Continuum Mechanics by D. S. Chandrasekharaiah and Lokenath Debnath (Auth.)

By D. S. Chandrasekharaiah and Lokenath Debnath (Auth.)

A close and self-contained textual content written for rookies, Continuum Mechanics bargains concise insurance of the elemental innovations, basic ideas, and purposes of continuum mechanics. with out sacrificing rigor, the transparent and easy mathematical derivations are made obtainable to loads of scholars with very little past historical past in good or fluid mechanics. With the inclusion of greater than 250 totally worked-out examples and 500 labored workouts, this e-book is sure to turn into a regular introductory textual content for college kids in addition to an necessary reference for pros.

Key Features
* presents a transparent and self-contained therapy of vectors, matrices, and tensors in particular adapted to the desires of continuum mechanics
* Develops the strategies and rules universal to all components in strong and fluid mechanics with a typical notation and terminology
* Covers the basics of elasticity idea and fluid mechanics

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Extra resources for Continuum Mechanics

Example text

1 0 . In the system of axes with base vectors ef, show that a = (a · ef) e, for every vector a. 1 1 . 18). 1 2 . The absolute value of the scalar triple product [a, b, c] represents the volume of the parallelopiped whose adjacent edges with a common corner are represented by a, b, c. Justify this statement. 30 1 SUFFIX NOTATION 1 3 . 20). Deduce that a x (b x c) = (a x b) x c if and only if b x (c x a) = 0. Interpret the condition geometrically. 1 4 . ,,, dijûji and 0 2 dijdij. 1 5 . Represent the following matrix as a sum of a symmetric matrix and a skewsymmetric matrix: \flu\ = 2 0 4 -6 8 0 8 10 - 8 1 6 .

Ii) Let [üij] be a 3 X 3 matrix related to the Jt, system. For an arbitrary vector with components bi9 if a^bj are components of a vector, then αϋ are components of a tensor. Proof (i) Since α& is a scalar, we have α,-ή,- = a\b\. 28) that ap = aipa·. Thus at obey the transformation rule of a vector. Hence at are components of a vector. (ii) Put Ci = dijbj in all coordinate systems. 29) because bx and c, are components of vectors, by data. 30) that arq = airajqa\j. Thus, au obey the transformation rule of a second-order tensor.

8 EXERCISES 1. State which of the following expressions are meaningful in the suffix notation. Write out the unabridged versions of the meaningful expressions: (i) «„ (ii) aubj (iii) aubi (iv) aubi (v) aubjj (vi) aubü (vii) arsbsr (viii) arsbss (ix) aijkbik 2 . Which of the following expressions have the same meaning? dijbj, arsbs, apqbp, a^bj, apqbpbq, asrbsbr 3 . State which of the following equations are meaningful in the suffix notation. (i) Xg = (Xijyj (ii) yâ = (iii) au = ctuOLjj (iv) au = otipotjp (v) au = oLimoijnbmn (vii) au = otimajnbrs aikxk (vi) ars =

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