4TH International Congress on Technology - Engineering & SCIENCE - Kuala Lumpur - Malaysia (2017-08-05)

Computer-based Mathematical Package For Solution Of The Euler-bernoulli Beam On Elastic Foundation By Collocation Method
The collocation method is a method for the numerical solution of ordinary and partial differential equations and integral equations. The idea is to choose a finite-dimensional space of candidate solutions and a number of points in the domain and to select that solution which satisfies the given equation at the collocation points. The current paper involves developing, and a comprehensive, step-by-step procedure for applying the Collocation Method to the solution of the response of the Euler-Bernoulli beam on Winkler foundation. The simplicity of this approximation method makes it an ideal candidate for computer implementation. The effect of the elastic coefficient of Winkler foundation and other parameters are assessed. Over the years, spline method is used for solving differential system of equations with different boundary conditions. An overview of the formulation, analysis and implementation of orthogonal spline collocation for the numerical solution of partial differential equations in two space variables is provided by B. Bialecki and Fairweather [1]. Also, the orthogonal spline collocation solution of hyperbolic and parabolic partial integro-differential equations is mentioned. The sextic spline function for the solution of a system of second-order boundary-value problems associated with unilateral, obstacle, and contact problems is presented by Rashidinia et al. [2]. The results are shown that the approximate solutions obtained using the sextic spline method are better than the finite difference methods. The quartic B-splines collocation method is applied for the numerical solutions of the Burgers’ equation by Saka and Dağ [3]. The natural frequencies of non-uniform Euler–Bernoulli beam on elastic foundation are obtained using the spline collocation method by Hsu [4]. The isogeometric collocation methods for the Timoshenko beam problem is presented by da Veiga et al. [5]. Mohammadi developed a numerical method based on sextic B-spline to solve the fourth-order time dependent partial differential equations [6]. The isogeometric analysis method for the solution of thin structural problems described by the Bernoulli–Euler beam and Kirchhoff plate models introduced by Reali and Gomez [7]. Kiendl et al. applied the isogeometric collocation methods for the numerical approximation of Reissner–Mindlin plate problems [8].
Keywords: Computer-based mathematical package, Euler-Bernoulli Beam, Collocation Method
Amin Ghannadiasl