正交异性简支矩形底双曲扁壳大挠度问题的解析解
An Analytical Solution to Large Deflection Equations of Slmply-Supported Rectangular Hyperboloidal Shallow Shells of Orthotropic Composites
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摘要: 本文在文献[1,2]的基础上,进一步研究了富里叶级数在求解板壳大挠度问题中的应用。文中导出了简支边界条件下正交异性矩底双曲扁壳大挠度微分方程组的解析解。这个解可通用于板与壳、大挠度与小挠度、各向同性与正交异性在直角坐标下的多种情况。其数值结果与实验数据和其它解法结果相吻合。Abstract: Based on the product rule of the Fourier series and some relevant results inreferences[1,2], a method on solving the large deflection equations of plates and shells by means of the fourier series is proposed in the present paper.Applying this method,we derive a type solution to the Navier's solution of the nonlinear differential equations of the rectangular hyperboloidal shallow shells of the orthotropic composites simply supported.This solution is suitable for plates and shells with large deflection or small deflection whether it is isotropic or orthotropic.Their data processing results are correlative with those found in the classical examples and from the experiments.
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Key words:
- shallow shell /
- large deflection equations /
- analytic solution /
- numerical results
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[1] Yen Kai-yuan,Zheng Xiao-Jing,An analytical formula of the enact solution to Von Karmaris equations of a circular plate under a concentrated load,Int,J. Non-linear Mechanics,24,6(1989),551-560. [2] 严宗达,咤结构力学中的富里叶级数解法》,天津大学出版社,天津(1989). [3] 沃耳密尔A.C.著,《柔韧板与柔韧壳》(庐文达等译),科学出版社,北京(1959). [4] Timoshenko,S and S.Woinowsky-krieger,Theory of Plate and Shells,second edition,McGraw-Hill Book company,Inc.,(1959). [5] 孙镇泰,《各向异性板壳理论》,东南大学出版社,南京(1993). -
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