By J. N. Reddy
This textbook on continuum mechanics displays the trendy view that scientists and engineers might be informed to imagine and paintings in multidisciplinary environments. The publication is perfect for complicated undergraduate and starting graduate scholars. The ebook positive factors: derivations of the elemental equations of mechanics in invariant (vector and tensor) shape and specializations of the governing equations to varied coordinate platforms; a variety of illustrative examples; chapter-end summaries; and workout difficulties to check and expand the knowledge of thoughts offered.
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Additional resources for An introduction to continuum mechanics: with applications
27) Since S0 is the projection of S along nˆ 0 (if the angle between nˆ and nˆ 0 is acute; otherwise the negative of it), S0 = S · nˆ 0 = Snˆ · nˆ 0 . 28) The scalar product nˆ · nˆ 0 is the cosine of the angle between the two unit normal vectors. 8(b). 4 Components of a Vector So far we have considered a geometrical description of a vector. We now embark on an analytical description based on the notion of its components of a vector. In following discussion, we shall consider a three-dimensional space, and the extensions to n dimensions will be evident.
In fact, the vector C may be considered to represent both the magnitude and the direction of the product A and B. Thus, a plane area may be looked upon as possessing a direction in addition to a magnitude, the directional character arising out of the need to specify an orientation of the plane in space. It is customary to denote the direction of a plane area by means of a unit vector drawn normal to that plane. To fix the direction of the normal, we assign a sense of travel along the contour of the boundary of the plane area in question.
7) Thus, we observe that we can obtain the components A1 , A2 , and A3 by taking the scalar product of the vector A with special vectors, which we denote as follows: e1 = e2 × e3 , [e1 e2 e3 ] e2 = e3 × e1 , [e1 e2 e3 ] e3 = e1 × e2 . 8) 10:34 P1: JzG Chapter02 CUFX197-Reddy 978 0 521 87044 3 October 3, 2007 34 Vectors and Tensors The set of vectors (e1 , e2 , e3 ) is called the dual basis or reciprocal basis. Notice from the basic definitions that we have the following relations: ei · e j = δ ij = 1, 0, i= j .