关于集中力作用线下的几个位移特解及评论

直接用应变积分的方法得到在集中力作用线下的几个弹性力学位移特解。定积分的一个端点离开集中力作用点有一微小的距离，说明当此距离趋近于0时这些位移解的渐近奇异性是合理的。对有关解答做了比较，说明了其之间的区别和联系。用应变积分求位移特解的解法容易将解推广到材料正交各向异性的情况。举出一个应用实例说明用应变积分求位移特解的方法，对解的物理意义有更直接更清楚的表示，从而指正一篇文献对集中力作用下岩石表面变形趋势的误解。

SEVERAL SPECIAL DISPLACEMENT SOLUTIONS AND COMMENTS UNDER CONCENTRATED FORCE

Using integration of the normal strain concerned, several special displacement solutions under the concentrated force for a few elastic problems are obtained. The end point of the finite integration is purposefully separated from the load application point. When this separation approaches to zero, the asymptotic singularity of the displacement solution is proved to be correct. Comparisons are made of the related solutions, and the difference and association are discussed. The solutions can be easily extended to orthotropic materials. An example is given to illustrate the application of present method for deriving special displacement solutions with integration method, where the physical meaning of the solution can be understood more directly and clearly. It is also pointed out in the example that the original solution presented in a reference for the deformation of rock surface under concentrated force is incorrect.