Isogeometric Topology Optimization of Multi-Material Structures under Thermal-Mechanical Loadings Using Neural Networks

An isogeometric topology optimization (ITO) model for multi-material structures under thermal-mechanical loadings using neural networks is proposed. In the proposed model, a non-uniform rational B-spline (NURBS) function is employed for geometric description and analytical calculation, which realizes the unification of the geometry and computational models. Neural networks replace the optimization algorithms of traditional topology optimization to update the relative densities of multi-material structures. The weights and biases of neural networks are taken as design variables and updated by automatic differentiation without derivation of the sensitivity formula. In addition, the grid elements can be refined directly by increasing the number of refinement nodes, resulting in high-resolution optimal topology without extra computational costs. To obtain comprehensive performance from ITO for multi-material structures, a weighting coefficient is introduced to regulate the proportion between thermal compliance and compliance in the loss function. Some numerical examples are given and the validity is verified by performance analysis. The optimal topological structures obtained based on the proposed model exhibit both excellent heat dissipation and stiffness performance under thermal-mechanical loadings.