Three Dimensional Problems Of The Mathematical Theory Of Elasticity And Thermoelasticity
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Three Dimensional Problems Of The Mathematical Theory Of Elasticity And Thermoelasticity
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Author : T. G. Gegelii︠a︡
language : en
Publisher:
Release Date : 1979
Three Dimensional Problems Of The Mathematical Theory Of Elasticity And Thermoelasticity written by T. G. Gegelii︠a︡ and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979 with Elasticity categories.
Three Dimensional Problems Of Elasticity And Thermoelasticity
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Author : V.D. Kupradze
language : en
Publisher: Elsevier
Release Date : 2012-12-02
Three Dimensional Problems Of Elasticity And Thermoelasticity written by V.D. Kupradze and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-02 with Science categories.
North-Holland Series in Applied Mathematics and Mechanics, Volume 25: Three-Dimensional Problems of the Mathematical Theory of Elasticity and Thermoelasticity focuses on the theory of three-dimensional problems, including oscillation theory, boundary value problems, and integral equations. The publication first tackles basic concepts and axiomatization and basic singular solutions. Discussions focus on fundamental solutions of thermoelasticity, fundamental solutions of the couple-stress theory, strain energy and Hooke’s law in the couple-stress theory, and basic equations in terms of stress components. The manuscript then examines uniqueness theorems and singular integrals and integral equations. The book ponders on the potential theory and boundary value problems of elastic equilibrium and steady elastic oscillations. Topics include basic theorems of the oscillation theory, existence of solutions of boundary value problems, integral equations of the boundary value problems, and boundary properties of potential-type integrals. The publication also reviews mixed dynamic problems, couple-stress elasticity, and boundary value problems for media bounded by several surfaces. The text is a dependable source of data for mathematicians and readers interested in three-dimensional problems of the mathematical theory of elasticity and thermoelasticity.
Three Dimensional Problems Of The Mathematical Theory Of Elasticity And Thermoelasticity
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Author :
language : en
Publisher:
Release Date : 1976
Three Dimensional Problems Of The Mathematical Theory Of Elasticity And Thermoelasticity written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976 with categories.
Trehmernye Zadaci Matematiceskoi Teorii Uprugosti I Termouprugosti
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Author : V.D. Kupradze
language : en
Publisher:
Release Date : 1976
Trehmernye Zadaci Matematiceskoi Teorii Uprugosti I Termouprugosti written by V.D. Kupradze and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976 with categories.
The Mathematical Theory Of Elasticity Second Edition
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Author : Richard B. Hetnarski
language : en
Publisher: CRC Press
Release Date : 2010-10-18
The Mathematical Theory Of Elasticity Second Edition written by Richard B. Hetnarski and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-10-18 with Science categories.
Through its inclusion of specific applications, The Mathematical Theory of Elasticity, Second Edition continues to provide a bridge between the theory and applications of elasticity. It presents classical as well as more recent results, including those obtained by the authors and their colleagues. Revised and improved, this edition incorporates additional examples and the latest research results. New to the Second Edition Exposition of the application of Laplace transforms, the Dirac delta function, and the Heaviside function Presentation of the Cherkaev, Lurie, and Milton (CLM) stress invariance theorem that is widely used to determine the effective moduli of elastic composites The Cauchy relations in elasticity A body force analogy for the transient thermal stresses A three-part table of Laplace transforms An appendix that explores recent developments in thermoelasticity Although emphasis is placed on the problems of elastodynamics and thermoelastodynamics, the text also covers elastostatics and thermoelastostatics. It discusses the fundamentals of linear elasticity and applications, including kinematics, motion and equilibrium, constitutive relations, formulation of problems, and variational principles. It also explains how to solve various boundary value problems of one, two, and three dimensions. This professional reference includes access to a solutions manual for those wishing to adopt the book for instructional purposes.
Mathematical Elasticity
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Author : Philippe G. Ciarlet
language : en
Publisher: SIAM
Release Date : 2022-01-22
Mathematical Elasticity written by Philippe G. Ciarlet and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-22 with Mathematics categories.
The first book of a three-volume set, Three-Dimensional Elasticity covers the modeling and mathematical analysis of nonlinear three-dimensional elasticity. It includes the known existence theorems, either via the implicit function theorem or via the minimization of the energy (John Ball’s theory). An extended preface and extensive bibliography have been added to highlight the progress that has been made since the volume’s original publication. While each one of the three volumes is self-contained, together the Mathematical Elasticity set provides the only modern treatise on elasticity; introduces contemporary research on three-dimensional elasticity, the theory of plates, and the theory of shells; and contains proofs, detailed surveys of all mathematical prerequisites, and many problems for teaching and self-study. These classic textbooks are for advanced undergraduates, first-year graduate students, and researchers in pure or applied mathematics or continuum mechanics. They are appropriate for courses in mathematical elasticity, theory of plates and shells, continuum mechanics, computational mechanics, and applied mathematics in general.
Potential Method In Mathematical Theories Of Multi Porosity Media
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Author : Merab Svanadze
language : en
Publisher: Springer Nature
Release Date : 2019-11-01
Potential Method In Mathematical Theories Of Multi Porosity Media written by Merab Svanadze and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-01 with Mathematics categories.
This monograph explores the application of the potential method to three-dimensional problems of the mathematical theories of elasticity and thermoelasticity for multi-porosity materials. These models offer several new possibilities for the study of important problems in engineering and mechanics involving multi-porosity materials, including geological materials (e.g., oil, gas, and geothermal reservoirs); manufactured porous materials (e.g., ceramics and pressed powders); and biomaterials (e.g., bone and the human brain). Proceeding from basic to more advanced material, the first part of the book begins with fundamental solutions in elasticity, followed by Galerkin-type solutions and Green’s formulae in elasticity and problems of steady vibrations, quasi-static, and pseudo-oscillations for multi-porosity materials. The next part follows a similar format for thermoelasticity, concluding with a chapter on problems of heat conduction for rigid bodies. The final chapter then presents a number of open research problems to which the results presented here can be applied. All results discussed by the author have not been published previously and offer new insights into these models. Potential Method in Mathematical Theories of Multi-Porosity Media will be a valuable resource for applied mathematicians, mechanical, civil, and aerospace engineers, and researchers studying continuum mechanics. Readers should be knowledgeable in classical theories of elasticity and thermoelasticity.
Mathematical Elasticity
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Author :
language : en
Publisher: Elsevier
Release Date : 1997-07-22
Mathematical Elasticity written by and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-07-22 with Mathematics categories.
The objective of Volume II is to show how asymptotic methods, with the thickness as the small parameter, indeed provide a powerful means of justifying two-dimensional plate theories. More specifically, without any recourse to any a priori assumptions of a geometrical or mechanical nature, it is shown that in the linear case, the three-dimensional displacements, once properly scaled, converge in H1 towards a limit that satisfies the well-known two-dimensional equations of the linear Kirchhoff-Love theory; the convergence of stress is also established. In the nonlinear case, again after ad hoc scalings have been performed, it is shown that the leading term of a formal asymptotic expansion of the three-dimensional solution satisfies well-known two-dimensional equations, such as those of the nonlinear Kirchhoff-Love theory, or the von Kármán equations. Special attention is also given to the first convergence result obtained in this case, which leads to two-dimensional large deformation, frame-indifferent, nonlinear membrane theories. It is also demonstrated that asymptotic methods can likewise be used for justifying other lower-dimensional equations of elastic shallow shells, and the coupled pluri-dimensional equations of elastic multi-structures, i.e., structures with junctions. In each case, the existence, uniqueness or multiplicity, and regularity of solutions to the limit equations obtained in this fashion are also studied.
Three Dimensional Mathematical Problems Of Thermoelasticity Of Anisotropic Bodies
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Author : Lothar Jentsch
language : en
Publisher:
Release Date : 1999
Three Dimensional Mathematical Problems Of Thermoelasticity Of Anisotropic Bodies written by Lothar Jentsch and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with categories.
The Mathematical Theory Of Elasticity
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Author : Richard B. Hetnarski
language : en
Publisher: CRC Press
Release Date : 2016-04-19
The Mathematical Theory Of Elasticity written by Richard B. Hetnarski and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-19 with Mathematics categories.
Through its inclusion of specific applications, The Mathematical Theory of Elasticity, Second Edition continues to provide a bridge between the theory and applications of elasticity. It presents classical as well as more recent results, including those obtained by the authors and their colleagues. Revised and improved, this edition incorporates add