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Computational Continuum Mechanics, 3rd Edition
book

Computational Continuum Mechanics, 3rd Edition

by Ahmed A. Shabana
February 2018
Intermediate to advanced content levelIntermediate to advanced
368 pages
11h 34m
English
Wiley
Content preview from Computational Continuum Mechanics, 3rd Edition

CHAPTER 1INTRODUCTION

Matrix, vector, and tensor algebras are often used in the theory of continuum mechanics in order to have a simpler and more tractable presentation of the subject. In this chapter, the mathematical preliminaries required to understand the matrix, vector, and tensor operations used repeatedly in this book are presented. Principles of mechanics and approximation methods that represent the basis for the formulation of the kinematic and dynamic equations developed in this book are also reviewed in this chapter. In the first two sections of this chapter, matrix and vector notations are introduced and some of their important identities are presented. Some of the vector and matrix results are presented without proofs with the assumption that the reader has some familiarity with matrix and vector notations. In Section 3, the summation convention, which is widely used in continuum mechanics texts, is introduced. This introduction is made despite the fact that the summation convention is rarely used in this book. Tensor notations, on the other hand, are frequently used in this book and, for this reason, tensors are discussed in Section 4. In Section 5, the polar decomposition theorem, which is fundamental in continuum mechanics, is presented. This theorem states that any nonsingular square matrix can be decomposed as the product of an orthogonal matrix and a symmetric matrix. Other matrix decompositions that are used in computational mechanics are also discussed. ...

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Publisher Resources

ISBN: 9781119293217Purchase book