Element subdivision technique for coupling-matrix-free iterative s-version FEM and investigation of sufficient element subdivision

In s-version finite element method (s-FEM), a local mesh is superposed on a global mesh, and they are solved monolithically. The local mesh represents the local feature such as a hole, whereas the global mesh does the shape of a structure. Since the two meshes are generated independently, mesh gener...

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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 numerical integration discontinuity local least squares interpolation sampling region numerical oscillations Mechanical engineering and machinery TJ1-1570
Acceso en línea:	https://doaj.org/article/e4327b7b9b3d432e852b22b509749916
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spelling	oai:doaj.org-article:e4327b7b9b3d432e852b22b5097499162021-11-26T06:55:30ZElement subdivision technique for coupling-matrix-free iterative s-version FEM and investigation of sufficient element subdivision2187-974510.1299/mej.16-00361https://doaj.org/article/e4327b7b9b3d432e852b22b5097499162016-09-01T00:00:00Zhttps://www.jstage.jst.go.jp/article/mej/3/5/3_16-00361/_pdf/-char/enhttps://doaj.org/toc/2187-9745In s-version finite element method (s-FEM), a local mesh is superposed on a global mesh, and they are solved monolithically. The local mesh represents the local feature such as a hole, whereas the global mesh does the shape of a structure. Since the two meshes are generated independently, mesh generation becomes very tractable. However, s-FEM has a difficulty that the generation of coupling stiffness matrices takes a lot of computational efforts. To overcome this difficulty, the authors proposed coupling-matrix-free iterative s-FEM. In this method, the coupling stiffness matrices are computed implicitly by stress integration on one mesh and stress transfer from one mesh to the other mesh. Converged solution is obtained by iteration. However, in practical cases, unnatural stress oscillations can occur with conventional Gaussian quadrature. In this paper, in order to smooth unnatural stress oscillations, element subdivision technique is applied. Element subdivision technique can deal with the discontinuity of discretized stress along element interfaces. The stress transfer scheme in coupling-matrix-free iterative s-FEM is designed to work harmoniously with element subdivision. Moreover, element subdivision strategy to obtain smooth stress distribution is investigated in the numerical experiments of a circular hole problem. We propose the element subdivision strategy as the following two items. First, at least 4×4 element subdivision should be adopted to obtain smooth stress distribution. Second, the local mesh should be fine enough to evaluate stress concentration accurately. To confirm this strategy, global and local meshes for elliptical hole problems are designed by following this strategy. Even in severe stress concentration problems, unnatural stress oscillations, which occur with conventional quadrature, is smoothed obviously with 4×4 element subdivision. In addition, stress concentration is evaluated accurately due to the second item of the strategy.Yosuke YUMOTOYasunori YUSAHiroshi OKADAThe Japan Society of Mechanical Engineersarticles-version finite element methodnumerical integrationdiscontinuitylocal least squares interpolationsampling regionnumerical oscillationsMechanical engineering and machineryTJ1-1570ENMechanical Engineering Journal, Vol 3, Iss 5, Pp 16-00361-16-00361 (2016)
institution	DOAJ
collection	DOAJ
language	EN
topic	s-version finite element method numerical integration discontinuity local least squares interpolation sampling region numerical oscillations Mechanical engineering and machinery TJ1-1570
spellingShingle	s-version finite element method numerical integration discontinuity local least squares interpolation sampling region numerical oscillations Mechanical engineering and machinery TJ1-1570 Yosuke YUMOTO Yasunori YUSA Hiroshi OKADA Element subdivision technique for coupling-matrix-free iterative s-version FEM and investigation of sufficient element subdivision
description	In s-version finite element method (s-FEM), a local mesh is superposed on a global mesh, and they are solved monolithically. The local mesh represents the local feature such as a hole, whereas the global mesh does the shape of a structure. Since the two meshes are generated independently, mesh generation becomes very tractable. However, s-FEM has a difficulty that the generation of coupling stiffness matrices takes a lot of computational efforts. To overcome this difficulty, the authors proposed coupling-matrix-free iterative s-FEM. In this method, the coupling stiffness matrices are computed implicitly by stress integration on one mesh and stress transfer from one mesh to the other mesh. Converged solution is obtained by iteration. However, in practical cases, unnatural stress oscillations can occur with conventional Gaussian quadrature. In this paper, in order to smooth unnatural stress oscillations, element subdivision technique is applied. Element subdivision technique can deal with the discontinuity of discretized stress along element interfaces. The stress transfer scheme in coupling-matrix-free iterative s-FEM is designed to work harmoniously with element subdivision. Moreover, element subdivision strategy to obtain smooth stress distribution is investigated in the numerical experiments of a circular hole problem. We propose the element subdivision strategy as the following two items. First, at least 4×4 element subdivision should be adopted to obtain smooth stress distribution. Second, the local mesh should be fine enough to evaluate stress concentration accurately. To confirm this strategy, global and local meshes for elliptical hole problems are designed by following this strategy. Even in severe stress concentration problems, unnatural stress oscillations, which occur with conventional quadrature, is smoothed obviously with 4×4 element subdivision. In addition, stress concentration is evaluated accurately due to the second item of the strategy.
format	article
author	Yosuke YUMOTO Yasunori YUSA Hiroshi OKADA
author_facet	Yosuke YUMOTO Yasunori YUSA Hiroshi OKADA
author_sort	Yosuke YUMOTO
title	Element subdivision technique for coupling-matrix-free iterative s-version FEM and investigation of sufficient element subdivision
title_short	Element subdivision technique for coupling-matrix-free iterative s-version FEM and investigation of sufficient element subdivision
title_full	Element subdivision technique for coupling-matrix-free iterative s-version FEM and investigation of sufficient element subdivision
title_fullStr	Element subdivision technique for coupling-matrix-free iterative s-version FEM and investigation of sufficient element subdivision
title_full_unstemmed	Element subdivision technique for coupling-matrix-free iterative s-version FEM and investigation of sufficient element subdivision
title_sort	element subdivision technique for coupling-matrix-free iterative s-version fem and investigation of sufficient element subdivision
publisher	The Japan Society of Mechanical Engineers
publishDate	2016
url	https://doaj.org/article/e4327b7b9b3d432e852b22b509749916
work_keys_str_mv	AT yosukeyumoto elementsubdivisiontechniqueforcouplingmatrixfreeiterativesversionfemandinvestigationofsufficientelementsubdivision AT yasunoriyusa elementsubdivisiontechniqueforcouplingmatrixfreeiterativesversionfemandinvestigationofsufficientelementsubdivision AT hiroshiokada elementsubdivisiontechniqueforcouplingmatrixfreeiterativesversionfemandinvestigationofsufficientelementsubdivision
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Element subdivision technique for coupling-matrix-free iterative s-version FEM and investigation of sufficient element subdivision

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