A Solution of Nonlinear Models for Concrete Beam

Abstract

This thesis provides solutions for nonlinear partial differential equations, obtained from Concrete Beams Design (CBD), by extracting three partial differential equations of the beam model. Including beam definition, types of beams, calculation of the equation of the elastic curve, and extract the equations from structure model by using Euler-Lagrange equation. The equations are solved by using Adomian's decomposition method, homotopy perturbation method, variational iteration method and finally it solved numerically by using finite differences method and spectral method, with design algorithms using MATLAB program. The Adomian's decomposition method, homotopy perturbation method and variational iteration method give the solution in power series form, but the finite differences method and spectral method give approximation solution, it gave satisfactory results in agreement with the analytical solutions.