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An adaptive finite element/meshless coupled method based on local maximum entropy shape functions for linear and nonlinear problems

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COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 2013年 267卷 111-132页

作者： Ullah, Z. Coombs, W. M. Augarde, C. E. Univ Durham Sch Engn & Comp Sci Durham DH1 3LE England

In this paper, an automatic adaptive coupling procedure is proposed for the finite element method (FEM) and the element-free Galerkin method (EFGM) for linear elasticity and for problems with both material and geometrical nonlinearities. In this new procedure, initially the whole of the problem domain is modelled using the FEM. During an analysis, those finite elements which violate a predefined error measure are automatically converted to an EFG zone. This EFG zone can be further refined by adding nodes, thus avoiding computationally expensive FE remeshing. Local maximum entropy shape functions are used in the EFG zone of the problem domain for two reasons: their weak Kronecker delta property at the boundaries allows straightforward imposition of essential boundary conditions and also provides a natural way to couple the EFG and FE regions compared to the use of moving least squares basis functions. The Zienkiewicz and Zhu error estimation procedure with the superconvergent patch method for strains and stresses recovery is used in the FE region of the problem domain, while the Chung and Belytschko error estimation procedure is used in the EFG region. (C) 2013 Elsevier B.V. All rights reserved.

关键词： Meshless method maximum entropy shape functions FE-EFGM coupling Error estimation Adaptivity Superconvergent patch recovery

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Parallel computations in nonlinear solid mechanics using adaptive finite element and meshless methods

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ENGINEERING COMPUTATIONS 2016年第4期33卷 1161-1191页

作者： Ullah, Zahur Coombs, Will Augarde, C. Univ Glasgow Sch Engn Glasgow Lanark Scotland Univ Durham Sch Engn & Comp Sci Durham England

Purpose - A variety of meshless methods have been developed in the last 20 years with an intention to solve practical engineering problems, but are limited to small academic problems due to associated high computational cost as compared to the standard finite element methods (FEM). The purpose of this paper is to develop an efficient and accurate algorithms based on meshless methods for the solution of problems involving both material and geometrical nonlinearities. Design/methodology/approach - A parallel two-dimensional linear elastic computer code is presented for a maximum entropy basis functions based meshless method. The two-dimensional algorithm is subsequently extended to three-dimensional adaptive nonlinear and three-dimensional parallel nonlinear adaptively coupled finite element, meshless method cases. The Prandtl-Reuss constitutive model is used to model elasto-plasticity and total Lagrangian formulations are used to model finite deformation. Furthermore, Zienkiewicz and Zhu and Chung and Belytschko error estimation procedure are used in the FE and meshless regions of the problem domain, respectively. The message passing interface library and open-source software packages, METIS and MUltifrontal Massively Parallel Solver are used for the high performance computation. Findings - Numerical examples are given to demonstrate the correct implementation and performance of the parallel algorithms. The agreement between the numerical and analytical results in the case of linear elastic example is excellent. For the nonlinear problems load-displacement curve are compared with the reference FEM and found in a very good agreement. As compared to the FEM, no volumetric locking was observed in the case of meshless method. Furthermore, it is shown that increasing the number of processors up to a given number improve the performance of parallel algorithms in term of simulation time, speedup and efficiency. Originality/value - Problems involving both material and geomet

关键词： Parallel computations Adaptively coupled finite element-meshless method Adaptivity Error estimation maximum entropy shape functions Meshless method

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