Nonstationary plane contact problem in theory of elasticity for conformal cylindrical surfaces
A numerical—analytical approach is described to investigate the process of impact interaction between a long smooth rigid body and the surface of a circular cylindrical cavity in elastic space. A non-stationary mixed initial boundary value problem is formulated with a priori unknown boundaries moving with variable velocity. The problem is solved using the methods of the theory of integral transforms, expansion of desired variables into a Fourier series, and the quadrature method to reduce the problem to solving a system of linear algebraic equations at each time step. Some concrete numerical computations are presented. The cylindrical body mass and radius impact on the profile of the transient process of contact interaction has been analysed.
KeywordsNon-stationary mixed problem Cylindrical cavity in elastic medium Rigid body Contact interaction Fourier expansion
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