A comparison of various 3-D approaches for the analysis of laminated composite structures

Abstract

Three computational approaches for 3-D analysis of laminated composite plates are presented. These are displacement assumed approach, displacement assumed/equilibrium approach and mixed two-field approach. The fundamental concept in all of the three approaches is that “deficient” polynomials have to be used for the through-the-thickness displacement approximation. Bernstein polynomials, having discontinuous first derivatives at the interfaces, are used as approximation functions in the through-the-thickness direction. The examples of a double-sine distributed surface load on 3-ply, 9-ply, and sandwich plates examined by Pagano are solved. It is shown that the results obtained with all three present approaches agree excellently with the closed form solution, for the length-to-thickness aspect ratios ranging from 2–100. A comparison between the results obtained with the deficient and with the continuously differentiable displacement approximations is also presented. This reveals that polynomial approximations that are continuously differentiable through the whole thickness of a laminate, provide qualitatively incorrect transverse stresses at the interfaces. By increasing the degree of the polynomial, one gets two distinct from the top and from the bottom limits for any transverse stress component on the interfaces. On the contrary, when using deficient approximation functions one obtains the same from the top and from the bottom limits for the transverse stresses on the interfaces.