不用克希霍夫—拉夫假设的弹性圆板理论再探

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A Further Study of the Theory of Elastic Circular Plates with Non-Kirchhoff-Love Assumptions

Shanghai University, Shanghai Institute of Applied Mathematics and Mechanics, Shanghai

摘要: 本文在不用克希霍夫一拉夫假设的弹性板一般理论的基础上,建立了不用克希霍夫一拉夫假设的弹性圆板的一级近似理论,对圆板在四周固定和均布载荷的条件下,得到了具体的轴对称分析解,并和经典的圆薄板解进行了比较,证明本文新解更加接近实验结果,本文也具体地讨论了理论结果中厚度增大时的影响。
- 弹性力学 /
- 圆板 /
- 克希霍夫—拉夫假设
Abstract: Based on the general theory of elastic plates which abandons Kirchhoff-Love assunption in the classical theory.this paper establishes a first order approximation theory of elastic circular plates with non-Kirchhoff-Love assumption,and presents ananalytic solution to the axisymmetric problem of elastic circular plates with clamped boundary under uniformly distributed load.By comparing with the classical solution of the thin circular plates,it is verified that the new solution is closer to the experiment results than the classical solution.By virtue of the new theory.the influence of thediameter-to-thickness ratio upon the precision of the classical theory is examined.
- elasticity /
- circular plates /
- Kirchhoff-Love assumption

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[2]	Kirchhoff,G.,Über das Gleichgewicht and die Bewegung einer elastischen Scheibe Journal fur die reine und angeirandte Math.(Crulle).40(1850),51-88.
[3]	Love,A.E.H.,A Treatise on the Mathematical Theory of Elasticitr,Cambridge(1927).
[4]	McPherson,A.E.,W.Ramberg and S.Levy,Normal Pressure Tests on Circular Plates with Clamped Edges,N.A.C.A.,Report,744(1942).