Eventos Anais de eventos
MecSol 2017
6th International Symposium on Solid Mechanics
COMPUTATIONAL IMPLEMENTATION OF THE ARC-LENGTH CONTROL METHOD BASED ON THE RATES OF ENERGY FOR PHYSICALLY NONLINEAR ANALYSIS
Submission Author:
Christian Jean , MG
Co-Authors:
Roque Luiz da Silva Pitangueira, Jamile Fuina
Presenter: Christian Jean
doi://10.26678/ABCM.MecSol2017.MSL17-0031
Abstract
This paper presents the computational implementation of the arc-length control method based on the rates of the internal and the dissipated energy for physically nonlinear analysis. This implementation has been fulfilled in the numerical core of the project INSANE (INteractive Structural ANalysis Environment), an open source project developed at the Structural Engineering Department of the Federal University of Minas Gerais. In nonlinear problems, most of the procedures for solving equilibrium equations are based on the iterative process of Newton-Raphson in which control methods are linked. The idea of these methods is to consider the loading parameter as a variable and to set a restraint condition into the system of equilibrium equations, in such a way that this parameter can be evaluated. In order to obtain a complete equilibrium path an arc-length method is often required due to the occurence of snap-through and snap-back phenomena. In this paper, an introduction to nonlinear analysis and the Newton-Raphson method responsible for the solution of incremental-iterative problems are presented. In this part, the classical control methods and their respective limitations are discussed. Next, the organization of the solution module of INSANE and the arc-length control method based on the rates of energy are presented. Finally, a comparative analysis with the classical control methods is presented along with general conclusions about the efficiency and the applicability of the energy rate control method.
Keywords
Arc-Length Control, Numerical Methods, Physically Nonlinear Analysis, Energy Rate, Incremental-Iterative Solutions
