Application of strong SaS formulation and enhanced DQ method to 3D stress analysis of rectangular plates

Abstract

The paper focuses on application of the strong sampling surfaces (SaS) formulation and the enhanced differential quadrature (EDQ) method to the three-dimensional (3D) stress analysis of rectangular plates with different boundary and loading conditions. The SaS formulation is based on choosing the arbitrary number of SaS parallel to the middle surface in order to introduce the displacements of these surfaces as basic plate unknowns. Such choice of unknowns with the use of Lagrange polynomials in assumed approximations of displacements through the thickness leads to a robust plate formulation. The feature of the proposed approach is that all SaS are located at Chebyshev polynomial nodes. The use of outer surfaces is avoided that makes 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 can be applied efficiently to the obtaining of 3D exact solutions for plates with simply supported edges. To consider general boundary conditions, the EDQ method is proposed in which the displacements, strains and stresses are interpolated inside a rectangular domain using the Chebyshev-Gauss-Lobatto grid. Such a technique allows one not to utilize the higher order derivatives in equilibrium equations that significantly simplifies the implementation of the EDQ method.