Download Cusped shell-like structures by George Jaiani PDF
By George Jaiani
The ebook is dedicated to an up-dated exploratory survey of effects pertaining to elastic cusped shells, plates, and beams and cusped prismatic shell-fluid interplay difficulties. It includes a few in the past non-published effects besides. Mathematically the corresponding difficulties bring about non-classical, more often than not, boundary worth and initial-boundary worth difficulties for governing degenerate elliptic and hyperbolic platforms in static and dynamical situations, respectively. Its makes use of essentially diversified techniques of research: 1) to get effects for two-dimensional and one-dimensional difficulties from result of the corresponding three-d difficulties and a couple of) to enquire at once governing degenerate and singular structures of second and 1D difficulties. In either the situations, you will need to research relation of second and 1D difficulties to 3D problems.
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Additional resources for Cusped shell-like structures
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). (Nauka, Moscow, 1970) B. Miara, G. Avalishvili, M. Avalishvili, D. Gordeziani, Hierarchical modeling of thermoelastic plates with variable thickness. Anal. Appl. 8(2), 125–159 (2010) P.
18) takes the following form ! 18) is not yet investigated. 6 Hierarchical Models of the First Type for Fluids Now, applying the above Vekua’s dimension reduction method, we construct hierarchical models for shallow fluids occupying non-Lipschitz, in general, prismatic domains within the scheme of small displacements linearized with respect to the rest state (see Chinchaladze and Jaiani 2007). As it is well known, motion of the Newtonian fluid is characterized by the following equations qf €ufi ðx1 ; x2 ; x3 ; tÞ ¼ rfij;j ðx1 ; x2 ; x3 ; tÞ þ Ufi ðx1 ; x2 ; x3 ; tÞ; i ¼ 1; 3; rfij ¼ Àdij p þ kf dij h_ f ðu_ f Þ þ 2lf e_ fij ðu_ f Þ; i; j ¼ 1; 3; e_ fij :¼ 1 f u_ i;j þ u_ fj;i ; i; j ¼ 1; 3; 2 ð3:19Þ ð3:20Þ ð3:21Þ h_ f :¼ e_ fii ¼ u_ fi;i ¼ divu_ f ; ð3:22Þ where uf :¼ uf1 ; uf2 ; uf3 is a displacement vector, rfij is a stress tensor, efij is a strain tensor, p is a pressure, Ufi ; i ¼ 1; 3; are components of the volume force, kf and lf are the coefficients of viscosity, qf is a density of the fluid, superscript f means fluid, and superscript dot means differentiation with respect to t.
8, 68, fasc. V. Jaiani, On some boundary value problems for prismatic cusped shells. Theory of Shells. Vekua, ed. T. K. Mikhailov, North-Holland Publishing Company, (1980b), pp. V. Jaiani, Solution of Some Problems for a Degenerate Elliptic Equation of Higher Order and Their Applications to Prismatic Shells (Russian). V. Jaiani, Boundary value problems of mathematical theory of prismatic shells with cusps (Russian). Proceedings of All-union Seminar in Theory and Numerical Methods in Shell and Plate Theory.