Difference Equations for Plane Thermal Elasticity
Author | : George N. White |
Publisher | : |
Total Pages | : 74 |
Release | : 1962 |
Genre | : Differential equations |
ISBN | : |
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Author | : George N. White |
Publisher | : |
Total Pages | : 74 |
Release | : 1962 |
Genre | : Differential equations |
ISBN | : |
Author | : Witold Nowacki |
Publisher | : Elsevier |
Total Pages | : 579 |
Release | : 2013-10-22 |
Genre | : Science |
ISBN | : 1483162486 |
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 | : M. Reza Eslami |
Publisher | : Springer Science & Business Media |
Total Pages | : 787 |
Release | : 2013-05-13 |
Genre | : Science |
ISBN | : 9400763565 |
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.
Author | : W. Nowacki |
Publisher | : Springer Science & Business Media |
Total Pages | : 462 |
Release | : 1975-12-31 |
Genre | : Science |
ISBN | : 9789028600454 |
Author | : J. R. Whiteman |
Publisher | : Academic Press |
Total Pages | : 535 |
Release | : 2014-05-10 |
Genre | : Mathematics |
ISBN | : 1483268845 |
The Mathematics of Finite Elements and Applications provides information pertinent to the mathematics of finite elements, applications, algorithms, and computational techniques. This book discusses the developments in the mathematics of finite elements. Organized into 32 chapters, this book begins with an overview of the basis of the finite element process as a general approximation tool. This text then examines the methods for obtaining bounds on the errors in finite element solutions to two-dimensional elliptic boundary value problems defined on simply connected polygonal regions. Other chapters consider the practical implementation of the Galerkin and the Rayleigh–Ritz methods to equations of importance to physics and engineering. This book discusses as well a fundamental investigation into the problem of convergence in the finite element method. The final chapter deals with an algorithm that is applicable to the analysis of arbitrary plane stress or plane strain configurations. This book is a valuable resource for numerical analysts, mathematical physicist, applied mathematicians, computer scientists, and engineers.
Author | : Luis Manuel Braga da Costa Campos |
Publisher | : CRC Press |
Total Pages | : 394 |
Release | : 2019-11-05 |
Genre | : Mathematics |
ISBN | : 0429644175 |
Higher-Order Differential Equations and Elasticity is the third book within Ordinary Differential Equations with Applications to Trajectories and Vibrations, Six-volume Set. As a set, they are the fourth volume in the series Mathematics and Physics Applied to Science and Technology. This third book consists of two chapters (chapters 5 and 6 of the set). The first chapter in this book concerns non-linear differential equations of the second and higher orders. It also considers special differential equations with solutions like envelopes not included in the general integral. The methods presented include special differential equations, whose solutions include the general integral and special integrals not included in the general integral for myriad constants of integration. The methods presented include dual variables and differentials, related by Legendre transforms, that have application in thermodynamics. The second chapter concerns deformations of one (two) dimensional elastic bodies that are specified by differential equations of: (i) the second-order for non-stiff bodies like elastic strings (membranes); (ii) fourth-order for stiff bodies like bars and beams (plates). The differential equations are linear for small deformations and gradients and non-linear otherwise. The deformations for beams include bending by transverse loads and buckling by axial loads. Buckling and bending couple non-linearly for plates. The deformations depend on material properties, for example isotropic or anisotropic elastic plates, with intermediate cases such as orthotropic or pseudo-isotropic. Discusses differential equations having special integrals not contained in the general integral, like the envelope of a family of integral curves Presents differential equations of the second and higher order, including non-linear and with variable coefficients Compares relation of differentials with the principles of thermodynamics Describes deformations of non-stiff elastic bodies like strings and membranes and buckling of stiff elastic bodies like bars, beams, and plates Presents linear and non-linear waves in elastic strings, membranes, bars, beams, and plates
Author | : Prem Kythe |
Publisher | : Springer Science & Business Media |
Total Pages | : 461 |
Release | : 2011-06-27 |
Genre | : Mathematics |
ISBN | : 0817681604 |
Modern finite element analysis has grown into a basic mathematical tool for almost every field of engineering and the applied sciences. This introductory textbook fills a gap in the literature, offering a concise, integrated presentation of methods, applications, software tools, and hands-on projects. Included are numerous exercises, problems, and Mathematica/Matlab-based programming projects. The emphasis is on interdisciplinary applications to serve a broad audience of advanced undergraduate/graduate students with different backgrounds in applied mathematics, engineering, physics/geophysics. The work may also serve as a self-study reference for researchers and practitioners seeking a quick introduction to the subject for their research.
Author | : United States. National Aeronautics and Space Administration |
Publisher | : |
Total Pages | : 1556 |
Release | : 1962 |
Genre | : Aeronautics |
ISBN | : |
Author | : |
Publisher | : Academic Press |
Total Pages | : 447 |
Release | : 2009-08-31 |
Genre | : Mathematics |
ISBN | : 008087312X |
Kernel Functions and Differential Equations