Bending of Nonconforming Thin Plates Based on the Mixed-Order Manifold Method with Background Cells for Integration
As it is very difficult to construct conforming plate elements and the solutions achieved with conforming elements yield inferior accuracy to those achieved with nonconforming elements on many occasions, nonconforming elements, especially Adini’s element (ACM element), are often recommended for prac...
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| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Advances in Materials Science and Engineering |
| Online Access: | http://dx.doi.org/10.1155/2020/6681214 |
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| author | Xin Qu Lijun Su Zhijun Liu Xingqian Xu Fangfang Diao Wei Li |
| author_facet | Xin Qu Lijun Su Zhijun Liu Xingqian Xu Fangfang Diao Wei Li |
| author_sort | Xin Qu |
| collection | DOAJ |
| description | As it is very difficult to construct conforming plate elements and the solutions achieved with conforming elements yield inferior accuracy to those achieved with nonconforming elements on many occasions, nonconforming elements, especially Adini’s element (ACM element), are often recommended for practical usage. However, the convergence, good numerical accuracy, and high computing efficiency of ACM element with irregular physical boundaries cannot be achieved using either the finite element method (FEM) or the numerical manifold method (NMM). The mixed-order NMM with background cells for integration was developed to analyze the bending of nonconforming thin plates with irregular physical boundaries. Regular meshes were selected to improve the convergence performance; background cells were used to improve the integration accuracy without increasing the degrees of freedom, retaining the efficiency as well; the mixed-order local displacement function was taken to improve the interpolation accuracy. With the penalized formulation fitted to the NMM for Kirchhoff’s thin plate bending, a new scheme was proposed to deal with irregular domain boundaries. Based on the present computational framework, comparisons with other studies were performed by taking several typical examples. The results indicated that the solutions achieved with the proposed NMM rapidly converged to the analytical solutions and their accuracy was vastly superior to that achieved with the FEM and the traditional NMM. |
| format | Article |
| id | doaj-art-4238713dbeca443c9de1eb9ca21eefb0 |
| institution | Kabale University |
| issn | 1687-8434 1687-8442 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Materials Science and Engineering |
| spelling | doaj-art-4238713dbeca443c9de1eb9ca21eefb02025-02-03T05:52:25ZengWileyAdvances in Materials Science and Engineering1687-84341687-84422020-01-01202010.1155/2020/66812146681214Bending of Nonconforming Thin Plates Based on the Mixed-Order Manifold Method with Background Cells for IntegrationXin Qu0Lijun Su1Zhijun Liu2Xingqian Xu3Fangfang Diao4Wei Li5School of Civil and Architecture Engineering, Anyang Institute of Technology, Anyang 455000, ChinaKey Laboratory of Mountain Hazards and Earth Surface Processes, Institute of Mountain Hazards and Environment, Chinese Academy of Sciences, Chengdu 610041, ChinaCollege of Civil Engineering and Mechanics, Lanzhou University, Lanzhou, Gansu 730000, ChinaCollege of Water Conservancy, Yunnan Agricultural University, Kunming 650201, ChinaSchool of Foreign Languages, Anyang Institute of Technology, Anyang 455000, ChinaInstitute of Civil Engineering and Architecture, Linyi University, Linyi 276005, ChinaAs it is very difficult to construct conforming plate elements and the solutions achieved with conforming elements yield inferior accuracy to those achieved with nonconforming elements on many occasions, nonconforming elements, especially Adini’s element (ACM element), are often recommended for practical usage. However, the convergence, good numerical accuracy, and high computing efficiency of ACM element with irregular physical boundaries cannot be achieved using either the finite element method (FEM) or the numerical manifold method (NMM). The mixed-order NMM with background cells for integration was developed to analyze the bending of nonconforming thin plates with irregular physical boundaries. Regular meshes were selected to improve the convergence performance; background cells were used to improve the integration accuracy without increasing the degrees of freedom, retaining the efficiency as well; the mixed-order local displacement function was taken to improve the interpolation accuracy. With the penalized formulation fitted to the NMM for Kirchhoff’s thin plate bending, a new scheme was proposed to deal with irregular domain boundaries. Based on the present computational framework, comparisons with other studies were performed by taking several typical examples. The results indicated that the solutions achieved with the proposed NMM rapidly converged to the analytical solutions and their accuracy was vastly superior to that achieved with the FEM and the traditional NMM.http://dx.doi.org/10.1155/2020/6681214 |
| spellingShingle | Xin Qu Lijun Su Zhijun Liu Xingqian Xu Fangfang Diao Wei Li Bending of Nonconforming Thin Plates Based on the Mixed-Order Manifold Method with Background Cells for Integration Advances in Materials Science and Engineering |
| title | Bending of Nonconforming Thin Plates Based on the Mixed-Order Manifold Method with Background Cells for Integration |
| title_full | Bending of Nonconforming Thin Plates Based on the Mixed-Order Manifold Method with Background Cells for Integration |
| title_fullStr | Bending of Nonconforming Thin Plates Based on the Mixed-Order Manifold Method with Background Cells for Integration |
| title_full_unstemmed | Bending of Nonconforming Thin Plates Based on the Mixed-Order Manifold Method with Background Cells for Integration |
| title_short | Bending of Nonconforming Thin Plates Based on the Mixed-Order Manifold Method with Background Cells for Integration |
| title_sort | bending of nonconforming thin plates based on the mixed order manifold method with background cells for integration |
| url | http://dx.doi.org/10.1155/2020/6681214 |
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