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Books > Science & Mathematics > Mathematics > Applied mathematics > Mathematical modelling
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Variational and Potential Methods in the Theory of Bending of Plates with Transverse Shear Deformation (Hardcover)
Loot Price: R5,522
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Variational and Potential Methods in the Theory of Bending of Plates with Transverse Shear Deformation (Hardcover)
Series: Monographs and Surveys in Pure and Applied Mathematics
Expected to ship within 12 - 19 working days
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Elastic plates form a class of very important mechanical structures
that appear in a wide range of practical applications, from
building bodies to microchip production. As the sophistication of
industrial designs has increased, so has the demand for greater
accuracy in analysis. This in turn has led modelers away from
Kirchoff's classical theory for thin plates and toward increasingly
refined models that yield not only the deflection of the middle
section, but also account for transverse shear deformation. The
improved performance of these models is achieved, however, at the
expense of a much more complicated system of governing equations
and boundary conditions. In this Monograph, the authors conduct a
rigorous mathematical study of a number of boundary value problems
for the system of partial differential equations that describe the
equilibrium bending of an elastic plate with transverse shear
deformation. Specifically, the authors explore the existence,
uniqueness, and continuous dependence of the solution on the data.
In each case, they give the variational formulation of the problems
and discuss their solvability in Sobolev spaces. They then seek the
solution in the form of plate potentials and reduce the problems to
integral equations on the contour of the domain. This treatment
covers an extensive range of problems and presents the variational
method and the boundary integral equation method applied
side-by-side. Readers will find that this feature of the book,
along with its clear exposition, will lead to a firm and useful
understanding of both the model and the methods.
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