Keywords: augmented splines, bubble polynomials, buckling, end restraints, internal restraints, plate stiffener, spline finite strip method.

The spline finite strip method (SFSM) [1] is an attractive numerical technique for the buckling analysis of folded plate structures where general loading regimes and boundary conditions need to be modelled. Its computational efficiency lies between that of the semi-analytical finite strip method [2] and the finite element method. The former numerical technique, although highly efficient computationally, is very restrictive in the loading and strip end conditions that may be modelled, while the finite element method is much less efficient, but is able to model almost any configuration of loading and restraint. In implementing splines as interpolation functions in the longitudinal direction of the strip, amended splines have been used conventionally to model the variety of end conditions that may occur (clamped, simply supported, sliding or free). These amended splines are somewhat difficult to implement in the simple fashion whereby freedoms are easily assigned in the finite element method and moreover are difficult to incorporate if internal restraints are to be specified. A restriction of the SFSM [1] that renders its formulation 'untidy' is the need for amended spline functions to model a variety of end conditions, and this becomes unduly complex for internal restraints. Rather than specify one member of a family of amended splines, it is easier and more rational to treat the variety of end conditions in the SFSM in much the same way as in the finite element method, where the specification of, for example, an integer '0' signifies 'fixed' and an integer '1' signifies 'free'.

This paper presents a simple technique for replacing the specification of dedicated amended splines, so that freedoms may be assigned in the same manner as is usually employed in the finite element method. The formulation of the SFSM is that of the bubble-augmented technique used elsewhere by the authors [3], but its use for the SFSM with conventional cubic transverse polynomials is straightforward.

The accuracy and validity of the method are investigated through the analysis of a representative set of local buckling problems, and the high degree of efficacy of the method is demonstrated. The method is then employed to study the local buckling of flat and stiffened plates under longitudinal and/or transverse compression with different boundary conditions at the ends and with internal supports, and the results of are compared with solutions reported elsewhere in the literature.

1

M. Azhari, S. Hoshdar, M.A. Bradford, "On the Use of Bubble Functions in the Local Buckling Analysis of Plate Structures by the Spline Finite Strip Method", International Journal of Numerical Methods in Engineering, 48(4), 503-593, 2000. doi:10.1002/(SICI)1097-0207(20000610)48:4<583::AID-NME898>3.0.CO;2-A

2

Y.K. Cheung, "Finite Strip Method in Structural Analysis", Pergamon Press, Oxford, UK, 1976.

3

Z. Vrcelj, M.A. Bradford, "Bubble Functions in the Analysis of Plates and Plate Assemblies by the Spline Finite Strip Method", UNICIV Report No. R-431, The University of New South Wales, Sydney, Australia, 2004.

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