By J. N. Reddy

ISBN-10: 1107025435

ISBN-13: 9781107025431

This best-selling textbook provides the options of continuum mechanics in an easy but rigorous demeanour. The ebook introduces the invariant shape in addition to the part kind of the elemental equations and their functions to difficulties in elasticity, fluid mechanics, and warmth move, and provides a quick creation to linear viscoelasticity. The booklet is perfect for complicated undergraduates and starting graduate scholars seeking to achieve a robust heritage within the simple rules universal to all significant engineering fields, and when you will pursue additional paintings in fluid dynamics, elasticity, plates and shells, viscoelasticity, plasticity, and interdisciplinary components reminiscent of geomechanics, biomechanics, mechanobiology, and nanoscience. The publication gains derivations of the fundamental equations of mechanics in invariant (vector and tensor) shape and specification of the governing equations to numerous coordinate platforms, and various illustrative examples, bankruptcy summaries, and workout difficulties. This moment version comprises extra motives, examples, and difficulties

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**Additional info for An Introduction to Continuum Mechanics**

**Sample text**

N (b) For reference purposes we label the sides of the tetrahedron by 1, 2, and 3 and the normals and surface areas by (ˆ n1 , S1 ), (ˆ n2 , S2 ), and(ˆ n3 , S3 ), respectively (that is, Si is the surface area of the plane perpendicular to the ith line or n ˆ i vector), as shown in Fig. 8(b). 1 Components of a vector So far we have considered a geometrical description of a vector. We now embark on an analytical description of a vector based on the notion of its components. In the following discussion, we shall consider a three-dimensional space, and the extensions to n dimensions will be evident.

It can be seen from Fig. 5 that the product A · (B × C), except for the algebraic sign, is the volume of the parallelepiped formed by the vectors A, B, and C. B×C A C B Fig. 5: Scalar triple product representation of the volume of a parallelepiped. We note the following properties of a scalar triple product: (1) The dot and cross can be interchanged without changing the value: A · B × C = A × B · C ≡ [ABC]. 20) (2) A cyclical permutation of the order of the vectors leaves the result unchanged: A · B × C = C · A × B = B · C × A ≡ [ABC].

Such a hypothetical continuous matter is termed a continuum. 1 The continuum assumption allows us to shrink an arbitrary volume of material to a point, in much the same way as we take the limit in defining a derivative, so that we can define quantities of interest at a point. For example, mass density (mass per unit volume) of a material at a point is defined as the ratio of the mass ∆m of the material to its volume ∆V surrounding the point in the limit that ∆V becomes a value 3 , where is small compared with the mean distance between molecules ∆m .

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