Solution and Verification for Multi-Objective Shape Optimization on Complicated Thermo-elastic Fields and Heat-convection Fields

线弹性体的形状优化问题、热传导场、粘性流场等是机械和结构设计中非常重要的问题。本研究针对黏性流场、热对流场、热弹性场等多目标形状优化问题，提出了数值分析方法。建立了多目标形状优化问题的数学模型，并从理论上推导了形状优化问题的形状灵敏度函数。针对形状优化问题开发了数值分析程序，二维数值分析结果验证了所提方法的有效性。

Shape optimization problems of linear elastic bodies, heat-conduction fields, viscous flow fields, etc. are very important problems in mechanical and structural design. In this study, numerical analyses method of some multi-objective shape optimization problems was proposed for improving performance in viscous flow fields, heat-convection fields, and thermo-elastic fields. These multi-objective shape optimization problems were formulated, then shape sensitivity functions for the shape optimization problems are derived theoretically. Numerical analyses program were developed for the shape optimization problems, and the validity of proposed method was confirmed by results of 2D numerical analyses.