Three-dimensional stress analysis of structures in instability conditions using nonlinear displacement-based and hybrid-mixed quadrilaterals based on SaS formulation

摘要

In this paper, the three-dimensional (3D) stress analysis of plate-type structures in instability conditions is presented. The displacement-based and hybrid-mixed four-node quadrilateral elements are developed taking the advantages of the sampling surfaces (SaS) method. The SaS formulation is based on considering inside the plate N not equally spaced SaS parallel to the middle surface to specify the displacements of these surfaces as primary plate unknowns. The displacements, strains and stresses are assumed to be distributed through the thickness using Lagrange polynomials of degree N-1 that lead to a well-set higher-order plate theory. The locations of SaS are based on the use of Chebyshev polynomial nodes that allow us to minimize uniformly the error due to Lagrange interpolation. To circumvent shear locking and have no spurious zero energy modes, the assumed transverse shear strains are employed. The nonlinear equilibrium equations are solved by the Newton-Raphson iterative method combined with the Crisfield arc-length algorithm. The accuracy and efficiency of both elements in different conditions such as coarse and distorted meshes are investigated. The developed assumed-natural strain (ANS) elements can be useful for the 3D stress analysis of thin and thick plates in whole states of equilibrium path involving bifurcation, snap-through, and/or snap-back phenomena.