A moving boundary finite element method-based numerical approach for the solution of one-dimensional problems in shape memory alloys

2000 ◽  
Vol 190 (13-14) ◽  
pp. 1741-1762 ◽  
Author(s):  
V. Stoilov ◽  
O. Iliev ◽  
A. Bhattacharyya
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Shape Memory Alloys ◽  
Shape Memory ◽  
Moving Boundary ◽  
Numerical Approach ◽  
One Dimensional ◽  
Element Method

Wave Finite Element Method Based on Reduced Model for One-Dimensional Periodic Structures

2015 ◽  
Vol 07 (02) ◽  
pp. 1550018 ◽  
Author(s):  
C. W. Zhou ◽  
J. P. Lainé ◽  
M. N. Ichchou ◽  
A. M. Zine
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Periodic Structures ◽  
Numerical Approach ◽  
Unit Cell ◽  
Cell Dynamics ◽  
One Dimensional ◽  
Ill Conditioning ◽  
Selection Of ◽  
Element Method

In this paper, an efficient numerical approach is proposed to study free and forced vibration of complex one-dimensional (1D) periodic structures. The proposed method combines the advantages of component mode synthesis (CMS) and wave finite element method. It exploits the periodicity of the structure since only one unit cell is modelled. The model reduction based on CMS improves the computational efficiency of unit cell dynamics, avoiding ill-conditioning issues. The selection of reduced modal basis can reveal the influence of local dynamics on global behavior. The effectiveness of the proposed approach is illustrated via numerical examples.

scholarly journals Finite Element Analysis of Thermoelastic Contact Stability

1994 ◽  
Vol 61 (4) ◽  
pp. 919-922 ◽  
Author(s):  
Taein Yeo ◽  
J. R. Barber
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Steady State ◽  
Eigenvalue Problem ◽  
Linear Perturbation ◽  
Dimensional System ◽  
The Finite Element Method ◽  
One Dimensional ◽  
Thermoelastic Contact ◽  
Element Method

When heat is conducted across an interface between two dissimilar materials, theimoelastic distortion affects the contact pressure distribution. The existence of a pressure-sensitive thermal contact resistance at the interface can cause such systems to be unstable in the steady-state. Stability analysis for thermoelastic contact has been conducted by linear perturbation methods for one-dimensional and simple two-dimensional geometries, but analytical solutions become very complicated for finite geometries. A method is therefore proposed in which the finite element method is used to reduce the stability problem to an eigenvalue problem. The linearity of the underlying perturbation problem enables us to conclude that solutions can be obtained in separated-variable form with exponential variation in time. This factor can therefore be removed from the governing equations and the finite element method is used to obtain a time-independent set of homogeneous equations in which the exponential growth rate appears as a linear parameter. We therefore obtain a linear eigenvalue problem and stability of the system requires that all the resulting eigenvalues should have negative real part. The method is discussed in application to the simple one-dimensional system of two contacting rods. The results show good agreement with previous analytical investigations and give additional information about the migration of eigenvalues in the complex plane as the steady-state heat flux is varied.

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