High-precision stress calculations for composite cylindrical shells with general boundary conditions using strong SaS formulation and extended DQ method

Abstract

This paper presents the three-dimensional (3D) stress analysis of cylindrical shells and panels with general boundary and loading conditions using the strong sampling surfaces (SaS) formulation and the extended differential quadrature (EDQ) method. 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 shell 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 shell formulation. The outer surfaces are not included into a set of SaS that allows one 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 cylindrical shells and panels with different 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 of the middle surface using the Chebyshev-Gauss-Lobatto grid and the Lagrange polynomials are also employed as basis functions. Such a technique allows the use of only first order derivatives in equilibrium equations (second order derivatives are not required) that significantly simplifies the implementation of the EDQ method.

Keywords:

• Cylindrical shells
• 3D stress analysis
• strong SaS formulation
• extended DQ method

Additional information

Funding

This work was supported by the Russian Science Foundation (Grant No. 18-19-00092).