Numerical Solution of Dynamic Problems in Couple-stressed Continuum on Multiprocessor Computer Systems

Computational algorithm for the solution of 2D and 3D dynamic problems of the Cosserat elasticity theory using multiprocessor computer systems is worked out. The algorithm is based on the two-cyclic splitting method with respect to the spatial variables in combination with the explicit monotone finite-difference ENO–scheme for solving 1D problems adapted for the calculation of discontinuities. Boundary conditions of symmetry, permitting to reduce computations many times, are formulated. Computations of 3D Lamb’s problem on the action of concentrated load on the surface of a homogeneous elastic half-space and the problem on the action of concentrated impulsive periodic load are performed. The shock waves of four types (longitudinal, transverse, torsional and rotational waves), characteristic of a couple-stressed elastic medium, are recognized numerically. The oscillations of rotational motion of particles on the wave fronts are also found.