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New analytic solutions for static problems of rectangular thin plates point-supported at three corners

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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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Acknowledgments

The authors gratefully acknowledge the support from the National Natural Science Foundation of China (Grant 11302038) and National Basic Research Program of China (973 Program, Grant 2014CB049000).

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Authors and Affiliations

  1. State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Dalian University of Technology, Dalian, 116024, China

    Rui Li, Yifan Lv, Qi Zhang, Haoyang Wang, Fengyu Jin, Fei Teng & Bo Wang

  2. Beijing Institute of Aerospace Systems Engineering, Beijing, 100076, China

    Bin Wang

Authors
  1. Rui Li
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  2. Bin Wang
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  3. Yifan Lv
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  4. Qi Zhang
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  5. Haoyang Wang
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  6. Fengyu Jin
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  7. Fei Teng
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  8. Bo Wang
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Correspondence to Rui Li or Bo Wang.

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Li, R., Wang, B., Lv, Y. et al. New analytic solutions for static problems of rectangular thin plates point-supported at three corners. Meccanica 52, 1593–1600 (2017). https://doi.org/10.1007/s11012-016-0500-5

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