Level‐wise strain recovery and error estimation for natural element hierarchical plate models

Abstract

AbstractDiffering from the finite element method, most of mesh‐free methods are restricted to two‐dimensional (2D) problems owing to the difficulty in constructing three‐dimensional (3D) grids. But, for 3D elastic structures, this limitation could be effectively overcome when hierarchical models are employed. In the hierarchical models of elastic structures, only the in‐plane displacement field is needed to be approximated because the thickness‐wise displacement field is assumed by polynomials. In this context, this paper is concerned with the reliable numerical implementation of hierarchical models for plate‐like structures using 2D natural element method (NEM). However, one critical problem in implementing the hierarchical model is to secure the continuity in strain and stress fields. To resolve this problem, this paper presents a level‐wise strain recovery method. In addition, a recovery‐based error estimation is introduced to predict the modeling error and the numerical approximation error. The proposed methods are illustrated and validated through the numerical experiments. It is confirmed that the level‐wise strain recovery successfully and CPU‐time effectively provides the continuous stress resultants and the proposed error estimator accurately predicts the modeling and approximation errors.