alexa Analysis of Second Degree of Freedom with Second Degree of Stiffness Based on Broyden’s Method
ISSN: 2165-784X

Journal of Civil & Environmental Engineering
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Research Article

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

Saad Essa*

Department of Civil Engineering, Erbil Technical Engineering College, Erbil Polytechnic University, Erbil, Iraq

*Corresponding Author:
Saad Essa,
Department of Civil Engineering
Erbil Technical Engineering College
Erbil Polytechnic University, Erbil, Iraq
Tel: 9647504823149
E-mail: [email protected]

Received date: January 27, 2017; Accepted date: February 27, 2017; Published date: February 28, 2017

Citation: Essa S (2017) Analysis of Second Degree of Freedom with Second Degree of Stiffness Based on Broyden’s Method. J Civil Environ Eng 7:266. doi:10.4172/2165-784X.1000266

Copyright: © 2017 Essa S, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Abstract

The main purpose of this study is comparing two methods to get the convergence of two series nonlinear spring system. The key method is Broyden’s method which based on the Jacobian matrix to update the inverse of the secant stiffness matrix and the results are compared with the Newton–Raphson’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 Broyden’s method is that it becomes unstable when the number of iterations increases.

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