By J. N. Reddy

ISBN-10: 1107025435

ISBN-13: 9781107025431

This best-selling textbook offers the techniques of continuum mechanics in an easy but rigorous demeanour. The booklet introduces the invariant shape in addition to the part type of the fundamental equations and their functions to difficulties in elasticity, fluid mechanics, and warmth move, and provides a short advent to linear viscoelasticity. The e-book is perfect for complex undergraduates and starting graduate scholars trying to achieve a robust heritage within the easy ideas universal to all significant engineering fields, and in the event you will pursue extra paintings in fluid dynamics, elasticity, plates and shells, viscoelasticity, plasticity, and interdisciplinary components equivalent to geomechanics, biomechanics, mechanobiology, and nanoscience. The ebook positive factors derivations of the fundamental equations of mechanics in invariant (vector and tensor) shape and specification of the governing equations to varied coordinate platforms, and various illustrative examples, bankruptcy summaries, and workout difficulties. This moment version comprises extra causes, examples, and difficulties

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**Extra info for An Introduction to Continuum Mechanics**

**Sample text**

For example, x1 {X} = x2 and {Y } = {y1 y2 y3 } x3 denote a column matrix and a row matrix, respectively. Row and column matrices can be used to represent the components of a vector. 2 Matrix Addition and Multiplication of a Matrix by a Scalar The sum of two matrices of the same size is defined to be a matrix of the same size obtained by simply adding the corresponding elements. If [A] is an m × n matrix and [B] is an m × n matrix, their sum is an m × n matrix, [C], with cij = aij + bij for all i, j.

42) m=1 The summation index i or m is arbitrary as long as the same index is used for both A and e. The expression can be shortened further by omitting the summation sign and understanding that a repeated index means summation over all values of that index. 43) 24 VECTORS AND TENSORS This notation is called the summation convention. For example, an arbitrary vector A can be expressed in terms of its components [see Eq. 36)] as A = A · ei ei = (A · ej ) ej . 1 Dummy index The repeated index is called a dummy index because it can be replaced by any other symbol that has not already been used in that expression.

Also, the interchange of dot product and cross product A × B · C = A · B × C, or a cyclical permutation of the order of the vectors A × B · C = B × C · A, leaves the result unchanged [see Eq. 20)]. 1 General transformation laws In addition to the basis (e1 , e2 , e3 ) and its dual (e1 , e2 , e3 ), consider a second ¯2 , e ¯3 ) and its dual (¯ ¯2 , e ¯3 ). Now we can express the same (barred) basis: (¯ e1 , e e1 , e vector in four ways: A = Ai ei = Aj ej , in unbarred basis, ¯m = A¯n e ¯n , in barred basis.

### An Introduction to Continuum Mechanics by J. N. Reddy

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