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In the past decades, automotive structure design has sought to minimize its mass while maintaining or improving structural performance. As such, topology optimization (TO) has become an increasingly popular tool during the conceptual design stage. While the designs produced by TO methods provide significant performance-to-mass ratio improvements, they require considerable computational resources when solving large-scale problems. An alternative for large-scale problems is to decompose the design domain into multiple scales that are coupled with homogenization. The problem can then be solved with hierarchical multiscale topology optimization (MSTO). The resulting optimal, homogenized macroscales are de-homogenized to obtain a high-fidelity, physically-realizable design. Even so MSTO methods are still computationally expensive due to the combined costs of solving nested optimization problems and performing de-homogenization.

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.