Journal
APPLIED MATHEMATICAL MODELLING
Volume 44, Issue -, Pages 614-639Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.apm.2017.02.013
Keywords
Mass redistributed finite element method; Finite element method; Eigenfrequency; Smoothed finite element method
Funding
- State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body [31315002, 31615002]
- Research Project of State Key Laboratory of Mechanical Systems and Vibration [MSV 201613, MSV201711]
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It is well known that the standard finite element method (FEM) with overly-stiff effect gives the upper bound solutions of natural frequencies in the free vibration analysis using triangular and tetrahedral elements. In this study, for the first time, this paper aims to improve the prediction of eigenfrequencies through the perfect match between the stiffness and mass matrices. With redistribution of mass in the system, we can tune the balance between stiffness and mass of a discrete model. This can be done by simply shifting the integration points away from the Gaussian locations, while ensuring the mass conservation. A number of numerical examples including 2D and 3D problems have demonstrated that the accuracy of eigenfrequencies is strongly determined by the location of integration points in the mass matrix. With appropriate selection of integration points in the mass matrix, even the exact solution of eigenfrequencies can be obtained in both FEM and smoothed finite element method (SFEM) models. (C) 2017 Elsevier Inc. All rights reserved.
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