Implementation of Thermomechanical Multiphysics in a Large-Scale Three-Dimensional Topology Optimization Code

Abstract

Due to the inherent computational cost of multiphysics topology optimization methods, it is a common practice to implement these methods in two-dimensions. However most real-world multiphysics problems are best optimized in three-dimensions, leading to the necessity for large-scale multiphysics topology optimization codes. To aid in the development of these codes, this paper presents a general thermomechanical topology optimization method and describes how to implement the method into a preexisting large-scale three-dimensional topology optimization code. The weak forms of the Galerkin finite element models are fully derived for mechanical, thermal, and coupled thermomechanical physics models. The objective function for the topology optimization method is defined as the weighted sum of the mechanical and thermal compliance. The corresponding sensitivity coefficients are derived using the direct differentiation method and are verified using the complex-step method. The design variables are updated using the method of moving asymptotes so that the objective function is minimized resulting in maximum performance of the structure. Solution of the linear systems of equation is scaled across several supercomputer nodes using the Portable, Extensible Toolkit for Scientific Computation (PETSc) developed by Argonne National Laboratory. The finite element models, sensitivity analysis, optimization algorithm, and solver are all implemented in a freeware, density-based, topology optimization code (written in C++) that has been modified for thermomechanical problems. As such, the implementation of the thermomechanical model is provided. The code is applied to solve an example problem under thermal, mechanical, and thermomechanical boundary conditions. The resulting topologies and field variables are shown with a corresponding discussion.