{ "cells": [ { "cell_type": "markdown", "id": "ed4a795b", "metadata": {}, "source": [ "# Post-buckling of an axially compressed cylinder with imperfections\n", "\n", "Simo, Fox and Rifai [1], Section 6.3.4 (pp. 54-57, Fig. 6.3.4 on p. 56),\n", "traced the post-buckling path of a simply supported cylinder under axial\n", "compression, with and without an initial geometric imperfection, with the\n", "Riks method and their geometrically exact shell element: radius $R = 36$,\n", "length $L = 100$, thickness $t = 0.125$, $E = 10^7$, $\\nu = 0.3$. As in\n", "Stanley [2], they modelled an $L/10 \\times 15°$ section of the cylinder,\n", "with symmetry conditions on the interior edges and a simple support on the\n", "loaded edge, with a $10 \\times 10$ mesh, such that the post-buckling path is\n", "that of the diamond mode of 5 axial half-waves and 12 circumferential\n", "waves. The imperfections, of 10 % and 50 % of the thickness, have the shape\n", "of the lowest linear buckling mode; the loads are normalized by the linear\n", "buckling load and plotted against the axial deflection of the loaded edge,\n", "its maximum in Fig. 6.3.4(a) and (d) and also its average in Fig.\n", "6.3.4(c). Fig. 6.3.4(a) also has the results of the 9-node ANS element of\n", "Stanley [2].\n", "\n", "Here the same section is meshed with the Donnell-type element\n", "`BFSCCylinder`, the imperfection is added exactly as described below, and\n", "the path is traced with the Riks method of\n", "[structsolve](https://saullocastro.github.io/structsolve/) (0.10.0 or\n", "newer) to an axial deflection of 0.04, the end of the axes of the figure.\n", "The model is in the module `simo1990_cylinder.py` of this folder, also used\n", "by `tests/test_simo1990_cylinder.py`.\n", "\n", "## The section\n", "\n", "The section has $x$ from 0, the loaded edge, to $a = L/10 = 10$, and $y$\n", "from 0 to $b = 15° \\, R = 9.425$. With the degrees of freedom $u$, $u_{,x}$,\n", "$u_{,y}$, $v$, $v_{,x}$, $v_{,y}$, $w$, $w_{,x}$, $w_{,y}$, $w_{,xy}$ of\n", "the nodes, the edges are:\n", "\n", "- $x = 0$, simply supported and loaded: $v = v_{,y} = w = w_{,y} = 0$, $u$\n", " free, with the consistent nodal forces of a uniform compressive force per\n", " unit length;\n", "- $x = a$, the middle of an axial half-wave of the diamond mode, a symmetry\n", " plane: $u = u_{,y} = v_{,x} = w_{,x} = w_{,xy} = 0$;\n", "- $y = 0$ and $y = b$, the crest and the trough of a circumferential wave,\n", " symmetry planes: $u_{,y} = v = v_{,x} = w_{,y} = w_{,xy} = 0$.\n", "\n", "The derivatives along an edge of a prescribed displacement are prescribed\n", "with it. A 15° section is half of a circumferential wave of 12 waves, and\n", "$L/10$ half of an axial half-wave of 5 half-waves. The axial deflection is\n", "the axial displacement $u$ of the loaded edge, the shortening of the\n", "section, whose other end does not move axially." ] }, { "cell_type": "code", "execution_count": 1, "id": "f444d758", "metadata": { "execution": { "iopub.execute_input": "2026-11-03T12:16:18.442519Z", "iopub.status.busy": "2026-11-03T12:16:18.442307Z", "iopub.status.idle": "2026-11-03T12:16:19.878874Z", "shell.execute_reply": "2026-11-03T12:16:19.877954Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "classical buckling load N_cl = E t^2/(R sqrt(3 (1 - nu^2))) = 2626.9\n", " 4 x 4 elements, 165 unknowns: N_cr/N_cl = [1.011 1.02163 1.02404], shortening at N_cl 0.02086\n", " 6 x 6 elements, 367 unknowns: N_cr/N_cl = [1.006 1.01673 1.0196 ], shortening at N_cl 0.02086\n", " 8 x 8 elements, 649 unknowns: N_cr/N_cl = [1.00491 1.01574 1.01862], shortening at N_cl 0.02086\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "12 x 12 elements, 1453 unknowns: N_cr/N_cl = [1.00439 1.01534 1.01808], shortening at N_cl 0.02086\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "16 x 16 elements, 2577 unknowns: N_cr/N_cl = [1.00427 1.01527 1.01793], shortening at N_cl 0.02086\n" ] } ], "source": [ "import time\n", "\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "import simo1990_cylinder as simo\n", "\n", "print('classical buckling load N_cl = E t^2/(R sqrt(3 (1 - nu^2))) = %.1f'\n", " % simo.N_CL)\n", "for n in (4, 6, 8, 12, 16):\n", " model = simo.SectionModel(n, n)\n", " eigvals, modes, ulin = simo.linear_buckling(model)\n", " print('%2d x %2d elements, %4d unknowns: N_cr/N_cl = %s, '\n", " 'shortening at N_cl %.5f'\n", " % (n, n, model.bu.sum(), np.array2string(eigvals[:3], precision=5),\n", " model.shortening(ulin)[0]))" ] }, { "cell_type": "markdown", "id": "29659138", "metadata": {}, "source": [ "The lowest buckling load converges to $1.0043 N_{cl}$, with a pre-buckling\n", "state that is not quite the membrane one, the simple support restraining\n", "the radial expansion at the loaded edge, and two more modes within 1.5 %\n", "above it. Under the linear buckling load the section shortens by\n", "$1.0043 \\times 0.020859 = 0.02095$, the abscissa at a load of 1 of the\n", "straight lines of Fig. 6.3.4, read as $0.0205 \\pm 0.0003$; the membrane\n", "value is $N_{cl} a/(E t) = 0.02101$. The lowest mode, plotted below, is\n", "the diamond mode: one half-wave $\\cos(\\pi y/b)$ around the circumference\n", "and, along $x$, the axial half-wave at $x = a$ with a boundary layer at the\n", "simple support." ] }, { "cell_type": "code", "execution_count": 2, "id": "b885f799", "metadata": { "execution": { "iopub.execute_input": "2026-11-03T12:16:19.881163Z", "iopub.status.busy": "2026-11-03T12:16:19.880835Z", "iopub.status.idle": "2026-11-03T12:16:20.574789Z", "shell.execute_reply": "2026-11-03T12:16:20.573396Z" } }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "model = simo.SectionModel(12, 12)\n", "eigvals, modes, ulin = simo.linear_buckling(model)\n", "w = modes[6::10, 0].reshape(13, 13)\n", "w /= w.flat[np.argmax(np.abs(w))]\n", "fig, ax = plt.subplots(figsize=(5, 4))\n", "cs = ax.contourf(model.x.reshape(13, 13), model.y.reshape(13, 13), w, 21,\n", " cmap='RdBu_r')\n", "fig.colorbar(cs, label='$w/w_{max}$')\n", "ax.set_xlabel('$x$, loaded edge at $x = 0$')\n", "ax.set_ylabel('$y$')\n", "ax.set_aspect('equal')\n", "ax.set_title('Lowest buckling mode, $N_{cr}/N_{cl}$ = %.5f' % eigvals[0])\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "0c558a8c", "metadata": {}, "source": [ "## Initial imperfection, exactly for the Donnell-type kinematics\n", "\n", "The element takes no initial geometric imperfection, but with the\n", "Donnell-type kinematics an imperfection $w_0$ of the normal displacement\n", "can be added exactly. In the strains of a shallow imperfect shell the\n", "non-linear terms are $(w_{,x}^2 + 2 w_{0,x} w_{,x})/2$, ..., which are\n", "those of $\\boldsymbol{u} + \\boldsymbol{u}_0$ minus those of\n", "$\\boldsymbol{u}_0$, with $\\boldsymbol{u}_0$ the vector of the degrees of\n", "freedom of $w_0$ ($u = v = 0$, $w = w_0$ with its derivatives); the linear\n", "membrane strains and the curvatures are linear, so that\n", "\n", "$$\n", "\\boldsymbol{\\varepsilon}_{imp}(\\boldsymbol{u}) =\n", "\\boldsymbol{\\varepsilon}(\\boldsymbol{u} + \\boldsymbol{u}_0) -\n", "\\boldsymbol{\\varepsilon}(\\boldsymbol{u}_0), \\qquad\n", "\\boldsymbol{\\kappa}_{imp}(\\boldsymbol{u}) =\n", "\\boldsymbol{\\kappa}(\\boldsymbol{u} + \\boldsymbol{u}_0) -\n", "\\boldsymbol{\\kappa}(\\boldsymbol{u}_0) = \\boldsymbol{\\kappa}(\\boldsymbol{u})\n", "$$\n", "\n", "and the imperfect shell is stress free at $\\boldsymbol{u} = \\boldsymbol{0}$.\n", "Its stress resultants are those of the perfect shell at\n", "$\\boldsymbol{u} + \\boldsymbol{u}_0$ minus $\\boldsymbol{N}_0$ and\n", "$\\boldsymbol{M}_0$, those of the state $\\boldsymbol{u}_0$, and since\n", "$\\boldsymbol{B}_{NL}(\\boldsymbol{u} + \\boldsymbol{u}_0) =\n", "\\boldsymbol{B}_{NL}(\\boldsymbol{u}) + \\boldsymbol{B}_{NL}(\\boldsymbol{u}_0)$\n", "and $\\int_A \\boldsymbol{B}_{NL}(\\boldsymbol{u})^\\top \\boldsymbol{N}_0 dA =\n", "\\boldsymbol{K}_G(\\boldsymbol{N}_0) \\boldsymbol{u}$, the gradient of the\n", "strain energy of the imperfect shell is\n", "\n", "$$\n", "\\boldsymbol{F}_{int,imp}(\\boldsymbol{u}) =\n", "\\boldsymbol{F}_{int}(\\boldsymbol{u} + \\boldsymbol{u}_0) -\n", "\\boldsymbol{F}_{int}(\\boldsymbol{u}_0) -\n", "\\boldsymbol{K}_G(\\boldsymbol{N}_0) \\boldsymbol{u}, \\qquad\n", "\\boldsymbol{K}_{T,imp}(\\boldsymbol{u}) =\n", "\\boldsymbol{K}_T(\\boldsymbol{u} + \\boldsymbol{u}_0) -\n", "\\boldsymbol{K}_G(\\boldsymbol{N}_0)\n", "$$\n", "\n", "with $\\boldsymbol{K}_T = \\boldsymbol{K}_{C0} + \\boldsymbol{K}_{CNL} +\n", "\\boldsymbol{K}_{GNL} + \\boldsymbol{K}_G$ and\n", "$\\boldsymbol{K}_G(\\boldsymbol{N}_0)$ the geometric stiffness matrix of the\n", "resultants $\\boldsymbol{N}_0$ of the **whole** strains of\n", "$\\boldsymbol{u}_0$, linear and non-linear. The identities hold for the\n", "quadrature sums of the elements, for any number of integration points, when\n", "$\\boldsymbol{K}_G(\\boldsymbol{N}_0)$ is integrated with the same points.\n", "\n", "`update_KG` builds its matrix from the resultants of the linear strains\n", "only, $\\boldsymbol{K}_G(\\boldsymbol{u}_0)$, which is linear in the\n", "displacements, see its Notes; the part of the non-linear strains,\n", "$\\boldsymbol{K}_{GNL,0}$, is computed by `SectionModel.calc_kG_N` from the\n", "resultants at the integration points, such that\n", "$\\boldsymbol{K}_G(\\boldsymbol{N}_0) = \\boldsymbol{K}_G(\\boldsymbol{u}_0) +\n", "\\boldsymbol{K}_{GNL,0}$. The callables of structsolve, in\n", "`ImperfectCylinder`, are then\n", "\n", "- `calc_fint`: $\\boldsymbol{F}_{int}(\\boldsymbol{u} + \\boldsymbol{u}_0) -\n", " \\boldsymbol{F}_{int}(\\boldsymbol{u}_0) - \\boldsymbol{K}_G(\\boldsymbol{u}_0)\n", " \\boldsymbol{u} - \\boldsymbol{K}_{GNL,0} \\boldsymbol{u}$;\n", "- `calc_kC`: $\\boldsymbol{K}_{C0} + \\boldsymbol{K}_{CNL}(\\boldsymbol{u} +\n", " \\boldsymbol{u}_0) + \\boldsymbol{K}_{GNL}(\\boldsymbol{u} + \\boldsymbol{u}_0)\n", " - \\boldsymbol{K}_{GNL,0}$, the matrix of `update_KCNL` minus\n", " $\\boldsymbol{K}_{GNL,0}$;\n", "- `calc_kG`: $\\boldsymbol{K}_G(\\boldsymbol{u} + \\boldsymbol{u}_0) -\n", " \\boldsymbol{K}_G(\\boldsymbol{u}_0) = \\boldsymbol{K}_G(\\boldsymbol{u})$,\n", " the geometric stiffness matrix of the perfect shell.\n", "\n", "The construction uses the Donnell-type element: `calc_kG_N` builds the\n", "geometric stiffness matrix with the rows of $w_{,x}$ and $w_{,y}$ of the\n", "Donnell-type kinematics. With the Sanders-type element the rotation is\n", "$-w_{,y} + v/R$, its geometric stiffness matrix has rows in $v$, and these\n", "identities, not verified here, would need that matrix for\n", "$\\boldsymbol{N}_0$.\n", "\n", "The checks below, on a $4 \\times 4$ mesh: the internal forces vanish at\n", "$\\boldsymbol{u} = \\boldsymbol{0}$; `calc_kG_N` with the resultants of the\n", "linear strains gives the matrix of `update_KG`; the tangent stiffness\n", "matrix is the Jacobian of the internal forces, by central differences; and\n", "the internal forces are the gradient of the strain energy of the strains\n", "$\\boldsymbol{\\varepsilon}(\\boldsymbol{u} + \\boldsymbol{u}_0) -\n", "\\boldsymbol{\\varepsilon}(\\boldsymbol{u}_0)$, computed by\n", "`SectionModel.strain_energy` from the interpolation of the element at the\n", "integration points, independently of its kernels. The same gradient with\n", "$\\boldsymbol{K}_G(\\boldsymbol{u}_0)$ alone in place of\n", "$\\boldsymbol{K}_G(\\boldsymbol{N}_0)$ is off by orders of magnitude more\n", "than the error of the central differences, which decreases with $h^2$." ] }, { "cell_type": "code", "execution_count": 3, "id": "a4f6237c", "metadata": { "execution": { "iopub.execute_input": "2026-11-03T12:16:20.578089Z", "iopub.status.busy": "2026-11-03T12:16:20.577766Z", "iopub.status.idle": "2026-11-03T12:16:20.794391Z", "shell.execute_reply": "2026-11-03T12:16:20.793170Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "calc_kG_N(N_L(u)) vs. update_KG(u): rel. diff 5.2e-16\n", "imperfection 0.1 t: |F_int,imp(0)| = 0.0e+00\n", " h = 1e-04: tangent 8.0e-09, energy gradient 2.8e-06, with K_G(u0) alone 3.3e-05\n", " h = 1e-05: tangent 8.0e-11, energy gradient 2.8e-08, with K_G(u0) alone 3.6e-05\n", "imperfection 0.5 t: |F_int,imp(0)| = 0.0e+00\n", " h = 1e-04: tangent 1.2e-08, energy gradient 4.0e-06, with K_G(u0) alone 1.5e-04\n", " h = 1e-05: tangent 1.2e-10, energy gradient 4.0e-08, with K_G(u0) alone 1.4e-04\n" ] } ], "source": [ "rng = np.random.default_rng(1)\n", "model, mode, lbd_cr = simo.normalized_model(4, 4)\n", "n = model.bu.sum()\n", "u = model.expand(rng.standard_normal(n)*1e-2)\n", "KG = model.calc_KG(u).toarray()\n", "KGN = model.calc_kG_N(model.membrane_resultants(u, nonlinear=False)).toarray()\n", "print('calc_kG_N(N_L(u)) vs. update_KG(u): rel. diff %.1e'\n", " % (np.abs(KGN - KG).max()/np.abs(KG).max()))\n", "for xi in (0.1, 0.5):\n", " u0 = simo.imperfection(model, mode, xi)\n", " imp = simo.ImperfectCylinder(model, u0)\n", " print('imperfection %g t: |F_int,imp(0)| = %.1e' %\n", " (xi, np.linalg.norm(imp.calc_fint(np.zeros(n)))))\n", " u = np.zeros(model.N)\n", " u[6::10] = rng.standard_normal(model.N//10)\n", " u *= 0.3*simo.t/np.abs(u).max()\n", " u[0::10] = 1e-3*rng.standard_normal(model.N//10)\n", " u[3::10] = 1e-3*rng.standard_normal(model.N//10)\n", " c = u[model.bu]\n", " U = model.expand(c)\n", " v = rng.standard_normal(n)\n", " KT = imp.calc_kC(c, NLgeom=True) + imp.calc_kG(c, NLgeom=True)\n", " fv = imp.calc_fint(c) @ v\n", " fv_L = (model.calc_fint(U + u0) - imp.fint0 - imp.KG0 @ U)[model.bu] @ v\n", " for h in (1e-4, 1e-5):\n", " dfd = (imp.calc_fint(c + h*v) - imp.calc_fint(c - h*v))/(2*h)\n", " dU = (model.strain_energy(model.expand(c + h*v), u0)\n", " - model.strain_energy(model.expand(c - h*v), u0))/(2*h)\n", " print(' h = %.0e: tangent %.1e, energy gradient %.1e, '\n", " 'with K_G(u0) alone %.1e'\n", " % (h, np.linalg.norm(dfd - KT @ v)/np.linalg.norm(KT @ v),\n", " abs(dU - fv)/abs(fv), abs(dU - fv_L)/abs(fv)))" ] }, { "cell_type": "markdown", "id": "13700d94", "metadata": {}, "source": [ "## Riks analyses with the imperfections\n", "\n", "The imperfection is the $w$ part of the lowest buckling mode, scaled to a\n", "largest $|w_0|$ of 10 % or 50 % of $t$. Its sign does not matter: the\n", "section is symmetric about $y = b/2$, and $-\\cos(\\pi y/b) = \\cos(\\pi (b -\n", "y)/b)$. The reference load of each mesh is its own linear buckling load,\n", "such that the load factor of structsolve is the normalized load of the\n", "figure. The Riks method of structsolve starts with an increment of 0.1 of\n", "the load factor, limited to 0.1, and stops at the first converged increment\n", "with a maximum axial deflection of 0.04, with `stop_criterion =\n", "value_reached(...)` (`run_riks` of the module). Three meshes, the finest\n", "one, $12 \\times 12$, being the one of the figures:" ] }, { "cell_type": "code", "execution_count": 4, "id": "59495ae5", "metadata": { "execution": { "iopub.execute_input": "2026-11-03T12:16:20.797628Z", "iopub.status.busy": "2026-11-03T12:16:20.797358Z", "iopub.status.idle": "2026-11-03T12:19:58.864994Z", "shell.execute_reply": "2026-11-03T12:19:58.863843Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "10 % 4 x 4: N_cr/N_cl 1.01100, 102 increments, 9.9 s, max. residual 8e-11, limit load 0.7294 at u_max 0.01657\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "10 % 8 x 8: N_cr/N_cl 1.00491, 101 increments, 38.9 s, max. residual 1e-10, limit load 0.7270 at u_max 0.01625\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "10 % 12 x 12: N_cr/N_cl 1.00439, 100 increments, 89.1 s, max. residual 1e-10, limit load 0.7269 at u_max 0.01625\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "50 % 4 x 4: N_cr/N_cl 1.01100, 65 increments, 6.6 s, max. residual 2e-10, limit load 0.3965 at u_max 0.01064\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "50 % 8 x 8: N_cr/N_cl 1.00491, 64 increments, 26.0 s, max. residual 2e-10, limit load 0.3905 at u_max 0.01070\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "50 % 12 x 12: N_cr/N_cl 1.00439, 64 increments, 44.7 s, max. residual 2e-10, limit load 0.3902 at u_max 0.01070\n" ] } ], "source": [ "runs = {}\n", "for xi in (0.1, 0.5):\n", " for n in (4, 8, 12):\n", " r = simo.run_riks(xi, n, n)\n", " runs[xi, n] = r\n", " an = r['an']\n", " fext = an.calc_fext()\n", " res = max(np.linalg.norm(an.calc_fint(c) - lbd*fext)\n", " for lbd, c in zip(an.increments, an.cs))/np.linalg.norm(fext)\n", " lbd_lim, u_lim = simo.limit_point(r['lbds'], r['umax'])\n", " print('%2d %% %2d x %2d: N_cr/N_cl %.5f, %3d increments, %5.1f s, '\n", " 'max. residual %.0e, limit load %.4f at u_max %.5f'\n", " % (100*xi, n, n, r['lbd_cr'], len(an.increments), r['elapsed'],\n", " res, lbd_lim, u_lim))" ] }, { "cell_type": "markdown", "id": "82bd568d", "metadata": {}, "source": [ "The limit loads change by less than 0.001 from the $8 \\times 8$ to the $12\n", "\\times 12$ mesh; a $16 \\times 16$ mesh, not run here (77 s and 52 s), gives\n", "0.7270 and 0.3902, at the same deflections within $10^{-5}$. The residual\n", "of every converged increment is below $10^{-9}$ of the reference load\n", "vector." ] }, { "cell_type": "code", "execution_count": 5, "id": "7f9ebec6", "metadata": { "execution": { "iopub.execute_input": "2026-11-03T12:19:58.869086Z", "iopub.status.busy": "2026-11-03T12:19:58.868711Z", "iopub.status.idle": "2026-11-03T12:19:59.156856Z", "shell.execute_reply": "2026-11-03T12:19:59.155676Z" } }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def plot_fig(ax, data, marker, label):\n", " d = np.array(data)\n", " ax.plot(d[:, 0], d[:, 1], marker, ms=4, mfc='none', color='k', mew=0.7,\n", " label=label)\n", "\n", "\n", "fig, axes = plt.subplots(1, 2, figsize=(11, 4.5), sharey=True)\n", "colors = {0.1: 'C0', 0.5: 'C3'}\n", "ax = axes[0]\n", "ax.plot([0, 0.04], [0, 0.04/simo.FIG_LINEAR_U1], color='0.6', lw=0.8)\n", "for xi in (0.1, 0.5):\n", " for n, ls, lw in ((4, ':', 0.8), (8, '--', 0.8), (12, '-', 1.5)):\n", " r = runs[xi, n]\n", " ax.plot(r['umax'], r['lbds'], ls=ls, lw=lw, color=colors[xi],\n", " label='%d %%, %d x %d' % (100*xi, n, n))\n", "plot_fig(ax, simo.FIG_A_SIMO_10, 'o', 'Simo et al., 10 %')\n", "plot_fig(ax, simo.FIG_A_SIMO_50, 's', 'Simo et al., 50 %')\n", "plot_fig(ax, simo.FIG_A_ANS_10, '^', 'Stanley, 9-ANS, 10 %')\n", "plot_fig(ax, simo.FIG_A_ANS_50, 'D', 'Stanley, 9-ANS, 50 %')\n", "ax.set_title('Fig. 6.3.4(a): maximum axial deflection')\n", "ax.set_ylabel('Axial load / linear buckling load')\n", "ax = axes[1]\n", "for xi in (0.1, 0.5):\n", " r = runs[xi, 12]\n", " ax.plot(r['uavg'], r['lbds'], '-', color=colors[xi],\n", " label='%d %%, average' % (100*xi))\n", " ax.plot(r['umax'], r['lbds'], ':', color=colors[xi],\n", " label='%d %%, maximum' % (100*xi))\n", "ax.set_title('Fig. 6.3.4(c): average and maximum, 12 x 12')\n", "for ax in axes:\n", " ax.set_xlim(0, 0.042)\n", " ax.set_ylim(0, 1)\n", " ax.set_xlabel('Axial deflection of the loaded edge')\n", " ax.grid(lw=0.3)\n", " ax.legend(fontsize=7, loc='upper right')\n", "fig.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "c2124f23", "metadata": {}, "source": [ "The values of Simo et al. and of Stanley are read from Fig. 6.3.4 on the\n", "page rendered at 300 dpi with a grid of $0.001 \\times 0.05$ drawn over the\n", "axes, to about $\\pm 0.0003$ in the deflection and $\\pm 0.01$ in the load.\n", "The table compares the limit loads, the minimum loads after them and the\n", "loads at a maximum deflection of 0.04, of the $12 \\times 12$ mesh:" ] }, { "cell_type": "code", "execution_count": 6, "id": "18df64aa", "metadata": { "execution": { "iopub.execute_input": "2026-11-03T12:19:59.160319Z", "iopub.status.busy": "2026-11-03T12:19:59.159944Z", "iopub.status.idle": "2026-11-03T12:19:59.168114Z", "shell.execute_reply": "2026-11-03T12:19:59.167195Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " P_lim u_lim P_min u_min P(0.04)\n", "BFSC 12 x 12, 10 % 0.727 0.0163 0.326 0.0203 0.441\n", "Simo et al., Fig. (a) 0.715 0.0168 0.326 0.0184 0.459\n", "Stanley 9-ANS, Fig. (a) 0.717 0.0159 0.319 0.0184 nan\n", "BFSC 12 x 12, 50 % 0.390 0.0107 0.324 0.0179 0.455\n", "Simo et al., Fig. (a) 0.411 0.0108 0.315 0.0150 0.449\n", "Stanley 9-ANS, Fig. (a) 0.402 0.0106 0.297 0.0175 nan\n" ] } ], "source": [ "def summary(r):\n", " lbds, u = r['lbds'], r['umax']\n", " ilim = np.flatnonzero(np.diff(lbds) < 0)[0]\n", " imin = ilim + np.argmin(lbds[ilim:])\n", " p04 = np.interp(0.04, u[-2:], lbds[-2:])\n", " return lbds[ilim], u[ilim], lbds[imin], u[imin], p04\n", "\n", "\n", "def fig_summary(data):\n", " d = np.array(data)\n", " ilim = np.flatnonzero(np.diff(d[:, 1]) < 0)[0]\n", " imin = ilim + np.argmin(d[ilim:, 1])\n", " p04 = d[-1, 1] if abs(d[-1, 0] - 0.04) < 1e-4 else np.nan\n", " return d[ilim, 1], d[ilim, 0], d[imin, 1], d[imin, 0], p04\n", "\n", "\n", "print('%-26s %7s %8s %7s %8s %7s' % ('', 'P_lim', 'u_lim', 'P_min', 'u_min',\n", " 'P(0.04)'))\n", "for xi, fsimo, fans in ((0.1, simo.FIG_A_SIMO_10, simo.FIG_A_ANS_10),\n", " (0.5, simo.FIG_A_SIMO_50, simo.FIG_A_ANS_50)):\n", " for label, s in (('BFSC 12 x 12, %d %%' % (100*xi), summary(runs[xi, 12])),\n", " ('Simo et al., Fig. (a)', fig_summary(fsimo)),\n", " ('Stanley 9-ANS, Fig. (a)', fig_summary(fans))):\n", " print('%-26s %7.3f %8.4f %7.3f %8.4f %7.3f' % ((label,) + s))" ] }, { "cell_type": "markdown", "id": "87a1b485", "metadata": {}, "source": [ "The limit loads are 0.727 and 0.390, against 0.715 and 0.411 of Simo et\n", "al. and 0.717 and 0.402 of Stanley's 9-ANS element, at deflections within\n", "0.0006 of theirs. The differences, 0.012 and 0.021, are larger than the\n", "reading precision, and of the size of the differences between the two\n", "elements of the figure; the Donnell-type kinematics of this model and the\n", "geometrically exact shell of [1] differ in the terms of the order of the\n", "waves over the radius, and their $10 \\times 10$ mesh of a low-order element\n", "is coarser than the converged meshes here. The post-buckling path is that\n", "of the figure: the load drops at a decreasing, then increasing, deflection\n", "to a minimum of 0.326 (10 %) and 0.324 (50 %), against 0.326 and 0.315 of\n", "Simo et al., and both curves rise again to 0.44-0.46 at a deflection of\n", "0.04 (0.459 and 0.449 in the figure). The average deflection, Fig.\n", "6.3.4(c), is smaller than the maximum one beyond the limit point, the\n", "section shortening most at the inward lobe of the mode.\n", "\n", "The Riks analyses of a Ritz model of the same section with panels, in the\n", "benchmark `benchmarks/simo1990_cylinder.py` of structsolve, give 1.00415\n", "$N_{cl}$ for the buckling load, and limit loads of 0.727 at 0.0163 and 0.390\n", "at 0.0107, the same as here to the digits given.\n", "\n", "## The perfect cylinder, branch switching\n", "\n", "Without imperfection the path is axisymmetric until a bifurcation. Fig.\n", "6.3.4(d) traces it with a branch switching technique; [1] notes the\n", "difficulties of a multiplicity of clustered critical points near the first\n", "bifurcation, the solution process often changing paths. Here the Riks\n", "method of structsolve runs with `inertia=True` and SuperLU, whose sign of\n", "the determinant of the tangent stiffness matrix locates the critical points\n", "crossed, and with `branch_switching=3`, which switches to the bifurcated\n", "branch, along the critical eigenvector, at most three times. Increments of\n", "at most 0.03 avoid stepping over the clustered critical points. The\n", "$8 \\times 8$ mesh:" ] }, { "cell_type": "code", "execution_count": 7, "id": "f7a2d871", "metadata": { "execution": { "iopub.execute_input": "2026-11-03T12:19:59.170204Z", "iopub.status.busy": "2026-11-03T12:19:59.170025Z", "iopub.status.idle": "2026-11-03T12:22:04.605458Z", "shell.execute_reply": "2026-11-03T12:22:04.604277Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "461 increments, 125 s, switched at the increments [33], of load factor [0.8241], maximum deflection [0.01815]\n", "sign of the determinant: +1 up to the increment 32, then [-1 1]\n", "bifurcation 0.8241 at 0.01815; minimum 0.3272 at 0.02091; 0.4384 at 0.04\n" ] } ], "source": [ "r0 = simo.run_riks(0., 8, 8, branch_switching=3)\n", "an0 = r0['an']\n", "bp = np.array(an0.branch_points)\n", "print('%d increments, %.0f s, switched at the increments %s, of load '\n", " 'factor %s, maximum deflection %s'\n", " % (len(an0.increments), r0['elapsed'], bp,\n", " np.array2string(r0['lbds'][bp + 1], precision=4),\n", " np.array2string(r0['umax'][bp + 1], precision=5)))\n", "signs = np.array(an0.det_signs)\n", "print('sign of the determinant: +1 up to the increment %d, then %s'\n", " % (np.argmax(signs < 0) - 1, np.unique(signs[np.argmax(signs < 0):])))\n", "lbds0, u0max = r0['lbds'], r0['umax']\n", "ilim = bp[0] + 1\n", "imin = ilim + np.argmin(lbds0[ilim:])\n", "print('bifurcation %.4f at %.5f; minimum %.4f at %.5f; %.4f at 0.04'\n", " % (lbds0[ilim], u0max[ilim], lbds0[imin], u0max[imin],\n", " np.interp(0.04, u0max[-2:], lbds0[-2:])))" ] }, { "cell_type": "code", "execution_count": 8, "id": "a62c052d", "metadata": { "execution": { "iopub.execute_input": "2026-11-03T12:22:04.607325Z", "iopub.status.busy": "2026-11-03T12:22:04.607183Z", "iopub.status.idle": "2026-11-03T12:22:04.747479Z", "shell.execute_reply": "2026-11-03T12:22:04.746205Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(6, 4.5))\n", "ax.plot([0, 0.04], [0, 0.04/simo.FIG_LINEAR_U1], color='0.6', lw=0.8)\n", "ax.plot(u0max, lbds0, '-', color='C2', lw=1.2,\n", " label='perfect, 8 x 8, branch switching')\n", "ax.plot(u0max[bp + 1], lbds0[bp + 1], 'x', color='C2', ms=8,\n", " label='switched to the bifurcated branch')\n", "ax.plot(runs[0.1, 12]['umax'], runs[0.1, 12]['lbds'], '--', color='C0',\n", " lw=0.8, label='10 %, 12 x 12')\n", "plot_fig(ax, simo.FIG_D_SIMO, 'o', 'Simo et al., Fig. (d)')\n", "ax.set_xlim(0, 0.042)\n", "ax.set_ylim(0, 1)\n", "ax.set_xlabel('Maximum axial deflection of the loaded edge')\n", "ax.set_ylabel('Axial load / linear buckling load')\n", "ax.set_title('Fig. 6.3.4(d): perfect cylinder')\n", "ax.grid(lw=0.3)\n", "ax.legend(fontsize=7, loc='upper right')\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "d971a1e5", "metadata": {}, "source": [ "The sign of the determinant changes on the axisymmetric path between the\n", "increments 32 and 33, where the analysis switches to the bifurcated branch,\n", "at a load of 0.824 and a maximum deflection of 0.0181, against 0.833 and\n", "0.0183 read from Fig. 6.3.4(d); the bifurcation is below the linear\n", "buckling load because of the non-linear axisymmetric pre-buckling state at\n", "the simple support. On the bifurcated branch the load first falls at an\n", "almost constant maximum deflection, 0.0179 to 0.0184, as in the figure,\n", "down to a limit point at 0.587, rises to another one at 0.748 and then\n", "falls with a decreasing maximum deflection, 0.0145 at a load of 0.45\n", "(0.0149 at 0.457 in the figure), to the minimum, 0.327 at 0.0209 (0.334\n", "at 0.020), and ends on the curve of the 10 % imperfection, 0.438 at 0.04\n", "(0.480 in the figure). The sign of the determinant changes at each of\n", "these three limit points of the branch, such that the analysis crosses no\n", "other bifurcation than the first, and it needed one switch only of the\n", "three allowed, in about 460 increments. Between the bifurcation and the\n", "descent the figure has a drop to about 0.74 followed by a dotted excursion\n", "to a deflection of about 0.0195, of a path that, according to [1], changes\n", "branches near clustered critical points; this part of the path differs\n", "from the loop computed here, and only the bifurcation load, the descent,\n", "the minimum and the end of the curves are compared.\n", "\n", "## References\n", "\n", "[1] Simo, J. C., Fox, D. D., and Rifai, M. S., On a stress resultant\n", "geometrically exact shell model. Part III: Computational aspects of the\n", "nonlinear theory, Computer Methods in Applied Mechanics and Engineering,\n", "79(1), 21-70, 1990, doi:10.1016/0045-7825(90)90094-3.\n", "\n", "[2] Stanley, G. M., Continuum-based shell elements, PhD thesis, Stanford\n", "University, 1985." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "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 }