A NEW LOOK AT SHEAR CORRECTION FACTORS AND WARPING FUNCTIONS OF ANISOTROPIC LAMINATES

Shear warpings of a composite laminate are shown to be functions of its stacking sequence, its ply angles, and the material properties of layers. Moreover, a new formulation of shear correction factors is derived by matching the exact shear stress resultants and shear strain energy with those of the equivalent first-order shear deformation theory. Without solving a plate problem with specified loading and boundary conditions, approximate analytical shear warping functions of a composite laminate can be derived by using the continuity conditions of in-plane displacements and interlaminar shear stresses and the free shear stress conditions on the bonding surfaces. The approach results in a layerwise higher-order shear deformation theory that contains most shear deformation theories as special cases and reveals the shear coupling effect of angle-ply laminates. A combination of the present method of deriving shear warping functions and the new formulation of shear correction factors can be used to obtain fairly accurate a priori estimates of shear correction factors for the use of the first-order shear deformation theory in analyzing highly anisotropic laminates. For isotropic plates, the shear correction factor obtained is 5/6. For orthotropic laminates, the shear correction factors obtained are compared with those results in the literature that are obtained by using predictor-corrector procedures. Shear correction factors for some symmetric and asymmetric angle-ply laminates, of which the shear correction factor accounting for the shear coupling effect is non-trivial, are also presented.