Topology Optimization of the Transient Heat Conduction Problem on a Triangular Mesh

Optimization design of the transient heat conduction problem is different from steady-state heat conduction because of varying temperature. This article proposes the integral of temperature gradient over a fixed time interval as an objective function. The shape sensitivity of the transient heat conduction problem is derived. The derivative information of the objective function about the element densities is used as a strategy to create holes. A narrow band on a triangular mesh is proposed to improve the computational efficiency. Numerical examples are presented to demonstrate the effectiveness of the proposed approach for optimal design of transient heat conduction problems.

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