Modeling of Size Effects in Bending of Perforated Cosserat Plates
This paper presents the numerical study of Cosserat elastic plate deformation based on the parametric theory of Cosserat plates, recently developed by the authors. The numerical results are obtained using the Finite Element Method used to solve the parametric system of 9 kinematic equations. We disc...
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| Format: | Article |
| Language: | English |
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Wiley
2017-01-01
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| Series: | Modelling and Simulation in Engineering |
| Online Access: | http://dx.doi.org/10.1155/2017/5246197 |
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| _version_ | 1850177024859045888 |
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| author | Roman Kvasov Lev Steinberg |
| author_facet | Roman Kvasov Lev Steinberg |
| author_sort | Roman Kvasov |
| collection | DOAJ |
| description | This paper presents the numerical study of Cosserat elastic plate deformation based on the parametric theory of Cosserat plates, recently developed by the authors. The numerical results are obtained using the Finite Element Method used to solve the parametric system of 9 kinematic equations. We discuss the existence and uniqueness of the weak solution and the convergence of the proposed FEM. The Finite Element analysis of clamped Cosserat plates of different shapes under different loads is provided. We present the numerical validation of the proposed FEM by estimating the order of convergence, when comparing the main kinematic variables with an analytical solution. We also consider the numerical analysis of plates with circular holes. We show that the stress concentration factor around the hole is less than the classical value, and smaller holes exhibit less stress concentration as would be expected on the basis of the classical elasticity. |
| format | Article |
| id | doaj-art-afcd97b4ea4a4cd692a320f8a0de10a1 |
| institution | OA Journals |
| issn | 1687-5591 1687-5605 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Modelling and Simulation in Engineering |
| spelling | doaj-art-afcd97b4ea4a4cd692a320f8a0de10a12025-08-20T02:19:06ZengWileyModelling and Simulation in Engineering1687-55911687-56052017-01-01201710.1155/2017/52461975246197Modeling of Size Effects in Bending of Perforated Cosserat PlatesRoman Kvasov0Lev Steinberg1Department of Mathematics, University of Puerto Rico at Aguadilla, Aguadilla, PR 00604, USADepartment of Mathematical Sciences, University of Puerto Rico at Mayagüez, Mayagüez, PR 00681, USAThis paper presents the numerical study of Cosserat elastic plate deformation based on the parametric theory of Cosserat plates, recently developed by the authors. The numerical results are obtained using the Finite Element Method used to solve the parametric system of 9 kinematic equations. We discuss the existence and uniqueness of the weak solution and the convergence of the proposed FEM. The Finite Element analysis of clamped Cosserat plates of different shapes under different loads is provided. We present the numerical validation of the proposed FEM by estimating the order of convergence, when comparing the main kinematic variables with an analytical solution. We also consider the numerical analysis of plates with circular holes. We show that the stress concentration factor around the hole is less than the classical value, and smaller holes exhibit less stress concentration as would be expected on the basis of the classical elasticity.http://dx.doi.org/10.1155/2017/5246197 |
| spellingShingle | Roman Kvasov Lev Steinberg Modeling of Size Effects in Bending of Perforated Cosserat Plates Modelling and Simulation in Engineering |
| title | Modeling of Size Effects in Bending of Perforated Cosserat Plates |
| title_full | Modeling of Size Effects in Bending of Perforated Cosserat Plates |
| title_fullStr | Modeling of Size Effects in Bending of Perforated Cosserat Plates |
| title_full_unstemmed | Modeling of Size Effects in Bending of Perforated Cosserat Plates |
| title_short | Modeling of Size Effects in Bending of Perforated Cosserat Plates |
| title_sort | modeling of size effects in bending of perforated cosserat plates |
| url | http://dx.doi.org/10.1155/2017/5246197 |
| work_keys_str_mv | AT romankvasov modelingofsizeeffectsinbendingofperforatedcosseratplates AT levsteinberg modelingofsizeeffectsinbendingofperforatedcosseratplates |