基于子结构法的大型结构数值敏度计算技术

针对大型结构直接精确敏度分析方法解方程规模大、求解时间长的问题,发展一套基于有限元子结构法的处理技术。大型结构中,数值敏度计算的伪载荷仅与涉及设计变量的结构单元有关,因此存在大量零元的可能性。根据此特点通过节点重排将与设计变量有关的节点位移排到总位移列阵序的后面,按重排后的顺序投放刚度矩阵,然后对其进行区域分块,并聚缩得到规模较小的矩阵。算例计算表明:利用此矩阵求解结构位移场的导数,不但保持了精确法的精度,而且在优化设计的敏度计算中,这些较小规模的数据又被多次使用,从而显著提高计算效率。

Numerical Sensitivity Computation Technique of Large-scale Structure based on Stiffness Matrix Domain Decomposition Method

The common analytical sensitivity method for the large-scale structure takes a lot of time for solving the large-scale equations.To solve this problem the substructure sensitivity method is developed.In the large structure,the pseud load of the numerical sensitivity calculation has a lot of zeros,and the displacement components which are relevant to design variables may have non-zeros.The displacement components can be reordered behind through reordering the nodes,by which the stiffness matrix is assembled.Then the stiffness matrix is decompressed to smaller matrix using the substructure method（SM）.The high accuracy of precise method can be kept by using these matrices to calculate the sensitivities of displacement.Meanwhile,these data can be used repeatedly in the optimization process,so the computational efficiency is improved greatly.