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According to the principle of the three-dimensional linearized theory of elastic waves in initially stressed bodies, a dynamical stress field in a pre-stressed bi-layered plate-strip under the action of an arbitrary inclined force resting on a rigid foundation is studied. It is assumed that the force applied to upper free surface of the plate-strip is time-harmonic and the materials used are linearly elastic, homogenous, and isotropic. By employing finite element method, the governing system of partial differential equations of motion is approximately solved. The different dependencies of the problem such as the ratio of height of plates and initial stress of the materials are numerically investigated. Particularly the effect of arbitrary inclined force is analyzed. It is observed that the numerical results obtained according to various angles converge to the ones in the previous studies.

a b s t r a c tIn this paper, the FEM modelling of the time-harmonic dynamical stress field problem for the pre-stressed plate-strip with finite length resting on a rigid foundation is developed. The mathematical formulation of the considered problem is made by the use of the equations and relations of the Three-dimensional Linearized Theory of Elastic Waves in Initially Stressed Bodies. The proposed modelling is tested on the concrete problems as an example. The numerical results testing the validity of the developed FEM modelling are presented. Moreover, the numerical results attained for the various values of the problem parameters are also presented.

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The numerical solution of linear Volterra-Stieltjes integral equations of the second kind by using the generalized trapezoid rule is established and investigated. Also, the conditions on estimation of the error are determined and proved. A selected example is solved employing the proposed method.