A Spline Finite Point Method for Nonlinear Bending Analysis of FG Plates in Thermal Environments Based on a Locking-free Thin/Thick Plate Theory
A spline finite point method (SFPM) based on a locking-free thin/thick plate theory, which is suitable for analysis of both thick and thin plates, is developed to study nonlinear bending behavior of functionally graded material (FGM) plates with different thickness in thermal environments. In the pr...
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| Veröffentlicht in: | Mathematical problems in engineering 2020, Vol.2020 (2020), p.1-22 |
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| creator | Wu, Hai Li, Shuang-Bei Huang, Jun Mo, Tian-Jing |
| description | A spline finite point method (SFPM) based on a locking-free thin/thick plate theory, which is suitable for analysis of both thick and thin plates, is developed to study nonlinear bending behavior of functionally graded material (FGM) plates with different thickness in thermal environments. In the proposed method, one direction of the plate is discretized with a set of uniformly distributed spline nodes instead of meshes and the other direction is expressed with orthogonal functions determined by the boundary conditions. The displacements of the plate are constructed by the linear combination of orthogonal functions and cubic B-spline interpolation functions with high efficiency for modeling. The locking-free thin/thick plate theory used by the proposed method is based on the first-order shear deformation theory but takes the shear strains and displacements as basic unknowns. The material properties of the FG plate are assumed to vary along the thickness direction following the power function distribution. By comparing with several published research studies based on the finite element method (FEM), the correctness, efficiency, and generality of the new model are validated for rectangular plates. Moreover, uniform and nonlinear temperature rise conditions are discussed, respectively. The effect of the temperature distribution, in-plane temperature force, and elastic foundation on nonlinear bending under different parameters are discussed in detail. |
| doi_str_mv | 10.1155/2020/2943705 |
| format | Article |
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In the proposed method, one direction of the plate is discretized with a set of uniformly distributed spline nodes instead of meshes and the other direction is expressed with orthogonal functions determined by the boundary conditions. The displacements of the plate are constructed by the linear combination of orthogonal functions and cubic B-spline interpolation functions with high efficiency for modeling. The locking-free thin/thick plate theory used by the proposed method is based on the first-order shear deformation theory but takes the shear strains and displacements as basic unknowns. The material properties of the FG plate are assumed to vary along the thickness direction following the power function distribution. By comparing with several published research studies based on the finite element method (FEM), the correctness, efficiency, and generality of the new model are validated for rectangular plates. Moreover, uniform and nonlinear temperature rise conditions are discussed, respectively. The effect of the temperature distribution, in-plane temperature force, and elastic foundation on nonlinear bending under different parameters are discussed in detail.</description><identifier>ISSN: 1024-123X</identifier><identifier>EISSN: 1563-5147</identifier><identifier>DOI: 10.1155/2020/2943705</identifier><language>eng</language><publisher>Cairo, Egypt: Hindawi Publishing Corporation</publisher><subject>Bending ; Boundary conditions ; Composite materials ; Elastic foundations ; Electric power distribution ; Finite element method ; Force distribution ; Functionally gradient materials ; Interpolation ; Locking ; Material properties ; Mathematical problems ; Methods ; Nonlinear analysis ; Orthogonal functions ; Parameter identification ; Plate theory ; Rectangular plates ; Research methodology ; Shear deformation ; Shear strain ; Stress concentration ; Temperature distribution ; Theory ; Thermal environments ; Thick plates ; Thickness ; Thin plates</subject><ispartof>Mathematical problems in engineering, 2020, Vol.2020 (2020), p.1-22</ispartof><rights>Copyright © 2020 Tian-Jing Mo et al.</rights><rights>Copyright © 2020 Tian-Jing Mo 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. http://creativecommons.org/licenses/by/4.0</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c360t-5fd7aed212aee1a6f77dc0b77399f81c82af8faee1e67de65beb440f318195f73</citedby><cites>FETCH-LOGICAL-c360t-5fd7aed212aee1a6f77dc0b77399f81c82af8faee1e67de65beb440f318195f73</cites><orcidid>0000-0002-8154-9163 ; 0000-0002-7930-2495</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>315,781,785,4025,27925,27926,27927</link.rule.ids></links><search><contributor>Yang, Mijia</contributor><contributor>Mijia Yang</contributor><creatorcontrib>Wu, Hai</creatorcontrib><creatorcontrib>Li, Shuang-Bei</creatorcontrib><creatorcontrib>Huang, Jun</creatorcontrib><creatorcontrib>Mo, Tian-Jing</creatorcontrib><title>A Spline Finite Point Method for Nonlinear Bending Analysis of FG Plates in Thermal Environments Based on a Locking-free Thin/Thick Plate Theory</title><title>Mathematical problems in engineering</title><description>A spline finite point method (SFPM) based on a locking-free thin/thick plate theory, which is suitable for analysis of both thick and thin plates, is developed to study nonlinear bending behavior of functionally graded material (FGM) plates with different thickness in thermal environments. In the proposed method, one direction of the plate is discretized with a set of uniformly distributed spline nodes instead of meshes and the other direction is expressed with orthogonal functions determined by the boundary conditions. The displacements of the plate are constructed by the linear combination of orthogonal functions and cubic B-spline interpolation functions with high efficiency for modeling. The locking-free thin/thick plate theory used by the proposed method is based on the first-order shear deformation theory but takes the shear strains and displacements as basic unknowns. The material properties of the FG plate are assumed to vary along the thickness direction following the power function distribution. By comparing with several published research studies based on the finite element method (FEM), the correctness, efficiency, and generality of the new model are validated for rectangular plates. Moreover, uniform and nonlinear temperature rise conditions are discussed, respectively. The effect of the temperature distribution, in-plane temperature force, and elastic foundation on nonlinear bending under different parameters are discussed in detail.</description><subject>Bending</subject><subject>Boundary conditions</subject><subject>Composite materials</subject><subject>Elastic foundations</subject><subject>Electric power distribution</subject><subject>Finite element method</subject><subject>Force distribution</subject><subject>Functionally gradient materials</subject><subject>Interpolation</subject><subject>Locking</subject><subject>Material properties</subject><subject>Mathematical problems</subject><subject>Methods</subject><subject>Nonlinear analysis</subject><subject>Orthogonal functions</subject><subject>Parameter identification</subject><subject>Plate theory</subject><subject>Rectangular plates</subject><subject>Research methodology</subject><subject>Shear deformation</subject><subject>Shear strain</subject><subject>Stress concentration</subject><subject>Temperature distribution</subject><subject>Theory</subject><subject>Thermal environments</subject><subject>Thick plates</subject><subject>Thickness</subject><subject>Thin plates</subject><issn>1024-123X</issn><issn>1563-5147</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><sourceid>RHX</sourceid><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GNUQQ</sourceid><recordid>eNqF0E1L7DAUBuAiXvDjunMtB1xqnXw27XIUxyuMH6CCu5JpTzTaScakepl_4U82pYJLN0ngPHnhvFm2T8kJpVJOGGFkwirBFZEb2TaVBc8lFWozvQkTOWX8cSvbifGFEEYlLbezzyncrTrrEGbW2R7h1lvXwxX2z74F4wNcezfMdYBTdK11TzB1ultHG8EbmF3Abad7jGAd3D9jWOoOzt2HDd4t0fURTnXEFrwDDXPfvKaA3ATEhK2bpKN5HROG3z6s_2Z_jO4i7n3fu9nD7Pz-7F8-v7m4PJvO84YXpM-laZXGllGmEakujFJtQxZK8aoyJW1Kpk1phhkWqsVCLnAhBDGclrSSRvHd7HDMXQX_9o6xr1_8e0ibxZoJJkqlhKySOh5VE3yMAU29Cnapw7qmpB46r4fO6-_OEz8aedqt1f_tb_pg1JgMGv2jaSUoJ_wLYgSLjw</recordid><startdate>2020</startdate><enddate>2020</enddate><creator>Wu, Hai</creator><creator>Li, Shuang-Bei</creator><creator>Huang, Jun</creator><creator>Mo, Tian-Jing</creator><general>Hindawi Publishing Corporation</general><general>Hindawi</general><general>Hindawi Limited</general><scope>ADJCN</scope><scope>AHFXO</scope><scope>RHU</scope><scope>RHW</scope><scope>RHX</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7TB</scope><scope>8FD</scope><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>CWDGH</scope><scope>DWQXO</scope><scope>FR3</scope><scope>GNUQQ</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K7-</scope><scope>KR7</scope><scope>L6V</scope><scope>M7S</scope><scope>P5Z</scope><scope>P62</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope><orcidid>https://orcid.org/0000-0002-8154-9163</orcidid><orcidid>https://orcid.org/0000-0002-7930-2495</orcidid></search><sort><creationdate>2020</creationdate><title>A Spline Finite Point Method for Nonlinear Bending Analysis of FG Plates in Thermal Environments Based on a Locking-free Thin/Thick Plate Theory</title><author>Wu, Hai ; Li, Shuang-Bei ; Huang, Jun ; Mo, Tian-Jing</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c360t-5fd7aed212aee1a6f77dc0b77399f81c82af8faee1e67de65beb440f318195f73</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Bending</topic><topic>Boundary conditions</topic><topic>Composite materials</topic><topic>Elastic foundations</topic><topic>Electric power distribution</topic><topic>Finite element method</topic><topic>Force distribution</topic><topic>Functionally gradient materials</topic><topic>Interpolation</topic><topic>Locking</topic><topic>Material properties</topic><topic>Mathematical problems</topic><topic>Methods</topic><topic>Nonlinear analysis</topic><topic>Orthogonal functions</topic><topic>Parameter identification</topic><topic>Plate theory</topic><topic>Rectangular plates</topic><topic>Research methodology</topic><topic>Shear deformation</topic><topic>Shear strain</topic><topic>Stress concentration</topic><topic>Temperature distribution</topic><topic>Theory</topic><topic>Thermal environments</topic><topic>Thick plates</topic><topic>Thickness</topic><topic>Thin plates</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Wu, Hai</creatorcontrib><creatorcontrib>Li, Shuang-Bei</creatorcontrib><creatorcontrib>Huang, Jun</creatorcontrib><creatorcontrib>Mo, Tian-Jing</creatorcontrib><collection>الدوريات العلمية والإحصائية - e-Marefa Academic and Statistical Periodicals</collection><collection>معرفة - المحتوى العربي الأكاديمي المتكامل - e-Marefa Academic Complete</collection><collection>Hindawi Publishing Complete</collection><collection>Hindawi Publishing Subscription Journals</collection><collection>Hindawi Publishing Open Access Journals</collection><collection>CrossRef</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>Advanced Technologies & Aerospace Collection</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>Middle East & Africa Database</collection><collection>ProQuest Central Korea</collection><collection>Engineering Research Database</collection><collection>ProQuest Central Student</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Computer Science Collection</collection><collection>Computer Science Database</collection><collection>Civil Engineering Abstracts</collection><collection>ProQuest Engineering Collection</collection><collection>Engineering Database</collection><collection>Advanced Technologies & Aerospace Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>Access via ProQuest (Open Access)</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering Collection</collection><jtitle>Mathematical problems in engineering</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Wu, Hai</au><au>Li, Shuang-Bei</au><au>Huang, Jun</au><au>Mo, Tian-Jing</au><au>Yang, Mijia</au><au>Mijia Yang</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A Spline Finite Point Method for Nonlinear Bending Analysis of FG Plates in Thermal Environments Based on a Locking-free Thin/Thick Plate Theory</atitle><jtitle>Mathematical problems in engineering</jtitle><date>2020</date><risdate>2020</risdate><volume>2020</volume><issue>2020</issue><spage>1</spage><epage>22</epage><pages>1-22</pages><issn>1024-123X</issn><eissn>1563-5147</eissn><abstract>A spline finite point method (SFPM) based on a locking-free thin/thick plate theory, which is suitable for analysis of both thick and thin plates, is developed to study nonlinear bending behavior of functionally graded material (FGM) plates with different thickness in thermal environments. In the proposed method, one direction of the plate is discretized with a set of uniformly distributed spline nodes instead of meshes and the other direction is expressed with orthogonal functions determined by the boundary conditions. The displacements of the plate are constructed by the linear combination of orthogonal functions and cubic B-spline interpolation functions with high efficiency for modeling. The locking-free thin/thick plate theory used by the proposed method is based on the first-order shear deformation theory but takes the shear strains and displacements as basic unknowns. The material properties of the FG plate are assumed to vary along the thickness direction following the power function distribution. By comparing with several published research studies based on the finite element method (FEM), the correctness, efficiency, and generality of the new model are validated for rectangular plates. Moreover, uniform and nonlinear temperature rise conditions are discussed, respectively. The effect of the temperature distribution, in-plane temperature force, and elastic foundation on nonlinear bending under different parameters are discussed in detail.</abstract><cop>Cairo, Egypt</cop><pub>Hindawi Publishing Corporation</pub><doi>10.1155/2020/2943705</doi><tpages>22</tpages><orcidid>https://orcid.org/0000-0002-8154-9163</orcidid><orcidid>https://orcid.org/0000-0002-7930-2495</orcidid><oa>free_for_read</oa></addata></record> |
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| subjects | Bending Boundary conditions Composite materials Elastic foundations Electric power distribution Finite element method Force distribution Functionally gradient materials Interpolation Locking Material properties Mathematical problems Methods Nonlinear analysis Orthogonal functions Parameter identification Plate theory Rectangular plates Research methodology Shear deformation Shear strain Stress concentration Temperature distribution Theory Thermal environments Thick plates Thickness Thin plates |
| title | A Spline Finite Point Method for Nonlinear Bending Analysis of FG Plates in Thermal Environments Based on a Locking-free Thin/Thick Plate Theory |
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