Symmetric tridiagonal structure preserving finite element model updating problem for the quadratic model

One of the most important yet difficult aspect of the Finite Element Model Updating Problem is to preserve the finite element inherited structures in the updated model. Finite element matrices are in general symmetric, positive definite (or semi-definite) and banded (tridiagonal, diagonal, penta-dia...

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Bibliographic Details
Published in:Mechanical systems and signal processing 2018-07, Vol.107, p.278-290
Main Authors: Rakshit, Suman, Khare, Swanand R., Datta, Biswa Nath
Format: Article
Language:English
Subjects:
Finite element analysis
Finite element method
Finite element model updating
Kronecker product of two matrices
Mathematical models
Matrix methods
Microelectronics
Model updating
Optimization
Quadratic matrix pencil
Signal processing
Stiffness
Symmetric tridiagonal matrix
Vibration
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Summary:One of the most important yet difficult aspect of the Finite Element Model Updating Problem is to preserve the finite element inherited structures in the updated model. Finite element matrices are in general symmetric, positive definite (or semi-definite) and banded (tridiagonal, diagonal, penta-diagonal, etc.). Though a large number of papers have been published in recent years on various aspects of solutions of this problem, papers dealing with structure preservation almost do not exist. A novel optimization based approach that preserves the symmetric tridiagonal structures of the stiffness and damping matrices is proposed in this paper. An analytical expression for the global minimum solution of the associated optimization problem along with the results of numerical experiments obtained by both the analytical expressions and by an appropriate numerical optimization algorithm are presented. The results of numerical experiments support the validity of the proposed method.
ISSN:0888-3270
1096-1216
DOI:10.1016/j.ymssp.2017.10.014