Keywords: thin-walled structures, bifurcation load, post-buckled states, harmonic coupled finite strip method.

It is well known that thin-walled structures when subjected to compression loads are susceptible to local buckling. Because of this, determining their strength often involves considering post-buckled states. The rigorous strength analysis must include elasto-plastic behaviour, and has been carried out for special cases using variational procedures and for more general cases using finite elements. However, elasto-plastic analyses are inevitably very expensive in computation. It is often found that for those structures a good estimate of the strength can be obtained by carrying out a purely elastic linear stability analysis, and coupling this with some inelastic theory. Again, finite elements must be used for the analysis of the more complex cases.

However, the finite strip method (FSM) using flat shell strips is ideally suited for the stability analysis of multiple-plate systems because of its ability to deal with a variety of different situations and also because of the small number of unknowns involved. For linear stability, a method has been developed for determining the initial stress matrices and bifurcation loads [1,2]. In linear theory, it takes advantage of the orthogonality properties of harmonic functions in the stiffness matrix formulation to yield a block diagonal stiffness matrix.

This method is also one of the many that can be applied to solving non-linear plate-structure problems. In recent studies [3,4] it has been developed to predict the geometrically non-linear response of folded plate structures. In these works the analyses have been based on the use of theory where an alternative formulation leads to uncoupled solutions.

The procedure for deriving the geometrically non-linear equations of balance regarding Kirchhoff's plates, which are based on a Lagrangean formulation for moderately large deflections, is explained in [2]. However, in the case of the geometrical stiffness matrix calculation, the integral expressions contain the products of trigonometric functions with higher-order exponents and here the orthogonality characteristics are no longer valid. All the terms of the series are thus coupled. Therefore, the only possible way to form the stiffness matrix is the one which takes into account all of the series. The object of the present paper is to extend and evaluate its application to the analysis of the problem of post-buckling of plate structures which have diaphragm ends and are subjected to compression loading.

1

Y.K. Cheung, L.G. Tham, "Finite strip method", CRC Press LLC, 1998.

2

D.D. Milašinovic, "The finite strip method in computational mechanics", Faculties of Civil Engng: Subotica, Budapest, Belgrade, 1997.

3

S. Wang, D.J. Dawe, "Finite strip large deflection and post-overall-buckling analysis of diaphragm-supported plate structures", Comp & Struct, 61(1), 155-170, 1996. doi:10.1016/0045-7949(96)00085-5

4

D.J. Dawe, S.S.E. Lam, Z.G. Azizian, "Finite strip post-buckling analysis of composite prismatic plate structures", Comp & Struct, 48, 1011-1023, 1993. doi:10.1016/0045-7949(93)90436-H

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