A Symplectic Superposition Method for Bending Problems of Free-Edge Rectangular Thick Plates Resting on Elastic Foundations

LI Rui; TIAN Yu; ZHENG Xinran; WANG Bo

doi:10.21656/1000-0887.390186

Volume 39 Issue 8

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Article Navigation > Applied Mathematics and Mechanics > 2018 > 39(8): 875-891

LI Rui, TIAN Yu, ZHENG Xinran, WANG Bo. A Symplectic Superposition Method for Bending Problems of Free-Edge Rectangular Thick Plates Resting on Elastic Foundations[J]. Applied Mathematics and Mechanics, 2018, 39(8): 875-891. doi: 10.21656/1000-0887.390186

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A Symplectic Superposition Method for Bending Problems of Free-Edge Rectangular Thick Plates Resting on Elastic Foundations

doi: 10.21656/1000-0887.390186

Department of Engineering Mechanics; International Research Center for Computational Mechanics, Dalian University of Technology; State Key Laboratory of Structural Analysis for Industrial Equipment(Dalian University of Technology), Dalian, Liaoning 116024, P.R.China

Funds: The National Basic Research Program of China(973 Program)（2014CB049000）；The National Natural Science Foundation of China（11302038）

Received Date: 2018-06-28
Publish Date: 2018-08-15

Abstract

Abstract

Based on the symplectic superposition method proposed in recent years, the bending problems of free-edge rectangular thick plates resting on elastic foundations were analytically solved. The original problem was split into 3 subproblems corresponding to the bending problems of rectangular thick plates with 2 opposite edges slidingly clamped and resting on elastic foundations, which were solved with the symplectic geometry method. The analytic solution of the original problem was then obtained through superposition. Compared to the conventional analytic approaches such as the semi-inverse method, the symplectic superposition method has the advantages of both rationality of the symplectic method and regularity of the superposition method. The solution procedure starts from the basic equations of elasticity, and a rigorous derivation yields the analytic solutions, thus extending the scope of problems to be solved. The present method can serve as an effective analytic approach to complex boundary value problems of high-order partial differential equations in elasticity, as represented by the rectangular plate problems.
- symplectic superposition method,
- elastic foundation,
- moderately thick plate,
- bending

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References(21)

References

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