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

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

An in depth and self-contained textual content written for novices, Continuum Mechanics bargains concise insurance of the elemental strategies, normal rules, and purposes of continuum mechanics. with out sacrificing rigor, the transparent and straightforward mathematical derivations are made available to various scholars with very little prior historical past in stable or fluid mechanics. With the inclusion of greater than 250 absolutely worked-out examples and 500 labored routines, this booklet is bound to develop into a typical introductory textual content for college students in addition to an critical reference for pros.

Key Features
* offers a transparent and self-contained remedy of vectors, matrices, and tensors in particular adapted to the desires of continuum mechanics
* Develops the strategies and ideas universal to all components in stable and fluid mechanics with a standard notation and terminology
* Covers the basics of elasticity idea and fluid mechanics

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Example text

Contraction operations are applicable to tensors of all orders (higher than 1); each such operation reduces the order of a tensor by 2. Some illustrations follow. PROPERTY 6 If au and bu are components of second-order tensors A and B and c,· are components of a vector c, then (i) auCj are components of a vector, called the product of A and c in that order and denoted Ac; (ii) aikbkj are components of a second-order tensor, called the product of A. and B in that order and denoted AB; (iii) a^b^ is a scalar, called the scalar product of A and B and denoted A · B.

17) show that [a 0 ] is a proper orthogonal matrix. The coordinate transformations determined by (Xij are therefore called proper orthogonal transformations. Only such coordinate transformations are dealt with in our further discussions; we will refer to them simply as coordinate transformations (with no adjective). 7). 7). We now show that precisely the same transformation rules hold for the components of an arbitrary vector when it is referred to two systems of coordinates (with the same fixed origin).

And B in that order and denoted AB; (iii) a^b^ is a scalar, called the scalar product of A and B and denoted A · B. Proof (i) We note that, by property 5(i), auck are components of a thirdorder tensor and a^Cj can be obtained from a^ck by a contraction operation (namely, changing k toy). We have to show that a^Cj are components of a vector. 15) This transformation rule shows that a^Cj are indeed components of a vector. The result illustrates that a third-order tensor reduces to a vector as a result of a contraction operation.

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