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CLC number: TU39

On-line Access: 2021-06-21

Received: 2020-09-06

Revision Accepted: 2020-11-29

Crosschecked: 2021-05-18

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Citations:  Bibtex RefMan EndNote GB/T7714


Himanshu Gaur


Lema Dakssa


Mahmoud Dawood


Nitin Kumar Samaiya


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Journal of Zhejiang University SCIENCE A 2021 Vol.22 No.6 P.481-491


A novel stress-based formulation of finite element analysis

Author(s):  Himanshu Gaur, Lema Dakssa, Mahmoud Dawood, Nitin Kumar Samaiya

Affiliation(s):  Institute of Structural Mechanics, BauhausUniversitt Weimar, Marienstrasse 15, D-99423 Weimar, Germany; more

Corresponding email(s):   himanshugaur82@gmail.com

Key Words:  Computational methods, Machine learning, Regression method, Material non-linear analysis, Finite element analysis

Himanshu Gaur, Lema Dakssa, Mahmoud Dawood, Nitin Kumar Samaiya. A novel stress-based formulation of finite element analysis[J]. Journal of Zhejiang University Science A, 2021, 22(6): 481-491.

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author="Himanshu Gaur, Lema Dakssa, Mahmoud Dawood, Nitin Kumar Samaiya",
journal="Journal of Zhejiang University Science A",
publisher="Zhejiang University Press & Springer",

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%T A novel stress-based formulation of finite element analysis
%A Himanshu Gaur
%A Lema Dakssa
%A Mahmoud Dawood
%A Nitin Kumar Samaiya
%J Journal of Zhejiang University SCIENCE A
%V 22
%N 6
%P 481-491
%@ 1673-565X
%D 2021
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.A2000397

T1 - A novel stress-based formulation of finite element analysis
A1 - Himanshu Gaur
A1 - Lema Dakssa
A1 - Mahmoud Dawood
A1 - Nitin Kumar Samaiya
J0 - Journal of Zhejiang University Science A
VL - 22
IS - 6
SP - 481
EP - 491
%@ 1673-565X
Y1 - 2021
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.A2000397

This paper demonstrates a novel formulation of structural analysis. A novel stress-based formulation of structural analysis for material nonlinear problems was proposed in earlier work. In this paper, this methodology is further extended for 3D finite element analysis. The approach avoids use of elastic moduli as the material input in the analysis procedure. It utilizes the whole stress-strain curve of the material. It can be shown that this analysis procedure solved the nonlinear or plasticity problem with relative ease. This paper solves a uniaxial bar, in which the results are compared with the solutions of Green-Lagrange strain and Piola-Kirchhoff stresses. The uniaxial bar is also solved by a regression model in the scikit-learn module in Python. The second problem solved is of a beam in pure bending for which the energy release rate is measured. For the beam in pure bending, the bending moment carrying capacity of the beam section is evaluated by this methodology as the crack propagates through the depth of the beam. It can be shown that the methodology is very simple, accurate, and clear in its physical steps.


创新点:1. 目前关于材料非线性分析的技术非常冗长、乏味和耗时,而本文提出的公式由于可以看作是积分公式而不是微分公式,所以非常适合解决断裂力学问题;2. 本文提出的公式对问题的求解是通过机器学习的回归模型完成.
方法:1. 应用本文所提出的新方法并在分析过程中消除经典方法的繁琐、冗长、逐步增量以及迭代的过程.2. 在分析过程中不需要使用弹性模量,直接使用由材料的应力-应变曲线导出的应力-应变函数作为材料输入.


Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article


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