关键词: 隔离非线性法, 平面应变单元, Woodbury公式, 组合近似法, 效率分析, Drucker-Prager准则

Abstract: In this paper, a plane-strain element analysis model is proposed on the basis of the inelasticity-separated finite element method (IS FEM). The 2×2 Gaussian points as the inelastic strain interpolation points are considered for the linear quadrilateral isoparametric plane-strain element. The inelastic strain field and the corresponding governing equation are established only in the in-plane three directions since there are no strain components out of the plane. In addition, the solving process of the governing equation only contains many times back-substitutions of the initial stiffness matrix and the sparse matrix and vector multiplication by using the Woodbury formula and the combined approximation approach. The computational efficiency of the proposed method based on the time complexity theory indicates that it significantly improves the total efficiency as compared with the conventional FEM with the updated stiffness matrix. The critical ratio of the inelastic degrees of freedom (IDOFs) is also improved by comparing with the exact Woodbury formula. The stress transfer method of the Drucker-Prager criterion is applied for the nonlinear analysis of the classical plane-strain model. Numerical examples verify the accuracy of the proposed model and the efficiency of the proposed algorithm for the nonlinear analysis of the plane-strain model.

Key words: inelasticity-separated finite element method, plane strain element, Woodbury formula, combined approximations approach, efficiency analysis, Drucker-Prager criterion