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Bending, buckling
and free vibration of Timoshenko beam-based plane frame via
FEM with nonlocal integral model
Yuan Tang and Hai Qing |
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Vol. 18 (2023), No. 3, 355–374
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Abstract |
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A finite element method is developed to study the size-dependent static bending, elastic buckling and free vibration of Timoshenko beam-based plane frame using two-phase local/nonlocal integral model. The explicit expression for the stiffness matrix, geometric stiffness matrix and mass matrix is derived. Coordinate transformation is employed to obtain the stiffness matrix, the geometric stiffness matrix and mass matrix for a plane frame element oriented around an arbitrary angle. The effects of the nonlocal parameters on static bending, elastic buckling and free vibration of Timoshenko beams as well as a clamped square frame are studied numerically under different boundary and loading conditions. The bending deflections obtained are validated against existing analytical and asymptotic results in literature. The numerical results show clearly that, with the application of the two-phase local/nonlocal integral model, a consistent softening effect can be obtained for both Timoshenko beams and plane frames. |
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Keywords
nonlocal integral model, finite element formulation,
Timoshenko beam, plane frame, mechanical response
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Milestones
Received: 4 August 2022
Revised: 20 December 2022
Accepted: 5 February 2023
Published: 5 May 2023
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Authors |
| Yuan Tang | |
| State Key Laboratory of Mechanics
and Control of Aerospace Structures Nanjing University of Aeronautics and Astronautics Nanjing China |
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| Hai Qing | |
| State Key Laboratory of Mechanics
and Control of Aerospace Structures Nanjing University of Aeronautics and Astronautics Nanjing China |
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| © 2023 The Author(s), under exclusive license to MSP (Mathematical Sciences Publishers). |
