No Cover Image

Journal article 548 views 157 downloads

High-performance geometric nonlinear analysis with the unsymmetric 4-node, 8-DOF plane element US-ATFQ4

Zhi Li, Song Cen, Cheng-Jin Wu, Yan Shang, Chen-Feng Li, Chenfeng Li Orcid Logo

International Journal for Numerical Methods in Engineering

Swansea University Author: Chenfeng Li Orcid Logo

Check full text

DOI (Published version): 10.1002/nme.5771

Abstract

A recent unsymmetric 4-node, 8-DOF plane element US-ATFQ4, which exhibits excellent precision and distortion-resistance for linear elastic problems, is extended to geometric nonlinear analysis. Since the original linear element US-ATFQ4 contains the analytical solutions for plane pure bending, how t...

Full description

Published in: International Journal for Numerical Methods in Engineering
ISSN: 00295981
Published: 2018
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa38853
Tags: Add Tag
No Tags, Be the first to tag this record!
Abstract: A recent unsymmetric 4-node, 8-DOF plane element US-ATFQ4, which exhibits excellent precision and distortion-resistance for linear elastic problems, is extended to geometric nonlinear analysis. Since the original linear element US-ATFQ4 contains the analytical solutions for plane pure bending, how to modify such formulae into incremental forms for nonlinear applications and design an appropriate updated algorithm become the key of the whole job. First, the analytical trial functions should be updated at each iterative step in the framework of updated Lagrangian formulation that takes the configuration at the beginning of an incremental step as the reference configuration during that step. Second, an appropriate stress update algorithm in which the Cauchy stresses are updated by the Hughes-Winget method is adopted to estimate current stress fields. Numerical examples show that the new nonlinear element US-ATFQ4 also possesses amazing performance for geometric nonlinear analysis, no matter whether regular or distorted meshes are used. It again demonstrates the advantages of the unsymmetric finite element method with analytical trial functions.
Keywords: analytical trial function; finite element; geometric nonlinear analysis; mesh distortion; UL formulation; unsymmetric 4-node plane element
College: College of Engineering