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

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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 J 2 plasticity theory with isotropic hardening are solved using the proposed procedure to demonstrate its robustness, accuracy and computational efficiency.

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Authors and Affiliations

  1. Department of Architectural Engineering, Kyung Hee University, Engineering Building, 1 Sochon-Dong Kihung-Gu, Yongin, Kyunggi-Do, 446-701, Korea

    D.-J. Kim

  2. Department of Civil and Environmental Engineering, Newmark Laboratory, University of Illinois at Urbana-Champaign, 205 North Mathews Avenue, Urbana, IL, 61801, USA

    C. A. Duarte

  3. Structural Engineering Department, School of Engineering at São Carlos, University of São Paulo, Av. Trabalhador São-carlense, 400 São Carlos, São Paulo, CEP 13566-590, Brazil

    S. P. Proenca

Authors
  1. D.-J. Kim
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  2. C. A. Duarte
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  3. S. P. Proenca
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Correspondence to D.-J. Kim.

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Kim, DJ., Duarte, C.A. & Proenca, S.P. A generalized finite element method with global-local enrichment functions for confined plasticity problems. Comput Mech 50, 563–578 (2012). https://doi.org/10.1007/s00466-012-0689-7

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  • DOI: https://doi.org/10.1007/s00466-012-0689-7

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