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By S.D. Akbarov

This publication is the frrst to target mechanical elements of fibrous and layered composite fabric with curved constitution. by way of mechanical points we suggest statics, vibration, balance loss, elastic and fracture difficulties. by means of curved constructions we suggest that the reinforcing layers or fibres will not be immediately: they've got a few preliminary curvature, bending or distortion. This curvature may possibly happen due to layout, or by reason of a few technological technique. over the last twenty years, we and our scholars have investigated difficulties in relation to curved composites intensively. those investigations have allowed us to check stresses and lines in areas of a composite that are small in comparison to the curvature wavelength. those new, actual, recommendations have been constructed within the framework of continuum theories for piecewise homogeneous our bodies. We use the precise equations of elasticity or viscoelasticity for anisotropic our bodies, and view linear and non-linear difficulties within the framework of this continuum idea in addition to within the framework of the piecewise homogeneous version. For the latter the strategy of resolution of comparable difficulties is proposed. we now have focussed our consciousness on self-balanced stresses which come up from the curvature, yet have supplied enough info for the learn of different results. We think that the reader is aware the idea of elasticity for anisotropic our bodies, with partial differential equations and imperative variations, and likewise with the Finite point Method.

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111112 ~1~2 + (~1 - ~2 )2111112 sin e . 5) . 5), we fmd cr23 ::::! -E't sin 8 . 6) The maximum values of the self-balanced stresses are of order E. 3. 5) are satisfied. 7) To estimate the results we assume that 1']0)::::! 8) shows that for tension-compression along the OXl axis, the selfbalanced stress is of order E2 PI . Thus, in this and the previous two sections we have given a complete study of the quasi-homogeneous stress states in composite materials with regular small-scale curvature in the structure under the influence of pure shear and tension-compression loads.

_ (0) (1). 2 (2) . l (2) , , respectively. t: j a. P P a. 0 + (1- 87 )(8:-8-:- + 8:-8-:-)G .. 3 -G~3) ){818~ +8~8~ )(8 3 8 2 + 8 2 8 3 ))8~8~ + 8~ 8~) (8 1 8 3 + 8 3 8 1 \1 L~ 1 J 1 J ~ a. P a. P ~ 1 J 1 J ~ a. P a. l(O) corresponds to a homogeneous body with rectilinear orthotropy. 4) Here L ja are the differential operators of Lame's equation for the rectilinear orthotropic body 24 CHAPTER 1 82 IJ. ) IJ. 8 2 82 +0-:- ( l-ocJ G 0.. --po-:--. ~~!! 8xilXIJ. ~ Ox ~ ~ 0. 2 _ 1 o IJ. = [ A. + ( 1-0-:- ) G.

7). 7). 2. THE SMALL PARAMETER METHOD We now consider the small parameter method for the solution of the equations. 7) we obtain the following equations for the n-th approximation: The equation of motion: L, u(n) JIJ. IJ. ~ sine~)u(n-l) _~[II~~) sin 2 e~lu(n-2) Ox~ IJ. Oxj rlJa~ Ox~ IJ. 8) the boundary conditions on the surface portion SI, where the stresses are given: _ (1). --N 1, [ 11"IJXI-'A sme _ "'-. (n-I) uU a :::>.. UX~ (2), 2 +11"IJXI-'A sm e _ "'-. 11) refer to an arbitrary approximation.

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