Eventos Anais de eventos
MecSol 2017
6th International Symposium on Solid Mechanics
Numerical Stability of GFEM Evaluation for Free Vibration Analysis in Trussed Structures
Submission Author:
Thamara Petroli , PR
Co-Authors:
Marcos Arndt, Paulo de Oliveira Weinhardt, ROBERTO Dalledone Machado
Presenter: Paulo de Oliveira Weinhardt
doi://10.26678/ABCM.MecSol2017.MSL17-0082
Abstract
Since 1960s, Finite Element Methods (FEM) has been studied with the purpose of solving problems in structural analysis. However, there are some limitations of the method when these problems involve discontinuities for example. In order to overcome these difficulties, the Generalized Finite Element Method (GFEM) was developed. In the specific case of dynamic analysis of structures, when applied numerical methods for the solution, the free vibration problems, fall back a problem of generalized eigenvalues and eigenvectors. Several numerical methods have been developed in recent decades to solve these problems, among which the GFEM stand out for the high convergence rates presented. However, it is observed that the solution of the GFEM is very sensitive to the precision used in numerical algorithms. Analytically, restricted matrices of stiffness (K) and mass (M) are positive definite, so the eigenvalue problem is stable and should not present sensitivity issues. In this context, the objective of this work is investigate possible causes of the observed numerical instability and to establish parameters that allow to evaluate the numerical stability of different version of the GFEM for analysis of free vibration unidimensional bar elements. The numerical results obtained indicate that the condition number of the mass matrix can be used to evaluate the numerical stability of the GFEM in free vibration analysis.
Keywords
stability, Generalized Eigenvalues and Eigenvectors Problems, dynamic analysis, Generalized Finite Element Method, stability, Generalized Eigenvalues and Eigenvectors Problems, dynamic analysis, Generalized Finite Element Method, stability, Generalized Eigenvalues and Eigenvectors Problems, dynamic analysis, Generalized Finite Element Method, stability, Generalized Eigenvalues and Eigenvectors Problems, dynamic analysis, Generalized Finite Element Method, stability, Generalized Eigenvalues and Eigenvectors Problems, dynamic analysis, Generalized Finite Element Method
