Topology-Optimization-of-Hierarchial-Structures

This repository contains all the codes and files developed for a research project on Topology Optimization done under guidance of Prof. Amuthan Ramabathiran from Department of Aerospace Engineering at Indian Institute of Technology Bombay

The initial part of the project contains numerical computations on numerical techniques like the finite difference, gradient descent, forward and backward euler, Constrained Optimization using Lagrange Multipliers finite element method and plotting results on python, matplotlib and GNUPlot.

Finite Element Codes - FEniCS

1. Finite Element Formulation 0001
2. Finite Element Method in 1D (Galerkin Approximation
3. 2D Linear Elastic Analysis of Cantilever Beam
4. Membrane Deflection Problem
5. Time Dependent Heat Equation

Some Numerical Techniques

1. Finite Difference Method in 1 Variable
2. Backward and Forward Euler
3. Gradient Descent
4. A General Polynomial Integrator based on the Simpson's Rule