A fully edge-based smoothed finite element method for static and dynamic elastoplastic analyses of axisymmetric structures

Abstract

A fully edge-based smoothed finite element method for static and dynamic elastoplastic analyses of axisymmetric structures is formulated in this paper, which incorporates a quasi-weak form of the smoothed integral into the edge-based smoothed finite element method framework. Based on the initial triangular meshes, an edge-based smoothing domain is constructed for each edge by connecting its two vertices to the centroids of adjacent triangular elements. To effectively tackle domain integrals related to the shape function in the strain and mass matrices, a quasi-weak form of the smoothed integral is introduced. This special integration necessitates the evaluation of indefinite integrals for shape functions without reducing the continuity requirements. Consequently, all the complex domain integrals can be transformed into the boundary integrals over the smoothing domains, thus completely eliminating the need for Jacobian calculations and isoparametric mapping throughout the solution process. Plastic strain evolution is governed by the associated flow rule, with isotropic hardening accounting for the increase in yield strength during plastic deformation. The resulting nonlinear governing equations are solved utilizing an unconditionally stable Newmark time integration scheme combined with the Newton–Raphson iterative algorithm. Numerical examples confirm that the proposed method yields optimal performance for both static and dynamic elastoplastic analyses of axisymmetric structures, especially relative to computational accuracy and robustness against mesh distortion.