Numerical analysis of natural frequency and stress intensity factor in Euler–Bernoulli cracked beam

In this paper, the evaluation procedures of the natural frequency and the stress intensity factor in the opening mode are established for the Euler–Bernoulli cracked beam by using (a) a technique in the framework of the finite element method, (b) a group method of data handling (GMDH), and (c) the s...

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Bibliographic Details
Published in:Acta mechanica 2019-12, Vol.230 (12), p.4391-4415
Main Authors: Alijani, A., Abadi, M. Kh, Razzaghi, J., Jamali, A.
Format: Article
Language:English
Subjects:
Algorithms
Analysis
Case studies
Classical and Continuum Physics
Computer simulation
Control
Design of experiments
Dynamical Systems
Energy release rate
Engineering
Engineering Fluid Dynamics
Engineering Thermodynamics
Finite element method
Group method of data handling
Heat and Mass Transfer
Identification methods
Mathematical analysis
Mathematical models
Neural networks
Numerical analysis
Original Paper
Resonant frequencies
Software
Solid Mechanics
Stiffness
Stress intensity factors
Theoretical and Applied Mechanics
Vibration
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Summary:In this paper, the evaluation procedures of the natural frequency and the stress intensity factor in the opening mode are established for the Euler–Bernoulli cracked beam by using (a) a technique in the framework of the finite element method, (b) a group method of data handling (GMDH), and (c) the software ABAQUS software. In the first one, the stiffness and mass matrices of the beam are enriched according to the depth and location of the crack for the determination of the natural frequency. A discrete spring model is used to simulate the crack in the structure based on the energy release rate. The continuity conditions in a cracked element are applied to connect two sub-elements of both sides of the crack. In the second method, the natural frequency and the stress intensity factor are determined using the GMDH algorithm. Design of experiments technique is employed to create an optimum arrangement for the application in the GMDH neural network. A few case studies are examined to investigate the results of the analysis, in addition, to identify the priority and the comparison of the three methods. The procedure of the analysis explains the advantages and limitations of the finite element-based technique, the GMDH method, and ABAQUS.
ISSN:0001-5970
1619-6937
DOI:10.1007/s00707-019-02492-x