On the Convergence of the Finite Element Solution of a Nonlinear Crack Type Problem in Finite Elasticity

Material type: 文書・図像類

Author: 大竹, 邦彦ほか

Publisher: 航空宇宙技術研究所

Publication date: 1985-08

Material Format: Digital

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Note (General)：: 高伸長弾性体中のクラック型の問題を考える。材料は等方性,非圧縮性で,大変形下で非線形構成関係を有する。この物体が体積力のもとでせん断変形をうける時,非線形境界値問題が導びかれる。この問題はクッラク状の先端部で,特異性のある解析解をもつ。この問題のガラーキン近似有限要素解の収束性につき,函数解析手法に...

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Material Type: 文書・図像類
Title: On the Convergence of the Finite Element Solution of a Nonlinear Crack Type Problem in Finite Elasticity
Author/Editor: 大竹, 邦彦
OHTAKE, Kunihiko
Author Heading: 大竹, 邦彦
OHTAKE, Kunihiko
Publication, Distribution, etc.: 航空宇宙技術研究所
Publication Date: 1985-08
Publication Date (W3CDTF): 1985-08
Periodical title: Technical Report of National Aerospace Laboratory TR-872T
No. or year of volume/issue: 872T
Volume: 872T
Pages: 13-
ISSN (Periodical Title): ISSN : 0389-4010
Text Language Code: eng
Target Audience: 一般
Note (General): 高伸長弾性体中のクラック型の問題を考える。材料は等方性,非圧縮性で,大変形下で非線形構成関係を有する。この物体が体積力のもとでせん断変形をうける時,非線形境界値問題が導びかれる。この問題はクッラク状の先端部で,特異性のある解析解をもつ。この問題のガラーキン近似有限要素解の収束性につき,函数解析手法における重みつきソボレフ空間を導入して調べた結果,grad u ～ r-i/4の特異性に対し,収束率
u-Uh
1w2 ～ h1/4を得た。
In this paper we consider the crack type problem in a hyperelastic body. The material is assumed to be isotropic, incompressible, and to have a special nonlinear constitutive equation under large deformation. This body is subjected to shear deformation under the action of body force. The problem leads to the nonlinear boundary value problem. The analytical solution of this problem exhibits the singularity at the crack tip. We investigate the convergence rate of the Galerkin approximation solution by introducing the weighted Sobolev space in functional analysis technique. The results show the convergence rate
1w2 ～ h1/4 for the singularity grad u ～ r-i/4.
資料番号: NALTR0872000
レポート番号: NAL TR-872T
Access Restrictions: 限定公開
Data Provider (Database): 国立情報学研究所 : 学術機関リポジトリデータベース（IRDB）（機関リポジトリ）
https://irdb.nii.ac.jp
Original Data Provider (Database): 宇宙航空研究開発機構 : 宇宙航空研究開発機構リポジトリ