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Adam J. Sadowski writes:
“The LBA, MNA etc. terminology is adopted from the Eurocode EN 1993-1-6 on metal shells where it is formally defined and managed.
“The definitions are as follows, in order of increasing complexity:
LA=linear elastic analysis to find the reference stresses;
LBA=linear bifurcation analysis to find the lowest linear buckling eigenvalue and eigenmode;
MNA=materially nonlinear analysis to find the reference plastic collapse load;
GNA=geometrically nonlinear analysis to find the lowest bifurcation load and associated buckling mode;
GNIA=geometrically nonlinear analysis with imperfections to find the same;
GMNA=geometrically and materially nonlinear analysis to find the same;
GMNIA=geometrically and materially nonlinear analysis with imperfections to find the same.
“Lambda is the linear bending half-wavelength, or ~2.444*sqrt(r*t)”
This and the next 2 images are from:
Jie Wang and Adam J. Sadowski, “Elastic imperfect tip-loaded cantilever cylinders of varying length”, International Journal of Mechanical Sciences, Vol. 140, pp 200-210, May 2018
ABSTRACT: A number of recent publications have explored the crucial relationship between the length of a thin cylindrical shell and the influence of pre-buckling cross-sectional ovalisation on its nonlinear elastic buckling capacity under bending. However, the research thus far appears to have focused almost exclusively on uniform bending, with ovalisation under moment gradients largely neglected.
This paper presents a comprehensive computational investigation into the nonlinear elastic buckling response of perfect and imperfect thin cantilever cylinders under global transverse shear. A complete range of practical lengths was investigated, from short cylinders which fail by shear buckling to very long ones which exhibit local meridional compression buckling with significant prior cross-section ovalisation. Two imperfection forms were applied depending on the length of the cylinder: the linear buckling eigenmode for short cylinders and a realistic weld depression imperfection for long cylinders. The weld depression imperfection was placed at the location where the cross-section of the perfect cylinder was found to undergo peak ovalisation under transverse shear, a location that approaches the base support with increasing length. Compact closed-form algebraic expressions are proposed to characterise the elastic buckling and ovalisation behaviour conservatively, suitable for direct application as design equations.
This study contributes to complete the understanding of cylindrical structures of varying length where the dominant load case is global transverse shear, including multi-strake aerospace shells with short individual segments between stiffeners and long near-cylindrical wind-turbine support towers and chimneys under wind or seismic action.
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