Generalized Finite Difference Method for Plate Bending Analysis of Functionally Graded Materials
In this paper, an easy-to-implement domain-type meshless method—the generalized finite difference method (GFDM)—is applied to simulate the bending behavior of functionally graded (FG) plates. Based on the first-order shear deformation theory (FSDT) and Hamilton’s principle, the governing equations a...
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MDPI AG
2020-11-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/11/1940 |
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| author | Yu-Dong Li Zhuo-Chao Tang Zhuo-Jia Fu |
| author_facet | Yu-Dong Li Zhuo-Chao Tang Zhuo-Jia Fu |
| author_sort | Yu-Dong Li |
| collection | DOAJ |
| description | In this paper, an easy-to-implement domain-type meshless method—the generalized finite difference method (GFDM)—is applied to simulate the bending behavior of functionally graded (FG) plates. Based on the first-order shear deformation theory (FSDT) and Hamilton’s principle, the governing equations and constrained boundary conditions of functionally graded plates are derived. Based on the multivariate Taylor series and the weighted moving least-squares technique, the partial derivative of the underdetermined displacement at a certain node can be represented by a linear combination of the displacements at its adjacent nodes in the GFDM implementation. A certain node of the local support domain is formed according to the rule of “the shortest distance”. The proposed GFDM provides the sparse resultant matrix, which overcomes the highly ill-conditioned resultant matrix issue encountered in most of the meshless collocation methods. In addition, the studies show that irregular distribution of structural nodes has hardly any impact on the numerical performance of the generalized finite difference method for FG plate bending behavior. The method is a truly meshless approach. The numerical accuracy and efficiency of the GFDM are firstly verified through some benchmark examples, with different shapes and constrained boundary conditions. Then, the effects of material parameters and thickness on FG plate bending behavior are numerically investigated. |
| first_indexed | 2024-03-10T15:07:49Z |
| format | Article |
| id | doaj.art-3a7fccdcfd224e75b467e29f6417ec6b |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T15:07:49Z |
| publishDate | 2020-11-01 |
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| series | Mathematics |
| spelling | doaj.art-3a7fccdcfd224e75b467e29f6417ec6b2023-11-20T19:37:07ZengMDPI AGMathematics2227-73902020-11-01811194010.3390/math8111940Generalized Finite Difference Method for Plate Bending Analysis of Functionally Graded MaterialsYu-Dong Li0Zhuo-Chao Tang1Zhuo-Jia Fu2Center for Numerical Simulation Software in Engineering & Sciences, College of Mechanics and Materials, Hohai University, Nanjing 211100, ChinaCenter for Numerical Simulation Software in Engineering & Sciences, College of Mechanics and Materials, Hohai University, Nanjing 211100, ChinaCenter for Numerical Simulation Software in Engineering & Sciences, College of Mechanics and Materials, Hohai University, Nanjing 211100, ChinaIn this paper, an easy-to-implement domain-type meshless method—the generalized finite difference method (GFDM)—is applied to simulate the bending behavior of functionally graded (FG) plates. Based on the first-order shear deformation theory (FSDT) and Hamilton’s principle, the governing equations and constrained boundary conditions of functionally graded plates are derived. Based on the multivariate Taylor series and the weighted moving least-squares technique, the partial derivative of the underdetermined displacement at a certain node can be represented by a linear combination of the displacements at its adjacent nodes in the GFDM implementation. A certain node of the local support domain is formed according to the rule of “the shortest distance”. The proposed GFDM provides the sparse resultant matrix, which overcomes the highly ill-conditioned resultant matrix issue encountered in most of the meshless collocation methods. In addition, the studies show that irregular distribution of structural nodes has hardly any impact on the numerical performance of the generalized finite difference method for FG plate bending behavior. The method is a truly meshless approach. The numerical accuracy and efficiency of the GFDM are firstly verified through some benchmark examples, with different shapes and constrained boundary conditions. Then, the effects of material parameters and thickness on FG plate bending behavior are numerically investigated.https://www.mdpi.com/2227-7390/8/11/1940meshless methodfunctionally graded materialfirst-order shear deformation theorybending of platesnumerical simulation |
| spellingShingle | Yu-Dong Li Zhuo-Chao Tang Zhuo-Jia Fu Generalized Finite Difference Method for Plate Bending Analysis of Functionally Graded Materials Mathematics meshless method functionally graded material first-order shear deformation theory bending of plates numerical simulation |
| title | Generalized Finite Difference Method for Plate Bending Analysis of Functionally Graded Materials |
| title_full | Generalized Finite Difference Method for Plate Bending Analysis of Functionally Graded Materials |
| title_fullStr | Generalized Finite Difference Method for Plate Bending Analysis of Functionally Graded Materials |
| title_full_unstemmed | Generalized Finite Difference Method for Plate Bending Analysis of Functionally Graded Materials |
| title_short | Generalized Finite Difference Method for Plate Bending Analysis of Functionally Graded Materials |
| title_sort | generalized finite difference method for plate bending analysis of functionally graded materials |
| topic | meshless method functionally graded material first-order shear deformation theory bending of plates numerical simulation |
| url | https://www.mdpi.com/2227-7390/8/11/1940 |
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