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p-Adaptive Ck generalized finite element method for arbitrary polygonal clouds

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Abstract

A p-Adaptive Generalized Finite Element Method (GFEM) based on a Partition of Unity (POU) of arbitrary smoothness degree is presented. The shape functions are built from the product of a Shepard POU and enrichment functions. Shepard functions have a smoothness degree directly related to the weighting functions adopted in their definition. Here the weighting functions are obtained from boolean R-functions which allow the construction of Ck approximations, with k arbitrarily large, defined over a polygonal patch of elements, named cloud. The Element Residual Method is used to obtain error indicators by taking into account the typical nodal enrichment scheme of the method. This procedure is enhanced by using approximations with a high degree of smoothness as it eliminates the discontinuity of the stress field in the interior of each cloud. Adaptive analysis of plane elasticity problems are presented, and the performance of the technique is investigated.

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Authors and Affiliations

  1. Department of Structural Engineering, Federal University of Minas Gerais, Av. Contorno, 842, 2º. andar, Centro, 30110-060, Belo Horizonte, MG, Brazil

    Felício B. Barros

  2. Graduate Program in Mechanical Engineering, Campus Universitrio - Trindade, Federal University of Santa Catarina, 88040-900, Florianpolis, SC, Brazil

    Clovis S. de Barcellos

  3. 2122 Newmark Civil Engineering Laboratory, University of Illinois at Urbana-Champaign, 205 North Mathews Ave., Urbana, IL, 61801-2352, USA

    Carlos A. Duarte

Authors
  1. Felício B. Barros
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  2. Clovis S. de Barcellos
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  3. Carlos A. Duarte
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Correspondence to Felício B. Barros.

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Barros, F.B., de Barcellos, C.S. & Duarte, C.A. p-Adaptive Ck generalized finite element method for arbitrary polygonal clouds. Comput Mech 41, 175–187 (2007). https://doi.org/10.1007/s00466-007-0177-7

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  • DOI: https://doi.org/10.1007/s00466-007-0177-7

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