Int. Conf. on Computational Methods for Coupled Problems in Science and Engineering COUPLED PROBLEMS 2005 M. Papadrakakis, E. Oñate and B. Schrefler (Eds)  CIMNE, Barcelona, 2005 FLEXURAL BUCKLING ANALYSIS OF COMPOSITE BEAMS OF VARIABLE CROSS-SECTION BY BEM E.J. Sapountzakis * and G.C. Tsiatas * * School of Civil Engineering, National Technical University, Zografou Campus, GR-157 80 Athens, Greece e-mail: cvsapoun@central.ntua.gr Key words: Flexural buckling, composite, variable cross-section, beam, boundary integral equation, analog equation method Abstract. In this paper a boundary element method is developed for the flexural buckling analysis of composite Euler-Bernoulli beams of arbitrary variable cross section. The composite beam consists of materials in contact each of which can surround a finite number of inclusions. Since the cross-sectional properties of the beam vary along its axis, the coefficients of the governing differential equation are variable. The beam is subjected to a compressive centrally applied load together with arbitrarily axial and transverse distributed loading, while its edges are restrained by the most general linear boundary conditions. The resulting boundary value problems are solved employing a boundary integral equation approach. Besides the effectiveness and accuracy of the developed method, a significant advantage is that the displacements as well as the stress resultants are computed at any cross-section of the beam using the respective integral representations as mathematical formulae. Several beams are analysed to illustrate the method and demonstrate its efficiency and wherever possible its accuracy. The influence of the boundary conditions on the buckling load is demonstrated through examples with great practical interest. The flexural buckling analysis of a homogeneous beam is treated as a special case. 1 INTRODUCTION Elastic stability of beams is one of the most important criteria in the design of structures subjected to compressive loads. The flexural buckling coupled analysis is much more complicated in the general case of a composite beam of variable cross-section. Namely, a beam consisting of a relatively weak matrix material reinforced by stronger inclusions or of materials in contact. The extensive use of the aforementioned structural elements necessitates a reliable and accurate analysis of the flexural buckling problem. Although there is an extensive research on the coupled flexural buckling analysis of homogeneous beams of variable cross-section using analytical 1-5 , semi analytical 6 or