Stability Analysis of Nonuniform Rectangular Beams Using Homotopy Perturbation Method

Abstract

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).

Elastic Stability Analysis of Euler Columns Using Analytical Approximate Techniques

“…A cubic polynomial with four unknown coefficients can be chosen as an initial guess which was shown previously to be an effective one in problems related to Euler beams and columns [23][24][25][26][27][28][29].…”

“…Coşkun [25,26] used the homotopy perturbation method for buckling of Euler columns on elastic foundations and tilt-buckling of variable stiffness columns. Pınarbaşı [27] also analyzed the stability of nonuniform rectangular beams using homotopy perturbation method. These techniques were also used successfully in the vibration analysis of Euler-Bernoulli beams and in the vibration of beams on elastic foundations.…”

Buckling Analysis of Steel Fiber Column with Different Cross-Section and Boundary Conditions Using Euler-Bernoulli Beam Theory

“…He has performed a buckling analysis. The researchers has used many analytical and numerical methods to model column and beam elements and compared their results with experimental results or to each other [19][20][21][22][23][24][25][26][27][28][29][30][31][32][33], similar to the approaches used in the column elements have been also studied in the beam elements [34][35][36][37][38][39][40][41].…”

On Critical Buckling Loads of Columns under End Load Dependent on Direction

“…Atay and Coşkun investigated the elastic stability of a homogenous and nonhomogenous Euler beam [ 33 – 39 ]. Pinarbasi investigated the buckling analysis of nonuniform columns with elastic end restraints [ 40 ]. Huang and Luo determined critical buckling loads of beams with arbitrarily axial inhomogeneity [ 41 ].…”