Abstract: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.