摘要
根据双解析函数可以得到单位圆内平面弹性问题应力函数的边界积分公式,但式中包含强奇异积分,不能用于直接计算· 将边界上的应力函数展开为Fourier级数,再利用广义函数论中的几个公式进行卷积计算,可以得到不含强奇异积分核的边界积分公式,通过边界的应力函数值和法向导数的积分,直接得到圆内应力函数值,并给出几个算例。
By bianalytic functions, the boundary integral formula of the stress function for the elastic problem in a circle plane is developed. But this integral formula includes a strongly singular integral and can not be directly calculated. After the stress function is expounded to Fourier series, making use of some formulas in generalized functions to the convolutions, the boundary integral formula which doesn't include strongly singular integral is derived further. Then the stress function can be got simply by the integration of the values of the stress function and its derivative on the boundary. Some examples are given. It shows that the boundary integral formula of the stress function for the elastic problem is convenient.
出处
《应用数学和力学》
CSCD
北大核心
2005年第5期556-560,共5页
Applied Mathematics and Mechanics
基金
中国科学院科学基金资助项目(AMIV20032C05)
关键词
圆内平面
弹性问题
双调和方程
应力函数
边界积分公式
elastic problem in circle plane
bi_harmonic equation
stress function
boundary integral formula