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You can also find papers in which spurious buckling modes are of concern by GOOGLING the string, “spurious buckling modes” or some such.
Some buckling modes look spurious, such as that shown here, but may actually inaccurately represent a real physical phenomenon, such as buckling between rings in this example. These modes are an inaccurate representation because the finite element mesh is not dense enough. Other spurious buckling modes, such as “hourglassing” (shown in the next image), may represent “zero energy” modes, that is, buckling modes permitted by the particular finite element model but not by Mother Nature. These spurious modes are not merely inaccurate representations of actual physical phenomena but result from an improperly formulated finite element model, such as the use of too few integration points within each finite element.
This image is from: David Bushnell and Charles Rankin, “Optimization of perfect and imperfect ring and stringer stiffened cylindricqal shells with PANDA2 and evaluation of the optimum designs with STAGS”, AIAA Paper 2002-1408, AIAA 43rd Structures, Dynamics and Materials Conference, 2002
ABSTRACT: Ring and stringer stiffened perfect and imperfect angle-ply cylindrical shells under combined axial compression and in-plane shear are optimized with a program called PANDA2 for the minimum weight design of stiffened panels, and the optimum designs are then evaluated with use of a general purpose finite element code called STAGS. The good agreement between PANDA2 and STAGS predictions for the nonlinear collapse of imperfect stiffened shells justifies the use of PANDA2 for preliminary design. A new PANDA2 processor called STAGSUNIT automatically generates STAGS input files for cylindrical panels and shells with both stringers and rings that have various open cross sections such as Blades, Zees, Jays, Tees and Is. In STAGSUNIT the edge conditions are formulated so that STAGS models of subdomains of a long cylindrical shell with many stiffeners can be constructed that do not have artificial prebuckling stress concentrations near the edges that might significantly affect predictions of bifurcation buckling and nonlinear collapse of the subdomain. Many STAGS models of optimized shells and subdomains of shells with Blade, Zee, and Tee stiffening are generated and explored, both with respect to linear bifurcation buckling and nonlinear collapse. The behavior of shells with an initial imperfection in the form of a general buckling mode of the imperfect shell is described from a physical point of view. Some difficulties encountered during this project are described.
This spurious buckling mode is a non-zero energy mode that significantly underpredicts the actual fundamental buckling mode. It can be eliminated by refinement of the finite element mesh.
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