FIG7_LOWER))\n", "P, w = paths['arc_length_riks']\n", "Pc = paths['arc_length_crisfield'][0]\n", "print(\"check: Riks' and Crisfield's methods, max difference of P %.1e\"\n", " % np.abs(P - Pc).max())\n", "\n", "fig, ax = plt.subplots(figsize=(7, 5))\n", "ax.plot(w, P, 'C0-', lw=1.5, label=\"16 BeamC/member, Riks\")\n", "ax.plot(paths['arc_length_crisfield'][1], Pc, 'C1x', ms=4,\n", " label=\"16 BeamC/member, Crisfield\")\n", "ax.plot(FIG7_W_P[:, 0], FIG7_W_P[:, 1], 'ko', mfc='none',\n", " label='Fig. 7, Karamanlidis et al. (1981), digitised')\n", "ax.set_xlabel('w')\n", "ax.set_ylabel('P')\n", "ax.set_xlim(0, 0.7)\n", "ax.set_ylim(0, 75)\n", "ax.grid(True, alpha=0.3)\n", "ax.legend(fontsize=8, loc='upper left')\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "9bccb98c", "metadata": {}, "source": [ "Both arc-length methods trace the same path, through the upper limit point,\n", "the snap-through and the lower limit point, to the load factor 1.0. The\n", "limit loads with 8 to 64 elements per member, compared with those read from\n", "Fig. 7:" ] }, { "cell_type": "code", "execution_count": 13, "id": "a6b0acf9", "metadata": { "execution": { "iopub.execute_input": "2026-10-25T10:41:07.929951Z", "iopub.status.busy": "2026-10-25T10:41:07.929794Z", "iopub.status.idle": "2026-10-25T10:41:11.390866Z", "shell.execute_reply": "2026-10-25T10:41:11.390164Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "BeamC/member upper limit lower limit upper % lower %\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "8 34.308 at 0.241 33.007 at 0.367 -0.27 +2.51\n", "16 33.957 at 0.236 31.717 at 0.389 -1.29 -1.50\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "32 33.871 at 0.231 31.354 at 0.389 -1.54 -2.63\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "64 33.851 at 0.231 31.260 at 0.394 -1.60 -2.92\n", "Fig. 7 34.4 at ~0.24 32.2 at ~0.40\n" ] } ], "source": [ "print('%-14s %16s %16s %9s %9s' % ('BeamC/member', 'upper limit',\n", " 'lower limit', 'upper %', 'lower %'))\n", "for n in [8, 16, 32, 64]:\n", " P_, w_ = (paths['arc_length_riks'] if n == 16\n", " else run_toggle_frame(n, 'arc_length_riks'))\n", " (Pa, wa), (Pb, wb) = toggle_limit_points(P_, w_)\n", " print('%-14d %7.3f at %5.3f %7.3f at %5.3f %+9.2f %+9.2f'\n", " % (n, Pa, wa, Pb, wb, 100*(Pa/FIG7_UPPER - 1),\n", " 100*(Pb/FIG7_LOWER - 1)))\n", "print('%-14s %7.1f at %5s %7.1f at %5s' % ('Fig. 7', FIG7_UPPER, '~0.24',\n", " FIG7_LOWER, '~0.40'))" ] }, { "cell_type": "markdown", "id": "32eb9834", "metadata": {}, "source": [ "The limit loads converge with the number of elements, the differences\n", "between successive meshes decreasing about four times at each refinement,\n", "to about 33.85 and 31.26 with 64 elements per member: 1.6 % and 2.9 % below\n", "the values read from Fig. 7, more than the reading uncertainty. Coarse\n", "meshes are too stiff, as in the cantilever above; with 4 elements per member\n", "the path has no limit point at all. The deflections of the limit points\n", "agree with Fig. 7 within the reading uncertainty." ] }, { "cell_type": "markdown", "id": "1363a891", "metadata": {}, "source": [ "Summary\n", "---\n", "\n", "| benchmark | reference | pyfe3d |\n", "|---|---|---|\n", "| cantilever under end moment | Table 3a, exact, rolls up into a circle | `Quad4R`: the von Karman solution, within 1 % of Table 3a at $M = 0.05 M_{max}$, no roll-up; `BeamC`, `BeamLR`: membrane locking, converging to the von Karman solution with the number of elements |\n", "| hinged roof, $h = 12.7$ | Table 9a | `Quad4R` with the default hourglass stiffness: limit loads within about 1 %; 7 % stiffer at the start, up to 0.06 $P_{max}$ lower on the descending branch |\n", "| hinged roof, $h = 6.35$ | Table 9d | snap-through and snap-back traced; `Quad4R` with the default hourglass stiffness: upper limit load within 0.5 %, lower limit load 0.015 $P_{max}$ lower |\n", "| Williams' toggle frame | Fig. 7 of Karamanlidis et al. (1981), digitised | `BeamC`, both arc-length methods: the same path, limit loads converging to 1.6 % (upper) and 2.9 % (lower) below those read from the figure |\n", "| sensitivity to `hgfactor_w` | Tables 9a and 9d, `Tria3DSG`, shallow-shell Kirchhoff Ritz solution | the default `Quad4R` is 6 to 7 % stiffer in the linear range; smaller values approach the references there, with mixed effects on the limit loads; the default is kept |\n", "\n", "The references of the first four rows are of Sze et al. (2004). The\n", "assertions of their comparisons are in\n", "`tests/test_nonlinear_benchmarks_sze2004.py`; the toggle frame is compared\n", "in this notebook only." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.13.13" } }, "nbformat": 4, "nbformat_minor": 5 }