Assessment of computational models for multilayered anisotropic plates

Abstract

A study is made of the effects of variation in the lamination and geometric parameters of multilayered anisotropic (nonorthotropic) plates on the accuracy of the static and vibrational responses predicted by eight modeling approaches, based on two-dimensional shear-deformation theories. Two key elements distinguish the present study from previous studies reported in the literature: (1) the standard of comparison is taken to be the exact three-dimensional elasticity solutions, and (2) quantities compared are not limited to gross response characteristics (e.g. vibration frequencies, strain energy components, average through-the-thickness displacements and rotations), but include detailed through-the-thickness distributions of displacements, stresses and strain energy densities. The modeling approaches considered include first-order shear-deformation theory (with five displacement parameters to characterize the deformation in the thickness direction); first-order theory with the transverse normal stresses and strains included (six displacement parameters); two higher-order theories (with 11 and 18 displacement parameters); a simplified higher-order theory (with five displacement parameters); discrete-layer theory (with piecewise linear variation of the in-plane displacements in the thickness direction); simplified discrete-layer theory with the continuity of transverse stresses imposed at layer interfaces to reduce the number of displacement parameters to five; and a predictor-corrector approach, used in conjunction with the first-order shear-deformation theory (with five displacement parameters in the predictor phase). Based on the numerical studies conducted, the predictor-corrector approach appears to be the most effective among the eight modeling approaches considered. For antisymmetrically laminated rectangular plates the response quantities obtained by the predictor-corrector approach are shown to be in close agreement with exact three-dimensional elasticity solutions for a wide range of lamination and geometric parameters. The potential of this approach for predicting the response of multilayered anisotropic plates with complicated geometry is also discussed.