Discussion on singularity in deducing lateral shear stress distribution along anchorage section theoretically based on Mindlin’s solution of displacement

Most recent study methods for precise mechanical deducing the lateral shear stress distribution along anchorage section are theoretically based on the Mindlin’s solution of displacement in elastic theory.However,the results obtained with different methods are not only different,but also deviate from the results of practice projects.For exploring their theoretical origin,a general integral equation for deducing lateral shear stress was put forward.It was concluded that,the singularity of Mindlin’s solution,which led to an enormous displacement in force point,was difficult to clear up in numerical approaches.Although the singularity might be minimized to an appreciable extent by setting an arbitrary tiny space or by introducing convertion of the lateral stress,precise theoretical analysis with exact mechanical model could not be carried out yet.Another method,the analytical deduction of integral equation actually included three simplified conditions that would brought some distortion to prototypical mechanical model.These results only expressed a mathematical phenomenon came from these special simplified conditions.Furthermore,the reason of difference of shear stress between the analytical results and the practices at the start-element of anchorage section was discussed.According to the finite deformation mechanics,symmetrical tensor of shear stress was not applicable at that position.The shear stress at the start-element of anchorage section might not be zero.