Development of High-Order Infinite Element Method for Bending Analysis of Mindlin–Reissner Plates
An approach is presented for solving plate bending problems using a high-order infinite element method (IEM) based on Mindlin–Reissner plate theory. In the proposed approach, the computational domain is partitioned into multiple layers of geometrically similar virtual elements which use only the dat...
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| Published in | Mathematical problems in engineering Vol. 2020; no. 2020; pp. 1 - 13 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Cairo, Egypt
Hindawi Publishing Corporation
2020
Hindawi John Wiley & Sons, Inc |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1024-123X 1026-7077 1563-5147 1563-5147 |
| DOI | 10.1155/2020/9142193 |
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| Abstract | An approach is presented for solving plate bending problems using a high-order infinite element method (IEM) based on Mindlin–Reissner plate theory. In the proposed approach, the computational domain is partitioned into multiple layers of geometrically similar virtual elements which use only the data of the boundary nodes. Based on the similarity, a reduction process is developed to eliminate virtual elements and overcome the problem that the conventional reduction process cannot be directly applied. Several examples of plate bending problems with complicated geometries are reported to illustrate the applicability of the proposed approach and the results are compared with those obtained using ABAQUS software. Finally, the bending behavior of a rectangular plate with a central crack is analyzed to demonstrate that the stress intensity factor (SIF) obtained using the high-order PIEM converges faster and closer than low-order PIEM to the analytical solution. |
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| AbstractList | An approach is presented for solving plate bending problems using a high-order infinite element method (IEM) based on Mindlin–Reissner plate theory. In the proposed approach, the computational domain is partitioned into multiple layers of geometrically similar virtual elements which use only the data of the boundary nodes. Based on the similarity, a reduction process is developed to eliminate virtual elements and overcome the problem that the conventional reduction process cannot be directly applied. Several examples of plate bending problems with complicated geometries are reported to illustrate the applicability of the proposed approach and the results are compared with those obtained using ABAQUS software. Finally, the bending behavior of a rectangular plate with a central crack is analyzed to demonstrate that the stress intensity factor (SIF) obtained using the high-order PIEM converges faster and closer than low-order PIEM to the analytical solution. |
| Author | Liu, D. S. Lu, C. J. Chen, Y. W. |
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| Copyright | Copyright © 2020 D. S. Liu et al. Copyright © 2020 D. S. Liu et al. This is an open access article distributed under the Creative Commons Attribution License (the “License”), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. https://creativecommons.org/licenses/by/4.0 |
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| References | 22 23 26 T. Yu (9) 2016; 101 L. A. Ying (24) 1995 S. P. Timoshenko (25) 1959 11 12 13 C. H. Thai (6) 2020; 117 17 18 H. D. Han (15) 1979; 1 19 L. A. Ying (14) 1978; 21 C. G. Go (16) 1991; 37 N. Nguyen‐Thanh (10) 2018; 62 1 2 D. S. Liu (21) 2013; 92 3 4 5 7 8 20 |
| References_xml | – volume: 21 start-page: 19 year: 1978 ident: 14 article-title: The infinite similar element method for calculating stress intensity factors publication-title: Scientia Sinica – volume: 1 start-page: 91 year: 1979 ident: 15 article-title: An iterative method in the finite element publication-title: Mathematica Numerica Sinica – ident: 11 doi: 10.1016/j.cma.2019.112613 – volume: 117 start-page: 346 year: 2020 ident: 6 article-title: A meshfree approach using naturally atabilized nodal integration for multilayer FG GPLRC complicated plate structures publication-title: Engineering Analysis with Boundary Elements doi: 10.1016/j.enganabound.2020.04.001 – ident: 2 doi: 10.1016/j.apm.2012.01.003 – ident: 4 doi: 10.1017/jmech.2016.3 – volume: 62 start-page: 1287 year: 2018 ident: 10 article-title: Static and free-vibration analyses of cracks in thin-shell structures based on an isogeometric-meshfree coupling approach publication-title: Computational Mechanics doi: 10.1007/s00466-018-1564-y – volume-title: Theory of Plates and Shells year: 1959 ident: 25 – ident: 3 doi: 10.1002/nme.1620370205 – ident: 20 doi: 10.1299/jmmp.4.1131 – ident: 19 doi: 10.1016/s0965-9978(03)00036-x – volume-title: Infinite Element Method year: 1995 ident: 24 – ident: 8 doi: 10.1016/j.finel.2014.11.003 – ident: 7 doi: 10.1016/j.cma.2004.10.008 – volume: 37 start-page: 547 year: 1991 ident: 16 article-title: Infinitely small element for the problem of stress singularity publication-title: Computers & Structures – ident: 22 doi: 10.1016/j.cma.2007.10.008 – ident: 17 doi: 10.1016/0045-7949(92)90341-v – ident: 13 doi: 10.1137/0715030 – ident: 23 doi: 10.1142/s1758825110000706 – ident: 26 doi: 10.1016/s0013-7944(01)00136-9 – ident: 1 doi: 10.1016/j.cma.2009.09.001 – ident: 5 doi: 10.1016/j.compstruct.2017.06.049 – ident: 12 doi: 10.1093/imamat/16.3.303 – ident: 18 doi: 10.1016/s0020-7683(03)00014-3 – volume: 101 start-page: 141 year: 2016 ident: 9 article-title: NURBS-based isogeometric analysis of buckling and free vibration problems for laminated composites plates with complicated cutouts using a new simple FSDT theory and level set method publication-title: Thin-Walled Structures doi: 10.1016/j.tws.2015.12.008 – volume: 92 start-page: 573 year: 2013 ident: 21 article-title: Coupled PIEM/FEM algorithm based on Mindlin-Reissner plate theory for bending analysis of plates with through-thickness hole publication-title: CMES: Computer Modeling in Engineering & Sciences |
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| SubjectTerms | Bending Deformation Exact solutions Finite element method Infinite elements Methods Mindlin plates Numerical analysis Plate theory Rectangular plates Reduction Stress intensity factors |
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| Title | Development of High-Order Infinite Element Method for Bending Analysis of Mindlin–Reissner Plates |
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