Journal of Civil and Environmental Engineering

Analysis of Second Degree of Freedom with Second Degree of Stiffness Based on Broyden’s Method

Abstract

Saad Essa *

The main purpose of this study is comparing two methods to get the convergence of two series nonlinear spring system. The key method is BroydenâÃ?â?¬Ã?â?¢s method which based on the Jacobian matrix to update the inverse of the secant stiffness matrix and the results are compared with the NewtonâÃ?â?¬Ã?â??RaphsonâÃ?â?¬Ã?â?¢s method. A constant force is applied to the second node in the system of two degrees of freedom (DOF). The results are compared with the first and second degree of nonlinear springs displacements differences that serially connected. The displacements at the first node are smaller than the second node and the number of iterations to reach the convergence for the second degree of difference displacements are greater than for the first degree. The main disadvantage of BroydenâÃ?â?¬Ã?â?¢s method is that it becomes unstable when the number of iterations increases.