Edge-Based Smoothed Finite Element Method Using Two-Step Taylor Galerkin Algorithm for Lagrangian Dynamic Problems

Abstract

An edge-based smoothed finite element method (ESFEM) using two-step Taylor Galerkin (TS-TG) algorithm is formulated for two-dimensional solid dynamics problems using linear elements. Although explicit method with classical displacement formulations is the traditional way to simulate fast impact, errors accumulate rapidly resulted from mass, momentum or energy nonconservation. The proposed method is momentum conservative so that energy fluctuations can be minimal and stay bounded for long time. In the present method, the problem areas are firstly discretized into a series of triangular cells, and edge-based smoothing domains are further formed associated with the cell edges. The strain field using the gradient smoothing technique over each smoothing domain is smoothed, which is used for performing the numerical integration. The triangular elements using ESFEM can work for extremely distorted meshes. The newly proposed method can present a good property of accuracy and conservation for a long time.