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Author: V.D. Kupradze
Publisher: Elsevier
ISBN: 0080984630
Category : Science
Languages : en
Pages : 951
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Book Description
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.
Author: V.D. Kupradze
Publisher: Elsevier
ISBN: 0080984630
Category : Science
Languages : en
Pages : 951
Get Book
Book Description
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.
Author: V. D. Kupradze
Publisher: North Holland
ISBN: 9780444851482
Category :
Languages : en
Pages : 930
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Book Description
Three-Dimensional Problems of Elasticity and Thermoelasticity ...
Author: T. G. Gegelii︠a︡
Publisher:
ISBN:
Category : Elasticity
Languages : en
Pages : 960
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Book Description
Author: Clifford Truesdell
Publisher: Springer
ISBN: 3662397765
Category : Technology & Engineering
Languages : en
Pages : 755
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Book Description
Author: Witold Nowacki
Publisher: Elsevier
ISBN: 1483162486
Category : Science
Languages : en
Pages : 578
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Book Description
Thermoelasticity, Second Edition reviews advances in thermoelasticity and covers topics ranging from stationary problems of thermoelasticity to variational theorems of stationary thermoelasticity; stresses due to the action of a discontinuous temperature field in an infinite elastic body; the action of heat sources in the elastic space; and thermal inclusions in an infinite disc and semi-infinite disc. Three different sets of differential equations describing the fields of strain and temperature are presented. This book is comprised of 12 chapters and begins with a discussion on basic relations and equations of thermoelasticity. Thermoelasticity is treated as a synthesis of the theory of elasticity and the theory of heat conduction. Some particular cases of thermoelasticity are then investigated, including stationary problems, the theory of thermal stresses, and classical dynamic elasticity. Dynamic effects due to the action of a non-stationary temperature field are examined, along with plane harmonic waves in an elastic space and thermal stresses in plates, shells, and viscoelastic bodies. The final chapter focuses on micropolar thermoelasticity, magnetothermoelasticity, and thermopiezoelectricity. This monograph will be of interest to physicists and mechanical engineers.
Author: Jan Awrejcewicz
Publisher: Springer Nature
ISBN: 303037663X
Category : Science
Languages : en
Pages : 615
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Book Description
From the reviews: "A unique feature of this book is the nice blend of engineering vividness and mathematical rigour. [...] The authors are to be congratulated for their valuable contribution to the literature in the area of theoretical thermoelasticity and vibration of plates." Journal of Sound and Vibration
Author: Vyacheslav Vikhrenko
Publisher: BoD – Books on Demand
ISBN: 9533074043
Category : Technology & Engineering
Languages : en
Pages : 366
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Book Description
The content of this book covers several up-to-date approaches in the heat conduction theory such as inverse heat conduction problems, non-linear and non-classic heat conduction equations, coupled thermal and electromagnetic or mechanical effects and numerical methods for solving heat conduction equations as well. The book is comprised of 14 chapters divided into four sections. In the first section inverse heat conduction problems are discuss. The first two chapters of the second section are devoted to construction of analytical solutions of nonlinear heat conduction problems. In the last two chapters of this section wavelike solutions are attained.The third section is devoted to combined effects of heat conduction and electromagnetic interactions in plasmas or in pyroelectric material elastic deformations and hydrodynamics. Two chapters in the last section are dedicated to numerical methods for solving heat conduction problems.
Author: Richard B. Hetnarski
Publisher: CRC Press
ISBN: 1439828881
Category : Science
Languages : en
Pages : 840
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Book Description
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.
Author: Yuriy Tokovyy
Publisher: Cambridge Scholars Publishing
ISBN: 1527565327
Category : Mathematics
Languages : en
Pages : 342
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Book Description
The direct integration method (a general approach to analysis for boundary value problems of mathematical physics with no implications for the potential functions of higher differential order) is presented in this book as a potential tool for the analysis of the elastic response of arbitrarily nonhomogeneous solids to thermal and force loadings. This method rests upon the correct integration of the local equilibrium equations, which results in an explicit relationship between the stress-tensor components and fundamental integral conditions of equilibrium for individual stresses, which can serve to assure the correctness of the solution and provide a simple verification of computational results. Making use of these relationships and conditions, which are irrespective of the material properties, allows for the reduction of the original elasticity and thermoelasticity problems for nonhomogeneous materials to integral equations of a second kind which implies the solution in a closed form. This feature makes the method efficient for the analysis of arbitrarily nonhomogeneous materials, among which the functionally graded materials are of particular interest for both academia and industry.
Author: Jan Awrejcewicz
Publisher: Springer Science & Business Media
ISBN: 3642556779
Category : Technology & Engineering
Languages : en
Pages : 432
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Book Description
From the reviews: "A unique feature of this book is the nice blend of engineering vividness and mathematical rigour. [...] The authors are to be congratulated for their valuable contribution to the literature in the area of theoretical thermoelasticity and vibration of plates." Journal of Sound and Vibration
