Space-Time Finite Element Method for Fully Intrinsic Equations of Geometrically Exact Beam
In this paper, a space-time finite element method based on a Galerkin-weighted residual method is proposed to solve the nonlinear fully intrinsic equations of geometrically exact beam which are first-order partial differential equations about time and space. Therefore, it is natural to discretize it...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-01-01
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| Series: | Aerospace |
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| Online Access: | https://www.mdpi.com/2226-4310/10/2/92 |
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| author | Lidao Chen Xin Hu Yong Liu |
| author_facet | Lidao Chen Xin Hu Yong Liu |
| author_sort | Lidao Chen |
| collection | DOAJ |
| description | In this paper, a space-time finite element method based on a Galerkin-weighted residual method is proposed to solve the nonlinear fully intrinsic equations of geometrically exact beam which are first-order partial differential equations about time and space. Therefore, it is natural to discretize it in time and space simultaneously. Considering the continuity and intrinsic boundary conditions in the spatial direction and the continuity and periodic boundary conditions in the time direction, the boundary value scheme of space-time finite element for solving the full intrinsic equations is derived. This method has been successfully applied to the static analysis and dynamic response solution of the fully intrinsic equations of nonlinear geometrically exact beam. The numerical results of several examples are compared with the analytical solution, existing algorithms, and literature to illustrate the applicability, accuracy and efficiency of this method. |
| first_indexed | 2024-03-11T09:18:52Z |
| format | Article |
| id | doaj.art-555aac43be534367bc027c9eebf0d388 |
| institution | Directory Open Access Journal |
| issn | 2226-4310 |
| language | English |
| last_indexed | 2024-03-11T09:18:52Z |
| publishDate | 2023-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Aerospace |
| spelling | doaj.art-555aac43be534367bc027c9eebf0d3882023-11-16T18:26:27ZengMDPI AGAerospace2226-43102023-01-011029210.3390/aerospace10020092Space-Time Finite Element Method for Fully Intrinsic Equations of Geometrically Exact BeamLidao Chen0Xin Hu1Yong Liu2College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, ChinaCollege of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, ChinaCollege of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, ChinaIn this paper, a space-time finite element method based on a Galerkin-weighted residual method is proposed to solve the nonlinear fully intrinsic equations of geometrically exact beam which are first-order partial differential equations about time and space. Therefore, it is natural to discretize it in time and space simultaneously. Considering the continuity and intrinsic boundary conditions in the spatial direction and the continuity and periodic boundary conditions in the time direction, the boundary value scheme of space-time finite element for solving the full intrinsic equations is derived. This method has been successfully applied to the static analysis and dynamic response solution of the fully intrinsic equations of nonlinear geometrically exact beam. The numerical results of several examples are compared with the analytical solution, existing algorithms, and literature to illustrate the applicability, accuracy and efficiency of this method.https://www.mdpi.com/2226-4310/10/2/92space-time finite methodtime finite methodfully intrinsic equationsgeometrically exact beamrotor dynamic response |
| spellingShingle | Lidao Chen Xin Hu Yong Liu Space-Time Finite Element Method for Fully Intrinsic Equations of Geometrically Exact Beam Aerospace space-time finite method time finite method fully intrinsic equations geometrically exact beam rotor dynamic response |
| title | Space-Time Finite Element Method for Fully Intrinsic Equations of Geometrically Exact Beam |
| title_full | Space-Time Finite Element Method for Fully Intrinsic Equations of Geometrically Exact Beam |
| title_fullStr | Space-Time Finite Element Method for Fully Intrinsic Equations of Geometrically Exact Beam |
| title_full_unstemmed | Space-Time Finite Element Method for Fully Intrinsic Equations of Geometrically Exact Beam |
| title_short | Space-Time Finite Element Method for Fully Intrinsic Equations of Geometrically Exact Beam |
| title_sort | space time finite element method for fully intrinsic equations of geometrically exact beam |
| topic | space-time finite method time finite method fully intrinsic equations geometrically exact beam rotor dynamic response |
| url | https://www.mdpi.com/2226-4310/10/2/92 |
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