Finite element analysis of hyperelastic shells without any local iterative calculations by block Newton method
The simultaneously iterative procedure proposed by the authors is extended to hyperelastic shells. The weak form of the equilibrium equation and the plane stress condition at every material point are defined as a coupled problem, and a numerical procedure based on the block Newton method to solve th...
| Main Authors: | , , |
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| Format: | Article |
| Language: | Japanese |
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The Japan Society of Mechanical Engineers
2022-07-01
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| Series: | Nihon Kikai Gakkai ronbunshu |
| Subjects: | |
| Online Access: | https://www.jstage.jst.go.jp/article/transjsme/88/912/88_22-00150/_pdf/-char/en |
| _version_ | 1811180261133516800 |
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| author | Takeki YAMAMOTO Takahiro YAMADA Kazumi MATSUI |
| author_facet | Takeki YAMAMOTO Takahiro YAMADA Kazumi MATSUI |
| author_sort | Takeki YAMAMOTO |
| collection | DOAJ |
| description | The simultaneously iterative procedure proposed by the authors is extended to hyperelastic shells. The weak form of the equilibrium equation and the plane stress condition at every material point are defined as a coupled problem, and a numerical procedure based on the block Newton method to solve them with simultaneous linearization is developed in this paper. In the proposed block Newton method, the tangent moduli can be constructed algebraically by eliminating the internal variables, which are also updated algebraically without any local iterative calculations. In addition, the pseudo-stress for the residuals of plane stress state is incorporated into the linearized weak form of the equilibrium equation. Hence, the proposed procedure enables us to decrease the residuals in the coupled boundary value problems simultaneously. Some numerical examples demonstrate the validity and the effectiveness of the procedures in hyperelastic shells. |
| first_indexed | 2024-04-11T06:48:24Z |
| format | Article |
| id | doaj.art-cf796e65ae794a5797d52f6c4aec7665 |
| institution | Directory Open Access Journal |
| issn | 2187-9761 |
| language | Japanese |
| last_indexed | 2024-04-11T06:48:24Z |
| publishDate | 2022-07-01 |
| publisher | The Japan Society of Mechanical Engineers |
| record_format | Article |
| series | Nihon Kikai Gakkai ronbunshu |
| spelling | doaj.art-cf796e65ae794a5797d52f6c4aec76652022-12-22T04:39:18ZjpnThe Japan Society of Mechanical EngineersNihon Kikai Gakkai ronbunshu2187-97612022-07-018891222-0015022-0015010.1299/transjsme.22-00150transjsmeFinite element analysis of hyperelastic shells without any local iterative calculations by block Newton methodTakeki YAMAMOTO0Takahiro YAMADA1Kazumi MATSUI2Graduate School of Advanced Science and Engineering, Hiroshima UniversityGraduate School of Environment and Information Science, Yokohama National UniversityGraduate School of Environment and Information Science, Yokohama National UniversityThe simultaneously iterative procedure proposed by the authors is extended to hyperelastic shells. The weak form of the equilibrium equation and the plane stress condition at every material point are defined as a coupled problem, and a numerical procedure based on the block Newton method to solve them with simultaneous linearization is developed in this paper. In the proposed block Newton method, the tangent moduli can be constructed algebraically by eliminating the internal variables, which are also updated algebraically without any local iterative calculations. In addition, the pseudo-stress for the residuals of plane stress state is incorporated into the linearized weak form of the equilibrium equation. Hence, the proposed procedure enables us to decrease the residuals in the coupled boundary value problems simultaneously. Some numerical examples demonstrate the validity and the effectiveness of the procedures in hyperelastic shells.https://www.jstage.jst.go.jp/article/transjsme/88/912/88_22-00150/_pdf/-char/enblock newton methodhyperelasticityplane stressfinite element analysislarge strains |
| spellingShingle | Takeki YAMAMOTO Takahiro YAMADA Kazumi MATSUI Finite element analysis of hyperelastic shells without any local iterative calculations by block Newton method Nihon Kikai Gakkai ronbunshu block newton method hyperelasticity plane stress finite element analysis large strains |
| title | Finite element analysis of hyperelastic shells without any local iterative calculations by block Newton method |
| title_full | Finite element analysis of hyperelastic shells without any local iterative calculations by block Newton method |
| title_fullStr | Finite element analysis of hyperelastic shells without any local iterative calculations by block Newton method |
| title_full_unstemmed | Finite element analysis of hyperelastic shells without any local iterative calculations by block Newton method |
| title_short | Finite element analysis of hyperelastic shells without any local iterative calculations by block Newton method |
| title_sort | finite element analysis of hyperelastic shells without any local iterative calculations by block newton method |
| topic | block newton method hyperelasticity plane stress finite element analysis large strains |
| url | https://www.jstage.jst.go.jp/article/transjsme/88/912/88_22-00150/_pdf/-char/en |
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