Elasto-plastic Stress Analysis with Nested Finite Element Method

• Published in: Transactions of the Japan Society of Mechanical Engineers Series A Vol. 70; no. 691; pp. 406 - 411
• Main Author: SASAKI, Koji
• Format: Journal Article
• Language: Japanese
• Published: The Japan Society of Mechanical Engineers 2004
• Subjects: Computational Mechanics; Finite Element Method; Implicit Analysis; Inelastic Analysis
• ISSN: 0387-5008; 1884-8338
• DOI: 10.1299/kikaia.70.406

Nested-finite-element methodology (NFEM) is an improved finite-element method to evaluate local concentrations of stress with nested sub-elements. NFEM was applied only to elastic and explicit inelastic problems, because it is unable to calculate residual forces accurately from stresses at integral points. I thus developed an algorithm that would allow implicit analysis of the elastic-plastic problem on the basis of NFEM. The algorithm has the following steps : (1) Calculate the displacements of nodes with elastic NFEM. (2) Calculate stresses at each integral point. (3) Modify stresses at “yielded” integral points in main-elements and sub-elements. (4) Extrapolate stresses from integral points in sub-elements to integral points in main elements, and (5) Calculate residual forces at nodes from stresses. All steps are repeated until the residual forces converge to an allowable limit. The stress extrapolation scheme is the most important part of the method. I developed the extrapolation algorithm based on the shape functions of an iso-parametric element. To conclude, elastic-plastic NFEM can be used to implicitly analyze the stress of inelastic materials.