两对边固支另两对边自由弹性矩形薄板理论解  

Theoretical Solution of Elastic Rectangular Thin Plate with Opposite Boundary Completely Clamped Support and Others Free

作　　者：钟阳[1] 殷建华[2] 

机构地区：[1]大连理工大学土木学院,大连116024 [2]香港理工大学土木学院

出　　处：《重庆建筑大学学报》2005年第6期29-32,共4页Journal of Chongqing Jianzhu University

基　　金：科学技术部重大基础研究项目资助(2004CCA03300)

摘　　要：利用辛几何的方法推导出了两对边固支另两对边自由支承条件情况下,弹性矩形薄板问题的理论解。在推导过程中并不需要事先人为的假定挠度函数,而是直接从弹性矩形薄板问题的控制方程出发,利用纯数学的手段推导出问题的解析解,使得求解过程更加理论化,从而为进一步解决了这类问题(例如动力问题)奠定了理论基础。文中还给出了算例来验证方法的正确性。In this paper, the analytical solutions for an elastic rectangular thin plate with opposite boundary completely clamped support and others free were derived by a Symplectic geometry method. Due to the fact that the basic elasticity equations of the thin plate were only used, it was not necessary to select the deformation function arbitrarily. Therefore, the solutions in this paper are much more general mathematically. In order to prove the validity of the formulations, numerical results were presented to be compared with those derived by other references.

关 键 词：两对边固支另两对边自由支承 弹性矩形薄板 辛几何法 理论解 

分 类 号：TB125[理学—工程力学]