{ "cells": [ { "cell_type": "raw", "metadata": { "collapsed": false }, "source": [ "Code provided under BSD 3-Clause license, all other content under a Creative Commons Attribution license, CC-BY 4.0. (c) 2023 Francesco Mario Antonio Mitrotta." ] }, { "attachments": {}, "cell_type": "markdown", "metadata": { "collapsed": true, "pycharm": { "name": "#%% md\n" } }, "source": [ "# Proof-of-concept of a Nonlinear Structural Stability Constraint for Aeroelastic Optimizations\n", "\n", "***\n", "\n", "This notebook shows how to produce the figures published in the paper titled _Proof-of-concept of a Nonlinear Structural Stability Constraint for Aeroelastic Optimizations_, presented at the RAeS 8th Aircraft Structural Design Conference in October 2023 and authored by Francesco M. A. Mitrotta, Alberto Pirrera, Terence Macquart, Jonathan E. Cooper, Alex Pereira do Prado and Pedro Higino Cabral.\n", "\n", "* [Nonlinear structural stability of canonical examples](#canonical-examples)\n", " * [Supercritical pitchfork bifurcation](#supercritical-pitchfork)\n", " * [Broken supercritical pitchfork](#broken-pitchfork)\n", " * [Limit point bifurcation](#limit-point)\n", "* [Nonlinear structural stability of a CRM-like box beam](#crm-like-box-beam)\n", "* [Optimization of the CRM-like box beam with nonlinear structural stability constraints](#optimization)" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import os\n", "\n", "# Define name of directory where to save analyses and figures\n", "analysis_directory_name = \"RAeS_2023\"\n", "ANALYSIS_DIRECTORY_PATH = os.path.join(os.getcwd(), \"analyses\", analysis_directory_name)" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "## Nonlinear structural stability of canonical examples \n", "\n", "***\n", "\n", "### Supercritical pitchfork bifurcation " ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "088bdd86f9614fd68f104ec79ca30369", "version_major": 2, "version_minor": 0 }, "image/png": 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", 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