Study of Material Desing via Topology optimization

In this thesis the Topology Optimization technique for optimal engineering mi-crostructure design is presented. Topology Optimization is a numerical technique based on the well-known Finite Element Method. The principles of this technique and a detailed explanation of its implementation is exposed and commented. Since its birth in 1988 topology optimization has become a multi-discipline research field which has experienced a huge growth in the past decades. It is expected to be a mandatory engineering development tool in the future for many industries such as aeronautics, automotive, etc. The purpose of this work is to develop a Topology Op-timization program in the MATLAB environment by means of the Finite Element Method and based on the Object Oriented programming philosophy. The developed code would have a general approach to a wide variety of Topology Optimizations problems but the aim of this study is the material design approach. Several types of microstructure designs would be computed according to di˙erent final proper-ties objectives. It would be introduced an incremental convergence scheme enabling the convergence of numerically diÿcult cases. Moreover, di˙erent optimization algo-rithms are implemented including the Method of Moving Asymptotes, the Level-Set based SLERP method, the interior point algorithm IPOPT and the Projected Gra-dient solver. In addition, the recent SIMP-ALL interpolation scheme which derives from the widely accepted SIMP interpolation and enables the homogenization of the microstructure properties is reviewed. Moreover, the developed code is done in collaboration with other master students performing their Masters’ Thesis using professional development tools such as GitHub. This thesis has also a focus on the code development methodology which has tried to be as professional as possible