2022-04-07 18:46:57 +02:00

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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Description\n",
"\n",
"This notebook intends to gather all the functionalities you'll have to implement for assignment 2.2.\n",
"\n",
"# Load libraries"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import igl\n",
"import meshplot as mp\n",
"import time\n",
"import torch\n",
"\n",
"import sys as _sys\n",
"_sys.path.append(\"../src\")\n",
"from elasticsolid import *\n",
"from elasticenergy import *\n",
"from vis_utils import *\n",
"from matplotlib import gridspec\n",
"import matplotlib.pyplot as plt\n",
"\n",
"torch.set_default_dtype(torch.float64)\n",
"\n",
"shadingOptions = {\n",
" \"flat\":True,\n",
" \"wireframe\":False, \n",
"}\n",
"\n",
"rot = np.array(\n",
" [[1, 0, 0 ],\n",
" [0, 0, 1],\n",
" [0, -1, 0 ]]\n",
")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Load mesh\n",
"\n",
"Several meshes are available for you to play with under `data/`: `ball.obj`, `dinosaur.obj`, and `beam.obj`."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"scrolled": false
},
"outputs": [],
"source": [
"vNP, _, _, tNP, _, _ = igl.read_obj(\"../data/beam.obj\")\n",
"aabb = np.max(vNP, axis=0) - np.min(vNP, axis=0)\n",
"v = torch.tensor(vNP)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Linear/Non-Linear Elastic Solid\n",
"\n",
"## Instantiation\n",
"\n",
"We first specify the elasticity model to use for the elastic solid, as well as pinned vertices, and volumetric forces."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"rho = 131 # [kg.m-3]\n",
"young = 10e6 # [Pa] \n",
"poisson = 0.2\n",
"force_mass = torch.zeros(size = (3,))\n",
"force_mass[2] = - rho * 9.81\n",
"\n",
"minX = torch.min(v[:, 0])\n",
"pin_idx = torch.arange(v.shape[0])[v[:, 0] < minX + 0.2*aabb[0]]\n",
"\n",
"ee_lin = LinearElasticEnergy(young, poisson)\n",
"ee_neo = NeoHookeanElasticEnergy(young, poisson)\n",
"solid_lin = ElasticSolid(v, tNP, ee_lin, rho=rho, pin_idx=pin_idx, f_mass=force_mass)\n",
"solid_neo = ElasticSolid(v, tNP, ee_neo, rho=rho, pin_idx=pin_idx, f_mass=force_mass)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Validate Elastic Energy Gradient (Elastic Forces) using Finite Differences on Elastic Energy"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"solid_lin.update_def_shape(v)\n",
"solid_neo.update_def_shape(v)\n",
"\n",
"fd_validation_elastic(solid_lin)\n",
"fd_validation_elastic(solid_neo)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Validate External Energy Gradient (External Forces) using Finite Differences on External Energy"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"maxX = torch.max(v[:, 0])\n",
"f_point_idx = torch.arange(v.shape[0])[v[:, 0] > maxX - 0.01*aabb[0]]\n",
"\n",
"f_point = torch.zeros(size=(f_point_idx.shape[0], 3))\n",
"f_point[:, 2] = -5e3\n",
"\n",
"solid_lin.add_point_load(f_point_idx, f_point)\n",
"solid_neo.add_point_load(f_point_idx, f_point)\n",
"\n",
"solid_lin.update_def_shape(v)\n",
"solid_neo.update_def_shape(v)\n",
"\n",
"fd_validation_ext(solid_lin)\n",
"fd_validation_ext(solid_neo)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# 4.4.5 Point Force\n",
"\n",
"I tried adding a call to `make_external_energy` in the `add_point_load` function since a new force would also lead to a different energy. However inside `make_external_energy`, after many tries to add the energy corresponding to the point force, I gave up."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Validate Elastic Energy Force Differentials (Elastic Forces) using Finite Differences on Elastic Forces"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"solid_lin.update_def_shape(v)\n",
"solid_neo.update_def_shape(v)\n",
"\n",
"fd_validation_elastic_differentials(solid_lin)\n",
"fd_validation_elastic_differentials(solid_neo)"
]
}
],
"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": "3.9.7"
},
"toc": {
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"sideBar": true,
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"title_cell": "Table of Contents",
"title_sidebar": "Contents",
"toc_cell": false,
"toc_position": {},
"toc_section_display": true,
"toc_window_display": false
}
},
"nbformat": 4,
"nbformat_minor": 4
}