On the limit equilibrium of a stamp with a rounded base on the boundary of an elastic semiplane

摘要

In this study we consider the problem of limit equilibrium of a stamp with a rounded base on the boundary of an elastic semiplane in the case of vertical force P applied to the middle of the stamp, horizontal force ρP (ρis the coefficient of friction between the stamp and the boundary of the semiplane) and moment M causing translational motion of the stamp. We assume that τ(x) = ρp(x), where p(x) is the pressure and τ(x) is the shear stress under the stamp. The problem is solved by means of Fourier integral transforms and the Wiener-Hopf method. It is shown that in the case of a variable interval of contact between the stamp and the base there exists such a state of limit equilibrium of the stamp (in contrast to the case of finite pressure at the ends of the contact interval) where pressure has singularity at one of the ends of the contact interval.