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Mathematical Methods for Elastic Plates (Hardcover, 2014 ed.)
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Mathematical Methods for Elastic Plates (Hardcover, 2014 ed.)
Series: Springer Monographs in Mathematics
Expected to ship within 12 - 17 working days
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Mathematical models of deformation of elastic plates are used by
applied mathematicians and engineers in connection with a wide
range of practical applications, from microchip production to the
construction of skyscrapers and aircraft. This book employs two
important analytic techniques to solve the fundamental boundary
value problems for the theory of plates with transverse shear
deformation, which offers a more complete picture of the physical
process of bending than Kirchhoff's classical one. The first method
transfers the ellipticity of the governing system to the boundary,
leading to singular integral equations on the contour of the
domain. These equations, established on the basis of the properties
of suitable layer potentials, are then solved in spaces of smooth
(Hoelder continuous and Hoelder continuously differentiable)
functions. The second technique rewrites the differential system in
terms of complex variables and fully integrates it, expressing the
solution as a combination of complex analytic potentials. The last
chapter develops a generalized Fourier series method closely
connected with the structure of the system, which can be used to
compute approximate solutions. The numerical results generated as
an illustration for the interior Dirichlet problem are accompanied
by remarks regarding the efficiency and accuracy of the procedure.
The presentation of the material is detailed and self-contained,
making Mathematical Methods for Elastic Plates accessible to
researchers and graduate students with a basic knowledge of
advanced calculus.
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