Three-dimensional FE-EFGM adaptive coupling with application to nonlinear adaptive analysis

Zahur Ullah, C. E. Augarde, W. M. Coombs

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Three-dimensional problems with both material and geometrical nonlinearities are of practical importance in many engi- neering applications, e.g. geomechanics, metal forming and biomechanics. Traditionally, these problems are simulated using an adaptive finite element method (FEM). However, the FEM faces many challenges in modeling these problems, such as mesh distortion and selection of a robust refinement algorithm. Adaptive meshless methods are a more recent technique for modeling these problems and can overcome the inherent mesh based drawbacks of the FEM but are com- putationally expensive. To take advantage of the good features of both methods, in the method proposed in this paper, initially the whole of the problem domain is modeled using the FEM. During an analysis those elements which violate a predefined error measure are automatically converted to a meshless zone. This zone can be further refined by adding nodes, overcoming computationally expensive FE remeshing. Therefore an appropriate coupling between the FE and the meshless zone is vital for the proposed formulation.One of the most widely used meshless methods, the element-free Galerkin method (EFGM), is used in this research. Maximum entropy shape functions are used instead of the conventional moving least squares based formulations‘. These shape functions posses a weak Kronecker delta property at the boundaries of the problem domain, which allows the essential boundary conditions to be imposed directly and also helps to avoid the use of a transition region in the coupling between the FE and the EFG regions. Total Lagrangian formulation is preferred over the update Lagrangian formulation for modeling finite deformation due to its computational efficiency. The well-established error estimation procedure of Zienkiewicz-Zhu is used in the FE region to determine the elements requiring conversion to the EFGM. The Chung and Belytschko error estimator is used in the EFG region for further adaptive refinement. Numerical examples are presented to demonstrate the performance of the current approach in three dimensional nonlinear problems.
LanguageEnglish
Title of host publicationUnknown Host Publication
Number of pages6
Publication statusAccepted/In press - 25 Mar 2013
EventInternational Conference on Computational Mechanics (CM13) - Durham University, UK
Duration: 25 Mar 2013 → …

Conference

ConferenceInternational Conference on Computational Mechanics (CM13)
Period25/03/13 → …

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Galerkin methods
Finite element method
Geomechanics
Biomechanics
Metal forming
Computational efficiency
Error analysis
Entropy
Boundary conditions

Keywords

  • FE-EFGM adaptive coupling
  • error estimation
  • finite deformation
  • elasto-plasticity
  • total Lagrangian

Cite this

Ullah, Z., Augarde, C. E., & Coombs, W. M. (Accepted/In press). Three-dimensional FE-EFGM adaptive coupling with application to nonlinear adaptive analysis. In Unknown Host Publication
Ullah, Zahur ; Augarde, C. E. ; Coombs, W. M. / Three-dimensional FE-EFGM adaptive coupling with application to nonlinear adaptive analysis. Unknown Host Publication. 2013.
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abstract = "Three-dimensional problems with both material and geometrical nonlinearities are of practical importance in many engi- neering applications, e.g. geomechanics, metal forming and biomechanics. Traditionally, these problems are simulated using an adaptive finite element method (FEM). However, the FEM faces many challenges in modeling these problems, such as mesh distortion and selection of a robust refinement algorithm. Adaptive meshless methods are a more recent technique for modeling these problems and can overcome the inherent mesh based drawbacks of the FEM but are com- putationally expensive. To take advantage of the good features of both methods, in the method proposed in this paper, initially the whole of the problem domain is modeled using the FEM. During an analysis those elements which violate a predefined error measure are automatically converted to a meshless zone. This zone can be further refined by adding nodes, overcoming computationally expensive FE remeshing. Therefore an appropriate coupling between the FE and the meshless zone is vital for the proposed formulation.One of the most widely used meshless methods, the element-free Galerkin method (EFGM), is used in this research. Maximum entropy shape functions are used instead of the conventional moving least squares based formulations‘. These shape functions posses a weak Kronecker delta property at the boundaries of the problem domain, which allows the essential boundary conditions to be imposed directly and also helps to avoid the use of a transition region in the coupling between the FE and the EFG regions. Total Lagrangian formulation is preferred over the update Lagrangian formulation for modeling finite deformation due to its computational efficiency. The well-established error estimation procedure of Zienkiewicz-Zhu is used in the FE region to determine the elements requiring conversion to the EFGM. The Chung and Belytschko error estimator is used in the EFG region for further adaptive refinement. Numerical examples are presented to demonstrate the performance of the current approach in three dimensional nonlinear problems.",
keywords = "FE-EFGM adaptive coupling, error estimation, finite deformation, elasto-plasticity, total Lagrangian",
author = "Zahur Ullah and Augarde, {C. E.} and Coombs, {W. M.}",
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Ullah, Z, Augarde, CE & Coombs, WM 2013, Three-dimensional FE-EFGM adaptive coupling with application to nonlinear adaptive analysis. in Unknown Host Publication. International Conference on Computational Mechanics (CM13), 25/03/13.

Three-dimensional FE-EFGM adaptive coupling with application to nonlinear adaptive analysis. / Ullah, Zahur; Augarde, C. E.; Coombs, W. M.

Unknown Host Publication. 2013.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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T1 - Three-dimensional FE-EFGM adaptive coupling with application to nonlinear adaptive analysis

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AU - Augarde, C. E.

AU - Coombs, W. M.

PY - 2013/3/25

Y1 - 2013/3/25

N2 - Three-dimensional problems with both material and geometrical nonlinearities are of practical importance in many engi- neering applications, e.g. geomechanics, metal forming and biomechanics. Traditionally, these problems are simulated using an adaptive finite element method (FEM). However, the FEM faces many challenges in modeling these problems, such as mesh distortion and selection of a robust refinement algorithm. Adaptive meshless methods are a more recent technique for modeling these problems and can overcome the inherent mesh based drawbacks of the FEM but are com- putationally expensive. To take advantage of the good features of both methods, in the method proposed in this paper, initially the whole of the problem domain is modeled using the FEM. During an analysis those elements which violate a predefined error measure are automatically converted to a meshless zone. This zone can be further refined by adding nodes, overcoming computationally expensive FE remeshing. Therefore an appropriate coupling between the FE and the meshless zone is vital for the proposed formulation.One of the most widely used meshless methods, the element-free Galerkin method (EFGM), is used in this research. Maximum entropy shape functions are used instead of the conventional moving least squares based formulations‘. These shape functions posses a weak Kronecker delta property at the boundaries of the problem domain, which allows the essential boundary conditions to be imposed directly and also helps to avoid the use of a transition region in the coupling between the FE and the EFG regions. Total Lagrangian formulation is preferred over the update Lagrangian formulation for modeling finite deformation due to its computational efficiency. The well-established error estimation procedure of Zienkiewicz-Zhu is used in the FE region to determine the elements requiring conversion to the EFGM. The Chung and Belytschko error estimator is used in the EFG region for further adaptive refinement. Numerical examples are presented to demonstrate the performance of the current approach in three dimensional nonlinear problems.

AB - Three-dimensional problems with both material and geometrical nonlinearities are of practical importance in many engi- neering applications, e.g. geomechanics, metal forming and biomechanics. Traditionally, these problems are simulated using an adaptive finite element method (FEM). However, the FEM faces many challenges in modeling these problems, such as mesh distortion and selection of a robust refinement algorithm. Adaptive meshless methods are a more recent technique for modeling these problems and can overcome the inherent mesh based drawbacks of the FEM but are com- putationally expensive. To take advantage of the good features of both methods, in the method proposed in this paper, initially the whole of the problem domain is modeled using the FEM. During an analysis those elements which violate a predefined error measure are automatically converted to a meshless zone. This zone can be further refined by adding nodes, overcoming computationally expensive FE remeshing. Therefore an appropriate coupling between the FE and the meshless zone is vital for the proposed formulation.One of the most widely used meshless methods, the element-free Galerkin method (EFGM), is used in this research. Maximum entropy shape functions are used instead of the conventional moving least squares based formulations‘. These shape functions posses a weak Kronecker delta property at the boundaries of the problem domain, which allows the essential boundary conditions to be imposed directly and also helps to avoid the use of a transition region in the coupling between the FE and the EFG regions. Total Lagrangian formulation is preferred over the update Lagrangian formulation for modeling finite deformation due to its computational efficiency. The well-established error estimation procedure of Zienkiewicz-Zhu is used in the FE region to determine the elements requiring conversion to the EFGM. The Chung and Belytschko error estimator is used in the EFG region for further adaptive refinement. Numerical examples are presented to demonstrate the performance of the current approach in three dimensional nonlinear problems.

KW - FE-EFGM adaptive coupling

KW - error estimation

KW - finite deformation

KW - elasto-plasticity

KW - total Lagrangian

M3 - Conference contribution

BT - Unknown Host Publication

ER -

Ullah Z, Augarde CE, Coombs WM. Three-dimensional FE-EFGM adaptive coupling with application to nonlinear adaptive analysis. In Unknown Host Publication. 2013