Eliminating End Effects for Theoretical Panel Buckling with FEM

This is a conference paper. It was presented at the 51st AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference [© AIAA]. The definitive published version can be found at: http://www.aiaa.org/content.cfm?pageid=2The theoretical buckling performance of thin walled panels under compression can be predicted using classical plate theory (CPT) and using tools such as the VICONOPT, which uses the finite strip method, and Abaqus, a finite element modelling program (FEM). VICONOPT is much more computationally efficient than FEM, and is able to optimise panel design for buckling and pseudo-postbuckling performance. This work forms part of a larger project to use VICONOPT to optimise panel designs that are allowed to buckle in a stable manner below the maximum allowed loading. Because VICONOPT can only make a first approximation of postbuckling performance, a method is required to validate the optimisation results against a more accurate method

Torsion and bending of swept and tapered wings with ribs parallel to the root

The problem considered is that of a swept wing, either conical or cylindrical, of arbitrary section, under any system of bending and torsion loads. The wing is assumed to consist of a non-buckling outer skin, a series of booms located along generators of the tube; and a series of closely spaced ribs all parallel to the root section. The ribs are assumed to be rigid in their own planes but to offer no resistance to warping out of their planes. No restriction is placed on either the taper or the sweep of the wing. The theory is developed in general terms, for arbitrary wing section, arbitrary variation of stress bearing area over the tube, and arbitrary applied loads. The fundamental equations are expressed in terms of a stress function which is found to satisfy a complicated integro-differential equation. Analytical solutions of this equation are obtained for certain simple types of tube and applied load by a process consisting essentially of separation of the variables. These solutions in some cases lead to formulae exactly analagous to thoso of the simple theories of bending and torsion for an unswopt wing. They are slightly more complicated than the latter formulae, in that they show an interaction between bonding and torsion which is characteristic of this type of wing. The Appendix gives detailed numerical applications of the theory to a highly tapered unswopt four boom tube of rectangular cross section, with a completely constrained root section, under varying bénding moment and torque. It is shown that when the taper is large the root effect is of prime importance and the analysis of a delta Wing would therefore be very tedious

Postbuckled Stability of Panels with Torsional Buckling

The panel analysis and optimization code VICONOPT, based on exact strip theory, is utilized to investigate the postbuckling stability of a stiffened aerospace panel in a torsional buckled state. The paper shows that the postbuckling characteristics of a panel buckling in a torsional mode has similarity to the postbuckling behavior of a panel with a skin initiated mode and a panel initiated mode. The postbuckled stiffness of the torsional mode is similar to the skin mode in terms of load versus end shortening and is similar to the panel postbuckling behavior in terms of load versus out-of-plane deflection. If the panel has stiffeners of more than one size then there are multiple torsional modes. For panel design it is suggested that small stiffener buckling, i.e., in a torsional mode, can have postbuckling stability with regard to the growth of the out-of-plane deflection. If the large stiffeners initiate the buckling then there is no postbuckling reserve of strength. This has implications for design of such panels as mass could be saved if allowance is made for small stiffener buckling in the optimization process