An adaptive strategy based on conforming quadtree meshes for kinematic limit analysis

Abstract

We propose a simple and efficient scheme based on adaptive finite elements over conforming quadtree meshes for collapse plastic analysis of structures. Our main interest in kinematic limit analysis is concerned with both purely cohesive-frictional and cohesive materials. It is shown that the most computational efficiency for collapse plastic problems is to employ an adaptive mesh strategy on quadtree meshes. However, a major difficulty in finite element formulations is the appearance of hanging nodes during adaptive process. This can be resolved by a definition of conforming quadtree meshes in the context of polygonal elements. Piecewise-linear shape functions in barycentric coordinates are used to approximate the velocity field. Numerical results prove the reliability and benefit of the present approach.

An extended polygonal finite element method for large deformation fracture analysis

“…Paulino et al [17] then established a framework for two dimensional mesh generator written in Matlab. Their applications have been widely utilized in various fields, such as simulation of incompressible fluid flows [18], contact problems [19,20], three dimensional linear elasticity [21], polycrystalline materials [22], and hyper-elastic materials [23], scaled boundary polygonal finite element method (SBPFEM) [24], linear strain smoothing [25], advanced virtual element techniques (VEM) [26,27], limit analysis [28,29] and so on.…”