Design of thermal meta-structures made of functionally graded materials using isogeometric density-based topology optimization

TL;DR

This paper presents a novel isogeometric density-based topology optimization method for designing thermal meta-structures made of functionally graded materials, enabling efficient heat flow control in complex geometries.

Contribution

It introduces an isogeometric approach that aligns with FGMs, allowing flexible design of thermal meta-structures without relying on transformation thermotics.

Findings

Successfully designed 2D and 3D thermal meta-structures.

Demonstrated versatility across different design scenarios.

Validated designs using numerical homogenization for cellular materials.

Abstract

The thermal conductivity of Functionally Graded Materials (FGMs) can be efficiently designed through topology optimization to obtain thermal meta-structures that actively steer the heat flow. Compared to conventional analytical design methods, topology optimization allows handling arbitrary geometries, boundary conditions and design requirements; and producing alternate designs for non-unique problems. Additionally, as far as the design of meta-structures is concerned, topology optimization does not need intuition-based coordinate transformation or the form invariance of governing equations, as in the case of transformation thermotics. We explore isogeometric density-based topology optimization in the continuous setting, which perfectly aligns with FGMs. In this formulation, the density field, geometry and solution of the governing equations are parameterized using non-uniform rational basis spline entities. Accordingly, the heat conduction problem is solved using Isogeometric Analysis. We design various 2D & 3D thermal meta-structures under different design scenarios to showcase the effectiveness and versatility of our approach. We also design thermal meta-structures based on architected cellular materials, a special class of FGMs, using their empirical material laws calculated via numerical homogenization.