291 lines
116 KiB
Plaintext
291 lines
116 KiB
Plaintext
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{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Description\n",
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"\n",
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"This notebook intends to gather all the functionalities you'll have to implement for assignment 2.2.\n",
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"\n",
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"# Load libraries"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 1,
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"metadata": {},
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"outputs": [],
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"source": [
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"import numpy as np\n",
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"import igl\n",
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"import meshplot as mp\n",
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"import time\n",
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"import torch\n",
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"\n",
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"import sys as _sys\n",
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"_sys.path.append(\"../src\")\n",
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"from elasticsolid import *\n",
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"from elasticenergy import *\n",
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"from vis_utils import *\n",
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"from matplotlib import gridspec\n",
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"import matplotlib.pyplot as plt\n",
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"\n",
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"torch.set_default_dtype(torch.float64)\n",
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"\n",
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"shadingOptions = {\n",
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" \"flat\":True,\n",
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" \"wireframe\":False, \n",
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"}\n",
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"\n",
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"rot = np.array(\n",
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" [[1, 0, 0 ],\n",
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" [0, 0, 1],\n",
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" [0, -1, 0 ]]\n",
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")"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Load mesh\n",
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"\n",
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"Several meshes are available for you to play with under `data/`: `ball.obj`, `dinosaur.obj`, and `beam.obj`."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"metadata": {
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"scrolled": false
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},
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"outputs": [],
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"source": [
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"vNP, _, _, tNP, _, _ = igl.read_obj(\"../data/beam.obj\")\n",
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"aabb = np.max(vNP, axis=0) - np.min(vNP, axis=0)\n",
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"v = torch.tensor(vNP)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Linear/Non-Linear Elastic Solid\n",
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"\n",
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"## Instantiation\n",
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"\n",
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"We first specify the elasticity model to use for the elastic solid, as well as pinned vertices, and volumetric forces."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"metadata": {},
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"outputs": [],
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"source": [
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"rho = 131 # [kg.m-3]\n",
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"young = 10e6 # [Pa] \n",
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"poisson = 0.2\n",
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"force_mass = torch.zeros(size = (3,))\n",
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"force_mass[2] = - rho * 9.81\n",
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"\n",
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"minX = torch.min(v[:, 0])\n",
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"pin_idx = torch.arange(v.shape[0])[v[:, 0] < minX + 0.2*aabb[0]]\n",
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"\n",
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"ee_lin = LinearElasticEnergy(young, poisson)\n",
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"ee_neo = NeoHookeanElasticEnergy(young, poisson)\n",
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"solid_lin = ElasticSolid(v, tNP, ee_lin, rho=rho, pin_idx=pin_idx, f_mass=force_mass)\n",
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"solid_neo = ElasticSolid(v, tNP, ee_neo, rho=rho, pin_idx=pin_idx, f_mass=force_mass)\n"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Validate Elastic Energy Gradient (Elastic Forces) using Finite Differences on Elastic Energy"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 4,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"image/png": "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"text/plain": [
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"<Figure size 432x288 with 1 Axes>"
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]
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},
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"metadata": {
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"needs_background": "light"
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},
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"output_type": "display_data"
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},
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{
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"data": {
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"image/png": "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
|
||
|
|
"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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
|
||
|
|
"text/plain": [
|
||
|
|
"<Figure size 432x288 with 1 Axes>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {
|
||
|
|
"needs_background": "light"
|
||
|
|
},
|
||
|
|
"output_type": "display_data"
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"image/png": "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
|
||
|
|
"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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
|
||
|
|
"text/plain": [
|
||
|
|
"<Figure size 432x288 with 1 Axes>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {
|
||
|
|
"needs_background": "light"
|
||
|
|
},
|
||
|
|
"output_type": "display_data"
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
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|
||
|
|
"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"
|
||
|
|
},
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||
|
|
"language_info": {
|
||
|
|
"codemirror_mode": {
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||
|
|
"name": "ipython",
|
||
|
|
"version": 3
|
||
|
|
},
|
||
|
|
"file_extension": ".py",
|
||
|
|
"mimetype": "text/x-python",
|
||
|
|
"name": "python",
|
||
|
|
"nbconvert_exporter": "python",
|
||
|
|
"pygments_lexer": "ipython3",
|
||
|
|
"version": "3.9.7"
|
||
|
|
},
|
||
|
|
"toc": {
|
||
|
|
"base_numbering": 1,
|
||
|
|
"nav_menu": {},
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|
|
"number_sections": true,
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"sideBar": true,
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|
|
"skip_h1_title": false,
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||
|
|
"title_cell": "Table of Contents",
|
||
|
|
"title_sidebar": "Contents",
|
||
|
|
"toc_cell": false,
|
||
|
|
"toc_position": {},
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||
|
|
"toc_section_display": true,
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||
|
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"toc_window_display": false
|
||
|
|
}
|
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|
|
},
|
||
|
|
"nbformat": 4,
|
||
|
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"nbformat_minor": 4
|
||
|
|
}
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