弹性圆板在一侧受均载而四周固定的条件下不用Kirchhoff-Love假设的一级近似理论(Ⅰ)

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The First Order Approximation of Non-Kirchhoff-Love Theory for Elastic Circular Plate with Fixed Boundary under Uniform Surface Loading(Ⅰ)

Shanghai University; Shanghai Institute of Applied Mathematics and Mechanics, Shanghai 20072, P. R. China

摘要: 根据一般形状的三维弹性板不用Kirchhoff-Love假设的近似理论^[1],[2],作者导出了三维弹性圆板的广义变分泛函,从而得到了圆板四周固定和一侧受均布载荷下的一级近似理论的微分方程和有关边界条件,其解析解答留待另文处理.
- 弹性圆板 /
- Kirchhoff-Love假设 /
- 广义变分原理
Abstract: Based on the approximation theory adopting non-Kirchhoff-Love assumption forthree dimensional elaslic plates with arbitrary shapes, the author derives afunctional of generalized variation for three dimensional elastic circular plates, therebyobtains a set of differtial equations and the relate boundary conditions to establish afirst order approximation theory for elastic circular plate with fixed boundary andunder uniform loading on one of its surface. The analytical solution of this problem will present in another paper.
- elastic circular plate /
- Kirchhoff-Love assumption /
- generalized variational principle

[1]	钱伟长,不用Kirchhof f-Love假定的三维弹性板近似理论及其边界条性,应用数学和力学,18(3)(1995), 189-206.
[2]	钱伟长,不用Kirchhoff-Love假定的三维弹性板二级近似理论及其边界条件,应用数学和力学,16(5)(1995), 38-394.
[3]	Chien Weizang, Further study of generalized variational principles in elasticty, Advance of Applied Mathematics and Mechamcs in China, Edited by Chien, W. Z and Fu. Z. Z.,1 (l987), 1-10.
[4]	Chien Weizang, Incompatible elements and generalized variational princples, Advances in Applted Mechanics, U. S. A., 14 (1984), 93-153.

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