一种基于复数变量求偏导的随机有限元可靠度法

提出一种基于复数变量求偏导的随机有限元可靠度法.将工程中的随机因素设置为复数变量,通过复数函数的泰勒级数展式得到一阶导数的近似计算式.这种求导方法效率高,精度高,应用简单方便,只需在复数空间进行有限元计算,无需对有限元方程进行偏导计算,便可求出响应量的偏导数,进而求得响应量的方差.在随机有限元一次二阶矩的迭代格式中,取复数空间有限元计算结果的实部作为响应量的值,这样在求可靠度系数的迭代过程中,无需再在实数空间进行计算.复数变量法大大简化了随机有限元(SFEM)和随机有限元可靠度(SFEMR)的计算和编程过程,为工程应用提供了一种现实可行的途径.

A Stochastic Finite Element Reliability Analysis Method Based on Complex variable Derivative Technique

A new approach is proposed for stochastic finite element method(SFEM) and reliability analysis by using a complex-variable technique.The random factors in engineering are defined as complex variables,the first derivative formulation can be obtained by the Taylor’s series of a complex function.This derivative method is computationally very accurate,efficient,and very easily implemented.In SFEM,to get the variances of responses,it only needs to implement FEM in complex variables space,without a need of partial derivatives of FEM functions.In the iteration scheme of SFEM reliability analysis,the real parts of complex response is considered as the response value to simplify the process.The complex-variable method greatly simplifies SFEM and reliability program,providing a feasible approach for engineering application.