A novel stress-based formulation of finite element analysis

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 3 D 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.