{ "cells": [ { "cell_type": "markdown", "id": "0ea15e99", "metadata": {}, "source": [ "Tutorial: Timoshenko beam benchmarks with BeamC and BeamLR\n", "===\n", "\n", "Static deflections and natural frequencies of Timoshenko cantilevers computed\n", "with the two beam elements of pyfe3d and compared with published values:\n", "\n", "- `BeamC`: consistent (interdependent) interpolation, cubic deflection and\n", " quadratic rotation that depend on the shear parameter, such that the\n", " element solves the homogeneous equilibrium equations of the Timoshenko beam\n", " exactly;\n", "- `BeamLR`: linear interpolation of the deflection and of the rotation,\n", " with reduced integration of the transverse shear;\n", "- the Euler-Bernoulli beam, without shear deformation, as a third reference.\n", "\n", "The references are:\n", "\n", "- Bathe, K. J., *Finite Element Procedures*, 2nd ed., K. J. Bathe,\n", " Watertown, MA, 2014, Section 1.2, Eq. (1.2) and Fig. 1.2;\n", "- Petyt, M., *Introduction to Finite Element Vibration Analysis*, 2nd ed.,\n", " Cambridge University Press, 2010,\n", " [doi:10.1017/CBO9780511761195](https://doi.org/10.1017/CBO9780511761195),\n", " Example 3.10 and Table 3.6.\n", "\n", "The models are those of `tests/test_timoshenko_beam_literature.py` and\n", "`tests/test_beamc_timoshenko_shape_functions.py`, imported below." ] }, { "cell_type": "code", "execution_count": 1, "id": "1f5dcf6d", "metadata": { "execution": { "iopub.execute_input": "2026-10-25T21:37:41.087709Z", "iopub.status.busy": "2026-10-25T21:37:41.087446Z", "iopub.status.idle": "2026-10-25T21:37:42.212665Z", "shell.execute_reply": "2026-10-25T21:37:42.211908Z" } }, "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", "from scipy.optimize import brentq\n", "\n", "from pyfe3d.beamprop import BeamProp\n", "from test_timoshenko_beam_literature import (bathe_prop, cantilever_tip,\n", " petyt_coefficients)\n", "import test_beamc_timoshenko_shape_functions as sf" ] }, { "cell_type": "markdown", "id": "1cecd521", "metadata": {}, "source": [ "Static deflection of a cantilever with shear deformation\n", "---\n", "\n", "Bathe (2014), Section 1.2, Fig. 1.2: cantilever of length $L = 28$ cm,\n", "rectangular cross section of height $h = 6$ cm and thickness $t = 0.4$ cm,\n", "$E = 2 \\times 10^7$ N/cm$^2$, $\\nu = 0.3$, tip force $W = 1000$ N. Eq. (1.2)\n", "gives the tip deflection with the bending and the shear contributions, with\n", "the shear correction factor $5/6$:\n", "\n", "$$\n", "\\delta = \\frac{W L^3}{3 E I} + \\frac{W L}{\\frac{5}{6} A G} = 0.053 \\text{ cm}\n", "$$\n", "\n", "The function `bathe_prop()` of the test puts the factor $5/6$ in `prop.G`.\n", "The Euler-Bernoulli deflection is the first term only." ] }, { "cell_type": "code", "execution_count": 2, "id": "9f9cc31d", "metadata": { "execution": { "iopub.execute_input": "2026-10-25T21:37:42.215218Z", "iopub.status.busy": "2026-10-25T21:37:42.214960Z", "iopub.status.idle": "2026-10-25T21:37:42.239406Z", "shell.execute_reply": "2026-10-25T21:37:42.238397Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "model delta [cm] error [%]\n", "Bathe (2014), published 0.0530000 \n", "Bathe (2014), Eq. (1.2) 0.0526348 \n", "Euler-Bernoulli 0.0508148 -3.458\n", "BeamC, 1 element(s) 0.0526348 -0.000\n", "BeamC, 3 element(s) 0.0526348 0.000\n", "BeamLR, 1 element(s) 0.0399311 -24.136\n", "BeamLR, 4 element(s) 0.0518408 -1.508\n", "BeamLR, 16 element(s) 0.0525852 -0.094\n", "BeamLR, 100 element(s) 0.0526335 -0.002\n", "\n", "check: one BeamC element against Eq. (1.2), relative difference 2.2e-16\n", "check: one BeamC element rounded to the published two digits: 0.053 cm\n" ] } ], "source": [ "L = 28. # cm\n", "W = 1000. # N\n", "prop = bathe_prop()\n", "delta_bending = W*L**3/(3*prop.E*prop.Izz)\n", "delta_ref = delta_bending + W*L/(prop.A*prop.G) # Eq. (1.2) of Bathe (2014)\n", "delta_published = 0.053 # cm\n", "\n", "print('%-28s %12s %10s' % ('model', 'delta [cm]', 'error [%]'))\n", "print('%-28s %12.7f %10s' % ('Bathe (2014), published', delta_published, ''))\n", "print('%-28s %12.7f %10s' % ('Bathe (2014), Eq. (1.2)', delta_ref, ''))\n", "print('%-28s %12.7f %10.3f' % ('Euler-Bernoulli', delta_bending,\n", " 100*(delta_bending - delta_ref)/delta_ref))\n", "for name, n in [('BeamC', 1), ('BeamC', 3), ('BeamLR', 1), ('BeamLR', 4),\n", " ('BeamLR', 16), ('BeamLR', 100)]:\n", " delta = W*cantilever_tip(name, prop, L, n)[0]\n", " print('%-28s %12.7f %10.3f' % ('%s, %d element(s)' % (name, n), delta,\n", " 100*(delta - delta_ref)/delta_ref))\n", "\n", "delta = W*cantilever_tip('BeamC', prop, L, 1)[0]\n", "print()\n", "print('check: one BeamC element against Eq. (1.2), relative difference %.1e'\n", " % abs(delta/delta_ref - 1))\n", "print('check: one BeamC element rounded to the published two digits: %.3f cm'\n", " % delta)" ] }, { "cell_type": "markdown", "id": "749451dd", "metadata": {}, "source": [ "One `BeamC` element gives Eq. (1.2) to round-off; the Euler-Bernoulli beam\n", "misses the shear deflection, 3.6 % of the bending deflection of this beam\n", "($L/h \\approx 4.7$).\n", "`BeamLR` converges with the number of elements. The convergence is plotted\n", "below for Bathe's cantilever and for a cantilever as long as deep, $L = h$,\n", "where the shear deflection is larger than the bending one (the second model of\n", "the test, `test_deep_cantilever_shear_deflection`)." ] }, { "cell_type": "code", "execution_count": 3, "id": "12aae748", "metadata": { "execution": { "iopub.execute_input": "2026-10-25T21:37:42.242312Z", "iopub.status.busy": "2026-10-25T21:37:42.242077Z", "iopub.status.idle": "2026-10-25T21:37:42.906683Z", "shell.execute_reply": "2026-10-25T21:37:42.905858Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Bathe (2014), L/h = 4.7: BeamLR error 2.4e-01 6.0e-02 1.5e-02 3.8e-03 9.4e-04 2.4e-04 5.9e-05 1.5e-05\n", "Bathe (2014), L/h = 4.7: BeamC error 2.2e-16 1.3e-15 1.9e-14 4.0e-14 2.5e-14 2.1e-13 9.4e-14 6.1e-13\n", "Bathe (2014), L/h = 4.7: BeamLR order between the last two meshes 2.00\n", "deep cantilever, L/h = 1: BeamLR error 1.5e-01 3.8e-02 9.5e-03 2.4e-03 5.9e-04 1.5e-04 3.7e-05 9.2e-06\n", "deep cantilever, L/h = 1: BeamC error 1.1e-16 0.0e+00 2.2e-16 1.6e-15 4.4e-16 6.1e-14 2.3e-13 5.2e-14\n", "deep cantilever, L/h = 1: BeamLR order between the last two meshes 2.00\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def deep_prop():\n", " E, nu, h = 1., 0.3, 1.\n", " p = BeamProp()\n", " p.A = h*h\n", " p.E = E\n", " p.G = E/(2*(1 + nu))\n", " p.Izz = p.Iyy = h**4/12\n", " p.J = 2*h**4/12\n", " return p\n", "\n", "cases = {\n", " 'Bathe (2014), L/h = 4.7': (bathe_prop(), 28.),\n", " 'deep cantilever, L/h = 1': (deep_prop(), 1.),\n", "}\n", "ns = np.array([1, 2, 4, 8, 16, 32, 64, 128])\n", "fig, ax = plt.subplots(figsize=(6, 4))\n", "for (label, (p, Lc)), marker in zip(cases.items(), ['o', 's']):\n", " ref = Lc**3/(3*p.E*p.Izz) + Lc/(p.A*p.G)\n", " err_lr = [abs(cantilever_tip('BeamLR', p, Lc, n)[0]/ref - 1) for n in ns]\n", " err_c = [abs(cantilever_tip('BeamC', p, Lc, n)[0]/ref - 1) for n in ns]\n", " ax.loglog(ns, err_lr, marker=marker, label='BeamLR, ' + label)\n", " print('%s: BeamLR error %s' % (label, ' '.join('%.1e' % e for e in err_lr)))\n", " print('%s: BeamC error %s' % (label, ' '.join('%.1e' % e for e in err_c)))\n", " print('%s: BeamLR order between the last two meshes %.2f'\n", " % (label, np.log(err_lr[-2]/err_lr[-1])/np.log(2)))\n", "ax.loglog(ns, 1./ns**2, 'k--', lw=1, label='slope 2')\n", "ax.set_xlabel('number of elements')\n", "ax.set_ylabel('relative error of the tip deflection')\n", "ax.grid(True, which='both', alpha=0.3)\n", "ax.legend()\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "51dbe504", "metadata": {}, "source": [ "`BeamC` is exact with any number of elements (errors at round-off, not\n", "plotted on the logarithmic scale); `BeamLR` converges quadratically.\n", "\n", "The shear parameter of BeamC\n", "---\n", "\n", "With $\\phi = 12 E I/(G A L^2)$, the shape functions of `BeamC` depend on\n", "$\\alpha = -\\phi$ and $\\beta = 1/(1 - \\alpha) = 1/(1 + \\phi)$, see the notes of\n", "`BeamC`. With this sign they solve the homogeneous equilibrium equations of\n", "the Timoshenko beam, the same solution as Eq. (3.236) of Petyt (2010), whose\n", "denominator $1 + 3\\beta_P$, with $\\beta_P = E I/(\\kappa A G a^2)$ and\n", "$a = L/2$, is $1 + \\phi$. Eq. (21) of Luo (2008), the source of the shape\n", "functions (Luo, Y., An Efficient 3D Timoshenko Beam Element with Consistent\n", "Shape Functions, Adv. Theor. Appl. Mech., 1(3), 95-106, 2008), gives\n", "$\\alpha$ with the positive sign, which `BeamC` used before version 0.11.0.\n", "\n", "The effect of the sign is shown with the shape functions of\n", "`tests/test_beamc_timoshenko_shape_functions.py`, written there for any\n", "$\\alpha$: the bending and shear stiffness matrix of one element,\n", "\n", "$$\n", "\\boldsymbol{K}_e = \\int_0^L \\left( E I \\boldsymbol{S}_{r_z,x}^\\top \\boldsymbol{S}_{r_z,x}\n", " + G A \\boldsymbol{S}_\\gamma^\\top \\boldsymbol{S}_\\gamma \\right) dx, \\qquad\n", "\\gamma_{xy} = v_{,x} - r_z\n", "$$\n", "\n", "is integrated with a 6-point Gauss quadrature, and the tip deflection of a\n", "cantilever with one element under a unit tip force is computed for\n", "$\\alpha = -\\phi$, $0$ and $+\\phi$ (the square cross section $0.3 \\times 0.3$,\n", "$E = 1$, $\\nu = 0.3$, $L = 1$ of that test)." ] }, { "cell_type": "code", "execution_count": 4, "id": "1afdfe14", "metadata": { "execution": { "iopub.execute_input": "2026-10-25T21:37:42.909351Z", "iopub.status.busy": "2026-10-25T21:37:42.909143Z", "iopub.status.idle": "2026-10-25T21:37:42.919877Z", "shell.execute_reply": "2026-10-25T21:37:42.919075Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "phi = 0.2340\n", "Euler-Bernoulli 493.827, Timoshenko (exact) 522.716\n", "alpha = -phi tip deflection 522.716, error -0.00 %\n", "alpha = 0 tip deflection 493.827, error -5.53 %\n", "alpha = +phi tip deflection 429.073, error -17.91 %\n", "BeamC, one element: 522.716, relative difference 6.7e-16\n" ] } ], "source": [ "def element_matrix(alpha, EI, GA):\n", " L = sf.L\n", " K = np.zeros((12, 12))\n", " points, weights = np.polynomial.legendre.leggauss(6)\n", " h = 1.e-6\n", " for p, w in zip(points, weights):\n", " xi = (p + 1)/2\n", " Nu, Nv, Nw, Nrx, Nry, Nrz, Sv_x, Sw_x = sf.shape_functions(xi, alpha)\n", " # NOTE r_z is quadratic in xi: the central difference is exact\n", " Srz_x = (sf.shape_functions(xi + h, alpha)[5]\n", " - sf.shape_functions(xi - h, alpha)[5])/(2*h*L)\n", " gamma = Sv_x - Nrz\n", " K += w*L/2*(EI*np.outer(Srz_x, Srz_x) + GA*np.outer(gamma, gamma))\n", " return K\n", "\n", "def one_element_tip(alpha, EI, GA):\n", " tip = [7, 11] # v and r_z of node 2\n", " K = element_matrix(alpha, EI, GA)\n", " return np.linalg.solve(K[np.ix_(tip, tip)], [1., 0.])[0]\n", "\n", "p = sf.get_prop()\n", "EI, GA = p.E*p.Izz, p.G*p.A\n", "phi = 12*EI/(GA*sf.L**2)\n", "exact = sf.L**3/(3*EI) + sf.L/GA\n", "print('phi = %.4f' % phi)\n", "print('Euler-Bernoulli %.3f, Timoshenko (exact) %.3f' % (sf.L**3/(3*EI), exact))\n", "for label, alpha in [('alpha = -phi', -phi), ('alpha = 0', 0.),\n", " ('alpha = +phi', +phi)]:\n", " tip = one_element_tip(alpha, EI, GA)\n", " print('%-13s tip deflection %.3f, error %+.2f %%'\n", " % (label, tip, 100*(tip/exact - 1)))\n", "tip, _ = sf.cantilever(1)\n", "print('BeamC, one element: %.3f, relative difference %.1e'\n", " % (tip[0], abs(tip[0]/exact - 1)))" ] }, { "cell_type": "markdown", "id": "d0099734", "metadata": {}, "source": [ "With $\\alpha = 0$ the interpolation is the cubic Hermite interpolation of the\n", "Euler-Bernoulli beam, with no shear strain. With $\\alpha = +\\phi$ the element\n", "of this beam, $L/b = 3.3$, is even stiffer than the Euler-Bernoulli beam,\n", "although the shear deformation can only make the beam more flexible. Over a\n", "range of slenderness, only $\\alpha = -\\phi$ gives the exact deflection:" ] }, { "cell_type": "code", "execution_count": 5, "id": "166c9733", "metadata": { "execution": { "iopub.execute_input": "2026-10-25T21:37:42.922208Z", "iopub.status.busy": "2026-10-25T21:37:42.922013Z", "iopub.status.idle": "2026-10-25T21:37:43.162692Z", "shell.execute_reply": "2026-10-25T21:37:43.161723Z" } }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "check: alpha = -phi exact for all L/b, max |ratio - 1| = 3.4e-11\n" ] } ], "source": [ "# NOTE sf.shape_functions() is written for the length sf.L = 1: the length is\n", "# kept and the side b of the square cross section varies\n", "slenderness = np.logspace(-0.5, 1.5, 40) # L/b\n", "ratios = {'alpha = -phi (BeamC)': [], 'alpha = 0 (Euler-Bernoulli)': [],\n", " 'alpha = +phi': []}\n", "for Lb in slenderness:\n", " b = sf.L/Lb\n", " EI_b, GA_b = p.E*b**4/12, p.G*b**2\n", " phi_b = 12*EI_b/(GA_b*sf.L**2)\n", " exact_b = sf.L**3/(3*EI_b) + sf.L/GA_b\n", " for key, alpha in zip(ratios, (-phi_b, 0., phi_b)):\n", " ratios[key].append(one_element_tip(alpha, EI_b, GA_b)/exact_b)\n", "fig, ax = plt.subplots(figsize=(6, 4))\n", "for (key, values), ls in zip(ratios.items(), ['-', '--', ':']):\n", " ax.semilogx(slenderness, values, ls, lw=2, label=key)\n", "ax.set_xlabel('L/b')\n", "ax.set_ylabel('one element / exact tip deflection')\n", "ax.grid(True, which='both', alpha=0.3)\n", "ax.legend()\n", "plt.tight_layout()\n", "plt.show()\n", "print('check: alpha = -phi exact for all L/b, max |ratio - 1| = %.1e'\n", " % np.abs(np.array(ratios['alpha = -phi (BeamC)']) - 1).max())" ] }, { "cell_type": "markdown", "id": "92f50c30", "metadata": {}, "source": [ "Natural frequencies with shear deformation and rotary inertia\n", "---\n", "\n", "Petyt (2010), Example 3.10 and Table 3.6: cantilever with radius of gyration\n", "$r_z/L = 0.08$, shear coefficient $\\kappa = 2/3$ and $E/G = 8/3$, with shear\n", "deformation and rotary inertia, in terms of the frequency coefficients\n", "$\\lambda = \\omega \\sqrt{\\rho A L^4/(E I)}$. One element with the same shape\n", "functions and consistent mass matrix as `BeamC` gives $3.322$ and $26.569$\n", "(p. 99-100); Table 3.6 lists the exact coefficients and the errors of three\n", "elements for $r_z/L = 0.08$ and $0.02$. The function `petyt_coefficients()`\n", "of the test assembles the cantilever and keeps the bending in the $xy$ plane." ] }, { "cell_type": "code", "execution_count": 6, "id": "51be04a7", "metadata": { "execution": { "iopub.execute_input": "2026-10-25T21:37:43.164882Z", "iopub.status.busy": "2026-10-25T21:37:43.164705Z", "iopub.status.idle": "2026-10-25T21:37:43.174557Z", "shell.execute_reply": "2026-10-25T21:37:43.173836Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "one BeamC element, r_z/L = 0.08\n", " mode Petyt BeamC\n", " 1 3.322 3.322\n", " 2 26.569 26.569\n", "check: max |difference| 3.0e-04 (published with three decimals)\n", "\n", "three BeamC elements, r_z/L = 0.08\n", " mode exact BeamC error Petyt % error BeamC %\n", " 1 3.284 3.288 0.12 0.12\n", " 2 15.488 15.871 2.47 2.47\n", " 3 34.301 37.320 8.80 8.80\n", "\n", "three BeamC elements, r_z/L = 0.02\n", " mode exact BeamC error Petyt % error BeamC %\n", " 1 3.500 3.500 0.02 0.01\n", " 2 21.353 21.480 0.59 0.59\n", " 3 57.474 58.839 2.37 2.37\n" ] } ], "source": [ "one = petyt_coefficients('BeamC', 0.08, 1, num_modes=2)\n", "print('one BeamC element, r_z/L = 0.08')\n", "print('%6s %10s %10s' % ('mode', 'Petyt', 'BeamC'))\n", "for i, (ref, c) in enumerate(zip([3.322, 26.569], one)):\n", " print('%6d %10.3f %10.3f' % (i + 1, ref, c))\n", "print('check: max |difference| %.1e (published with three decimals)'\n", " % np.abs(one - [3.322, 26.569]).max())\n", "\n", "table_3_6 = {\n", " 0.08: ([3.284, 15.488, 34.301], [0.12, 2.47, 8.80]),\n", " 0.02: ([3.500, 21.353, 57.474], [0.02, 0.59, 2.37]),\n", "}\n", "for rz_L, (exact, errors) in table_3_6.items():\n", " coef = petyt_coefficients('BeamC', rz_L, 3)\n", " err = 100*(coef - exact)/np.array(exact)\n", " print()\n", " print('three BeamC elements, r_z/L = %.2f' % rz_L)\n", " print('%6s %10s %10s %14s %14s' % ('mode', 'exact', 'BeamC',\n", " 'error Petyt %', 'error BeamC %'))\n", " for i in range(3):\n", " print('%6d %10.3f %10.3f %14.2f %14.2f'\n", " % (i + 1, exact[i], coef[i], errors[i], err[i]))" ] }, { "cell_type": "markdown", "id": "fe644cd7", "metadata": {}, "source": [ "The Euler-Bernoulli cantilever, without shear deformation and rotary inertia,\n", "has $\\lambda = x^2$ with $x$ the roots of $\\cos x \\cosh x = -1$. Its\n", "coefficients show how much the shear deformation and the rotary inertia lower\n", "the frequencies of these deep beams. The convergence of `BeamC` and `BeamLR`\n", "to the exact values of Table 3.6, $r_z/L = 0.08$:" ] }, { "cell_type": "code", "execution_count": 7, "id": "7e0bdc56", "metadata": { "execution": { "iopub.execute_input": "2026-10-25T21:37:43.177206Z", "iopub.status.busy": "2026-10-25T21:37:43.177022Z", "iopub.status.idle": "2026-10-25T21:37:43.660647Z", "shell.execute_reply": "2026-10-25T21:37:43.659676Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Euler-Bernoulli lambda: 3.516 22.034 61.697\n", "Petyt (2010), exact with shear and rotary inertia, r_z/L = 0.08: 3.284 15.488 34.301\n", "BeamC, 160 elements: 3.2837 15.4885 34.3020\n", "BeamLR, 160 elements: 3.2837 15.4893 34.3053\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "check: 160 BeamC elements against the exact values of Table 3.6, max relative difference 9.0e-05\n" ] } ], "source": [ "f = lambda x: np.cos(x)*np.cosh(x) + 1\n", "roots = [brentq(f, a, b) for a, b in [(1, 3), (4, 6), (7, 9)]]\n", "lambda_eb = np.array(roots)**2\n", "exact = np.array(table_3_6[0.08][0])\n", "print('Euler-Bernoulli lambda: %s' % ' '.join('%.3f' % l for l in lambda_eb))\n", "print('Petyt (2010), exact with shear and rotary inertia, r_z/L = 0.08: %s'\n", " % ' '.join('%.3f' % l for l in exact))\n", "\n", "ns = np.array([3, 5, 10, 20, 40, 80, 160])\n", "fig, ax = plt.subplots(figsize=(6, 4))\n", "markers = ['o', 's', '^']\n", "for name, ls in [('BeamC', '-'), ('BeamLR', '--')]:\n", " errs = np.array([np.abs(petyt_coefficients(name, 0.08, n)/exact - 1)\n", " for n in ns])\n", " for mode in range(3):\n", " ax.loglog(ns, errs[:, mode], ls, marker=markers[mode],\n", " label='%s, mode %d' % (name, mode + 1))\n", " print('%s, 160 elements: %s' % (name, ' '.join(\n", " '%.4f' % c for c in petyt_coefficients(name, 0.08, 160))))\n", "ax.set_xlabel('number of elements')\n", "ax.set_ylabel('relative error of the frequency')\n", "ax.grid(True, which='both', alpha=0.3)\n", "ax.legend(ncol=2, fontsize=8)\n", "plt.tight_layout()\n", "plt.show()\n", "coef = petyt_coefficients('BeamC', 0.08, 160)\n", "print('check: 160 BeamC elements against the exact values of Table 3.6, '\n", " 'max relative difference %.1e' % np.abs(coef/exact - 1).max())" ] }, { "cell_type": "markdown", "id": "dc628bb2", "metadata": {}, "source": [ "Three `BeamC` elements reproduce the errors of Table 3.6 within their\n", "rounding (the exact values have three decimals and the errors two). Both\n", "elements converge to the exact values of Table 3.6; the difference left with\n", "160 elements is within the rounding of the three published decimals, which\n", "is where the errors of the plot level off. `BeamC`\n", "starts much closer, because its interpolation solves the static equilibrium\n", "equations; the error left comes from the interpolation of the inertia\n", "forces.\n", "\n", "Summary\n", "---\n", "\n", "| benchmark | reference | pyfe3d |\n", "|---|---|---|\n", "| cantilever tip deflection with shear | Bathe (2014), Eq. (1.2), 0.053 cm | one `BeamC`: Eq. (1.2) to round-off; `BeamLR`: second-order convergence |\n", "| frequency coefficients, one element | Petyt (2010), Example 3.10: 3.322, 26.569 | one `BeamC`: the same three decimals |\n", "| errors of three elements | Petyt (2010), Table 3.6 | three `BeamC`: the same errors, within their rounding |\n", "| exact frequency coefficients | Petyt (2010), Table 3.6 | `BeamC` and `BeamLR` converge to them |" ] } ], "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 }