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Indexed by:期刊论文

Date of Publication:2010-01-01

Journal:IES Journal Part A: Civil and Structural Engineering

Included Journals:EI、Scopus

Volume:3

Issue:1

Page Number:28-37

ISSN No.:19373260

Abstract:Based on an appropriate definition of symplectic inner product, we establish a symplectic space formed by generalised displacements and their dual variables for the bending of rectangular plates on Winkler foundation. By using the Hellinger-Reissner variational principle, dual equations in the symplectic space are obtained and its operator matrix proved to be a Hamilton operator matrix. So the original plate bending problem is converted into the symplectic system. By using separation of variables and symplectic eigenfunction expansion, a novel analytical method is presented for solving the aforementioned plate bending problem. The symplectic eigenvalue problems for rectangular plates with two opposite sides simply supported and the other two opposite sides clamped are discussed. The transcendental equation of its eigenvalues and symplectic eigenvectors is derived in analytical forms. Analytical solutions of two examples are presented by using this method. The solution for a simply supported plate under uniformly distributed load is compared with classical Navier's method, and the result shows that this method has good convergence characteristic and high accuracy. © 2010 The Institution of Engineers, Singapore.