By J. N. Reddy
This best-selling textbook provides the innovations of continuum mechanics in an easy but rigorous demeanour. The publication introduces the invariant shape in addition to the part kind of the elemental equations and their purposes to difficulties in elasticity, fluid mechanics, and warmth move, and gives a short advent to linear viscoelasticity. The publication is perfect for complicated undergraduates and starting graduate scholars seeking to achieve a robust historical past within the uncomplicated ideas universal to all significant engineering fields, and if you happen to will pursue additional paintings in fluid dynamics, elasticity, plates and shells, viscoelasticity, plasticity, and interdisciplinary components comparable to geomechanics, biomechanics, mechanobiology, and nanoscience. The e-book beneficial properties derivations of the elemental equations of mechanics in invariant (vector and tensor) shape and specification of the governing equations to varied coordinate platforms, and diverse illustrative examples, bankruptcy summaries, and workout difficulties. This moment variation comprises extra motives, examples, and difficulties
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Extra info for An Introduction to Continuum Mechanics
An identity matrix, denoted by [I], is a diagonal matrix whose elements are all 1’s. Examples of a diagonal and an identity matrix are given below: 5 0 0 0 1 0 0 0 0 −2 0 0 0 1 0 0 [I] = 0 0 1 0, 0 0 1 0. 0 0 0 3 0 0 0 1 The sum of the diagonal elements is called the trace of the matrix. 1 The word “matrix” was first used in 1850 by James Sylvester (1814–1897), an English algebraist. However, Arthur Caley (1821–1895), professor of mathematics at Cambridge, was the first one to explore properties of matrices.
We do not consider such situations in this book. 1 2 INTRODUCTION covered in this book, are described in the examples discussed next. At this stage of discussion, it is sufficient to rely on the reader’s intuitive understanding of concepts from basic courses in fluid mechanics, heat transfer, and mechanics of materials about the meaning of stress and strain and what constitutes viscosity, conductivity, modulus, and so on used in the examples. Problem 1 (solid mechanics) We wish to design a diving board (which enables a swimmer to gain momentum before jumping into the pool) of given length L, assumed to be fixed at one end and free at the other end (see Fig.
One can show that (a) eijk eijk = 6, (b) Ai Aj eijk = 0, and (c) eimn ejmn = 2δij . An alternative formula [to Eq. 50)] to determine the value of eijk is eijk = 12 (i − j)(j − k)(k − i) for any i, j, k = 1, 2, 3. 51) 26 VECTORS AND TENSORS j k i• + i• •j + j k • • • • •k i• - i• •j (a) - •k (b) Fig. 10: (a) A natural cyclic order is going from any index to the next in the order it appears alphabetically (going from k to i makes it cyclic). (b) Opposite to a natural cyclic order is going in a direction opposite to that of a natural cyclic order.
An Introduction to Continuum Mechanics by J. N. Reddy