By J. N. Reddy
This best-selling textbook provides the recommendations of continuum mechanics in an easy but rigorous demeanour. The publication 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 advent to linear viscoelasticity. The ebook is perfect for complicated undergraduates and starting graduate scholars seeking to achieve a powerful history within the uncomplicated rules universal to all significant engineering fields, and if you will pursue additional paintings in fluid dynamics, elasticity, plates and shells, viscoelasticity, plasticity, and interdisciplinary parts akin to geomechanics, biomechanics, mechanobiology, and nanoscience. The booklet 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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Extra info for An Introduction to Continuum Mechanics
Constitutive equations describe thermomechanical behavior of the material of the continuum, and they relate the dependent variables introduced in the kinetic description to those introduced in the kinematic and thermodynamic descriptions. 1 provides a brief summary of the relationship between physical principles and governing equations and physical entities involved in the equations. 1: The major four topics of study, physical principles used, resulting governing equations, and variables involved.
69) Next, we establish the relationship between the components of two different orthonormal coordinate systems, say, unbarred and barred [see Fig. 11(b)]. Consider the unbarred coordinate basis ˆ2 , e ˆ3 ) (ˆ e1 , e and the barred coordinate basis ˆ¯1 , e ˆ¯2 , e ˆ¯3 ). (e Then Eq. 70) where ij z = x3 ˆ¯i · e ˆj . =e x3 . 71) x3 b x3 x1 a y = x2 x1 x = x1 (a) x2 l11 = cos q l31 = cos a l23 = cos b q x1 x2 (b) Fig. 11: (a) A rectangular Cartesian coordinate system. (b) Barred and unbarred coordinate systems.
25) gives the same result with A = C = ˆ eB and B = A: ˆ eB × (A × ˆ eB ) = A − (ˆ eB · A)ˆ eB or A = (A · ˆ eB )ˆ eB + ˆ eB × (A × ˆ eB ). 3 Plane Area as a Vector The magnitude of the vector C = A×B is equal to the area of the parallelogram formed by the vectors A and B, as shown in Fig. 7(a). In fact, the vector C may be considered to represent both the magnitude and the direction of the product of 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.