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Discrete variable topology optimization for simplified convective heat transfer via sequential approximate integer programming with trust‐region
Author(s) -
Yan Xin Yu,
Liang Yuan,
Cheng Geng Dong
Publication year - 2021
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.6775
Subject(s) - discretization , topology optimization , topology (electrical circuits) , interpolation (computer graphics) , convective heat transfer , boundary (topology) , mathematics , mathematical optimization , convection , variable (mathematics) , integer programming , heat transfer , computer science , mathematical analysis , mechanics , physics , finite element method , thermodynamics , animation , computer graphics (images) , combinatorics
This 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.