Discrete variable topology optimization for simplified convective heat transfer via sequential approximate integer programming with trust‐region

Abstract

AbstractThis article presents a discrete variable topology optimization method to solve the simplified convective heat transfer (SCHT) design optimization modeled by Newton's law of cooling. The discrete variable topology optimization is based on the proposed sequential approximate integer programming with trust‐region. Due to the discrete variables, identifying the convective boundary, and implementing this design‐dependent convective boundary condition can be precisely undertaken. As a result, the consistent precise temperature field compared with the commercial software is captured. Besides, the interpolation scheme of the convective coefficient is unnecessary to analyze this SCHT problem. Furthermore, an analytical sensitivity formulation that can simultaneously incorporate the conductive and convective effect is also deduced. Finally, several 2D and 3D valid thermal designs are presented to illustrate the effectiveness of the method. Based on the optimized designs, we find that favorable configurations for a simplified convective problem may be hollowed structure or the dense needle‐like structure. Further, the checkerboard pattern should be interpreted as a convection oscillatory feature but not the discretization error because it cannot be eliminated by using higher‐order elements.