Abstract:
In the article, based on the equations of the theory of poroelastic bodies of Cowin-Nunziato, an axisymmetric contact problem of the interaction of a rigid stamp with a poroelastic cylinder of finite dimensions lying on a Winkler foundation is considered. It is assumed that the stamp base has a flat shape and a paraboloid of revolution, there is no friction in the contact zone. The cylinder rests on the Winkler foundation, and on the lateral surface of the cylinder there are no normal displacements and tangential stresses. The stamp moves vertically by a certain value using a given force. The problem posed, based on the representation of unknown displacements in the cylinder and the function, describing the change of the volume fraction of pores, in the form of series in Bessel functions, is reduced relative to the distribution function of contact stresses under the stamp to an integral equation of the first kind, the transform of the kernel of which is given in explicit form. To solve the integral equation, the collocation method is used, which allows finding contact stresses and the dependence of the value of the applied force on the displacement of the stamp. A comparative analysis of the studied values for different values of the Winkler foundation parameters, the porosity of the cylinder and its geometric parameters is carried out.
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