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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 
International Journal for Numerical Methods in Engineering
Swansea University Author:
Chenfeng Li
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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...
| Published in: | International Journal for Numerical Methods in Engineering |
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| ISSN: | 00295981 |
| Published: |
2018
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| Online Access: |
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa38853 |
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| 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. |
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| Keywords: |
analytical trial function; finite element; geometric nonlinear analysis; mesh distortion; UL formulation; unsymmetric 4-node plane element |
| College: |
Faculty of Science and Engineering |