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极坐标下弹性力学的一个新解答
引用本文:周建方,卓家寿.极坐标下弹性力学的一个新解答[J].力学学报,2001,33(6):839-846.
作者姓名:周建方  卓家寿
作者单位:1. 河海大学常州校区,
2. 河海大学土木工程学院,
摘    要:在极坐标下将Hamilton体系下的分离变量法应用到弹性力学的非齐次边界情况,得到了一个新解答,利用这个新解可以求解一类弹性力学问题。文中给出了具体例子。

关 键 词:极坐标  Hamilton体系  分离变量法  弹性力学
修稿时间:1999年4月29日

A NEW SOLUTION OF ELASTICITY IN POLAR COORDINATE
Zhou Jianfang.A NEW SOLUTION OF ELASTICITY IN POLAR COORDINATE[J].chinese journal of theoretical and applied mechanics,2001,33(6):839-846.
Authors:Zhou Jianfang
Abstract:In the present method of variables of separation of elastic mechanics in Hamilton system, homogeneous boundary conditions are only considered, nonhomogeneous boundary conditions are hardly taken into account, and the solutions are also found in the books of classical mechanics of elasticity. In this paper, the method of separation of variables in Hamilton system is extended, i.e. it is applied to nonhomogeneous boundary conditions. It is different form the classical method of separation of variables of mathematical physics problems, and it does not first homogenized nonhomogeneous boundary conditions, but solves equation, then boundary conditions are satisfied. A new solution of elasticity in polar coordinate is obtained in such method. A group of elasticity problem such as thick-walled cylinder subjected to internal water pressure that water weight is reckoned in can be solved by using this new solution. Two specific examples are given. The results those are obtained in this paper are not only of theoretical significance but also of applied significance.
Keywords:polar coordinate  Hamilton system  separation of variables  a new solution
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