A novel stress-based formulation of finite element analysis

Abstract

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.

Abstract

目的

本文旨在提出一种新的基于应力的结构分析公式, 以期可以相对轻松地解决材料非线性分析问题并对材料的线性行为及非线性行为直接给出结果。另外, 期望该方法可以扩展到三维有限元分析中。

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。

结论

本文提出的方法在物理步骤上非常简单, 准确和清晰, 适合材料非线性和断裂力学问题的求解。