Topology Optimization Based Material Design for 3D Domains Using MATLAB

Abstract

In this work, a simple, easy to use MATLAB code is presented for the optimal design of materials for 3D domains. For the optimal design of materials, the theoretical framework of topology optimization and that of homogenization were utilized to develop a formulation where the design of the micro-structure of the material is affected among others by the loading and boundary conditions of the 3D macro domain. The final result of the micro-scale can then be converted into an stl file, which can be utilized for 3D printing; however, the continuity of the unit cells when assembled to form the macro structure should be taken into account. The transition of the design of the material problem formulation from 2D to 3D domains generates drastically increased computational needs in order to perform the design procedures, which might narrow its formulation scales and the corresponding sizes of the adopted finite element discretization. Thus, in addition to the optimal design of materials implementation, the utilization of three different model order reduction (MOR) approaches is presented, aiming to assist towards the reduction of the computational cost of the two scales formulation. On-the-fly reduced order model, proper orthogonal decomposition (POD), and approximate reanalysis (AR) following the combined approximations are the three approaches adopted for the purposes of this study, while the code implementation enables the addition of new ones easily.

Keywords

• topology optimization
• microstructure
• homogenization
• MATLAB
• reduced order models
• reduced basis