Application of Differential Transform Method to Buckling Problems at Clamped-Clamped Boundary Conditions

Abstract

Differential Transform Method (DTM) is a new semi-analytical, semi-numerical algorithm, which transforms differential equations to the form of Taylor series. The method derives an approximate numerical solution based on Taylor series expansion, which is an analytical solution built on polynomial form. Traditional Taylor series method is used for symbolic computation, while Differential Transform Method obtained the solution of the polynomials through itineration calculations. Applying DTM to buckling problems, the critical length of a bar at clamped-clamped boundary is studied. The computational results are compared with analytical solutions and shown excellent agreement between those two algorithms. The method adds a new tool to the fields of computational engineering mechanics. Differential Transform Method is much easier, and more efficient when compared with other computational methods.