2020 Volume 76 Issue 1 Pages 7-21
The author has developed a non-intrusive spectral projection (NISP) stochastic finite element method (NISP-SFEM) that incorporates a NISP method as part of the intrusive spectral stochastic finite element method (intrusive SSFEM), and has analyzed elasto-plastic problems in the range of small strain deformations. NISP-SFEM is a hybrid method that uses the NISP method to calculate the element stiffness matrix and internal force matrix, and uses an intrusive SSFEM to solve the global stiffness matrix.
In this paper, NISP-SFEM is extended to be applicable to the problem of quasi-static finite deformation. Then the expanded NISP-SFEM is used to solve simple tension problems in which displacement is applied gradually to both sides of an elasto-plastic body with yield stress that varies stochastically. By examining the stochastic variation of the internal force-nominal strain curve, it is observed whether the stochastic variation of the stress in the stable or unstable region is accurately tracked. Furthermore, the numerical verification of NISP-SFEM is performed through comparison with the Monte Carlo method.