On the accuracy of one-dimensional models for multilayered composite beams

The accuracy of 1-D models for composite beams made of linearly elastic orthotropic layers is estimated by means of the Prager-Synge hypercircle method. Statically admissible and kinematically afdmissible stress fields are derived, and asymptotic forms for the error bounds of 0(/z/i) and 0(/r/1)’ for h/l approaching zero are obtained for displacement-based laminated beam theories where the axial displacement is represented in terms of a given set of coordinate functions defined over the beam height. The condition of vanishing of relative mean-square error for h/l+ 0 is used to derive the constitutive law for the 1-D model. Explicit forms for the error bounds are given for the classical lamination theory, first order shear deformation theory and two higher order theories. Quantitative error bounds are calculated for simply supported multilayered beams under sinusoidal transverse loading. It is shown that, starting from a wise choice of coordinate functions, the accuracy of higher order theories can be almost independent of the beam lamination and up to 150 and 80 times higher than CLT and FSDT, respectively