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.

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.

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

This book comprises select peer-reviewed articles submitted for the proceedings of the International Conference on Mathematics and Computing (ICMC 2022), held by the School of Advanced Sciences, Vellore Institute of Technology, Vellore, India, in association with Ramanujan Mathematical Society, India, Cryptology Research Society of India and Society for Electronic Transactions and Security, India, from 6–8 January 2022. With an aim to identify the existing challenges in the areas of mathematics and computing, the book emphasizes the importance of establishing new methods and algorithms to address these challenges. The book includes topics on diverse applications of cryptology, network security, cyber security, block chain, IoT, mobile network, data analytics, applied algebra, mathematical analysis, mathematical modelling, fluid dynamics, fractional calculus, multi-optimization, integral equations, dynamical systems, numerical analysis and scientific computing. Divided into five major parts—applied algebra and analysis, fractional calculus and integral equations, mathematical modelling and fluid dynamics, numerical analysis, and computer science and applications—the book is a useful resource for students, researchers and faculty as well as practitioners.

This book contains the elements of the theory and the problems of Elasticity and Thermal Stresses with full solutions. The emphasis is placed on problems and solutions and the book consists of four parts: one part is on The Mathematical Theory of Elasticity, two parts are on Thermal Stresses and one part is on Numerical Methods. The book is addressed to higher level undergraduate students, graduate students and engineers and it is an indispensable companion to all who study any of the books published earlier by the authors. This book links the three previously published books by the authors into one comprehensive entity.

Although the study of classical thermoelasticity has provided information on linear systems, only recently have results on the asymptotic behavior completed our basic understanding of the generic behavior of solutions. Through systematic work that began in the 80s, we now also understand the basic features of nonlinear systems. Yet some questions r

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

A unique monograph in a fast developing field of generalized thermoelasticity, an area of active research in continuum mechanics, focusing on thermoelasticity governed by hyperbolic equations, rather than on a wide range of continuum theories.

The theory of thermoelasticity studies the interaction between thermal and mechan ical fields in elastic bodies. This theory is of interest both for the mathematical and technical point of view. Intense interest has been shown recently in this field owing to the great practical importance of dynamical effects in aeronautics, nu clear reactors, and its potential importance in cryogenic applications. This work is concerned mainly with basic problems of the theory of thermoelasticity. Ther moelasticity of polar materials and the theories of thermoelasticity with finite wave speeds are not considered here. The reader interested in these subjects will find a full account in the works of Nowacki [280], Chandrasekharaiah [60] and Ignaczak [195]. Our purpose in this work is to present a systematic treatment of some results established in the theory of thermoelasticity. On the whole, the subject matter is directed towards recent developments. Chapter 1 is concerned mainly with the development of the fundamental equa tions of the theory of thermoelasticity. The kinematics and primitive concepts associated with the basic principles are developed and emphasized only to the ex tent that they are needed in our treatment of the subject. Chapter 2 is devoted to a study of linear thermoelastic deformations for prestressed bodies. We have at tempted to isolate those conceptual and mathematical difficulties which arise over and above those inherent in the problems concerned with unstressed bodies.