By J. N. Reddy

ISBN-10: 1107025435

ISBN-13: 9781107025431

This best-selling textbook provides the innovations of continuum mechanics in an easy but rigorous demeanour. The ebook introduces the invariant shape in addition to the part kind of the fundamental equations and their functions to difficulties in elasticity, fluid mechanics, and warmth move, and gives a short advent to linear viscoelasticity. The e-book is perfect for complex undergraduates and starting graduate scholars trying to achieve a powerful heritage within the easy rules universal to all significant engineering fields, and should you will pursue additional paintings in fluid dynamics, elasticity, plates and shells, viscoelasticity, plasticity, and interdisciplinary parts comparable to geomechanics, biomechanics, mechanobiology, and nanoscience. The publication positive aspects derivations of the fundamental equations of mechanics in invariant (vector and tensor) shape and specification of the governing equations to numerous coordinate structures, and various illustrative examples, bankruptcy summaries, and workout difficulties. This moment version contains extra factors, examples, and difficulties

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Example text

8 Rewrite the expression eijk Ai Bj Ck in vector form. Solution: Examining the indices in the permutation symbol and those of the coefficients, it is clear that there are three possibilities: (1) A and B must have a cross product between them and the resulting vector must have a dot product with C; (2) B and C must have a cross product between them and the resulting vector must have a dot product with A; or (3) C and A must have a cross product between them and the resulting vector must have a dot product with B.

2 Let A and B be any two vectors in space. , parallel) and perpendicular to vector B. Solution: The component of A along B is given by (A · ˆ eB ), where ˆ eB = B/B is the unit vector in the direction of B. The component of A perpendicular to B and in the plane of A and B is given by the vector triple product ˆ eB × (A × ˆ eB ). Thus, A = (A · ˆ eB )ˆ eB + ˆ eB × (A × ˆ eB ). 26) Alternatively, Eq. 25) gives the same result with A = C = ˆ eB and B = A: ˆ eB × (A × ˆ eB ) = A − (ˆ eB · A)ˆ eB or A = (A · ˆ eB )ˆ eB + ˆ eB × (A × ˆ eB ).

A] =   .  ··· ··· ··· ··· . . .   .. αam1 αam2 . . αamn am1 am2 . . amn Matrix addition has the following properties: (1) Addition is commutative: [A] + [B] = [B] + [A]. (2) Addition is associative: [A] + ([B] + [C]) = ([A] + [B]) + [C]. (3) There exists a unique matrix [0], such that [A] + [0] = [0] + [A] = [A]. The matrix [0] is called zero matrix when all elements are zeros. (4) For each matrix [A], there exists a unique matrix −[A] such that [A] + (−[A]) = [0]. (5) Addition is distributive with respect to scalar multiplication: α([A] + [B]) = α[A] + α[B].

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An Introduction to Continuum Mechanics by J. N. Reddy

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