Modification of boundary integral equation method for investigation of dynamic stresses for couple stress elasticity

Abstract The paper presents studies on the application of the boundary integral equation method for investigation of dynamic stresses in Cosserat continuum with constrained microrotations. For the solution of the non-stationary problem, the Fourier transform for time variable was used. The fundamental functions for the two-dimensional case of Cosserat continuum with constrained micro-rotations are built. Thus, the fundamental functions for the time-domain problem are derived as the functions of the two-dimensional isotropic continuum and the functions, which are responsible for the effect of shear-rotation deformations. The method of mechanical quadrature and collocation technique are applied for numerical calculations. Several numerical examples show the comparison of distribution of dynamic stresses in the foam medium with the cavity under the action of impulse loads accounting for the shear-rotation deformations effect and without accounting for this effect.