基于灵敏度分析的三维结构等几何形状优化方法

Three Dimensional Structural Shape Optimization Based on Sensitivity Analysis Using Isogeometric Analysis

以等几何分析为数值分析方法,针对三维结构的线弹性问题,以优化边界控制点坐标为设计变量,通过Coons体插值方法得到插值控制点对优化边界控制点的坐标导数,推导了单元刚度矩阵对控制点坐标变量的形状优化灵敏度方程,并对应力灵敏度和位移灵敏度方程进行了推导。数值算例证明该方法具有较高的优化效率,优化结果良好。

An isogeometric analysis method was used as numerical analysis method.As for threedimensional structures of linear elastic problem,boundary control points that needed to be optimized were regarded as design variables,derivatives of internal control points as to design variables might be obtained by using Coons interpolation method.In shape optimization,sensitivity equation of element stiffness matrix as to control points coordinates was derived,and sensitivity equations of stresses and displacements were deduced.Numerical examples show that the method has high efficiency and good results.