等几何壳体分析与形状优化

首先基于Reissner-Mindlin理论进行了三维壳体等几何分析，而后基于此对三维壳体进行形状优化，提出了形状优化中灵敏度的全解析计算方法，包括位移应变阵、雅克比阵和刚度阵等相对控制顶点位置的灵敏度解析计算公式；通过实例验证了壳体等几何分析和灵敏度全解析计算方法的有效性。与传统的基于网格的灵敏度半解析计算方法相比，基于NURBS的灵敏度全解析计算具有精确、计算效率高的特点，且可以避免优化迭代中的网格畸变。

Isogeometric shell analysis and shape optimization

The isogeometric shell analysis is implemented based on Reissner-Mindlin theory,and then the shape optimization of 3D shells is carried out.The analytical computation method of sensitivity is presented including the analytical computational formulae of the strain-displacement matrix,the Jacobin matrix and the stiffness matrix with respect to the positions of the control points.Effectiveness of the isogeometric shell analysis and the presented analytical computation methods of sensitivity are demonstrated with numerical examples.Compared with the conventional mesh based semi-analytical method,the NURBS based analytical computational method of sensitivity is more precise and more efficient,and can avoid the mesh distortion as well.