Hierarchic layer models for anisotropic laminated plates

Abstract

Hierarchic p-refined formulations based on several macroscopic layer models are presented to analyze anisotropic laminated plates. Analysis of composite laminated plates is implemented with full discrete-layer, partial discrete-layer, and equivalent single-layer models, respectively. In the first approach all three displacement components are expressed as the product of one- and two-dimensional interpolation functions for applying the three-dimensional elasticity theory to each layer. Second approach considers thickness-wise variation of in-plane displacement in individual layers and a constant value of out-of-plane displacement across the plate thickness. The third approach assumes that a heterogeneous laminated plate stacked with several laminae is treated as a shell element using hierarchic interpolation functions. The integrals of Legendre polynomials and Gauss-Lobatto technique are adopted to interpolate displacement fields and to implement numerical quadrature, respectively. The validity and characteristics of the proposed numerical layer models are tested on anisotropic multilayered plates and sandwich plates, and compared with the values available in the published literature based on analytical methods and h-refined layer models.