The ‘panel analysis’ technique in the computational study of axisymmetric thin-walled shell systems

Abstract

Thin-walled shells of revolution under circumferentially uniform pre-buckling stress states are important fundamental systems, often serving as reference 'base cases' to which the behaviour of more complex unsymmetrical systems can be related. However, the same simplicity that often permits closed-form algebraic expressions for the critical buckling load is also often responsible for a lack of localisation and significant ambiguity in the critical buckling mode. The computation of the linear or nonlinear buckling loads requires the systematic trial of many potential buckling modes to identify the one which minimises the necessary strain energy. In times when researchers used custom-written tools usually based on circumferential Fourier series expansions, this operation was relatively straightforward. However, today's analysts using 'general' commercial 3D finite element packages must apply careful safeguards to correctly identify the correct buckling load and associated mode in axisymmetric shell systems. This paper presents a detailed computational strategy to accurately and efficiently investigate the correct buckling load and mode number of axisymmetric shell systems using the technique of a 'panel analysis'. This is implemented in the ABAQUS finite element solver controlled by the SIMULIA TM Isight automation software and the Python object-oriented programming language. The methodology is illustrated on three classical benchmark problems from the scientific literature on the buckling of cylindrical shells under meridional compression, with special attention given to meshing considerations.

Imperfection sensitivity of unstiffened cylindrical shells under external pressure

“…For the determination of the elastic critical buckling load using computational analysis, the circumferential mesh resolution must be optimised so that the buckling half-waves of the modelled geometry can be accurately represented and the critical circumferential wave number can be provided in the numerical model, see Figure 1. This is important to ensure that the numerically estimated buckling load is not unconservatively overpredicted [16].…”

Elastic Imperfect Cylindrical Shells of Varying Length under Combined Axial Compression and Bending

“…The elastic buckling behaviour of cylindrical shells under uniform compression has been the subject of a very large number of previous research studies, and it is well established that these shells present different buckling modes according to the length (Yamaki, 1984;Rotter, 2004;Rotter and Al-Lawati, 2016;Sadowski et al, 2018). The elastic nonlinear finite element calculations presented in Fig.…”

“…Such models have been widely used in the absence of torsion (Teng and Song, 2001;Cai et al, 2003;Jayadevan et al, 2004;Song et al, 2004;Østby et al, 2005;Limam et al, 2010;Rotter et al, 2011;2014;Sadowski et al, 2018). A state of combined loading was achieved by applying a point load N in the meridional direction through a reference point located at a known eccentricity e away from the centroid of the cross-section and linked via a rigid coupling to the circumferential edge of the cylinder, thus additionally inducing an edge moment M = e•N on the cylinder.…”

On the advantages of hybrid beam-shell structural finite element models for the efficient analysis of metal wind turbine support towers

“…Detailed discussions on the mesh design of cylindrical shells subject to meridional compression were presented in Sadowski et al [20]. Specifically, it was shown how the theory of the Koiter circle [21,22] may be used to design a mesh capable of accurately capturing all theoretically permissible critical non-axisymmetric buckling modes for a particular cylindrical geometry.…”

“…Equation 3 naturally reduces to the 'Koiter circle' in ṁ•r vs n space for a cylindrical shell (β → 0, secβ → 1, ρ ɺ → r). An illustration of the linear buckling surface on the mn plane computed with LBAs using the 'panel analysis' technique of Sadowski et al [20] is shown in Fig. 3 for a single truncated conical shell with a purposefully accentuated shallow angle of β = 45°, unit thickness, r1 / t = 500 (with 'ring' conditions: u = w and v = 0; Fig.…”