A new iterative technique of the finite element method for the analysis of the steady state incompressible viscous flow based on the transformation of variables

1993 ◽  
Vol 12 (3) ◽  
pp. 181-196
Author(s):  
Hiroshi Okuda ◽  
Laszlo Fuchs ◽  
Genki Yagawa
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Steady State ◽  
Viscous Flow ◽  
Iterative Technique ◽  
The Finite Element Method ◽  
Incompressible Viscous Flow ◽  
Transformation Of Variables ◽  
Element Method

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.

scholarly journals COMPARISON OF THE THEORETICAL AND NUMERICAL SOLUTION BY THE FINITE ELEMENT METHOD FOR STEADY STATE AIR FLOW IN SOIL TOWARD AN EXTRACTION WELL

2006 ◽  
Vol 62 (4) ◽  
pp. 391-402 ◽  
Author(s):  
Yoshihiko HIBI ◽  
Kenji JINNO ◽  
Nobuyuki EGUSA ◽  
Junichi KAWABATA ◽  
Masanori SHIMOMURA
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Steady State ◽  
Numerical Solution ◽  
Air Flow ◽  
The Finite Element Method ◽  
Element Method

A Computational Method for Modeling Interface Corner Crack under Steady-State Delamination

2012 ◽  
Vol 486 ◽  
pp. 457-463
Author(s):  
Badrinath Veluri ◽  
Henrik Myhre Jensen
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Steady State ◽  
Crack Front ◽  
Strain Energy Release ◽  
Computational Method ◽  
The Finite Element Method ◽  
Corner Crack ◽  
Corner Cracks ◽  
Element Method

Corner cracks under steady-state delamination were investigated. The fracture mechanics parameters that include the strain energy release rate and the three-dimensional mode-mixity along the interface crack front are estimated. A numerical approach was then applied for coupling the far field solutions based on the Finite Element Method to the near field (crack tip) solutions based on the J-integral methodology. A quantitative approach was formulated based on the finite element method with iterative adjustment of the crack front nodal coordinates to estimate the critical delamination stresses as a function of the fracture criterion and corner angles.

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