Author: Stuart Antman
Publisher: Springer Science & Business Media
ISBN: 1475741472
Category : Mathematics
Languages : en
Pages : 762
Get Book Here
Book Description
The scientists of the seventeenth and eighteenth centuries, led by Jas. Bernoulli and Euler, created a coherent theory of the mechanics of strings and rods undergoing planar deformations. They introduced the basic con cepts of strain, both extensional and flexural, of contact force with its com ponents of tension and shear force, and of contact couple. They extended Newton's Law of Motion for a mass point to a law valid for any deformable body. Euler formulated its independent and much subtler complement, the Angular Momentum Principle. (Euler also gave effective variational characterizations of the governing equations. ) These scientists breathed life into the theory by proposing, formulating, and solving the problems of the suspension bridge, the catenary, the velaria, the elastica, and the small transverse vibrations of an elastic string. (The level of difficulty of some of these problems is such that even today their descriptions are sel dom vouchsafed to undergraduates. The realization that such profound and beautiful results could be deduced by mathematical reasoning from fundamental physical principles furnished a significant contribution to the intellectual climate of the Age of Reason. ) At first, those who solved these problems did not distinguish between linear and nonlinear equations, and so were not intimidated by the latter. By the middle of the nineteenth century, Cauchy had constructed the basic framework of three-dimensional continuum mechanics on the founda tions built by his eighteenth-century predecessors.
Author: R. W. Ogden
Publisher: Courier Corporation
ISBN: 0486318710
Category : Technology & Engineering
Languages : en
Pages : 562
Get Book Here
Book Description
Classic in the field covers application of theory of finite elasticity to solution of boundary-value problems, analysis of mechanical properties of solid materials capable of large elastic deformations. Problems. References.
Author: Clifford Truesdell
Publisher: Springer
ISBN: 3662397765
Category : Technology & Engineering
Languages : en
Pages : 755
Get Book Here
Book Description
Author: Y. B. Fu
Publisher: Cambridge University Press
ISBN: 0521796954
Category : Mathematics
Languages : en
Pages : 541
Get Book Here
Book Description
Comprehensive introduction to nonlinear elasticity for graduates and researchers, covering new developments in the field.
Author: Jerrold E. Marsden
Publisher: Courier Corporation
ISBN: 0486142272
Category : Technology & Engineering
Languages : en
Pages : 578
Get Book Here
Book Description
Graduate-level study approaches mathematical foundations of three-dimensional elasticity using modern differential geometry and functional analysis. It presents a classical subject in a modern setting, with examples of newer mathematical contributions. 1983 edition.
Author:
Publisher: Elsevier
ISBN: 0080875416
Category : Technology & Engineering
Languages : en
Pages : 495
Get Book Here
Book Description
This volume is a thorough introduction to contemporary research in elasticity, and may be used as a working textbook at the graduate level for courses in pure or applied mathematics or in continuum mechanics. It provides a thorough description (with emphasis on the nonlinear aspects) of the two competing mathematical models of three-dimensional elasticity, together with a mathematical analysis of these models. The book is as self-contained as possible.
Author: Basile Audoly
Publisher: Oxford University Press
ISBN: 0198506252
Category : Mathematics
Languages : en
Pages : 597
Get Book Here
Book Description
We experience elasticity everywhere in everyday life. This book covers several modern aspects of the established field of elasticity theory, applying general methods of classical analysis including advanced nonlinear aspects to derive detailed solutions to specific problems. It can serve as an introduction to nonlinear methods in science.
Author: Arabinda Roy
Publisher: CRC Press
ISBN: 1000758885
Category : Technology & Engineering
Languages : en
Pages : 407
Get Book Here
Book Description
Linear and Non-Linear Deformations of Elastic Solids aims to compile the advances in the field of linear and non-linear elasticity through discussion of advanced topics. Broadly classified into two parts, it includes crack, contact, scattering and wave propagation in linear elastic solids and bending vibration, stability in non-linear elastic solids supported by MATLAB examples. This book is aimed at graduate students and researchers in applied mathematics, solid mechanics, applied mechanics, structural mechanics and includes comprehensive discussion of related analytical/numerical methods.
Author: J. T. Oden
Publisher: Courier Corporation
ISBN: 0486317900
Category : Technology & Engineering
Languages : en
Pages : 517
Get Book Here
Book Description
Geared toward undergraduate and graduate students, this text extends applications of the finite element method from linear problems in elastic structures to a broad class of practical, nonlinear problems in continuum mechanics. It treats both theory and applications from a general and unifying point of view. The text reviews the thermomechanical principles of continuous media and the properties of the finite element method, and then brings them together to produce discrete physical models of nonlinear continua. The mathematical properties of these models are analyzed, along with the numerical solution of the equations governing the discrete model. Though the theory and methods are sufficiently general to be applied to any nonlinear problem, emphasis has been placed on problems in finite elasticity, viscoelasticity, heat conduction, and thermoviscoelasticity. Problems in rarefied gas dynamics and nonlinear partial differential equations are also examined. Other topics include topological properties of finite element models, applications to linear and nonlinear boundary value problems, and discrete models of nonlinear thermomechanical behavior of dissipative media. This comprehensive text is valuable not only to students of structural analysis and continuum mechanics but also to professionals researching the numerical analysis of continua
Author: Adnan Ibrahimbegovic
Publisher: Springer Science & Business Media
ISBN: 9048123305
Category : Computers
Languages : en
Pages : 588
Get Book Here
Book Description
This book offers a recipe for constructing the numerical models for representing the complex nonlinear behavior of structures and their components, represented as deformable solid bodies. Its appeal extends to those interested in linear problems of mechanics.
