An efficient adaptive polygonal finite element method for plastic collapse analysis of solids

TL;DR

This paper introduces an adaptive polygonal finite element method for plastic collapse analysis that improves computational efficiency and accuracy through innovative mesh strategies and shape functions, validated by numerical experiments.

Contribution

The paper presents a novel adaptive polygonal finite element formulation with a dual-mesh approach and a new primal-mesh strategy, enhancing collapse analysis of solids.

Findings

Performs well for volumetric locking problems

Efficiently solves large-scale optimization problems

Demonstrates excellent numerical validation results

Abstract

We propose an adaptive polygonal finite element formulation for collapse plastic analysis of solids. The article contributes into four crucial points: 1) Wachspress shape functions at vertex and bubble nodes handled at a primal-mesh level; 2) plastic strain rates and dissipation performed over a dual-mesh level; 3) a new adaptive primal-mesh strategy driven by the L^2 -norm-based indicator of strain rates; and 4) a spatial decomposition structure obtained from a so-called polytree mesh scheme. We investigate both purely cohesive and cohesive-frictional materials. We prove numerically that the present method performs well for volumetric locking problem. In addition, the optimization formulation of limit analysis is written by the form of second-order cone programming (SOCP) in order to exploit the high efficiency of interior-point solvers. The present method retains a low number of optimization variables. This convenient approach allows us to design and solve the large-scale optimization problems effectively. Numerical validations show the excellent performance of the proposed method.