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The Theory of Anisotropic Elastic Plates (Paperback, Softcover reprint of hardcover 1st ed. 1999)
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The Theory of Anisotropic Elastic Plates (Paperback, Softcover reprint of hardcover 1st ed. 1999)
Series: Mathematics and Its Applications, 476
Expected to ship within 10 - 15 working days
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The main purpose of this work is construction of the mathematical
theory of elastic plates and shells, by means of which the
investigation of basic boundary value problems of the spatial
theory of elasticity in the case of cylindrical do mains reduces to
the study of two-dimensional boundary value problems (BVP) of
comparatively simple structure. In this respect in sections 2-5
after the introductory material, methods of re duction, known in
the literature as usually being based on simplifying hypotheses,
are studied. Here, in contradiction to classical methods, the
problems, connected with construction of refined theories of
anisotropic nonhomogeneous plates with variable thickness without
the assumption of any physical and geometrical re strictions, are
investigated. The comparative analysis of such reduction methods
was carried out, and, in particular, in section 5, the following
fact was established: the error transition, occuring with
substitution of a two-dimensional model for the initial problem on
the class of assumed solutions is restricted from below. Further,
in section 6, Vekua's method of reduction, containing regular pro
cess of study of three-dimensional problem, is investigated. In
this direction, the problems, connected with solvability,
convergence of processes, and construction of effective algorithms
of approximate solutions are studied."
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