Mathematical Methods for Elastic Plates by Christian Constanda
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 (Hölder continuous and Hölder 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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The Higher Infinite
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Fredholm Theory in Topological Vector Spaces
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Combinatorial Set Theory of C*-Algebras
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Classical Lie Algebras at Infinity
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Representation Theory of Finite Group Extensions
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Geometric Approximation Theory
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Determinants, Grobner Bases and Cohomology
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Topics in Global Real Analytic Geometry
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Self-Adjoint Extension Schemes and Modern Applications to Quantum Hamiltonians
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The Weierstrass Sigma Function in Higher Genus and Applications to Integrable Equations
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The Riordan Group and Applications
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Domination in Graphs: Core Concepts
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Real Algebraic Varieties
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Curvature Measures of Singular Sets
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Structure and Regularity of Group Actions on One-Manifolds
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Superconcentration and Related Topics
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Extremal Polynomials and Riemann Surfaces
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Simplicial Partitions with Applications to the Finite Element Method
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Modular Forms
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Microstructured Materials: Inverse Problems
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Projective and Cayley-Klein Geometries
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Monotone Complete C*-algebras and Generic Dynamics
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Logical Foundations of Mathematics and Computational Complexity
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Arithmetic of Quadratic Forms
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Hardy Spaces on the Euclidean Space
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Functional Analytic Techniques for Diffusion Processes
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Harnack's Inequality for Degenerate and Singular Parabolic Equations
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Structure and Geometry of Lie Groups
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Inverse Linear Problems on Hilbert Space and their Krylov Solvability
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Modular Forms: Basics and Beyond
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The Absolute Galois Group of a Semi-Local Field
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Hardy Operators, Function Spaces and Embeddings
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Random Fields and Geometry
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Positive Polynomials
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Classical Fine Potential Theory
From the book reviews:
“This is a nice short and self-contained book on mathematical methods in the linear theory of plates… The book is strongly recommended to those who are interested in mathematical problems of elasticity and applications of the theory of potentials in mathematical physics.” (Leonid P. Lebedev, zbMATH, Vol. 1301, 2015)| SKU | Unavailable |
| ISBN 13 | 9781447164333 |
| ISBN 10 | 1447164334 |
| Title | Mathematical Methods for Elastic Plates |
| Author | Christian Constanda |
| Series | Springer Monographs In Mathematics |
| Condition | Unavailable |
| Binding Type | Hardback |
| Publisher | Springer London Ltd |
| Year published | 2014-07-10 |
| Number of pages | 209 |
| Cover note | Book picture is for illustrative purposes only, actual binding, cover or edition may vary. |
| Note | Unavailable |