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Download e-book for kindle: An Introduction to Continuum Mechanics by J. N. Reddy

By J. N. Reddy

ISBN-10: 1107025435

ISBN-13: 9781107025431

This best-selling textbook provides the ideas 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 provides a quick advent to linear viscoelasticity. The booklet is perfect for complex undergraduates and starting graduate scholars trying to achieve a powerful historical past within the simple ideas universal to all significant engineering fields, and should you will pursue extra paintings in fluid dynamics, elasticity, plates and shells, viscoelasticity, plasticity, and interdisciplinary components resembling geomechanics, biomechanics, mechanobiology, and nanoscience. The booklet positive factors 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 version comprises extra reasons, examples, and difficulties

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Sample text

2) If two vectors A and B are parallel to each other, then θ = 0, π, and sin θ = 0. Thus A × B = 0. Conversely, if A × B = 0, then either A or B is zero, or they are parallel vectors. It follows that the vector product of a vector with itself is zero; that is, A × A = 0. 16 VECTORS AND TENSORS (3) The distributive law still holds, but the order of the factors must be maintained: (A + B) × C = (A × C) + (B × C). 5 A(B · C), A · (B × C), A × (B × C). 19) The product A(B · C) is merely a multiplication of the vector A by the scalar B · C.

2 Free index A free index is one that appears in every expression of an equation, except for expressions that contain real numbers (scalars) only. Index i in the equation Fi = Ai Bj Cj and k in the equation Gk = Hk (2 − 3Ai Bi ) + Pj Qj Fk are free indices. 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.

Liquid is supplied to the tank at a rate of qi (m3 /day) and drained at a rate of q0 (m3 /day). , constant mass density ρ) and use the principle of conservation of mass to obtain a differential equation governing h(x, t). 5 (Surface tension). Forces develop at the interface between two immiscible liquids, causing the interface to behave as if it were a membrane stretched over the fluid mass. , inside the imaginary membrane) are subjected to a net force toward the interior. This force imbalance creates a tensile force in the membrane and is called surface tension (measured per unit length).

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An Introduction to Continuum Mechanics by J. N. Reddy

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