New analytic solutions for static problems of rectangular thin plates point-supported at three corners |
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Authors: | Rui Li Bin Wang Yifan Lv Qi Zhang Haoyang Wang Fengyu Jin Fei Teng Bo Wang |
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Institution: | 1.State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics,Dalian University of Technology,Dalian,China;2.Beijing Institute of Aerospace Systems Engineering,Beijing,China |
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Abstract: | This paper deals with the bending of rectangular thin plates point-supported at three corners using an analytic symplectic superposition method. The problems are of fundamental importance in both civil and mechanical engineering, but there were no accurate analytic solutions reported in the literature. This is attributed to the difficulty in seeking the solutions that satisfy the governing fourth-order partial differential equation with the free boundary conditions at all the edges as well as the support conditions at the corners. In the following, the Hamiltonian system-based equation for plate bending is formulated, and two types of fundamental problems are analytically solved by the symplectic method. The analytic solutions of the plates point-supported at three corners are then obtained by superposition, where the constants are obtained by a set of linear equations. The solution procedure presented in this paper offers a rigorous way to yield analytic solutions of similar problems. Some numerical results, validated by the finite element method, are shown to provide useful benchmarks for comparison and validation of other solution methods. |
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