{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# A comparison of the static displacement of Mindlin-Reissner and Kirchhoff-Love plates under the effect of a uniformly distributed constant load" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this notebook, we explore the differences in calculating the same plate using the Kirchhoff-Love and Uflyand-Mindlin theories. The vertical displacements at the center of the plates are compared across varying thickness values and for two different side length ratios." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First we create a helper function that returns the value of the vertical displacement for a uniformly distributed load." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "\n", "from sigmaepsilon.solid.material import (\n", " MindlinPlateSection,\n", " KirchhoffPlateSection,\n", " ElasticityTensor,\n", " LinearElasticMaterial,\n", ")\n", "from sigmaepsilon.solid.fourier import (\n", " NavierPlate,\n", " LoadGroup,\n", " RectangleLoad,\n", ")\n", "from sigmaepsilon.solid.material.utils import elastic_stiffness_matrix\n", "\n", "\n", "def calculate_UZ(size: tuple, shape: tuple, model: str) -> float:\n", " # geometry\n", " length_X, length_Y, thickness = size\n", "\n", " # material\n", " young_modulus = 2890.0\n", " poisson_ratio = 0.2\n", "\n", " # material stiffness matrix\n", " hooke = elastic_stiffness_matrix(E=young_modulus, NU=poisson_ratio)\n", " stiffness = ElasticityTensor(hooke, tensorial=False)\n", " material = LinearElasticMaterial(stiffness=stiffness)\n", " section_type = MindlinPlateSection if model == \"MR\" else KirchhoffPlateSection\n", " section = section_type(\n", " layers=[\n", " section_type.Layer(material=material, thickness=thickness),\n", " ]\n", " )\n", " ABDS_matrix = section.elastic_stiffness_matrix()\n", " bending_stiffness, shear_stiffness = (\n", " np.ascontiguousarray(ABDS_matrix[:3, :3]),\n", " np.ascontiguousarray(ABDS_matrix[3:, 3:]),\n", " )\n", " if not model == \"MR\":\n", " shear_stiffness = None\n", "\n", " # uniform distributed load\n", " loads = LoadGroup(\n", " LC1=RectangleLoad([[0, 0], [length_X, length_Y]], [-0.1, 0, 0]),\n", " )\n", " loads.lock()\n", "\n", " # coordinates of the point of evaluation\n", " coords = np.array([[length_X / 2, length_Y / 2]], dtype=float)\n", " \n", " plate = NavierPlate(\n", " (length_X, length_Y), shape, D=bending_stiffness, S=shear_stiffness\n", " )\n", " results = plate.linear_static_analysis(coords, loads)\n", "\n", " # return results[\"LC1\"][0, 0].values # this would return the same value\n", " return results[\"LC1\"].to_xarray().sel(index=0, component=\"UZ\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We create another helper function to calculate the normalized ratio of the results obtained for Kirchhoff-Love and Uflyand-Mindlin setups." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from typing import Iterable\n", "\n", "\n", "def generate_plot_data(\n", " size: Iterable[float], thicknesses: Iterable[float]\n", ") -> list[float]:\n", "\n", " Lx, Ly = size\n", " nx, ny = 20, 20\n", " absdiff = []\n", " for t in thicknesses:\n", " UZ_MR = calculate_UZ((Lx, Ly, t), (nx, ny), \"MR\")\n", " UZ_KL = calculate_UZ((Lx, Ly, t), (nx, ny), \"KL\")\n", " absdiff.append(UZ_MR / UZ_KL - 1)\n", " return absdiff" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally, we prepare the data and plot the results using ``matplotlib``." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "\n", "fig, axs = plt.subplots(1, 1, figsize=(6, 3), dpi=400, sharex=True)\n", "\n", "thicknesses = (2, 5, 10, 15, 20, 25, 30)\n", "\n", "# calculate plot data for square plate\n", "size = (800, 800)\n", "width_ratio = size[0] / size[1]\n", "absdiff = generate_plot_data(size, thicknesses)\n", "axs.plot(thicknesses, absdiff, label=\"Lx/Ly={}\".format(width_ratio))\n", "\n", "# calculate plot data for rectangular plate\n", "size = (400, 800)\n", "width_ratio = size[0] / size[1]\n", "absdiff = generate_plot_data(size, thicknesses)\n", "axs.plot(thicknesses, absdiff, label=\"Lx/Ly={}\".format(width_ratio))\n", "\n", "axs.set_xlabel(\"thickness\")\n", "axs.set_ylabel(\"$UZ_{MR}/UZ_{KL} - 1 $\")\n", "axs.legend()\n", "\n", "plt.rcParams.update(\n", " {\n", " \"text.usetex\": True,\n", " \"font.family\": \"sans-serif\",\n", " }\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The results show that:\n", "\n", "* for small thicknesses, the results are about the same, regardless of the side ratio\n", "* the differences are more significant for the rectangular plate" ] } ], "metadata": { "kernelspec": { "display_name": "sigmaepsilon-solid-fourier-2jj81J8s-py3.12", "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": "3.12.7" }, "orig_nbformat": 4 }, "nbformat": 4, "nbformat_minor": 2 }