Analytic bending solutions of free rectangular thin plates resting on elastic foundations by a new symplectic superposition method

被引:74
作者
Li, Rui [1 ]
Zhong, Yang [2 ]
Li, Ming [1 ]
机构
[1] Dalian Univ Technol, Dept Engn Mech, State Key Lab Struct Anal Ind Equipment, Dalian 116024, Peoples R China
[2] Dalian Univ Technol, Fac Infrastruct Engn, Dalian 116024, Peoples R China
来源
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES | 2013年 / 469卷 / 2153期
基金
中国博士后科学基金;
关键词
analytic solution; rectangular plate; elastic foundation; symplectic superposition method; INTEGRAL-EQUATION METHOD; BOUNDARY ELEMENT METHOD; HAMILTONIAN SYSTEM; WINKLER FOUNDATION; CLAMPED PLATES; FREE-VIBRATION; GEOMETRY; SHELLS;
D O I
10.1098/rspa.2012.0681
中图分类号
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号
07 ; 0710 ; 09 ;
摘要
Analytic bending solutions of free rectangular thin plates resting on elastic foundations, based on the Winkler model, are obtained by a new symplectic superposition method. The proposed method offers a rational elegant approach to solve the problem analytically, which was believed to be difficult to attain. By way of a rigorous but simple derivation, the governing differential equations for rectangular thin plates on elastic foundations are transferred into Hamilton canonical equations. The symplectic geometry method is then introduced to obtain analytic solutions of the plates with all edges slidingly supported, followed by the application of superposition, which yields the resultant solutions of the plates with all edges free on elastic foundations. The proposed method is capable of solving plates on elastic foundations with any other combinations of boundary conditions. Comprehensive numerical results validate the solutions by comparison with those obtained by the finite element method.
引用
收藏
页数:18
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