{ "cells": [ { "cell_type": "markdown", "id": "a904a713", "metadata": {}, "source": [ "# Transverse shear stresses through the thickness\n", "\n", "The FSDT gives constant transverse shear strains through the thickness. The\n", "stresses that satisfy equilibrium, vanish at the faces and are continuous at\n", "the ply interfaces are given by `calc_transverse_shear_stress`, for given\n", "shear forces, and by `calc_equilibrium_transverse_shear`, from the strain\n", "gradients of an actual solution. This tutorial also compares the shear\n", "correction methods. SI units are used throughout." ] }, { "cell_type": "code", "execution_count": 1, "id": "af3922ee", "metadata": { "execution": { "iopub.execute_input": "2026-10-22T13:32:03.707820Z", "iopub.status.busy": "2026-10-22T13:32:03.707585Z", "iopub.status.idle": "2026-10-22T13:32:04.226614Z", "shell.execute_reply": "2026-10-22T13:32:04.225621Z" } }, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "from composites import laminated_plate, isotropic_plate\n", "\n", "laminaprop = (142e9, 8.7e9, 0.28, 5.1e9, 5.1e9, 3.2e9)\n", "plyt = 0.25e-3" ] }, { "cell_type": "markdown", "id": "64c4580c", "metadata": {}, "source": [ "## Stresses for given shear forces\n", "\n", "For a cross-ply $[0/90]_s$ laminate and a homogeneous plate of the same\n", "thickness, the stresses of the shear force $Q_x$ are compared with the\n", "parabola $\\tau_{xz} = 3 Q_x/(2h) (1 - 4z^2/h^2)$. The arguments are\n", "`(z, Qy, Qx)` and the results `(tau_yz, tau_xz)`." ] }, { "cell_type": "code", "execution_count": 2, "id": "e7a2b152", "metadata": { "execution": { "iopub.execute_input": "2026-10-22T13:32:04.229315Z", "iopub.status.busy": "2026-10-22T13:32:04.228993Z", "iopub.status.idle": "2026-10-22T13:32:04.403041Z", "shell.execute_reply": "2026-10-22T13:32:04.401748Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cp = laminated_plate([0, 90, 90, 0], plyt=plyt, laminaprop=laminaprop)\n", "h = cp.h\n", "Qx = 1e3 # N/m\n", "zs = np.linspace(-h/2, h/2, 201)\n", "tau_xz = [cp.calc_transverse_shear_stress(z, 0., Qx)[1] for z in zs]\n", "tau_yz = [cp.calc_transverse_shear_stress(z, Qx, 0.)[0] for z in zs]\n", "parabola = 3*Qx/(2*h)*(1 - 4*zs**2/h**2)\n", "\n", "fig, ax = plt.subplots(figsize=(4.5, 4))\n", "ax.plot(np.array(tau_xz)/1e6, zs*1e3, label='tau_xz, Qx = %g' % Qx)\n", "ax.plot(np.array(tau_yz)/1e6, zs*1e3, label='tau_yz, Qy = %g' % Qx)\n", "ax.plot(parabola/1e6, zs*1e3, 'k--', label='homogeneous')\n", "for zi in np.linspace(-h/2, h/2, 5):\n", " ax.axhline(zi*1e3, color='gray', lw=0.5)\n", "ax.set_xlabel('stress [MPa]')\n", "ax.set_ylabel('z [mm]')\n", "ax.legend()\n", "fig.tight_layout()" ] }, { "cell_type": "markdown", "id": "dadc7c5d", "metadata": {}, "source": [ "The stresses vanish at the faces and change slope at the interfaces. The\n", "shear correction of `'rohwer'` is the ratio between the strain energy of\n", "these stresses and the one of constant strains:" ] }, { "cell_type": "code", "execution_count": 3, "id": "5a9bd953", "metadata": { "execution": { "iopub.execute_input": "2026-10-22T13:32:04.405957Z", "iopub.status.busy": "2026-10-22T13:32:04.405462Z", "iopub.status.idle": "2026-10-22T13:32:04.411590Z", "shell.execute_reply": "2026-10-22T13:32:04.410843Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "scf_k13 = A55/Abar55 = 0.7454\n", "scf_k23 = A44/Abar44 = 0.6685\n" ] } ], "source": [ "print('scf_k13 = A55/Abar55 = %.4f' % cp.scf_k13)\n", "print('scf_k23 = A44/Abar44 = %.4f' % cp.scf_k23)" ] }, { "cell_type": "markdown", "id": "cb159993", "metadata": {}, "source": [ "## Angle-ply coupling\n", "\n", "In a $[45/-45]_s$ laminate, a shear force $Q_x$ also creates $\\tau_{yz}$,\n", "through the bending-twisting coupling $D_{16}$, $D_{26}$. The coupling term\n", "`A45` of `Ats` is not zero, although `Abar45` is." ] }, { "cell_type": "code", "execution_count": 4, "id": "9d125987", "metadata": { "execution": { "iopub.execute_input": "2026-10-22T13:32:04.414361Z", "iopub.status.busy": "2026-10-22T13:32:04.414130Z", "iopub.status.idle": "2026-10-22T13:32:04.536777Z", "shell.execute_reply": "2026-10-22T13:32:04.535912Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Ats =\n", " [[3136030.33223062 122955.17981668]\n", " [ 122955.17981668 3136030.33223062]]\n", "Abar_ts =\n", " [[4150000. 0.]\n", " [ 0. 4150000.]]\n" ] }, { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ap = laminated_plate([45, -45, -45, 45], plyt=plyt, laminaprop=laminaprop)\n", "tau = np.array([ap.calc_transverse_shear_stress(z, 0., Qx) for z in zs])\n", "fig, ax = plt.subplots(figsize=(4.5, 4))\n", "ax.plot(tau[:, 1]/1e6, zs*1e3, label='tau_xz')\n", "ax.plot(tau[:, 0]/1e6, zs*1e3, label='tau_yz')\n", "ax.set_xlabel('stress [MPa]')\n", "ax.set_ylabel('z [mm]')\n", "ax.set_title('Qx = %g N/m' % Qx)\n", "ax.legend()\n", "fig.tight_layout()\n", "print('Ats =\\n', ap.Ats)\n", "print('Abar_ts =\\n', ap.Abar_ts)" ] }, { "cell_type": "markdown", "id": "099ef989", "metadata": {}, "source": [ "## Stresses recovered from strain gradients\n", "\n", "`calc_equilibrium_transverse_shear` integrates the equilibrium equations\n", "from the bottom face with the derivatives of the generalized strains\n", "$\\{\\varepsilon^{(0)}, \\varepsilon^{(1)}\\}$, e.g. of an FSDT solution. In\n", "cylindrical bending about $y$, with $M_{xx,x} = Q_x$ and the other\n", "derivatives of the resultants equal to zero, the strain gradients are\n", "`inv(ABD) @ {0, 0, 0, Qx, 0, 0}`, and the recovered stresses coincide with\n", "those of `calc_transverse_shear_stress`." ] }, { "cell_type": "code", "execution_count": 5, "id": "990aa40c", "metadata": { "execution": { "iopub.execute_input": "2026-10-22T13:32:04.538725Z", "iopub.status.busy": "2026-10-22T13:32:04.538464Z", "iopub.status.idle": "2026-10-22T13:32:04.547875Z", "shell.execute_reply": "2026-10-22T13:32:04.547071Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "max difference [Pa]: 6.984919309616089e-10\n" ] } ], "source": [ "grad_x = np.linalg.solve(cp.ABD, [0, 0, 0, Qx, 0, 0])\n", "grad_y = np.zeros(6)\n", "z, tyz, txz = cp.calc_equilibrium_transverse_shear(grad_x, grad_y, z=zs)\n", "print('max difference [Pa]:',\n", " np.abs(txz[0] - np.array(tau_xz)).max())" ] }, { "cell_type": "markdown", "id": "db6fb800", "metadata": {}, "source": [ "`calc_aposteriori_energy` gives the transverse shear strain energies of the\n", "recovered stresses, from which the a posteriori factor of Noor and Peters,\n", "$k_{13} = Q_x^2 / (2 \\bar{A}_{55} U_{13})$, follows:" ] }, { "cell_type": "code", "execution_count": 6, "id": "2a948452", "metadata": { "execution": { "iopub.execute_input": "2026-10-22T13:32:04.550067Z", "iopub.status.busy": "2026-10-22T13:32:04.549820Z", "iopub.status.idle": "2026-10-22T13:32:04.554799Z", "shell.execute_reply": "2026-10-22T13:32:04.553945Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "resultant of the recovered stresses: Qx = 1000.000000 N/m\n", "a posteriori k13 = 0.7454\n", "'rohwer' scf_k13 = 0.7454\n" ] } ], "source": [ "U13, U23, Qy_r, Qx_r = cp.calc_aposteriori_energy(grad_x, grad_y)\n", "print('resultant of the recovered stresses: Qx = %.6f N/m' % Qx_r[0])\n", "print('a posteriori k13 = %.4f' % (Qx**2/(2*cp.Abar55*U13[0])))\n", "print(\"'rohwer' scf_k13 = %.4f\" % cp.scf_k13)" ] }, { "cell_type": "markdown", "id": "56851946", "metadata": {}, "source": [ "## Comparison of the shear correction methods\n", "\n", "The methods are selected with the argument `shear_correction`. For a\n", "homogeneous plate most of them give 5/6; they differ for laminates, in\n", "particular for a sandwich with a soft core. `'thickness_shear'` requires the\n", "densities of the plies." ] }, { "cell_type": "code", "execution_count": 7, "id": "b7aa6c76", "metadata": { "execution": { "iopub.execute_input": "2026-10-22T13:32:04.557321Z", "iopub.status.busy": "2026-10-22T13:32:04.557101Z", "iopub.status.idle": "2026-10-22T13:32:04.577376Z", "shell.execute_reply": "2026-10-22T13:32:04.576603Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "k13 rohwer vlachoutsis birman_bert thickness_shear constant\n", "isotropic 0.8333 0.8333 1.0000 0.8225 0.8333\n", "[0/90]s 0.7454 0.7453 0.8882 0.6788 0.8333\n", "sandwich 0.1010 0.1010 0.1036 0.0959 0.8333\n" ] } ], "source": [ "core = (0.1e9, 0.1e9, 0.3, 0.04e9, 0.04e9, 0.04e9)\n", "laminates = {\n", " 'isotropic': dict(stack=[0], plyt=1e-3, laminaprop=(70e9, 0.3),\n", " rho=2700.),\n", " '[0/90]s': dict(stack=[0, 90, 90, 0], plyt=plyt, laminaprop=laminaprop,\n", " rho=1600.),\n", " 'sandwich': dict(stack=[0, 90, 0, 90, 0], plyts=[plyt, plyt, 10e-3,\n", " plyt, plyt],\n", " laminaprops=[laminaprop, laminaprop, core, laminaprop,\n", " laminaprop],\n", " rhos=[1600., 1600., 50., 1600., 1600.]),\n", "}\n", "methods = ['rohwer', 'vlachoutsis', 'birman_bert', 'thickness_shear',\n", " 'constant']\n", "print('%-12s' % 'k13' + ''.join('%17s' % m for m in methods))\n", "for name, kwargs in laminates.items():\n", " k13 = [laminated_plate(shear_correction=m, **kwargs).scf_k13\n", " for m in methods]\n", " print('%-12s' % name + ''.join('%17.4f' % k for k in k13))" ] } ], "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 }