4th International Engineering Conference on Developments in Civil & Computer Engineering Applications (IEC2018)
Title: ANALYSIS OF ELASTIC BEAMS ON LINEAR AND NONLINEAR FOUNDATIONS USING FINITE DIFFERENCE METHOD
Authors: Saad Essa
DOI: 10.23918/iec2018.18
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 is used to solve the elastic differential equation of beam and beam-column based on linear elastic supports and the results are compared with the finite difference method. Two types of beams are 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 are assumed and based on these forces, the equivalent displacements are obtained from an assumed power law equation by using the finite difference method. Central finite difference scheme has a second order is 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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