By H. benisty, J. Gerard
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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.