Keywords: post-buckling, finite strip, full-analytical, semi-energy, semi-analytical, von-Karman equations.

Prismatic plates and plate structures are increasingly used as structural components in various branches of engineering, chief of which are aerospace and marine engineering. These structures are often employed in situations where they are subjected to in-plane compressive loading. In aerospace, in particular, the quest for efficient, light-weight structures often leads to allowing for the possibility of local buckling and post-local-buckling at design load levels. Thus it is important to accurately predict the buckling and post buckling behavior of such structures. More recently, Ghannadpour and Ovesy [1,2,3,4] have developed a full-analytical post-local-buckling finite strip method (FSM) in which the solution of the von-Karman's equilibrium equation was substituted into the von-Karman's compatibility equation. It is noted that in their analysis, only one of the calculated out-of-plane buckling deflection modes, corresponding to the lowest buckling load, i.e. the first mode is used for the initial post-buckling study. For this reason, their method was designated by the name single-term full-analytical finite strip method (F-a FSM). It is worth mentioning that the single-term assumption within F-a FSM analysis corresponds to the fact that the shape of the plate in the post-buckling region is unchangeable in both longitudinal and transverse directions. Thus, the relationship between load and end-shortening becomes a linear function.

In the current paper, the theoretical developments of a high accuracy multi-term F-a FSM for the post-buckling analyses of isotropic box section struts are attempted. The strip is developed based on the concept that it is effectively a plate, and thus the von-Karman's equilibrium equation is solved exactly to obtain the buckling loads and the corresponding forms of out-of-plane buckling deflection modes. In order to solve the von-Karman's compatibility equation, the deflected form after the buckling is assumed as a combination of first, second and higher (if required) modes of buckling. Subsequently, the general form of in-plane displacement fields in a post-buckling region can be obtained. This method is characterized by the use of buckling mode shapes, obtained from the von-Karman's equilibrium equation, as global shape functions for representing displacements in a geometrically non-linear analysis.

The method developed is subsequently applied to analyze with high accuracy the post-buckling behaviour of isotropic box section struts for which the results were also available through the application of the semi-energy finite strip and semi-analytical finite strip methods. Through the comparison of the results and the appropriate discussion, the knowledge of the level of capability of these methods is significantly developed.

1

H.R. Ovesy, S.A.M. Ghannadpour, "An exact finite strip for the calculation of relative post-buckling stiffness of isotropic plates", Structural Engineering and Mechanics, 31(2), 181-210, 2009.

2

S.A.M. Ghannadpour, H.R. Ovesy, "The application of an exact finite strip to the buckling of symmetrically laminated composite rectangular plates and prismatic plate structures", Composite Structures, 89(1), 151-158, 2009. doi:10.1016/j.compstruct.2008.07.014

3

S.A.M. Ghannadpour, H.R. Ovesy, "An exact finite strip for the calculation of relative post-buckling stiffness of I-section struts", International Journal of Mechanical Sciences, 50(9), 1354-1364, 2008. doi:10.1016/j.ijmecsci.2008.07.010

4

S.A.M. Ghannadpour, H.R. Ovesy, "Exact post-buckling stiffness calculation of box section struts", Engineering Computations, 26(7), 868-893, 2009. doi:10.1108/02644400910985224

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