Mathematical Modeling of Dynamical Stress Field Problem for a Pre-stressed Bi-layered Plate-Strip

Abstract

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.

Dynamic response of a bi-axially pre-stressed bi-layered plate resting on a rigid foundation under a harmonic force

“…In addition, to obtain concrete numerical results, we consider Aluminum-(Al) in the upper layer, with ν(Al)=0.35 and ρ(Al)=2.7×103kg/m3, and Steel-(St) in the lower layer, with ν(St)=0.29 and ρ(St)=7.86×103 kg/m3, as investigated by Daşdemir and Eröz. 18…”

“…15 (for plate-strip subjected to a perpendicular force), Akbarov et al. 16 (for bi-layered plate-strip subjected to a perpendicular force), Eröz 17 (for plate-strip subjected to an inclined force), and Daşdemir and Eröz 18 (for bi-layered plate-strip subjected to an inclined force). However, Daşdemir and Eröz only investigated the influence of the initial tension on the problem parameters.…”

“…However, Daşdemir and Eröz only investigated the influence of the initial tension on the problem parameters. 18 To address this issue, Daşdemir considered the case where there exists the initial compression force in the layers. 19 Further, Daşdemir 20 extended the problem to the case mentioned in Daşdemir and Eröz 18 and Daşdemir 19 , which is the investigation of plate-strip with elastic multi-layers under the action of an inclined time-harmonic loading.…”

“…18 To address this issue, Daşdemir considered the case where there exists the initial compression force in the layers. 19 Further, Daşdemir 20 extended the problem to the case mentioned in Daşdemir and Eröz 18 and Daşdemir 19 , which is the investigation of plate-strip with elastic multi-layers under the action of an inclined time-harmonic loading. Note that it is infeasible to investigate the effect of pre-stresses on the dynamic response of the layered system according to the classical linear theory of elastodynamics because the system is nonlinear.…”

A Spring-Layer Model for a Bi-Layered Plate-Strip with Initial Stress Through Imperfect Contact Interface

“…The numerical calculations are done by using the FEM. The problems studied by Akbarov et al [1,2,3,6,7] are special cases of the current problem. Therefore, the findings presented in this paper can also be regarded as a development of the aforementioned papers, because imperfect contact conditions between the layers of the plate-strip for both the shear-and normal-spring types are satisfied.…”