Anisotropic Elastic Plates by Chyanbin Hwu

By Chyanbin Hwu

Anisotropic Elastic Plates locate huge functions as structural parts in glossy know-how. The plates are thought of to be subjected not to basically inplane a lot but in addition transverse so much. aircraft difficulties, plate bending difficulties in addition to stretching-bending coupling difficulties are all handled during this booklet. as well as the advent of the idea of anisotropic elasticity that comes with complicated variable tools - Lekhnitiskii formalism and Stroh formalism- a number of very important matters also are mentioned resembling wedges, interfaces, cracks, holes, inclusions, touch difficulties, piezoelectric fabrics, thermal stresses and boundary point research.

Anisotropic Elastic Plates additionally collects over 100 difficulties and options. This e-book is an invaluable source for engineers and researchers in composite materials.

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2 Plane Deformation Let us assume that the body considered in the case of generalized plane deformation has at each point a plane of elastic symmetry normal to the generator, that is, normal to the z-axis. In other words, the body is composed of the monoclinic materials with the symmetry plane at z=0 for which C14 = C15 = C24 = C25 = C34 = C35 = C46 = C56 = 0. 40), we have u = U(x, y) − ω3 y + u0 , v = V(x, y) + ω3 x + v0 , w = w0 . 41) Consequently, γyz = γxz = εz = 0, and on the basis of the equations of the generalized Hook’s law, τxz = τyz = 0 and σz = − 1 (S13 σx + S23 σy + S36 τxy ).

In the literature, there are two different complex variable formulations for two-dimensional linear anisotropic elasticity. One is the Lekhnitskii formalism (Lekhnitskii, 1963, 1968) which starts with the equilibrated stress functions followed by compatibility equations, and the other is the Stroh formalism (Stroh, 1958, 1962; Ting, 1996) which starts with the compatible displacements followed by equilibrium equations. The Lekhnitskii formalism excerpted from the two well-known books (Lekhnitskii, 1963, 1968) will be presented in this chapter, whereas the Stroh formalism excerpted from the other well-known book (Ting, 1996) will be presented in the next chapter.

Since the variable x3 may appear as a parameter in the elasticity equations (for example, if ε33 = 0 through integration we get u3 which will depend on x3 ), the problem of plane stress is not truly two dimensional. However, by dealing with the mean values of the displacements and stresses, and supposing that the faces of the thin plates are free of applied loads and all external surface forces acting on the edge of the plate lie in the plane parallel to the middle plane, a mathematical truly two-dimensional problem can be obtained for a thin plate (Sokolnikoff, 1956), which is called the problems of generalized plane stress.

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