### Analysis of Elastic Beams on Linear and Nonlinear Foundations Using Finite Difference Method

1Erbil Polytechnic University, Iraq
2Ishik University, Erbil, Iraq

Abstract:  An approximate method is developed to analyze the deflection in beams and beam-column by solving the differential equation for the elastic deformation of beam and beam-column. The analysis is performed using the central difference of finite difference method for the Euler-Bernoulli beam and beam-column supported on an elastic, nonlinear foundation with rigid or elastic discrete supports. To make a verification of the results, Laplace Transformation method was used to solve the elastic differential equation of beam and beam-column based on linear elastic supports and the results were compared with the finite difference method. Two types of beams were selected, simply supported and fixed-fixed with five elastic supports of an idealized soil. In the nonlinear idealization, the division of force into many levels were assumed and based on these forces, the equivalent displacements were obtained from an assumed power law equation by using the finite difference method. Central finite difference scheme, which has a second order, was used throughout the numerical analysis with five nonlinear behavior of springs separated by an equal distance between them.

Keywords: Finite Difference Method, Euler-Bernoulli Beam, Laplace Transformation

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