An s-version finite element method without generation of coupling stiffness matrix by using iterative technique

In s-version finite element method (s-FEM) proposed by Fish (1992), a local mesh that represents the local feature such as a hole or a crack is superposed on a global mesh that represents the shape of the whole analysis model. The interaction between global and local meshes is represented by couplin...

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Autores principales:	Yosuke YUMOTO, Yasunori YUSA, Hiroshi OKADA
Formato:	article
Lenguaje:	EN
Publicado:	The Japan Society of Mechanical Engineers 2016
Materias:	s-version finite element method coupling stiffness matrix iterative method initial stress local least squares interpolation nearest neighbor interpolation stress concentration stress intensity factor Mechanical engineering and machinery TJ1-1570
Acceso en línea:	https://doaj.org/article/8f4eff6549634c9b920a1839ed75f574
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spelling	oai:doaj.org-article:8f4eff6549634c9b920a1839ed75f5742021-11-26T06:55:30ZAn s-version finite element method without generation of coupling stiffness matrix by using iterative technique2187-974510.1299/mej.16-00001https://doaj.org/article/8f4eff6549634c9b920a1839ed75f5742016-08-01T00:00:00Zhttps://www.jstage.jst.go.jp/article/mej/3/5/3_16-00001/_pdf/-char/enhttps://doaj.org/toc/2187-9745In s-version finite element method (s-FEM) proposed by Fish (1992), a local mesh that represents the local feature such as a hole or a crack is superposed on a global mesh that represents the shape of the whole analysis model. The interaction between global and local meshes is represented by coupling stiffness matrices. Since the global and local meshes can be generated independently, mesh generation efforts are reduced remarkably. However, s-FEM has a common issue. The generation of coupling stiffness matrices takes a considerable amount of program development efforts, which include constructing accurate cross-element integration methodology and programming it for various element types. For such an issue, we propose an iterative s-FEM that does not require the generation of coupling stiffness matrices at all. The coupling term is now evaluated by global and local stresses that are computed on the respective mesh and then transferred to the other by interpolation techniques. The global and local stresses are treated as initial stress in the finite element computations. The global and local analyses are performed alternately under assumed initial stress, and converged solution is achieved by iteration with a monitored residual being sufficiently small. In proposed iterative s-FEM, an issue about linear independence of global and local elements, which is known to occur in the original s-FEM, does not occur. In numerical experiments, converged solution was successfully obtained within several hundred iteration counts. Accurate stress distribution for a stress concentration problem and an accurate stress intensity factor for a linear elastic fracture mechanics problem were computed by proposed iterative s-FEM. In addition, several stress interpolation techniques were compared in the numerical experiments. Nearest neighbor interpolation for the global stress and local least squares interpolation for the local stress showed good convergence and accurate solution.Yosuke YUMOTOYasunori YUSAHiroshi OKADAThe Japan Society of Mechanical Engineersarticles-version finite element methodcoupling stiffness matrixiterative methodinitial stresslocal least squares interpolationnearest neighbor interpolationstress concentrationstress intensity factorMechanical engineering and machineryTJ1-1570ENMechanical Engineering Journal, Vol 3, Iss 5, Pp 16-00001-16-00001 (2016)
institution	DOAJ
collection	DOAJ
language	EN
topic	s-version finite element method coupling stiffness matrix iterative method initial stress local least squares interpolation nearest neighbor interpolation stress concentration stress intensity factor Mechanical engineering and machinery TJ1-1570
spellingShingle	s-version finite element method coupling stiffness matrix iterative method initial stress local least squares interpolation nearest neighbor interpolation stress concentration stress intensity factor Mechanical engineering and machinery TJ1-1570 Yosuke YUMOTO Yasunori YUSA Hiroshi OKADA An s-version finite element method without generation of coupling stiffness matrix by using iterative technique
description	In s-version finite element method (s-FEM) proposed by Fish (1992), a local mesh that represents the local feature such as a hole or a crack is superposed on a global mesh that represents the shape of the whole analysis model. The interaction between global and local meshes is represented by coupling stiffness matrices. Since the global and local meshes can be generated independently, mesh generation efforts are reduced remarkably. However, s-FEM has a common issue. The generation of coupling stiffness matrices takes a considerable amount of program development efforts, which include constructing accurate cross-element integration methodology and programming it for various element types. For such an issue, we propose an iterative s-FEM that does not require the generation of coupling stiffness matrices at all. The coupling term is now evaluated by global and local stresses that are computed on the respective mesh and then transferred to the other by interpolation techniques. The global and local stresses are treated as initial stress in the finite element computations. The global and local analyses are performed alternately under assumed initial stress, and converged solution is achieved by iteration with a monitored residual being sufficiently small. In proposed iterative s-FEM, an issue about linear independence of global and local elements, which is known to occur in the original s-FEM, does not occur. In numerical experiments, converged solution was successfully obtained within several hundred iteration counts. Accurate stress distribution for a stress concentration problem and an accurate stress intensity factor for a linear elastic fracture mechanics problem were computed by proposed iterative s-FEM. In addition, several stress interpolation techniques were compared in the numerical experiments. Nearest neighbor interpolation for the global stress and local least squares interpolation for the local stress showed good convergence and accurate solution.
format	article
author	Yosuke YUMOTO Yasunori YUSA Hiroshi OKADA
author_facet	Yosuke YUMOTO Yasunori YUSA Hiroshi OKADA
author_sort	Yosuke YUMOTO
title	An s-version finite element method without generation of coupling stiffness matrix by using iterative technique
title_short	An s-version finite element method without generation of coupling stiffness matrix by using iterative technique
title_full	An s-version finite element method without generation of coupling stiffness matrix by using iterative technique
title_fullStr	An s-version finite element method without generation of coupling stiffness matrix by using iterative technique
title_full_unstemmed	An s-version finite element method without generation of coupling stiffness matrix by using iterative technique
title_sort	s-version finite element method without generation of coupling stiffness matrix by using iterative technique
publisher	The Japan Society of Mechanical Engineers
publishDate	2016
url	https://doaj.org/article/8f4eff6549634c9b920a1839ed75f574
work_keys_str_mv	AT yosukeyumoto ansversionfiniteelementmethodwithoutgenerationofcouplingstiffnessmatrixbyusingiterativetechnique AT yasunoriyusa ansversionfiniteelementmethodwithoutgenerationofcouplingstiffnessmatrixbyusingiterativetechnique AT hiroshiokada ansversionfiniteelementmethodwithoutgenerationofcouplingstiffnessmatrixbyusingiterativetechnique AT yosukeyumoto sversionfiniteelementmethodwithoutgenerationofcouplingstiffnessmatrixbyusingiterativetechnique AT yasunoriyusa sversionfiniteelementmethodwithoutgenerationofcouplingstiffnessmatrixbyusingiterativetechnique AT hiroshiokada sversionfiniteelementmethodwithoutgenerationofcouplingstiffnessmatrixbyusingiterativetechnique
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An s-version finite element method without generation of coupling stiffness matrix by using iterative technique

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