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Concurrent topology and anisotropy optimisation of continua for heat conduction problems
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DOI：10.1016/j.cma.2026.119274.png)
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Abstract
En 中文
We present a new methodology to concurrently design the topology and the anisotropy of thin-walled structures for heat conduction problems. Our method is based on the Verchery’s polar formalism to represent the anisotropic thermal response of the continuum and the pseudo-density as a topology descriptor. The design variables are the pseudo-density, thickness and the polar parameters of the thin-walled structure. Their distribution across the design domain is described using non-uniform rational basis spline (NURBS) entities. Specifically, we leverage NURBS properties to calculate the gradient of the thermal responses and accelerate the optimisation process. We apply this methodology to heat conduction problems, taking into consideration also design-dependent thermal sources. The goal is to minimise the thermal compliance, by satisfying a set of requirements including lightness and feasibility of the polar parameters. The effectiveness of our method is verified on test cases taken from the literature. Finally, we conduct a series of sensitivity analyses to assess the impact of various factors on the optimised solution. These factors include the penalisation scheme used for the element thermal conductivity matrix, the optimisation strategy (sequential vs. concurrent), the initial guess, the integer parameters of the NURBS entity, the element size, and the incorporation of the local thickness among the design variables.
Keywords:
Topology optimisation
Anisotropy optimisation
Heat conduction
NURBS
Polar method
Density-based method
Journal
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7.3
Papers:
1.3W
Citations:
5.6W
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