中文摘要：

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。

英文摘要：

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 presen- ted 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 isogeo- metric 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 NURI3S based analytical computational method of sensitivity is more precise and more efficient,and can avoid the mesh distortion as well.