Motion of the spherical shell of medium thickness on solid surface under conditions of the combined kinematics

A contact problem for an elastic spherical shell of medium thickness and a rigid plane is considered. The shell model is formulated as a 2D constrained continuum on the background of a general higher-order shell theory. To find the contact pressure distribution, a static axisymmetric contact problem for a spherical shell and an absolutely solid surface is solved. The main governing equation is an integral equation using the transient function for a shell as a kernel. To close the system, the main governing equation is supplemented by the equilibrium condition and an additional relation determining the position of the contact area boundary. This system is solved iteratively using the quadrature method. The transient function is found by solving the corresponding auxiliary problem using series with respect to Legendre and Gegenbauer polynomials. By orthogonal expansion the formulated problem is reduced to the system of algebraic equations for the coefficients of the orthogonal series. The convergence of the constructed solution for the transient function is studied. The test problem on the given pressure impact on the spherical shell has been solved. Finally, the implementation of the theory of multicomponent dry friction in some engineering problems of the dynamics of composite shells interacting with rigid rough planes is proposed. The main attention is paid to the construction of analytical models of combined dry friction, taking into account the real distribution of normal and tangential contact stresses.