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Topology optimization of thermal problems in a nonsmooth variational setting: closed-form optimality criteria. (English) Zbl 1466.74034

Summary: This paper extends the nonsmooth Relaxed Variational Approach (RVA) to topology optimization, proposed by the authors in a preceding work [Comput. Methods Appl. Mech. Eng. 355, 779–819 (2019; Zbl 1441.74167)], to the solution of thermal optimization problems. First, the RVA topology optimization method is briefly discussed and, then, it is applied to a set of representative problems in which the thermal compliance, the deviation of the heat flux from a given field and the average temperature are minimized. For each optimization problem, the relaxed topological derivative and the corresponding adjoint equations are presented. This set of expressions are then discretized in the context of the finite element method and used in the optimization algorithm to update the characteristic function. Finally, some representative (3D) thermal topology optimization examples are presented to asses the performance of the proposed method and the Relaxed Variational Approach solutions are compared with the ones obtained with the level set method in terms of the cost function, the topology design and the computational cost.

MSC:

74P15 Topological methods for optimization problems in solid mechanics
74F05 Thermal effects in solid mechanics
74S05 Finite element methods applied to problems in solid mechanics

Citations:

Zbl 1441.74167
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References:

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