Introduction to Continuum Mechanics 3E pptx

[...]... the general approach to the subject matter of continuum mechanics We are pleased that many instructors of continuum mechanics have found this little book serves that purpose well However, we have also understood that many instructors have used this book as one of the texts for a beginning graduate course in continuum mechanics It is this latter knowledge that has motivated us to write this new edition... base vectors as follows: Tex = 4CJ+C2 Te2 = 2e! +3e3 Te3 = e1 +3e2 +e3 Solution By Eq (2B2.1a) it is clear that: [T]= 4 2 -1~ 1 0 3 [0 3 1 Example 2B2.2 Let T transform every vector into its mirror image with respect to a fixed plane If ej is normal to the reflection plane (e2 and 63 are parallel to this plane), find a matrix of T Solution Since the normal to the reflection plane is transformed into its... understanding of the continuum theory, the point to be made is simply that whether the continuum theory is justified in a given situation is a matter of experimental test, not of philosophy Suffice it to say that more than a hundred years of experience have justified such a theory in a wide variety of situations 1.2 Contents of Continuum Mechanics Continuum mechanics studies the response of materials to different... property: where a and b are two arbitrary vectors and a and ft are arbitrary scalars If two tensors, T and S, transform any arbitrary vector a in an identical way, then these tensors are equal to each other, i.e., Ta=Sa -» T=S Let T be a transformation which transforms every vector into a fixed vector n Is this transformation a tensor? Solution Let a and b be any two vectors, then by the definition of T, Ta... 520 523 526 532 537 Answer to Problems 543 References 550 Index 552 Preface to the Third Edition The first edition of this book was published in 1974, nearly twenty years ago It was written as a text book for an introductory course in continuum mechanics and aimed specifically at the junior and senior level of undergraduate engineering curricula which choose to introduce to the students at the undergraduate... Chairman of Mechanics Division at RPI, to whom the authors wish to express their heartfelt thanks Gratefully acknowledged is the financial support of the Ford Foundation under a grant which is directed by Dr S W Yerazunis, Associate Dean of Engineering The authors also wish to thank Drs V C Mow and W B Browner, Jr for their many useful suggestions Special thanks are given to Dr H A Scarton for painstakingly... states We wish to state that notwithstanding the additions, the present edition is still intended to be "introductory" in nature, so that the coverage is not extensive We hope that this new edition can serve a dual purpose: for an introductory course at the undergraduate level by omitting some of the "intermediate level" material in the book and for a beginning graduate course in continuum mechanics at... Transformation 11 Part B Tensors 281 Tensor - A Linear Transformation Let T be a transformation, which transforms any vector into another vector If T transforms a into c and b into d, we write Ta = c and Tb = d If T has the following linear properties: where a and b are two arbitrary vectors and a is an arbitrary scalar then T is called a linear transformation It is also called a second-order tensor or... July, 1993 xii Preface to the First Edition This text is prepared for the purpose of introducing the concept of continuum mechanics to beginners in the field Special attention and care have been given to the presentation of the subject matter so that it is within the grasp of those readers who have had a good background in calculus, some differential equations, and some rigid body mechanics For pedagogical... previous example, if fc=0 then the tensor T transforms all vectors into zero This tensor is the zero tensor and is symbolized by 0 Example 2B1.3 Consider a transformation T that transforms every vector into its mirror image with respect to a fixed plane Is T a tensor? Solution Consider a parallelogram in space with its sides represented by vectors a and b and its diagonal represented the resultant a + . class="bi x0 y0 w0 h0" alt="" Introduction to Continuum Mechanics This page intentionally left blank Introduction to Continuum Mechanics Third Edition W. . 1930- Introduction to continuum mechanics/ W.Michael Lai, David Rubin, Erhard Krempl - 3 rd ed. p. cm. ISBN 0 7506 2894 4 1. Contiuum mechanics