普遍的平面断裂配点法和超奇异性问题的讨论

A GENERALIZED COLLOCATION METHOD FORSTRESS ANALYSIS OF CRACKED PLATES ANDSOME DISCUSSIONS ABOUT THE SUPERSINGULARITIES

本文对平面断裂中的应力分析问题建立了普遍的配点计算法,并用巴波柯维奇—纽勃通解代替威廉斯应力函数,文中所得公式适于计算机的编程和计算。文中使用的试函数既可用于应力边界条件问题,又可用于位移边界条件问题。本方法中全部边界上的边界条件都是近似满足的。由于在计算中使用了较多的试函数,所以能分析复杂的边界条件问题,文中算例说明了这一方法的计算精度和广泛用途。 本文还讨论了平面断裂的超奇异性问题。

A generalized collocation method for stress analysis of cracked plates is developed in this paper. The Papkovich-Neuber general solution has been used instead of the Williams stress function. The expressions obtained are very suit able for computer programming. The triae functions can be used for force-boundary conditions as well as displacement -boundary conditions. In this method the conditions on all boundaries are satisfied approximately. As more trial functions are used, more complicated boundary value problems may be analysed. The accuracy and versatility of the method are demonstrated by several interesting examples. In this paper question of super singularities has also been discussed.