基于有限元分析计算设计灵敏度和网格更新的三维形状优化算法

该文提出一种用于含涡流电磁装备三维形状优化设计的新算法。在三维涡流场有限元分析的基础上，推导了复数形式的设计灵敏度和伴随向量计算公式。根据刚体弹性形变原理及其有限元分析，提出了形状优化计算过程中三维有限元网格更新的新方法，该方法适用于各种形状优化系统，足以获得良好的网格质量和光滑的设计表面。该算法将性能分析、最速下降法与灵敏度计算以及网格更新有效结合，构成集成化设计系统，并成功地用于电磁屏蔽钢板和变压器油箱屏蔽的最优形状设计。

3D SHAPE OPTIMIZATION METHOD BASED ON FINITE ELEMENT ANALYSIS TO CALCULATE DESIGN SENSITIVITY AND MESH RELOCATION

3D shape optimization algorithm is presented for the electromagnetic devices carrying eddy current. The formulae for the design sensitivity and the adjoint variable are derived in complex form in terms of 3D finite element method for eddy current problems. The proposed 3D mesh regeneration method based on the structural deformation analysis is problem independent and sufficient to obtain a smooth contour with proper mesh quality. The algorithm integrates 3D finite element performance analysis, steepest descent method with design sensitivity and mesh relocation method. Numerical applications to the shape optimum design of shielding plates show the effectiveness of the proposed algorithm and optimal design system.