应力函数一般解的补充

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The Improvement of the General Expression for the Stress Function φ of the Two-Dimensional Problem

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

摘要: 本文指出平面问题极坐标形式应力函数一般解并不完备,不能处理曲杆受任意边界分布力的问题.为此,提出两个新的应力函数,将一般解作若干补充之后,能解曲杆r=a,b上受任意分布力的问题.这是包含区域边界几何参数的新的应力函数.

Abstract: In this paper, it is pointed that the general expression for the stress function of the plane problem in polar coordinates is incomplete. The problems of the curved bar with an arbitrary distributive load at the boundries can't he solved by this stress function. For this reason, we suggest two new stress functions and put them into the general expression. Then, the problems of the curved bar applied with an arbitrary distributive load at r=a,b boundaries can be solved. This is a new stress function including geometric boundary constants.

[1]	Timoshenko,S.and J.N.Goodier,Theory of Elasticity(1951).
[2]	赵兴华、蒋智翔、景士都,弹性波形厚壳应力和变形的渐近分析,清华大学科技报告(1973).