The transverse stiffness of such plates may be enhanced by welded radial/circumferential stiffeners rather than increasing the plate thickness. However, existing orthotropic plate analysis is not appropriate for analysis/design of plates with few stiffeners. A more rational analysis/design approach, based on elasto-plastic large deflection discretely stiffened plate theory, is suggested. Such theories have been developed for rectangular [1,2] and axisymmetric circular [3,4] plates. The paper describes the generalisation of the theory to include non-axisymmetric deformations and its application to cross-stiffened circular plates.

First, the geometric parameters and the material properties are defined. Then the large deflection equilibrium equations for the stiffened plate are introduced and the force interaction between stiffener and plate is explained. Thereafter, Ilyushin full-section and volume yield criteria for the plate and stiffener respectively are explained. Subsequently, strain and curvature relations and the plate-stiffener compatibility equations are presented. The yield criteria and elasto-plastic constitutive equations then follow. Theoretical considerations are concluded with the definition of the plate edge conditions.

The stiffened plate equations are solved numerically using finite differences and the dynamic relaxation algorithm, details of which are given elsewhere.

A parametric study of the elasto-plastic large deflection response of circular plates stiffened by a pair of rectangular cross-section stiffeners in an orthogonal cross arrangement is described. The study encompasses: two plate slendernesses, two stiffener depths and four plate edge conditions. Dimensionless first yield pressures for both plate and stiffener are tabulated together with centre deflection etc values. Graphs of centre deflection etc. versus pressure are presented as well as radial cross-sections which show the 'spread of plasticity' within the plate and stiffeners. Finally, the effects of plate slenderness, stiffener depth and plate edge conditions on cross-stiffened circular plate response are highlighted and their practical implications discussed.

1

P. Djahani, "Large-deflection elasto-plastic behaviour of discretely stiffened plates", PhD Thesis, University of London (Imperial College), London, United Kingdom, 1977.

2

S.E. Webb, P.J. Dowling, "Large-deflexion elasto-plastic behaviour of discretely stiffened plates", Proceedings of the Institution of Civil Engineers, Part 2 (Research and Theory), 69, 375-401, 1980. doi:10.1680/iicep.1980.2543

3

G.J. Turvey, N.G.V. Der Avanessian, "Elastic large deflection analysis of ring-stiffened circular plates using graded finite-differences", in J. Middleton, G.N. Pande, (Editors), "Proceedings of the First International Conference on Numerical Methods in Engineering: Theory and Applications", Balkema, Doordrecht, The Netherlands, 875-884, 1985.

4

G.J. Turvey, N.G.V. Der Avanessian, "Axisymmetric elasto-plastic large deflection response of ring stiffened circular plates", International Journal of Mechanical Sciences, 31, 905-924, 1989. doi:10.1016/0020-7403(89)90032-5

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