By A. J. M. Spencer
The mechanics of fluids and the mechanics of solids symbolize the 2 significant parts of physics and utilized arithmetic that meet in continuum mechanics, a box that varieties the basis of civil and mechanical engineering. This unified method of the instructing of fluid and sturdy mechanics specializes in the overall mechanical ideas that practice to all fabrics. scholars who've familiarized themselves with the elemental ideas can move directly to specialise in any of the several branches of continuum mechanics. this article opens with introductory chapters on matrix algebra, vectors and Cartesian tensors, and an research of deformation and rigidity. Succeeding chapters research the mathematical statements of the legislation of conservation of mass, momentum, and effort in addition to the formula of the mechanical constitutive equations for numerous periods of fluids and solids. as well as many labored examples, this quantity contains a graded collection of difficulties (with solutions, the place appropriate). aimed toward undergraduate scholars of utilized arithmetic, it is going to additionally turn out helpful to physicists and engineers.
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Spencer All rights reserved. Bibliographical Note This Dover edition, first published in 2004, is an unabridged republication of the edition originally published by the Longman Group UK Limited, Essex, England, in 1980. Library of Congress Cataloging-in-Publication Data Spencer, A. J. M. M. Spencer. p. cm. Originally published: London ; New York : Longman, 1980. (Longman mathematical texts) Includes bibliographical references and index. 9780486139470 1. Continuum mechanics. 1. Title. com Table of Contents Title Page Copyright Page Preface 1 - Introduction 2 - Introductory matrix algebra 3 - Vectors and cartesian tensors 4 - Particle kinematics 5 - Stress 6 - Motions and deformations 7 - Conservation laws 8 - Linear constitutive equations 9 - Further analysis of finite deformation 10 - Non-linear constitutive equations 11 - Cylindrical and spherical polar coordinates Appendix - Representation theorem for an isotropic tensor function of a tensor Answers Further reading Index Preface The aim of this book is to provide an introduction to the theory of continuum mechanics in a form which is suitable for undergraduate students.
Vectors a, b, ... , and tensors A, B, . . ; or in component form, as relations between scalars α, β, . . , vector components ai, bi, ... , and tensor components Aij, Bij, . . The direct notation has the advantage that it emphasizes that physical statements are independent of the choice of the coordinate system. However, this advantage is not entirely lost when the component notation is used, because relations in component notation must be written in such a way that they preserve their form under coordinate transformations.
11) represents a set of six relations between the nine quantities Mij. Now regard Mij as the elements of a square matrix M. 12) Thus M = (Mij) is an orthogonal matrix; that is, the matrix which determines the new base vectors in terms of the old base vectors is an orthogonal matrix. For a transformation from one right-handed system to another right-handed system, M is a proper orthogonal matrix. The rows of M are the direction cosines of ēi in the first coordinate system. 13) and so the columns of M are the direction cosines of the ej in the coordinate system with base vectors ēi.