A material based model for topology optimization of thermoelastic structures

TLDR

The study develops a computational model for topology optimization of a 2‑D linear‑elastic solid under thermal loads, targeting compliance minimization with a volume constraint. The authors formulate an augmented Lagrangian, analytically derive optimality conditions, implement them in a code, and solve the problem through successive linearized subproblems, validating the approach on example cases. Analysis shows that both temperature distribution and finite element discretization significantly influence the resulting optimal topology.

Abstract

Abstract This paper presents the development of a computational model for the topology optimization problem, using a material distribution approach, of a 2‐D linear‐elastic solid subjected to thermal loads, with a compliance objective function and an isoperimetric constraint on volume. Defining formally the augmented Lagrangian associated with the optimization problem, the optimality conditions are derived analytically. The results of analysis are implemented in a computer code to produce numerical solutions for the optimal topology, considering the temperature distribution independent of design. The design optimization problem is solved via a sequence of linearized subproblems. The computational model developed is tested in example problems. The influence of both the temperature and the finite element model on the optimal solution obtained is analysed.