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

Abstract:

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.