An Introduction to Continuum Mechanics by J. N. Reddy

By J. N. Reddy

This best-selling textbook offers the thoughts of continuum mechanics in an easy but rigorous demeanour. The booklet introduces the invariant shape in addition to the part type of the elemental equations and their purposes to difficulties in elasticity, fluid mechanics, and warmth move, and gives a short creation to linear viscoelasticity. The booklet is perfect for complex undergraduates and starting graduate scholars seeking to achieve a powerful history within the uncomplicated ideas universal to all significant engineering fields, and in case you will pursue extra paintings in fluid dynamics, elasticity, plates and shells, viscoelasticity, plasticity, and interdisciplinary parts akin to geomechanics, biomechanics, mechanobiology, and nanoscience. The booklet beneficial properties derivations of the elemental equations of mechanics in invariant (vector and tensor) shape and specification of the governing equations to numerous coordinate platforms, and diverse illustrative examples, bankruptcy summaries, and workout difficulties. This moment variation contains extra factors, examples, and difficulties

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These four topics are the subjects of Chapters 3 through 6, respectively. Mathematical formulation 6 INTRODUCTION of the governing equations of a continuous medium necessarily requires the use of vectors and tensors, objects that facilitate invariant analytical formulation of the natural laws. Therefore, it is useful to study certain operational properties of vectors and tensors first. Chapter 2 is dedicated for this purpose. Although the present book is self-contained for an introduction to continuum mechanics or elasticity, other books are available that may provide an advanced treatment of the subject.

2(a). 9) where is the perpendicular distance from the point O to the force F (called lever arm). If r denotes the vector OP and θ the angle between r and F such that 0 ≤ θ ≤ π, we have = r sin θ and thus M = F r sin θ. 10) A direction can now be assigned to the moment. Drawing the vectors F and r from the common origin O, we note that the rotation due to F tends to bring r into F, as can be seen from Fig. 2(b). We now set up an axis of rotation eM F (a) O r  M θ P F (b) O θ r Fig. 2: (a) Representation of a moment about a point.

Another example is Ai = 2 + Bi + Ci + Di + (Fj Gj − Hj Pj )Ei . This expression contains three equations (i = 1, 2, 3). The expressions Ai = Bj Ck , Ai = Bj , and Fk = Ai Bj Ck do not make sense and should not arise, because the indices on both sides of the equal sign do not match. One must be careful when substituting a quantity with an index into an expression with indices or solving for one quantity with index in terms of the others with indices in an equation. For example, consider the equations pi = ai bj cj and ck = di ei qk .

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