Efficient linear transverse normal stress analysis of layered composite plates

Abstract

Based on the first order shear deformation theory (FSDT) a method is developed for calculating the transverse normal stress (in thickness direction) in layered composite plate structures. Two steps are necessary. First, the transverse shear stress calculation, and second, relying on the results of the first step, the transverse normal stress evaluation. In the first step strain derivatives are substituted with transverse shear forces which in turn are obtained from the corresponding material law. This leads to a derivative-free process which is numerically more accurate than a pure equilibrium approach. As a second step the transverse normal stress is equilibrated to the derivatives of the transverse shear stresses with respect to the in-plane coordinates. As compared to the standard equilibrium approach, the proposed procedure reduces the order of differentiation by one. Thus, only quadratic shape functions are necessary for evaluating the required derivatives on the element level. Numerical examples for symmetric cross-ply and antisymmetric angle-ply laminates show that the exact three-dimensional elasticity solution is very closely approximated. This holds for thin as well as rather thick plates with a slenderness ratio down to five. In contrast to many recently established methods, either higher order lamination theories or layerwise theories, the approach is easily applicable to finite elements, since only C 0-continuity is necessary and the numerical effort is low.