NDLI: Symplectic system based analytical solution for bending of rectangular orthotropic plates on Winkler elastic foundation

Content Provider	Springer Nature Link
Author	Yao, Wei An Hu, Xiao Fei Xiao, Feng
Copyright Year	2011
Abstract	This paper analyses the bending of rectangular orthotropic plates on a Winkler elastic foundation. Appropriate definition of symplectic inner product and symplectic space formed by generalized displacements establish dual variables and dual equations in the symplectic space. The operator matrix of the equation set is proven to be a Hamilton operator matrix. Separation of variables and eigenfunction expansion creates a basis for analyzing the bending of rectangular orthotropic plates on Winkler elastic foundation and obtaining solutions for plates having any boundary condition. There is discussion of symplectic eigenvalue problems of orthotropic plates under two typical boundary conditions, with opposite sides simply supported and opposite sides clamped. Transcendental equations of eigenvalues and symplectic eigenvectors in analytical form given. Analytical solutions using two examples are presented to show the use of the new methods described in this paper. To verify the accuracy and convergence, a fully simply supported plate that is fully and simply supported under uniformly distributed load is used to compare the classical Navier method, the Levy method and the new method. Results show that the new technique has good accuracy and better convergence speed than other methods, especially in relation to internal forces. A fully clamped rectangular plate on Winkler foundation is solved to validate application of the new methods, with solutions compared to those produced by the Galerkin method.
Starting Page	929
Ending Page	937
Page Count	9
File Format	PDF
ISSN	05677718
Journal	Acta Mechanica Sinica
Volume Number	27
Issue Number	6
e-ISSN	16143116
Language	English
Publisher	The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences
Publisher Date	2011-11-28
Publisher Place	Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Orthotropic plate Symplectic space Winkler elastic foundation Analytical solution Theoretical and Applied Mechanics Engineering Fluid Dynamics Computational Intelligence Classical Continuum Physics
Content Type	Text
Resource Type	Article
Subject	Mechanical Engineering Computational Mechanics

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