Generalized finite element method in structural nonlinear analysis – a p-adaptive strategy

This paper is concerned with an extension of the generalized finite element method, GFEM, to nonlinear analysis and to the proposition of a p-adaptive strategy. The p-adaptivity is considered due to the nodal enrichment scheme of the method. Here, such scheme consists of multiplying the partition of unity functions by a set of polynomials. In a first part, the performance of the method in nonlinear analysis of a reinforced concrete beam with progressive damage is presented. The adaptive strategy is then proposed on basis of a control over the approximation error. Aiming to estimate the approximation error, the equilibrated element residual method is adapted to the GFEM and to the nonlinear approach. Then, global and local error measures are defined. A numerical example is presented outlining the effectivity index of the error estimator proposed. Finally, a p-adaptive procedure is described and its good performance is illustrated by a numerical example.

[1]  I. Babuska,et al.  The design and analysis of the Generalized Finite Element Method , 2000 .

[2]  J. Mazars.  APPLICATION DE LA MECANIQUE DE L'ENDOMMAGEMENT AU COMPORTEMENT NON LINEAIRE ET A LA RUPTURE DU BETON DE STRUCTURE , 1984 .

[3]  Oden,et al.  An h-p adaptive method using clouds , 1996 .

[4]  I. Babuska,et al.  Special finite element methods for a class of second order elliptic problems with rough coefficients , 1994 .

[5]  Ted Belytschko,et al.  Elastic crack growth in finite elements with minimal remeshing , 1999 .

[6]  O. C. Zienkiewicz,et al.  A new cloud-based hp finite element method , 1998 .

[7]  L Davenne,et al.  UN CODE DE CALCUL POUR LA PREVISION DU COMPORTEMENT DE STRUCTURES ENDOMMAGEABLES EN BETON, EN BETON ARME, OU EN BETON DE FIBRES , 1989 .

[8]  J. Oden,et al.  H‐p clouds—an h‐p meshless method , 1996 .

[9]  T. Liszka,et al.  A generalized finite element method for the simulation of three-dimensional dynamic crack propagation , 2001 .

[10]  J. Melenk.  The Partition of Unity MethodI , 1996 .

[11]  J. Oden,et al.  Toward a universal h - p adaptive finite element strategy: Part 2 , 1989 .

[12]  C. S. de Barcellos,et al.  On error estimator and p‐adaptivity in the generalized finite element method , 2004 .

[13]  CLOUDS , CRACKS AND FEM ' , 1997 .

[14]  Pierre Ladevèze,et al.  A general method for recovering equilibrating element tractions , 1996 .

[15]  Ted Belytschko,et al.  A finite element method for crack growth without remeshing , 1999 .

[16]  A. Ranjbaran,et al.  Embedding of reinforcements in reinforced concrete elements implemented in DENA , 1991 .

[17]  I. Babuska,et al.  The generalized finite element method , 2001 .

[18]  J. Oden,et al.  A Posteriori Error Estimation in Finite Element Analysis , 2000 .

[19]  Ivo Babuška,et al.  Generalized finite element methods for three-dimensional structural mechanics problems , 2000 .

[20]  Roland Glowinski,et al.  An introduction to the mathematical theory of finite elements , 1976 .