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

## TL;DR

This paper introduces an adaptive finite element method using conforming quadtree meshes for efficient kinematic limit analysis of structures with cohesive and frictional materials, addressing computational challenges like hanging nodes.

## Contribution

It presents a novel adaptive mesh strategy with conforming quadtree meshes and enhanced shape functions to improve efficiency and reliability in collapse plastic analysis.

## Key findings

- Adaptive mesh strategy improves computational efficiency.
- Conforming quadtree meshes resolve hanging node issues.
- Numerical results validate the approach's reliability.

## 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 enhanced with generalized bubble functions in barycentric coordinates are used to approximate the velocity field. Numerical results prove the reliability and benefit of the present approach.