Multi-material isogeometric topology optimization for thermoelastic metamaterials

Abstract

The design of thermoelastic metamaterials has traditionally relied on finite element analysis. This paper introduces a high-precision isogeometric topology optimization method specifically tailored for thermoelastic metamaterials. By leveraging non-uniform rational B-spline (NURBS) basis functions within isogeometric analysis (IGA), the proposed method significantly enhances computational accuracy and efficiency. A numerical homogenization approach is integrated with IGA to evaluate the effective material properties of microstructures, enabling seamless integration with computer-aided design and computer-aided engineering. To formulate the optimization problem for thermoelastic metamaterials, a multi-material interpolation model is constructed, with a focus on minimizing the effective thermal expansion coefficient. Sensitivity analysis of the discrete multi-material variables are conducted within this framework. To overcome challenges such as convergence to local optima and the emergence of isolated ‘island’ in multi-material designs, innovative strategies are introduced, including a random density distribution technique and a variable-intensity threshold projection method. The proposed method's effectiveness and advantages are demonstrated through several two-dimensional and three-dimensional numerical examples. Furthermore, simulations performed using the commercial finite element software ANSYS validate the feasibility and robustness of the approach.