By J. N. Reddy
This best-selling textbook offers the techniques of continuum mechanics in an easy but rigorous demeanour. The ebook 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 quick advent to linear viscoelasticity. The e-book is perfect for complicated undergraduates and starting graduate scholars trying to achieve a robust historical past within the uncomplicated rules universal to all significant engineering fields, and in case 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 booklet positive aspects 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 causes, examples, and difficulties
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Additional info for An Introduction to Continuum Mechanics
3 The Euler–Bernoulli hypothesis concerning the kinematics of bending deformation of a beam assumes that straight lines perpendicular to the beam axis before deformation remain (1) straight, (2) perpendicular to the tangent line to the beam axis, and (3) inextensible during deformation. These assumptions lead to the following displacement field: dv u1 (x, y) = −y , u2 = v(x), u3 = 0, (1) dx 7 PROBLEMS where (u1 , u2 , u3 ) are the displacements of a point (x, y, z) along the x, y, and z coordinates, respectively, and v is the vertical displacement of the beam at point (x, 0, 0).
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.
Thus the scalar product of a vector multiplied with itself is equal to the square of its magnitude (|A| = A): A · A = AA = A2 . 7) ˆ is given by A · ˆ (4) The orthogonal projection of a vector A in direction e e. (5) The scalar product also follows the distributive law: A·(B + C) = (A · B) + (A · C). 2 Vector product To see the need for the vector product, consider the concept of the moment due to a force about a point. 2at a point P, such as shown in Fig. 2(a). 9) where is the perpendicular distance from the point O to the force F (called lever arm).
An Introduction to Continuum Mechanics by J. N. Reddy