On the Boundary Conditions in Out-of-Plane Analysis of Thin Plates by the Finite Point Method
The finite point method (FPM) is a numerical, mesh-free technique for solving differential equations, particularly in fluid dynamics. While the FPM has been previously applied in solid mechanics to analyze plates under in-plane loading, there remains a notable scarcity of research exploring the out-...
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2025-01-01
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| author | Sadegh Tavakoliyan Mohamad Najar Parham Memarzadeh Tadeh Zirakian |
| author_facet | Sadegh Tavakoliyan Mohamad Najar Parham Memarzadeh Tadeh Zirakian |
| author_sort | Sadegh Tavakoliyan |
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| description | The finite point method (FPM) is a numerical, mesh-free technique for solving differential equations, particularly in fluid dynamics. While the FPM has been previously applied in solid mechanics to analyze plates under in-plane loading, there remains a notable scarcity of research exploring the out-of-plane analysis of elastic plates using this method. This study thoroughly investigates the elastic FPM analysis of thin plates subjected to transverse loadings, focusing specifically on various boundary conditions (BCs). Boundary conditions represent a significant challenge in the out-of-plane analysis of thin plates within the FPM framework. To address this challenge, the approach incorporates additional nodal points positioned close to each boundary node, supplementing the points distributed throughout the plate’s interior and along its edges. The strong form of the governing equation is employed for the interior points, while the analysis also includes the scenario of a plate resting on boundary columns. Both distributed and concentrated external loads are examined to provide a comprehensive understanding of the behavior under different loading conditions. Furthermore, the optimal placement of the extra boundary nodes is briefly discussed, alongside a focus on the number of nodes within the finite point clouds. An appropriate range for this number is proposed, although the determination of the optimal distance for the extra boundary nodes and the ideal number of cloud points is earmarked for future research. The contribution of this work is to enhance the understanding of the FPM in the context of thin plates, particularly concerning the critical influence of boundary conditions. |
| format | Article |
| id | doaj-art-91e06cd734784932a113a02be60d1996 |
| institution | Kabale University |
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| language | English |
| publishDate | 2025-01-01 |
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| spelling | doaj-art-91e06cd734784932a113a02be60d19962025-01-24T13:26:18ZengMDPI AGBuildings2075-53092025-01-0115224110.3390/buildings15020241On the Boundary Conditions in Out-of-Plane Analysis of Thin Plates by the Finite Point MethodSadegh Tavakoliyan0Mohamad Najar1Parham Memarzadeh2Tadeh Zirakian3Department of Civil Engineering, Isfahan (Khorasgan) Branch, Islamic Azad University, Isfahan 81551-39998, IranDepartment of Civil Engineering, Isfahan (Khorasgan) Branch, Islamic Azad University, Isfahan 81551-39998, IranDepartment of Civil Engineering, Najafabad Branch, Islamic Azad University, Najafabad 85141-43131, IranDepartment of Civil Engineering and Construction Management, California State University, Northridge, CA 91330, USAThe finite point method (FPM) is a numerical, mesh-free technique for solving differential equations, particularly in fluid dynamics. While the FPM has been previously applied in solid mechanics to analyze plates under in-plane loading, there remains a notable scarcity of research exploring the out-of-plane analysis of elastic plates using this method. This study thoroughly investigates the elastic FPM analysis of thin plates subjected to transverse loadings, focusing specifically on various boundary conditions (BCs). Boundary conditions represent a significant challenge in the out-of-plane analysis of thin plates within the FPM framework. To address this challenge, the approach incorporates additional nodal points positioned close to each boundary node, supplementing the points distributed throughout the plate’s interior and along its edges. The strong form of the governing equation is employed for the interior points, while the analysis also includes the scenario of a plate resting on boundary columns. Both distributed and concentrated external loads are examined to provide a comprehensive understanding of the behavior under different loading conditions. Furthermore, the optimal placement of the extra boundary nodes is briefly discussed, alongside a focus on the number of nodes within the finite point clouds. An appropriate range for this number is proposed, although the determination of the optimal distance for the extra boundary nodes and the ideal number of cloud points is earmarked for future research. The contribution of this work is to enhance the understanding of the FPM in the context of thin plates, particularly concerning the critical influence of boundary conditions.https://www.mdpi.com/2075-5309/15/2/241meshless methodsfinite point methodthin plateboundary conditionsout-of-plane analysis |
| spellingShingle | Sadegh Tavakoliyan Mohamad Najar Parham Memarzadeh Tadeh Zirakian On the Boundary Conditions in Out-of-Plane Analysis of Thin Plates by the Finite Point Method Buildings meshless methods finite point method thin plate boundary conditions out-of-plane analysis |
| title | On the Boundary Conditions in Out-of-Plane Analysis of Thin Plates by the Finite Point Method |
| title_full | On the Boundary Conditions in Out-of-Plane Analysis of Thin Plates by the Finite Point Method |
| title_fullStr | On the Boundary Conditions in Out-of-Plane Analysis of Thin Plates by the Finite Point Method |
| title_full_unstemmed | On the Boundary Conditions in Out-of-Plane Analysis of Thin Plates by the Finite Point Method |
| title_short | On the Boundary Conditions in Out-of-Plane Analysis of Thin Plates by the Finite Point Method |
| title_sort | on the boundary conditions in out of plane analysis of thin plates by the finite point method |
| topic | meshless methods finite point method thin plate boundary conditions out-of-plane analysis |
| url | https://www.mdpi.com/2075-5309/15/2/241 |
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