High-precision computation in mechanics of composite structures by a strong sampling surfaces formulation: Application to angle-ply laminates with arbitrary boundary conditions

Abstract

This paper presents the three-dimensional analysis of laminated composite rectangular plates with general boundary and loading conditions using the strong sampling surfaces (SaS) formulation and the extended differential quadrature (EDQ) method proposed by the first author. The strong SaS formulation is based on the choice of SaS parallel to the middle surface and located at Chebyshev polynomial nodes to introduce the displacements of these surfaces as plate unknowns. This choice of unknowns with the use of Lagrange polynomials in the through-thickness approximations of displacements, strains and stresses leads to an efficient laminated plate formulation. The outer surfaces and interfaces are not included into a set of SaS that makes it possible to minimize uniformly the error due to Lagrange interpolation. Therefore, the strong SaS formulation based on direct integration of the equilibrium equations of elasticity in the transverse direction in conjunction with the EDQ method can be applied effectively to high-precision calculations for the composite rectangular plates with different boundary conditions. This due to the fact that in the SaS/EDQ formulation the displacements, strains and stresses of SaS are interpolated in a rectangular domain using the Chebyshev-Gauss-Lobatto grid and Lagrange polynomials are also utilized as basis functions. Such a technique allows the use of only first order derivatives in the equilibrium equations that simplifies the implementation of the EDQ method.