By B. M. Fraeijs de Veubeke (auth.)
This ebook relies on lecture notes of the overdue Professor de Veubeke. the topic is gifted at a degree compatible for graduate scholars in engineering, physics, or arithmetic. a few publicity to linear algebra, complicated research, variational calculus, or simple continuum mechanics will be valuable. the 1st 3rd of the publication comprises the basics of the idea of elasticity. Kinematics of constant media, the notions of pressure and equilibrium, conservation of strength, 'and the elastic constitutive legislation are each one taken care of first in a nonlinear context, then really expert to the linear case. the rest of the booklet is given to 3 vintage purposes of the speculation, each one supplemented by way of unique re sults according to using complicated variables. every one of the 3 themes - Saint-Venant's conception of prismatic beams, airplane deformations, and the bending of plates - is first pre sented and analyzed mostly, then rounded out with a variety of particular and infrequently novel examples. the subsequent notational conventions are mostly in strength, other than the place famous on the contrary: decrease case boldface letters denote vectors or triples of Cartesian co ordinates, top case boldface letters denote three x three matrices, repeated reduce case Latin subscripts are summed over (1,2,3), and non-repeated reduce case Latin subscripts are assumed to variety over (1,2,3).
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Extra info for A Course in Elasticity
9) should be transformed to material coordinates associated with each layer using the transformation relations. 4. 1. Introduction Historically, two distinct approaches have been followed in developing nonlinear finite element models of structural problems. Each of the approaches can be used to develop the displacement type, force type, or mixed/hybrid type finite element models. The first approach is based on a laminate theory, in which the 3-D elasticity equations are reduced to 2-D equations through certain kinematic assumptions, as described in section 2.
5 ::; alb ::; 5. The effect of bending-stretching coupling is the most for two-layer laminates, and the orthotropic solution is rapidly approached as the number of plies is increased. 17. 3US side-to-thickness ratio a/h for simpl) supported symmetric cross-ply (0/90/90/0) square laminates. 0 I~ "ift -..... 18. Buckling load (N) versus side-to-thickness ratio a/h for simpl) supported antisymmetric cross-ply (0/90)n square laminates. 19. Buckling load (N = N cr b2 I E 2 h 3 ) versus plate aspect ratio (alb) of antisymmetric angle-ply laminates under uniaxial compressive edge load.
1" ro 5 1 I IIII M I 1 I I I I 1 1 "! 28. Fundamental frequency versus lamination antisymmetric angle-ply square laminates. 29. Fundamental frequency (w) versus modulus ratio EI/E2 of antisymmetric angle-ply square laminates. 31. , exz i= 0 and eyz i= 0), and rotary inertia is to lower the fundamental frequencies. As the number of layers increases, the coupling decreases. The effect of shear deformation decreases with increasing values of a/h. This decrease is slower for eight-layer plates than two-layer plates.
A Course in Elasticity by B. M. Fraeijs de Veubeke (auth.)