Non-linear Elastic Deformations

Non-linear Elastic Deformations
Author: R. W. Ogden
Publisher: Courier Corporation
Total Pages: 562
Release: 1997-01-01
Genre: Technology & Engineering
ISBN: 0486696480

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.

Non-Linear Elastic Deformations

Non-Linear Elastic Deformations
Author: R. W. Ogden
Publisher: Courier Corporation
Total Pages: 562
Release: 2013-04-26
Genre: Technology & Engineering
ISBN: 0486318710

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.

Nonlinear Elasticity

Nonlinear Elasticity
Author: Y. B. Fu
Publisher: Cambridge University Press
Total Pages: 541
Release: 2001-05-07
Genre: Mathematics
ISBN: 0521796954

Comprehensive introduction to nonlinear elasticity for graduates and researchers, covering new developments in the field.

Linear and Non-Linear Deformations of Elastic Solids

Linear and Non-Linear Deformations of Elastic Solids
Author: Arabinda Roy
Publisher: CRC Press
Total Pages: 407
Release: 2019-12-06
Genre: Technology & Engineering
ISBN: 1000758885

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.

Non-Linear Theory of Elasticity and Optimal Design

Non-Linear Theory of Elasticity and Optimal Design
Author: L.W. Ratner
Publisher: Elsevier
Total Pages: 281
Release: 2003-11-12
Genre: Science
ISBN: 008053760X

In order to select an optimal structure among possible similar structures, one needs to compare the elastic behavior of the structures. A new criterion that describes elastic behavior is the rate of change of deformation. Using this criterion, the safe dimensions of a structure that are required by the stress distributed in a structure can be calculated. The new non-linear theory of elasticity allows one to determine the actual individual limit of elasticity/failure of a structure using a simple non-destructive method of measurement of deformation on the model of a structure while presently it can be done only with a destructive test for each structure. For building and explaining the theory, a new logical structure was introduced as the basis of the theory. One of the important physical implications of this logic is that it describes mathematically the universal domain of the possible stable physical relations.

Nonlinear Theory of Elasticity

Nonlinear Theory of Elasticity
Author: Larry Alan Taber
Publisher: World Scientific
Total Pages: 417
Release: 2004
Genre: Science
ISBN: 9812387358

Soft biological tissues often undergo large (nearly) elastic deformations that can be analyzed using the nonlinear theory of elasticity. Because of the varied approaches to nonlinear elasticity in the literature, some aspects of the subject may be difficult to appreciate. This book attempts to clarify and unify those treatments, illustrating the advantages and disadvantages of each through various examples in the mechanics of soft tissues. Applications include muscle, arteries, the heart, and embryonic tissues.

Non-Linear Theory of Elasticity

Non-Linear Theory of Elasticity
Author: A.I. Lurie
Publisher: Elsevier
Total Pages: 632
Release: 2012-12-02
Genre: Science
ISBN: 0444597239

This book examines in detail the Theory of Elasticity which is a branch of the mechanics of a deformable solid. Special emphasis is placed on the investigation of the process of deformation within the framework of the generally accepted model of a medium which, in this case, is an elastic body. A comprehensive list of Appendices is included providing a wealth of references for more in depth coverage. The work will provide both a stimulus for future research in this field as well as useful reference material for many years to come.

Nonlinear Problems of Elasticity

Nonlinear Problems of Elasticity
Author: Stuart Antman
Publisher: Springer Science & Business Media
Total Pages: 762
Release: 2013-03-14
Genre: Mathematics
ISBN: 1475741472

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.

Mathematical Foundations of Elasticity

Mathematical Foundations of Elasticity
Author: Jerrold E. Marsden
Publisher: Courier Corporation
Total Pages: 578
Release: 2012-10-25
Genre: Technology & Engineering
ISBN: 0486142272

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.