Computational Mechanics

, Volume 50, Issue 5, pp 563–578 | Cite as

A generalized finite element method with global-local enrichment functions for confined plasticity problems

Original Paper

Abstract

The main feature of partition of unity methods such as the generalized or extended finite element method is their ability of utilizing a priori knowledge about the solution of a problem in the form of enrichment functions. However, analytical derivation of enrichment functions with good approximation properties is mostly limited to two-dimensional linear problems. This paper presents a procedure to numerically generate proper enrichment functions for three-dimensional problems with confined plasticity where plastic evolution is gradual. This procedure involves the solution of boundary value problems around local regions exhibiting nonlinear behavior and the enrichment of the global solution space with the local solutions through the partition of unity method framework. This approach can produce accurate nonlinear solutions with a reduced computational cost compared to standard finite element methods since computationally intensive nonlinear iterations can be performed on coarse global meshes after the creation of enrichment functions properly describing localized nonlinear behavior. Several three-dimensional nonlinear problems based on the rate-independent J2 plasticity theory with isotropic hardening are solved using the proposed procedure to demonstrate its robustness, accuracy and computational efficiency.

Keywords

Generalized FEM Extended FEM Global-local analysis Confined plasticity Nonlinear analysis 

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Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Department of Architectural EngineeringKyung Hee UniversityYonginKorea
  2. 2.Department of Civil and Environmental EngineeringNewmark Laboratory, University of Illinois at Urbana-ChampaignUrbanaUSA
  3. 3.Structural Engineering DepartmentSchool of Engineering at São Carlos, University of São PauloSão PauloBrazil

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