In this project for MAT 548 - Continuous Models and MAT 554 - Scientific Computing, I implemented the Solid Isotropic Material with Penalization (SIMP) model for topology optimization in FORTRAN 90. The goal was to create the most rigid possible structure for a bracket mounted to a wall on the left that bears a load on the bottom right. To do this, the compliance of the structure is computed in each iteration and the amount of material in each grid cell changed so as to reduce the compliance in the next iteration subject to a volume constraint. Additionally, I performed a sensitivity analysis of final compliance against changes in the volume constraint and changes in the penalty term of SIMP.
As part of the implementation of SIMP, the FORTRAN code also contains a basic implementation of the simplex method, which is used to minimize compliance, and a basic implementation of Cholesky decomposition, which is used during the computation of compliance.
Source code, slides, and report can be found in the repo.