Finite Particle Method for Progressive Failure Simulation of Truss Structures

Abstract

A structural analysis framework called the finite particle method (FPM) for structure failure simulation is presented in this paper. The traditional finite-element method is generated from continuum mechanics and the variational principle; vector mechanics form the basis of FPM. It discretizes the domain with finite particles whose motions are described by Newton’s second law. Instead of imposing a global equilibrium of the entire continuous system, FPM enforces equilibrium on each particle. Thus, particles are free to separate from one another, which is advantageous in the simulation of structural failure. One of the features of this approach is that no iterations to follow nonlinear laws are necessary, and no global matrices are formed or solved in this method. A convected material frame is used to evaluate the structure deformation and internal force. The explicit time integration is adopted to solve the equation of motion. To simulate the truss structure failure, a failure criterion on the basis of the ideal plastic constitutive model and a failure modeling algorithm are proposed by using FPM. According to the energy conservation study of a two-dimensional (2D) truss, the energy is decomposed and balanced during the failure process. Also, a more complicated three-dimensional (3D) structure failure simulation is given. The comparison of the simulation results and the practical failure mode shows the capability of this method.