Z. Naturforsch. 68a, 355 – 361
A Nonlinear Model Arising in the Buckling Analysis and its New Analytic Approximate Solution
1 Department of Mathematics, Zhejiang University, Hangzhou 310027, China
2 Departamento de Matemáticas, Escuela Politécnica Superior, Universidad Carlos III de Madrid, Avenida de la Universidad, 30, 28911 Leganés, Madrid, Spain
3 Department of Mathematics, College of Computer Science and Mathematics, University of Mosul, Mosul-Iraq
Received July 3, 2012 / revised November 26, 2012 / published online April 10, 2013
An analytical nonlinear buckling model where the rod is assumed to be an inextensible column and prismatic is studied. The dimensionless parameters reduce the constitutive equation to a nonlinear ordinary differential equation which is solved using the Adomian decomposition method (ADM) through Green's function technique. The nonlinear terms can be easily handled by the use of Adomian polynomials. The ADM technique allows us to obtain an approximate solution in a series form. Results are presented graphically to study the efficiency and accuracy of the method. To the author's knowledge, the current paper represents a new approach to the solution of the buckling of the rod problem. The fact that ADM solves nonlinear problems without using perturbations and small parameters can be judged as a lucid benefit of this technique over the other methods.
Key words: Adomian Decomposition Method; Adomian Polynomials; Green's Function; Buckling Phenomena.