High-precision computation in mechanics of composite structures by a strong SaS formulation: Implementation for laminated cylindrical shells and panels with clamped and free edges

Abstract

The paper focuses on the three-dimensional (3D) stress analysis of laminated composite cylindrical shells and panels with general boundary and loading conditions using the strong sampling surfaces (SaS) formulation and the extended differential quadrature (EDQ) method, recently developed by the first author. In the strong SaS formulation, the SaS parallel to the middle surface and located at Chebyshev polynomial nodes in layers are utilized to introduce displacements of these surfaces as shell unknowns. This choice of unknowns with the use of Lagrange polynomials in the approximation of displacements, strains and stresses through the thickness leads to an efficient shell formulation. The outer surfaces 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 thickness direction in conjunction with the EDQ method can be effectively applied to high-precision calculations for laminated composite cylindrical shells and panels with arbitrary boundary conditions. This is due to the fact that in the SaS/EDQ formulation the displacements, strains and stresses of SaS are interpolated in a rectangular domain, which is mapped into the middle surface by using the Chebyshev-Gauss-Lobatto grid and the Lagrange polynomials are also utilized as basis functions.