Numerical solution of the wave problem in an elastic medium with transparent boundaries

When waves of different nature pass through a half-space and impact them on objects, the problem of numerical simulation of the dynamical processes taking place arises. The plane problem of elasticity theory is considered and it is suggested to limit the domain by artificial boundaries and provide transparency of boundaries for incoming and outgoing waves. A dynamic model of longitudinal and shear waves propagation in a given domain with artificial boundaries is described. To solve this problem, one dimensional problem with analogous physical properties for the basic medium and special boundary conditions are used additionally. Transparency conditions are set for the boundaries of the medium using the solution obtained for the one dimensional case. The problem posed is solved by the finite element method (FEM) (by coordinates) and implicit Newmark and Bathe finite-difference schemes for solving systems of differential equations.

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