Linear Theories Of Elasticity And Thermoelasticity
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Linear Theories Of Elasticity And Thermoelasticity
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Author : Clifford Truesdell
language : en
Publisher: Springer
Release Date : 2013-12-17
Linear Theories Of Elasticity And Thermoelasticity written by Clifford Truesdell and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-17 with Technology & Engineering categories.
Mechanics Of Solids
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Author : C. Truesdell
language : en
Publisher: Springer
Release Date : 1984-06-01
Mechanics Of Solids written by C. Truesdell and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984-06-01 with Science categories.
Reissue of Encyclopedia of Physics / Handbuch der Physik, Volume VIa The mechanical response of solids was first reduced to an organized science of fairly general scope in the nineteenth century. The theory of small elastic deformations is in the main the creation of CAUCHY, who, correcting and simplifying the work of NAVIER and POISSON, through an astounding application of conjoined scholarship, originality, and labor greatly extended in breadth the shallowest aspects of the treatments of par ticular kinds of bodies by GALILEO, LEIBNIZ, JAMES BERNOULLI, PARENT, DANIEL BER NOULLI, EULER, and COULOMB. Linear elasticity became a branch of mathematics, culti vated wherever there were mathematicians. The magisterial treatise of LOVE in its second edition, 1906 - clear, compact, exhaustive, and learned - stands as the summary of the classical theory. It is one of the great "gaslight works" that in BOCHNER'S words! "either do not have any adequate successor[ s] . . . or, at least, refuse to be super seded . . . ; and so they have to be reprinted, in ever increasing numbers, for active research and reference", as long as State and Society shall permit men to learn mathe matics by, for, and of men's minds. Abundant experimentation on solids was done during the same century. Usually the materials arising in nature, with which experiment most justly concerns itself, do not stoop easily to the limitations classical elasticity posits.
Heat Conduction Within Linear Thermoelasticity
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Author : William A. Day
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-07
Heat Conduction Within Linear Thermoelasticity written by William A. Day and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-07 with Science categories.
J-B. J. FOURIER'S immensely influential treatise Theorie Analytique de la Chaleur [21J, and the subsequent developments and refinements of FOURIER's ideas and methods at the hands of many authors, provide a highly successful theory of heat conduction. According to that theory, the growth or decay of the temperature e in a conducting body is governed by the heat equation, that is, by the parabolic partial differential equation Such has been the influence of FOURIER'S theory, which must forever remain the classical theory in that it sets the standard against which all other theories are to be measured, that the mathematical investigation of heat conduction has come to be regarded as being almost identicalt with the study of the heat equation, and the reader will not need to be reminded that intensive analytical study has t But not entirely; witness, for example, those theories which would replace the heat equation by an equation which implies a finite speed of propagation for the temperature. The reader is referred to the article [9] of COLEMAN, FABRIZIO, and OWEN for the derivation of such an equation from modern Continuum Thermody namics and for references to earlier work in this direction. viii Introduction amply demonstrated that the heat equation enjoys many properties of great interest and elegance.
Thermoelastic Models Of Continua
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Author : D. Iesan
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-19
Thermoelastic Models Of Continua written by D. Iesan and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-19 with Science categories.
This volume is concerned with the basic problems of the theory of thermoelasticity for three models of continuous bodies: materials with voids, micropolar solids and nonsimple bodies. Beginning with the basic laws of thermodynamics, the theory of thermoelastic materials with voids is treated. Two subsequent chapters cover the analysis of the linear theory of micropolar thermoelastic bodies. The book concludes with a study of nonsimple thermoelastic materials, which are characterised by the inclusion of higher gradients of displacement in the basic postulates. Relevant examples and exercises which illustrate the theory are given throughout the text. The book should be of interest to mathematicians and specialists working in the fields of elasticity, thermoelasticity, civil engineering and geophysics.
Linear Theories Of Elasticity And Thermoelasticity Linear And Nonlinear Theories Of Rods Plates And Shells
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Author :
language : en
Publisher:
Release Date : 1984
Linear Theories Of Elasticity And Thermoelasticity Linear And Nonlinear Theories Of Rods Plates And Shells written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Mechanics categories.
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.
Elastic And Thermoelastic Problems In Nonlinear Dynamics Of Structural Members
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Author : Jan Awrejcewicz
language : en
Publisher: Springer Nature
Release Date : 2020-04-06
Elastic And Thermoelastic Problems In Nonlinear Dynamics Of Structural Members written by Jan Awrejcewicz and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-04-06 with Science categories.
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
Continuum Mechanics Volume Iii
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Author : José Merodio
language : en
Publisher: EOLSS Publications
Release Date : 2011-11-30
Continuum Mechanics Volume Iii written by José Merodio and has been published by EOLSS Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-11-30 with categories.
The main objective of continuum mechanics is to predict the response of a body that is under the action of external and/or internal influences, i.e. to capture and describe different mechanisms associated with the motion of a body that is under the action of loading. A body in continuum mechanics is considered to be matter continuously distributed in space. Hence, no attention is given to the microscopic (atomic) structure of real materials although non-classical generalized theories of continuum mechanics are able to deal with the mesoscopic structure of matter (i.e. defects, cracks, dispersive lengths, ...). Matter occupies space in time and the response of a body in continuum mechanics is restricted to the Newtonian space-time of classical mechanics in this volume. Einstein’s theory of relativity is not considered. In the classical sense, loading is considered as any action that changes the motion of the body. This includes, for instance, a change in temperature or a force applied. By introducing the concept of configurational forces a load may also be considered as a force that drives a change in the material space, for example the opening of a crack. Continuum mechanics refers to field descriptions of phenomena that are usually modeled by partial differential equations and, from a mathematical point of view, require non-standard knowledge of non-simple technicalities. One purpose in this volume has been to present the different subjects in a self-contained way for a general audience. The organization of the volume is as follows. Mathematically, to predict the response of a body it is necessary to formulate boundary value problems governed by balance laws. The theme of the volume, that is an overview of the subject, has been written with this idea in mind for beginners in the topic. Chapter 1 is an introduction to continuum mechanics based on a one-dimensional framework in which, simultaneously, a more detailed organization of the chapters of this volume is given. A one-dimensional approach to continuum mechanics in some aspects maybe misleading since the analysis is oversimplified. Nevertheless, it allows us to introduce the subject through the early basic steps of the continuum analysis for a general audience. Chapters 3, 4 and 5 are devoted to the mathematical setting of continuum analysis: kinematics, balance laws and thermodynamics, respectively. Chapters 6 and 7 are devoted to constitutive equations. Chapters 8 and 9 deal with different issues in the context of linear elastostatics and linear elastodynamics and waves, respectively, for solids. Linear Elasticity is a classical and central theory of continuum mechanics. Chapter 10 deals with fluids while chapter 11 analyzes the coupled theory of thermoelasticity. Chapter 12 deals with nonlinear elasticity and its role in the continuum framework. Chapters 13 and 14 are dedicated to different applications of solid and fluid mechanics, respectively. The rest of the chapters involve some advanced topics. Chapter 15 is dedicated to turbulence, one of the main challenges in fluid mechanics. Chapter 16 deals with electro-magneto active materials (a coupled theory). Chapter 17 deals with specific ideas of soft matter and chapter 18 deals with configurational forces. In chapter 19, constitutive equations are introduced in a general (implicit) form. Well-posedness (existence, time of existence, uniqueness, continuity) of the equations of the mechanics of continua is an important topic which involves sophisticated mathematical machinery. Chapter 20 presents different analyses related to these topics. Continuum Mechanics is an interdisciplinary subject that attracts the attention of engineers, mathematicians, physicists, etc., working in many different disciplines from a purely scientific environment to industrial applications including biology, materials science, engineering, and many other subjects.
Thermoelasticity
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Author : Witold Nowacki
language : en
Publisher: Elsevier
Release Date : 2013-10-22
Thermoelasticity written by Witold Nowacki and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-22 with Science categories.
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.
Foundations Of Micropolar Thermoelasticity
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Author : Cemal Eringen
language : en
Publisher: Springer
Release Date : 2014-05-04
Foundations Of Micropolar Thermoelasticity written by Cemal Eringen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-04 with Science categories.