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A strain smoothing formulation for NURBS-based isogeometric finite element analysis

Science China(Physics,Mechanics & Astronomy) 2012年第1期55卷 132-140页

作者： WANG DongDong ZHANG HanJie XUAN JunChang Department of Civil Engineering Xiamen University Xiamen 361005 China

A strain smoothing formulation for NURBS (non-uniform rational B-splines) based isogeometric finite element analysis is presented. This approach is formulated within the framework of assumed strain methods and strain smoothing operations. The strain smoothing is defined through strain averaging in the element sub-domains which are subsequently used for numerical integration of the Galerkin weak form. This formulation satisfies the orthogonality condition of the assumed strain methods. Meanwhile the present formulation totally avoids the gradient computation of the rational NURBS basis functions in the formulation of stiffness matrix. A transformation method is employed to accurately enforce the displacement boundary conditions. Numerical results demonstrate that the present formation gives very satisfactory solution accuracy simultaneously with improved computational efficiency.

关键词： NURBS basis functions isogeometric finite element analysis meshfree method strain smoothing sub-domain integration

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Bubble-Enriched Smoothed Finite Element Methods for Nearly-Incompressible Solids

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Computer Modeling in Engineering & Sciences 2021年第5期127卷 411-436页

作者： Changkye Lee Sundararajan Natarajan Jack S.Hale Zeike A.Taylor Jurng-Jae Yee Stephane P.A.Bordas University Core Research Center for Disaster-Free and Safe Ocean City Construction Dong-A UniversityBusan49315Korea Department of Mechanical Engineering Indian Institute of Technology MadrasChennai600036India Faculty of Science Technology and CommunicationUniversity of LuxembourgEsch-sur-AlzetteL-4364Luxembourg CISTIB-Center for Computational Imaging&Simulation Technologies in Biomedicine School of EngineeringLeedsLS29JTUK

This work presents a locking-free smoothed finite element method(S-FEM)for the simulation of soft matter modelled by the equations of quasi-incompressible *** proposed method overcomes well-known issues of standard finite element methods(FEM)in the incompressible limit:the over-estimation of stiffness and sensitivity to severely distorted *** concepts of cell-based,edge-based and node-based S-FEMs are extended in this paper to ***,a cubic bubble function is utilized to improve accuracy and *** the bubble function,an additional displacement degree of freedom is added at the centroid of the *** numerical studies are performed demonstrating the stability and validity of the proposed *** obtained results are compared with standard FEM and with analytical solutions to show the effectiveness of the method.

关键词： strain smoothing smoothed finite element method bubble functions hyperelasticity mesh distortion

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Selective Smoothed Finite Element Method

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Tsinghua Science and Technology 2007年第5期12卷 497-508页

作者： T. T. Nauven G. R. Liu K. Y. Dai K. Y. Lam Center for Advanced Computations in Engineering Science Department of Mechanical Engineering National University of Singapore 9 Engineering Drive 1 Singapore 117576 Singapore Singapore-MIT Alliance (SMA) E4-04-10 4 Engineering Drive 3 Singapore 117576 Singapore School of Mechanical and Aerospace Engineering Nanyang Technological University 50 Nanyang Avenue Singapore 639798 Singapore

The paper examines three selective schemes for the smoothed finite element method （SFEM） which was formulated by incorporating a cell-wise strain smoothing operation into the standard compatible finite element method （FEM）. These selective SFEM schemes were formulated based on three selective integration FEM schemes with similar properties found between the number of smoothing cells in the SFEM and the number of Gaussian integration points in the FEM. Both scheme 1 and scheme 2 are free of nearly incompressible locking, but scheme 2 is more general and gives better results than scheme 1. In addition, scheme 2 can be applied to anisotropic and nonlinear situations, while scheme 1 can only be applied to isotropic and linear situations. Scheme 3 is free of shear locking. This scheme can be applied to plate and shell problems. Results of the numerical study show that the selective SFEM schemes give more accurate results than the FEM schemes.

关键词： finite element method (FEM) smoothed finite element method (SFEM) strain smoothing smoothing cell selective

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