CONTACT PROBLEM FOR A SPHERICAL SHELL SUPPORTED ON TWO FLAT SURFACES

Abstract

An effective numerical and analytical method is proposed for studying the force state inside the contact spots of elastic composite spherical shells resting on two flat surfaces inclined at an angle to each other. The method is based on constructing the influence function for the shell in an axisymmetric formulation, followed by its expansion into a Fourier series using the Legendre and Gegenbauer polynomials. A resolving system of equations for the corresponding coefficients is obtained. The developed methodology will allow for a more correct study of the dynamics of various robotic systems, the main controlled elements of which are elastic spherical shells that carry out complex kinematic movements on various surfaces. These systems, in particular, include a “butterfly robot”, the main controlled element of which is a thin spherical shell, rolling with simultaneous spinning and sliding along two parallel plates, as if on rails.

Keywords

• pherical composite shell; contact problem; theory of the multicomponent anisotropic dry friction