By J. N. Reddy

This best-selling textbook provides the options of continuum mechanics in an easy but rigorous demeanour. The booklet introduces the invariant shape in addition to the part kind of the fundamental equations and their purposes to difficulties in elasticity, fluid mechanics, and warmth move, and provides a quick creation to linear viscoelasticity. The publication is perfect for complex undergraduates and starting graduate scholars seeking to achieve a powerful heritage within the easy rules 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 components reminiscent of geomechanics, biomechanics, mechanobiology, and nanoscience. The booklet good points derivations of the elemental equations of mechanics in invariant (vector and tensor) shape and specification of the governing equations to numerous coordinate structures, and various illustrative examples, bankruptcy summaries, and workout difficulties. This moment variation comprises extra motives, examples, and difficulties.

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The governing equations for the study of deformation and stress of a continuous material are nothing but an analytical representation of the global laws of conservation of mass and balance of momenta and energy and the constitutive response of the continuum. They are applicable to all materials that are treated as a continuum. Tailoring these equations to particular problems and solving them constitutes the bulk of engineering analysis and design. The study of motion and deformation of a continuum (or a “body” consisting of continuously distributed material) can be broadly classified into four basic categories: (1) Kinematics (strain-displacement equations) (2) Kinetics (balance of linear and angular momentum) (3) Thermodynamics (first and second laws of thermodynamics) (4) Constitutive equations (stress–strain relations) Kinematics is the study of geometric changes or deformations in a continuum, without consideration of forces causing the deformation.

From Eq. 58) and from Eqs. 58) it follows that ¯m )Ai = (ej · e ¯m )Aj , A¯m = (ei · e ¯n )Aj = (ei · e ¯n )Ai . 60) The first two terms of Eqs. 60) give the transformation rules between the contragredient and the cogredient components in the two basis systems. By means of Eq. 44) we find that the basis systems are related by ¯s = (¯ e es · ej )ej = (¯ es · ej )ej . 61) ¯s = (¯ e es · e )ej = (¯ es · ej )e . 63) If we now write ¯s · ei , bsi ≡ e then we have in summary ¯s = ajs ej , e s ¯ = e bsi ei , A¯s = ajs Aj , cogredient law.

VECTOR ALGEBRA The following simple results follow from the definition in Eq. 6): (1) The scalar product is commutative: A · B = B · A. (2) If the vectors A and B are perpendicular to each other, then A · B = AB cos(π/2) = 0. Conversely, if A · B = 0, then either A or B is zero or A is perpendicular, or orthogonal, to B. (3) If two vectors A and B are parallel and in the same direction, then A · B = AB cos 0 = AB, because cos 0 = 1. Thus the scalar product of a vector multiplied with itself is equal to the square of its magnitude (|A| = A): A · A = AA = A2 .

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