Hindawi Publishing Corporation Mathematical Problems in Engineering Volume 2012, Article ID 197483, 18 pages doi:10.1155/2012/197483 Research Article Stability Analysis of Nonuniform Rectangular Beams Using Homotopy Perturbation Method Seval Pinarbasi Department of Civil Engineering, Kocaeli University, 41380 Kocaeli, Turkey Correspondence should be addressed to Seval Pinarbasi, sevalp@gmail.com Received 4 October 2011; Accepted 21 November 2011 Academic Editor: Alexander P. Seyranian Copyright q 2012 Seval Pinarbasi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The design of slender beams, that is, beams with large laterally unsupported lengths, is commonly controlled by stability limit states. Beam buckling, also called “lateral torsional buckling,” is different from column buckling in that a beam not only displaces laterally but also twists about its axis during buckling. The coupling between twist and lateral displacement makes stability analysis of beams more complex than that of columns. For this reason, most of the analytical studies in the literature on beam stability are concentrated on simple cases: uniform beams with ideal boundary conditions and simple loadings. This paper shows that complex beam stability problems, such as lateral torsional buckling of rectangular beams with variable cross-sections, can successfully be solved using homotopy perturbation method HPM. 1. Introduction A beam is a structural element which spans large distances between supports and which primarily carries transverse loads with negligible axial loads. If a beam has sufficient lateral bracing, it can easily be designed by selecting the most economical “compact” cross-section satisfying the strength and serviceability limit states. However, just like slender columns which buckle under compressive loads much smaller than their “stable” load carrying capacities, a “laterally unbraced” slender beam can also buckle under transverse loads. For this reason, the design of slender beams has to consider stability limit states as well. Beam buckling, which is also called “lateral torsional buckling,” differs from column buckling in that a beam not only displaces laterally but also rotates about its axis during buckling. The coupling between twist and outward lateral displacement makes stability analysis of beams more complex than that of columns. For this reason, most of the analytical studies in the literature are concentrated on simple cases: uniform beams with ideal boundary conditions and simple loadings. For exact solutions to simple beam buckling problems, one can refer to one of the well-known structural stability books, such as 1–4.