Proceedings of the 17th Nordic Seminar on Computational Mechanics (NSCM-17) KTH Mechanics, Stockholm, 15-16 october 2004, p.50-53. Approximate buckling strength analysis of plates with arbitrarily oriented stiffeners Lars Brubak and Jostein Hellesland Mechanics Division, Department of Mathematics University of Oslo, Norway e–mail: lbrubak@math.uio.no Eivind Steen and Eirik Byklum Section of Hydrodynamics and Structures, DNV Maritime Det Norske Veritas, Norway e–mail: eivind.steen@dnv.com Summary Buckling of stiffened plates with arbitrarily oriented stiffeners are considered. The main objective of the work has been to develop a computational model for direct calculation of the structural response using a semi-analytical method. The deflections are represented by trigonometric functions. All combinations of in-plane shear, and biaxial in-plane compression or tension are included in the formulations. Estimation of the buckling strength is made using first yield as the strength criterion. The formulations derived are implemented in a Fortran computer code. Numerical results are obtained for a variety of stiffener orientations and geometries. The results are compared to finite element analysis results and are found, in most cases, to be conservative compared to the finite element calculation results. Introduction Stiffened plates are used extensively in ships, aircrafts, bridges and offshore installations. Tra- ditionally, explicit design formulas [1, 6] have been used to provide quick strength estimates of stiffened plates. These formulas are relatively simple to use, but they are normally not very appli- cable with respect to arbitrary orientations of the stiffeners. This paper presents a semi-analytical model 1) for calculation of the elastic buckling load (eigen- value) of stiffened, simply supported plates with in-plane loading and arbitrarily oriented stiffen- ers, and 2) for a conservative buckling load assessment of such plates with specified imperfections using the first yield as the strength criterion. The present method provides relatively high numeri- cal accuracy with low computational effort. As an alternative, the finite element method could have been used, but this method is still unpractical and too time consuming for most design purposes at present. The stiffeners are assumed to be sniped at their ends and only their out-of plane bending (beam) stiffness are included in strain energy. Thus their axial stiffness and its influence on the internal membrane stress distribution is neglected. Elastic buckling limit state (ELS) Ideal elastic buckling loads (eigenvalues) of a perfectly plane plate are computed using the Rayleigh- Ritz method for the plate in Fig. . It is simply supported and subjected to in-plane shear and biaxial compression or tension. It may have several arbitrarily oriented stiffeners, but only one is shown in the figure. The assumed displacement field, which satisfies the boundary conditions, is given by sin sin where (1)