New PDF release: An Expedition to Continuum Theory

By Wolfgang H. Müller

ISBN-10: 9400777981

ISBN-13: 9789400777989

ISBN-10: 940077799X

ISBN-13: 9789400777996

This ebook introduces box concept as required in sturdy and fluid mechanics in addition to in electromagnetism. It comprises the mandatory utilized mathematical framework of tensor algebra and tensor calculus, utilizing an inductive procedure relatively fitted to newbies. it truly is aimed at undergraduate periods in continuum thought for engineers typically, and extra in particular to classes in continuum mechanics. scholars will achieve a legitimate uncomplicated realizing of the topic in addition to the facility to resolve engineering difficulties by way of utilizing the final legislation of nature when it comes to the balances for mass, momentum, and effort together with material-specific kin when it comes to constitutive equations, therefore studying find out how to use the speculation in perform for themselves. this can be facilitated by means of various examples and difficulties supplied in the course of the text.

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Extra resources for An Expedition to Continuum Theory

Sample text

Observe that bound indices always appear in co-/contravariant pairs. 15). 5: The co-/contravariant components of the position vector in cylindrical and spherical coordinates Show by using the Eqs. 15) that the following relations hold for the co-contravariant components of the position vector, x, in cylindrical and spherical coordinates, respectively: x1 ¼ r ; x2 ¼ 0 ; x3 ¼ z; ðzÞ ðzÞ ðzÞ x1 ðzÞ ¼ r; x2 ¼ 0; x3 ¼ 0: ðzÞ ð2:4:19Þ ðzÞ Explain the difference between coordinate lines and the position vector.

In what follows we shall learn about the corresponding mathematical tools. However, we must realize that mathematics has nothing to do with reality and we should never forget that it is nothing more but a neat ‘‘language’’ conceived by the human brain to model reality. Obviously, in order to determine the five fields, five equations are required, the so-called field equations. The foundation of these equations are the balance of mass (a scalar relation), the balance of momentum (a vector equation with three components), and the balance of energy (a scalar equation).

In general the tensor concepts presented so far have been known for a long time. ’’ In this context the article by Ericksen [6] in the Encyclopedia of Physics, Sects. I, II, and (in parts) III should be mentioned first. Moreover, the book by Green and Zerna [7] is to be recommended, in particular Sects. 10. Finally Chaps. 1, 12 and, notably, Sect. 13 (with many exotic coordinate transformations) in the book by Flügge [8] should be pointed out. Several notions, such as Mohr’s circle or yield stress, were used in this section without further explanations.

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An Expedition to Continuum Theory by Wolfgang H. Müller

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