Analysis of Second Degree of Freedom with Second Degree of Stiffness Based on BroydenÃ¢ÂÂs MethodSaad 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
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 Broydenâs 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.
The main purpose of this study is comparing two methods to get the convergence of two series nonlinear spring system. The key method is BroydenâÂÂs method which based on the Jacobian matrix to update the inverse of the secant stiffness matrix and the results are compared with the NewtonâÂÂRaphsonâÂÂs 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 BroydenâÂÂs method is that it becomes unstable when the number of iterations increases.