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Applications of tensor analysis in c...

Eremeyev, Victor A.

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Applications of tensor analysis in continuum mechanics

Record Type:	Electronic resources : Monograph/item
Title/Author:	Applications of tensor analysis in continuum mechanics/ Victor A. Eremeyev, Michael J. Cloud, Leonid P. Lebedev.
Author:	Eremeyev, Victor A.
other author:	Cloud, Michael J.
Published:	Singapore ;World Scientific, : c2018.,
Description:	1 online resource (ix, 415 p.) :ill.
Subject:	Continuum mechanics. -
Online resource:	https://www.worldscientific.com/worldscibooks/10.1142/10959#t=toc
ISBN:	9789813238978

Applications of tensor analysis in continuum mechanics
Eremeyev, Victor A.

Applications of tensor analysis in continuum mechanics[electronic resource] /Victor A. Eremeyev, Michael J. Cloud, Leonid P. Lebedev. - 1st ed. - Singapore ;World Scientific,c2018. - 1 online resource (ix, 415 p.) :ill.

Includes bibliographical references and index.

"A tensor field is a tensor-valued function of position in space. The use of tensor fields allows us to present physical laws in a clear, compact form. A byproduct is a set of simple and clear rules for the representation of vector differential operators such as gradient, divergence, and Laplacian in curvilinear coordinate systems. The tensorial nature of a quantity permits us to formulate transformation rules for its components under a change of basis. These rules are relatively simple and easily grasped by any engineering student familiar with matrix operators in linear algebra. More complex problems arise when one considers the tensor fields that describe continuum bodies. In this case general curvilinear coordinates become necessary. The principal basis of a curvilinear system is constructed as a set of vectors tangent to the coordinate lines. Another basis, called the dual basis, is also constructed in a special manner. The existence of these two bases is responsible for the mysterious covariant and contravariant terminology encountered in tensor discussions. This book provides a clear, concise, and self-contained treatment of tensors and tensor fields. It covers the foundations of linear elasticity, shell theory, and generalized continuum media, offers hints, answers, and full solutions for many of the problems and exercises, and Includes a handbook-style summary of important tensor formulas. The book can be useful for beginners who are interested in the basics of tensor calculus. It also can be used by experienced readers who seek a comprehensive review on applications of the tensor calculus in mechanics"--

ISBN: 9789813238978

LCCN: 2018028400Subjects--Topical Terms:

535472
Continuum mechanics.

LC Class. No.: QA808.2 / .E699 2018

Dewey Class. No.: 531

Applications of tensor analysis in continuum mechanics
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020 $z 9789813238961 $q (hardcover)
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050 0 0 $a QA808.2 $b .E699 2018
082 0 4 $a 531 $2 23
100 1 $a Eremeyev, Victor A. $3 1572832
245 1 0 $a Applications of tensor analysis in continuum mechanics $h [electronic resource] / $c Victor A. Eremeyev, Michael J. Cloud, Leonid P. Lebedev.
250 $a 1st ed.
260 $a Singapore ; $a Hackensack, NJ : $b World Scientific, $c c2018.
300 $a 1 online resource (ix, 415 p.) : $b ill.
504 $a Includes bibliographical references and index.
520 $a "A tensor field is a tensor-valued function of position in space. The use of tensor fields allows us to present physical laws in a clear, compact form. A byproduct is a set of simple and clear rules for the representation of vector differential operators such as gradient, divergence, and Laplacian in curvilinear coordinate systems. The tensorial nature of a quantity permits us to formulate transformation rules for its components under a change of basis. These rules are relatively simple and easily grasped by any engineering student familiar with matrix operators in linear algebra. More complex problems arise when one considers the tensor fields that describe continuum bodies. In this case general curvilinear coordinates become necessary. The principal basis of a curvilinear system is constructed as a set of vectors tangent to the coordinate lines. Another basis, called the dual basis, is also constructed in a special manner. The existence of these two bases is responsible for the mysterious covariant and contravariant terminology encountered in tensor discussions. This book provides a clear, concise, and self-contained treatment of tensors and tensor fields. It covers the foundations of linear elasticity, shell theory, and generalized continuum media, offers hints, answers, and full solutions for many of the problems and exercises, and Includes a handbook-style summary of important tensor formulas. The book can be useful for beginners who are interested in the basics of tensor calculus. It also can be used by experienced readers who seek a comprehensive review on applications of the tensor calculus in mechanics"-- $c Provided by publisher.
588 $a Description based on print version record.
650 0 $a Continuum mechanics. $3 535472
650 0 $a Calculus of tensors. $3 533863
650 0 $a Engineering mathematics. $3 516847
700 1 $a Cloud, Michael J. $3 816286
700 1 $a Lebedev, L. P. $3 815914
856 4 0 $u https://www.worldscientific.com/worldscibooks/10.1142/10959#t=toc