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By George Jaiani

The booklet is dedicated to an up-dated exploratory survey of effects bearing on elastic cusped shells, plates, and beams and cusped prismatic shell-fluid interplay difficulties. It comprises a few in past times non-published effects besides. Mathematically the corresponding difficulties result in non-classical, often, boundary price and initial-boundary price difficulties for governing degenerate elliptic and hyperbolic structures in static and dynamical circumstances, respectively. Its makes use of essentially various ways of research: 1) to get effects for two-dimensional and one-dimensional difficulties from result of the corresponding third-dimensional difficulties and a couple of) to enquire without delay governing degenerate and singular platforms of second and 1D difficulties. In either the situations, you will need to learn relation of second and 1D difficulties to 3D problems.

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Initial conditions have the following form   ujr t¼0 ¼ ujr ; u_ jr t¼0 ¼ wjr ; j ¼ 1; 3; r ¼ 0; N; 8ðx1 ; x2 Þ 2 x :¼ xs [ xf ; where ujr and wjr are prescribed functions. So, we get hierarchical models for structures occupying prismatic domains and consisting of elastic solid and fluid parts. References N. Chinchaladze, G. Jaiani, Hierarchical Mathematical Models for Solid–Fluid Interaction Problems (Georgian). Materials of the International Conference on Non-Classic Problems of Mechanics, Kutaisi, Georgia, 25–27 October, Kutaisi, vol.

V. Jaiani, Application of Vekua’s dimension reduction method to cusped plates and bars. Bull. TICMI 5, 27–34 (2001a) G. Jaiani, On a mathematical model of bars with variable rectangular cross-sections. ZAMM Z. Angew. Math. Mech. 81(3), 147–173 (2001b) M. Lucchesi, Longitudinal oscillations of bi-modular rods. Int. J. Struct. Stab. Dyn. N. Vekua, On one method of calculating of prismatic shells (Russian). Trudy Tbilis. Mat. Inst. N. Vekua, Theory of shallow shells of variable thickness (Russian).

Avalishvili, Dynamical hierarchical models for elastic shells. Appl. Math. Inform. Mech. 10(1), 19–38 (2005) D. Gordeziani, M. Avalishvili, G. Avalishvili, Hierarchical models of elastic shells in curvilinear coordinates. Comput. Math. Appl. V. Jaiani, On the deflections of thin wedge-shaped shells (Russian). Bull. Georgian Acad. Sci. V. Jaiani, On one problem of an elastic wedge-shaped body (Russian). Bull. Georgian Acad. Sci. V. Jaiani, On one problem for the fourth-order degenerate equation (Russian).

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