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By George Jaiani

The ebook 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 during the past non-published effects to boot. Mathematically the corresponding difficulties bring about non-classical, quite often, boundary price and initial-boundary worth difficulties for governing degenerate elliptic and hyperbolic structures in static and dynamical instances, respectively. Its makes use of essentially various techniques 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 instances, it is very important learn relation of 2nd and 1D difficulties to 3D problems.

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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). Bull. Georgian Acad. Sci. V. Jaiani, On a wedge-shaped body arbitrarily loaded along the cusped edge (Russian).

This matter will be discussed in the forthcoming paper of G. Jaiani. A qualitative part of G. Jaiani’s above-mentioned results can be summarized as follows. 1 Let n be the inward normal of the prismatic shell projection boundary. In the case of the tension-compression (N ¼ 0) problem on the cusped edge, where (see Figs. 15) this means k2 ! 1), which will be called a sharp cusped edge, the displacement vector can not be prescribed, while on the cusped edge, where (see Figs. 15) this means k2 \1], which will be called a blunt cusped edge, the displacement vector can be prescribed.

Mat. R. Khvoles, The general representation for solutions of equilibrium equations of prismatic shell with variable thickness (Russian). Semin. I. Vekua Inst. Appl. Math. Rep. Annot. Rep. V. Makhover, Bending of a plate of variable thickness with a cusp edge (Russian). Sci. Notes of Leningrad State Ped. Inst. V. Makhover, On the spectrum of the fundamental frequencies of a plate with a cusped edge (Russian). Sci. Notes of Leningrad State Ped. Inst. G. Mikhlin, Variational Methods in Mathematical Physics (Russian).

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