Interval finite element method based on the element for eigenvalue analysis of structures with interval parameters

2001 ◽  
Vol 12 (6) ◽  
pp. 669-684 ◽  
Author(s):  
Xiaowei Yang ◽  
Suhuan Chen ◽  
Huadong Lian
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Eigenvalue Analysis ◽  
Interval Parameters ◽  
Interval Finite Element Method ◽  
Element Method

A homogenization-based Chebyshev interval finite element method for periodical composite structural-acoustic systems with multi-scale interval parameters

2018 ◽  
Vol 233 (10) ◽  
pp. 3444-3458 ◽  
Author(s):  
Ning Chen ◽  
Jiaojiao Chen ◽  
Jian Liu ◽  
Dejie Yu ◽  
Hui Yin
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Sound Pressure ◽  
Acoustic System ◽  
Interval Parameters ◽  
Multi Scale ◽  
Small Uncertainty ◽  
Interval Finite Element Method ◽  
Scale Interval ◽  
Element Method

For the periodical composite structural-acoustic system with multi-scale interval uncertainties, a new interval analysis approach is presented in this study. In periodical composites structural-acoustic systems with multi-scale interval parameters, the variation ranges of the sound pressure response can be calculated using the homogenization-based interval finite element method. However, the homogenization-based interval finite element method that is based on Taylor series can only suit periodical composites structural-acoustic problems with small uncertainty degree. To consider larger uncertainty degree, by combining the Chebyshev polynomial series and the homogenization-based finite element, a homogenization-based Chebyshev interval finite element method is presented to predict the sound pressure responses of the structural-acoustic system involving periodical composite and multi-scale interval parameters. Compared with homogenization-based interval finite element method, homogenization-based Chebyshev interval finite element method can obtain higher accurate numerical solutions in the approximate process. Besides, homogenization-based Chebyshev interval finite element method can be implemented without conducting the complex derivation process. Numerical results verify the validity and practicability of the presented homogenization-based Chebyshev interval finite element method for the periodical composite structural-acoustic problem.

scholarly journals A substructure-based interval finite element method for problems with uncertain but bounded parameters

2017 ◽  
Vol 9 (1) ◽  
pp. 168781401668407
Author(s):  
Yihuan Zhu ◽  
Guojian Shao ◽  
Jingbo Su ◽  
Ang Li
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Evaluation System ◽  
Nonlinear Problems ◽  
Expansion Method ◽  
Constant Matrix ◽  
Approximation Solution ◽  
Interval Finite Element Method ◽  
Necessary Constraints ◽  
Element Method

In this article, the dependency between different elements in solid structures is considered and a substructure-based interval finite element method is used to model the interval properties. The penalty method is applied to impose the necessary constraints for compatibility. In order to obtain the interval stresses, an approximation solution based on the Taylor expansion method is presented. Then, the proposed interval substructure model is expanded to nonlinear problems. In consideration of the nonlinear property of the elasticity modulus, an interval elastoplastic substructure analysis method using constant matrix based on the incremental theory is proposed and the interval expression of the interval stress updated formation is derived. Finally, numerical examples are carried out to demonstrate the reasonability and feasibility of the proposed method and evaluation system.

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