scholarly journals Two simple finite element methods for Reissner–Mindlin plates with clamped boundary condition

2013 ◽  
Vol 72 ◽  
pp. 91-98 ◽  
Author(s):  
Bishnu P. Lamichhane
Keyword(s):  
Boundary Condition ◽  
Finite Element ◽  
Finite Element Methods

scholarly journals Finite element methods for compressible Stokes equations with inflow boundary condition

1997 ◽  
Vol 56 (2) ◽  
pp. 217-225
Author(s):  
Jae Ryong Kweon
Keyword(s):  
Finite Element Method ◽  
Boundary Condition ◽  
Finite Element ◽  
Error Analysis ◽  
Finite Element Methods ◽  
Stokes Equations ◽  
Discrete Problem ◽  
Unique Existence ◽  
Inflow Boundary Condition ◽  
The One

A finite element method for solving the compressible viscous Stokes equation with an inflow boundary condition is presented. The unique existence of the solution of the discrete problem is established, and an error analysis is given. It is shown that the error in pressure is dominated by the one in velocity and an error at the inflow portion of the boundary.

Order of Accuracy and Sensitivity to Freestream Conditions of a Modified k-ω Turbulence Model for High-Order Finite Element Methods

2020 ◽  
Author(s):  
Nojan Bagheri-Sadeghi ◽  
Brian T. Helenbrook ◽  
Kenneth D. Visser
Keyword(s):  
Boundary Condition ◽  
Finite Element ◽  
Flat Plate ◽  
Turbulence Model ◽  
Finite Element Methods ◽  
Incompressible Flows ◽  
Grid Point ◽  
High Order ◽  
Surface Boundary ◽  
Wall Distance

Abstract Using turbulence models with finite element methods (FEM) can be challenging as the turbulence variables can assume negative non-physical values and hinder solution convergence. A modified k–ω model was recently proposed by Stefanski et al. (2018) to be used with finite element solvers of compressible flows. The model overcomes this issue by replacing k and ω with working variables that ensure positivity and smoothness of k and ω. In this work the applicability of this model for high-order FEM simulations of incompressible flows was examined. The model was implemented for incompressible flow in an hp-FEM solver using streamline Petrov-Galerkin discretization and was validated and verified using a fully-developed channel flow and a boundary layer flow over a flat plate. Several aspects of the turbulence model behavior were studied. These included the possibilitty of getting orders of accuracy higher than 2, and the model’s sensitivity to freestream values of k and ω. The results suggested that higher orders of accuracy are possible when quadratic and quartic basis functions are used. However, this depended on the way the boundary condition for ω was defined. The commonly used boundary condition for ω, which depends on the wall-distance of the first grid point resulted in poor orders of accuracy compared to the so-called slightly-rough-surface boundary condition which is independent of the wall distance of the first grid point. Additionally, results indicated that increasing the nondimensional wall distance of the first gridpoint makes it more sensitive to the value of ω on the wall. Adding a cross-diffusion term to the transport equation for ω is known to significantly improve the accuracy of turbulence model prediction for certain flows and reduce the sensitivity of the original k–ω model to freestream values of turbulence variables. Following a more recent version of k–ω model, this term was added to the turbulence model and some other modifications including a different production term with a stress-limiter were applied. The drag coefficient of the flat plate from the new turbulence model showed similar sensitivity to the freestream values of turbulence variables as the model of Stefanski et al. (2018).

Equilibrium Profile of Modern Belted Radial Ply Tires: Its Determination and Performance Benefits

2013 ◽  
Vol 41 (2) ◽  
pp. 127-151
Author(s):  
Rudolf F. Bauer
Keyword(s):  
Finite Element ◽  
Aspect Ratio ◽  
Finite Element Methods ◽  
Mathematical Analysis ◽  
Internal Stresses ◽  
Stress Concentrations ◽  
Equilibrium Profiles ◽  
Equilibrium Profile ◽  
And Performance ◽  
Beneficial Property

ABSTRACT The benefits of a tire's equilibrium profile have been suggested by several authors in the published literature, and mathematical procedures were developed that represented well the behavior of bias ply tires. However, for modern belted radial ply tires, and particularly those with a lower aspect ratio, the tire constructions are much more complicated and pose new problems for a mathematical analysis. Solutions to these problems are presented in this paper, and for a modern radial touring tire the equilibrium profile was calculated together with the mold profile to produce such tires. Some construction modifications were then applied to these tires to render their profiles “nonequilibrium.” Finite element methods were used to analyze for stress concentrations and deformations within all tires that did or did not conform to equilibrium profiles. Finally, tires were built and tested to verify the predictions of these analyses. From the analysis of internal stresses and deformations on inflation and loading and from the actual tire tests, the superior durability of tires with an equilibrium profile was established, and hence it is concluded that an equilibrium profile is a beneficial property of modern belted radial ply tires.

Finite element methods for internal flow calculations

1983 ◽  
Author(s):  
W. HABASHI ◽  
M. HAFEZ ◽  
P. KOTIUGA
Keyword(s):  
Finite Element ◽  
Finite Element Methods ◽  
Internal Flow
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