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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Vydáno v:Acta mechanica Ročník 226; číslo 12; s. 4223 - 4245
Hlavní autoři: Li, Eric, He, Z. C., Xu, Xu, Liu, G. R., Gu, Y. T.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Vienna Springer Vienna 01.12.2015
Springer
Springer Nature B.V
Témata:
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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Shrnutí: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.
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ISSN:0001-5970
1619-6937
DOI:10.1007/s00707-015-1456-6