A three-dimensional hybrid smoothed finite element method (H-SFEM) for nonlinear solid mechanics problems

This paper presents a novel three-dimensional hybrid smoothed finite element method (H-SFEM) for solid mechanics problems. In 3D H-SFEM, the strain field is assumed to be the weighted average between compatible strains from the finite element method (FEM) and smoothed strains from the node-based smo...

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Veröffentlicht in:	Acta mechanica Jg. 226; H. 12; S. 4223 - 4245
Hauptverfasser:	Li, Eric, He, Z. C., Xu, Xu, Liu, G. R., Gu, Y. T.
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	Vienna Springer Vienna 01.12.2015 Springer Springer Nature B.V
Schlagworte:	Analysis Classical and Continuum Physics Control Dynamical Systems Eigenfrequencies Engineering Engineering Thermodynamics Finite element analysis Finite element method Heat and Mass Transfer Mathematical analysis Mathematical models Mechanical engineering Methods Nonlinearity Original Paper Solid Mechanics Strain Theoretical and Applied Mechanics Three dimensional Vibration Incompressible Material Meshfree Method Solid Mechanic Problem Tetrahedral Element Nonlinear Deformation
ISSN:	0001-5970, 1619-6937
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Abstract	This paper presents a novel three-dimensional hybrid smoothed finite element method (H-SFEM) for solid mechanics problems. In 3D H-SFEM, the strain field is assumed to be the weighted average between compatible strains from the finite element method (FEM) and smoothed strains from the node-based smoothed FEM with a parameter α equipped into H-SFEM. By adjusting α, the upper and lower bound solutions in the strain energy norm and eigenfrequencies can always be obtained. The optimized α value in 3D H-SFEM using a tetrahedron mesh possesses a close-to-exact stiffness of the continuous system, and produces ultra-accurate solutions in terms of displacement, strain energy and eigenfrequencies in the linear and nonlinear problems. The novel domain-based selective scheme is proposed leading to a combined selective H-SFEM model that is immune from volumetric locking and hence works well for nearly incompressible materials. The proposed 3D H-SFEM is an innovative and unique numerical method with its distinct features, which has great potential in the successful application for solid mechanics problems.
AbstractList	This paper presents a novel three-dimensional hybrid smoothed finite element method (H-SFEM) for solid mechanics problems. In 3D H-SFEM, the strain field is assumed to be the weighted average between compatible strains from the finite element method (FEM) and smoothed strains from the node-based smoothed FEM with a parameter a equipped into H-SFEM. By adjusting a, the upper and lower bound solutions in the strain energy norm and eigenfrequencies can always be obtained. The optimized α value in 3D H-SFEM using a tetrahedron mesh possesses a close-to-exact stiffness of the continuous system, and produces ultra-accurate solutions in terms of displacement, strain energy and eigenfrequencies in the linear and nonlinear problems. The novel domain-based selective scheme is proposed leading to a combined selective H-SFEM model that is immune from volumetric locking and hence works well for nearly incompressible materials. The proposed 3D H-SFEM is an innovative and unique numerical method with its distinct features, which has great potential in the successful application for solid mechanics problems. This paper presents a novel three-dimensional hybrid smoothed finite element method (H-SFEM) for solid mechanics problems. In 3D H-SFEM, the strain field is assumed to be the weighted average between compatible strains from the finite element method (FEM) and smoothed strains from the node-based smoothed FEM with a parameter [alpha] equipped into H-SFEM. By adjusting [alpha], the upper and lower bound solutions in the strain energy norm and eigenfrequencies can always be obtained. The optimized [alpha] value in 3D H-SFEM using a tetrahedron mesh possesses a close-to-exact stiffness of the continuous system, and produces ultra-accurate solutions in terms of displacement, strain energy and eigenfrequencies in the linear and nonlinear problems. The novel domain-based selective scheme is proposed leading to a combined selective H-SFEM model that is immune from volumetric locking and hence works well for nearly incompressible materials. The proposed 3D H-SFEM is an innovative and unique numerical method with its distinct features, which has great potential in the successful application for solid mechanics problems. This paper presents a novel three-dimensional hybrid smoothed finite element method (H-SFEM) for solid mechanics problems. In 3D H-SFEM, the strain field is assumed to be the weighted average between compatible strains from the finite element method (FEM) and smoothed strains from the node-based smoothed FEM with a parameter α equipped into H-SFEM. By adjusting α, the upper and lower bound solutions in the strain energy norm and eigenfrequencies can always be obtained. The optimized α value in 3D H-SFEM using a tetrahedron mesh possesses a close-to-exact stiffness of the continuous system, and produces ultra-accurate solutions in terms of displacement, strain energy and eigenfrequencies in the linear and nonlinear problems. The novel domain-based selective scheme is proposed leading to a combined selective H-SFEM model that is immune from volumetric locking and hence works well for nearly incompressible materials. The proposed 3D H-SFEM is an innovative and unique numerical method with its distinct features, which has great potential in the successful application for solid mechanics problems.
Audience	Academic
Author	Li, Eric Xu, Xu He, Z. C. Liu, G. R. Gu, Y. T.
Author_xml	– sequence: 1 givenname: Eric surname: Li fullname: Li, Eric email: ericsg2012@gmail.com organization: State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University – sequence: 2 givenname: Z. C. surname: He fullname: He, Z. C. organization: State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University – sequence: 3 givenname: Xu surname: Xu fullname: Xu, Xu organization: College of Mathematics, Jilin University – sequence: 4 givenname: G. R. surname: Liu fullname: Liu, G. R. organization: School of Aerospace Systems, University of Cincinnati – sequence: 5 givenname: Y. T. surname: Gu fullname: Gu, Y. T. organization: School of Engineering Systems, Queensland University of Technology
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Cites_doi	10.1007/s00466-006-0075-4 10.1002/nme.2050 10.1093/acprof:oso/9780198525295.001.0001 10.1002/nme.2204 10.1201/9781420082104 10.1002/nme.2719 10.1016/j.compstruc.2008.09.003 10.1016/j.cma.2008.03.011 10.1002/nme.1968 10.1016/0045-7825(78)90005-1 10.1201/9781482270211 10.1017/CBO9780511605345 10.1002/(SICI)1097-0207(20000510)48:1<79::AID-NME869>3.0.CO;2-D 10.1016/0045-7825(90)90168-L 10.1002/1097-0207(20010120)50:2<435::AID-NME32>3.0.CO;2-A 10.1016/S0045-7825(01)00281-X 10.1142/S0219876208001510 10.1016/j.jsv.2008.08.027 10.1002/nme.1620370205 10.1007/s00466-012-0809-4 10.1007/978-1-4612-3172-1 10.1002/nme.1620200911 10.1017/CBO9780511791253
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Snippet	This paper presents a novel three-dimensional hybrid smoothed finite element method (H-SFEM) for solid mechanics problems. In 3D H-SFEM, the strain field is...
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SubjectTerms	Analysis Classical and Continuum Physics Control Dynamical Systems Eigenfrequencies Engineering Engineering Thermodynamics Finite element analysis Finite element method Heat and Mass Transfer Mathematical analysis Mathematical models Mechanical engineering Methods Nonlinearity Original Paper Solid Mechanics Strain Theoretical and Applied Mechanics Three dimensional Vibration
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Title	A three-dimensional hybrid smoothed finite element method (H-SFEM) for nonlinear solid mechanics problems
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