The Lamb's problem for a half-space covered with the pre-stretched layer

Time-harmonic dynamical stress field in a system comprising a pre-stressed orthotropic layer and pre-stressed orthotropic half-plane

“…In this case, the integral in Eq. (28) is calculated with the algorithm developed and employed in papers [4,[7][8][9][10][11][12][13]. Nevertheless, we here detail the main particularities of the noted algorithm.…”

“…at |x 1 / h| → ∞. Satisfying the complete contact conditions for the initial stress-strain state and neglecting the "edge effects" of the initial stresses in the covering layer and half-plane can be determined by the expressions σ (2),0 11 11). Consequently, the case for which is assumed that the complete contact conditions are also satisfied for the initial stress-strain state is a particular case determined by Eq.…”

“…In the study of the dynamical response of such systems to the dynamical external loading, in many cases the materials of the member constructions can be modeled as anisotropic with normalized mechanical properties. Consequently, the foregoing statements (and similar arguments) require the development of studies [7][8][9][10][11][12][13] for the cases where the materials of the covering layer and half-plane are anisotropic (orthotropic). This development is the subject of the present paper.…”

“…It is evident that those investigations concerned with the study of the influence of the initial strains (or stresses) on the time-harmonic dynamical stress field in the homogeneous and layered materials have also had great significance in the theoretical and practical sense. In papers [7][8][9][10][11][12][13][14] and others, this type of study was conducted for the system comprising a pre-stressed covering layer and a pre-stressed half-space.…”

“…In studies [7][8][9][10][11], the axisymmetric stress state, and in [12,13] the plane strain state, are considered and it was assumed that the materials of the constituents of the systems are isotropic and these systems are composed of either: (i) a stiffer covering layer + soft half-plane; or (ii) a soft covering layer + stiffer half-plane. According to the numerical results attained in these studies, it was established that in the quantitative sense the main response (for example, the dominant absolute values of the normal stress acting on the interface plane between the covering layer and half-plane) for system (ii) occurs only in the near vicinity of the point (x 1 = 0.0; x 2 = −h; Fig.…”