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.

An analytical solution to the problem of seepage into counterfort drains

1984 ◽  
Vol 21 (4) ◽  
pp. 657-662 ◽  
Author(s):  
Edward Nicholas Bromhead
Keyword(s):  
Finite Element ◽  
Numerical Methods ◽  
Analytical Solution ◽  
Finite Element Methods ◽  
Theoretical Approach ◽  
Small Study ◽  
Full Thickness ◽  
Slope Stabilization ◽  
Design Chart ◽  
And Performance

Recently, J. N. Hutchinson has collected data on the design and performance of trench and counterfort drains. This article presents an analytical solution to one of these cases, that of seepage into counterfort drains which penetrate the full thickness of a layer of soil, down to the impermeable base on which it rests. The soil is assumed to have uniform permeability.The findings of a small study, by Hutchinson, of seepage patterns to such drains, made with the use of finite element methods, are found to be validated by the theoretical approach in this article. This solution also provides a convenient benchmark against which approximate numerical methods can be assessed.Finally, a design chart based on the theory is presented, with examples of its application to the design of counterfort drain installations for slope stabilization.

scholarly journals Stabilised finite element methods for the Oseen problem on anisotropic quadrilateral meshes

2018 ◽  
Vol 52 (1) ◽  
pp. 99-122
Author(s):  
Gabriel R. Barrenechea ◽  
Andreas Wachtel
Keyword(s):  
Finite Element ◽  
Aspect Ratio ◽  
Error Estimates ◽  
Finite Element Methods ◽  
A Priori ◽  
Oseen Equation ◽  
Quadrilateral Meshes ◽  
Oseen Problem ◽  
Two Space Dimensions ◽  
Element Pair

In this work we present and analyse new inf-sup stable, and stabilised, finite element methods for the Oseen equation in anisotropic quadrilateral meshes. The meshes are formed of closed parallelograms, and the analysis is restricted to two space dimensions. Starting with the lowest order ℚ12 × ℙ0 pair, we first identify the pressure components that make this finite element pair to be non-inf-sup stable, especially with respect to the aspect ratio. We then propose a way to penalise them, both strongly, by directly removing them from the space, and weakly, by adding a stabilisation term based on jumps of the pressure across selected edges. Concerning the velocity stabilisation, we propose an enhanced grad-div term. Stability and optimal a priori error estimates are given, and the results are confirmed numerically.

Stress Analysis of a Tire Under Vertical Load by a Finite Element Method

1977 ◽  
Vol 5 (2) ◽  
pp. 102-118 ◽  
Author(s):  
H. Kaga ◽  
K. Okamoto ◽  
Y. Tozawa
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Computer Program ◽  
Temperature Rise ◽  
Strain Energy ◽  
Internal Stresses ◽  
Vertical Load ◽  
The Finite Element Method ◽  
Internal Temperature ◽  
Element Method

Abstract An analysis by the finite element method and a related computer program is presented for an axisymmetric solid under asymmetric loads. Calculations are carried out on displacements and internal stresses and strains of a radial tire loaded on a road wheel of 600-mm diameter, a road wheel of 1707-mm diameter, and a flat plate. Agreement between calculated and experimental displacements and cord forces is quite satisfactory. The principal shear strain concentrates at the belt edge, and the strain energy increases with decreasing drum diameter. Tire temperature measurements show that the strain energy in the tire is closely related to the internal temperature rise.

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

SOME FEATURES OF THE EQUILIBRIUM COASTAL PROFILE FOR DIFFERENT INITIAL BED SLOPES BASED ON MODELLING STUDY

2017 ◽  
Author(s):  
Dmitry Korzinin ◽  
Dmitry Korzinin ◽  
Igor Leontiev ◽  
Igor Leontiev
Keyword(s):  
Time Scales ◽  
Wave Impact ◽  
Grain Sizes ◽  
Equilibrium Profiles ◽  
Equilibrium Profile ◽  
The Mean ◽  
Wave Conditions ◽  
Bed Slope ◽  
Coastal Profile ◽  
Modelling Study

Modelling study of the equilibrium profiles formed on sandy coasts of different bed slopes and grain sizes under the various wave conditions was realized by using the CROSS-P and Xbeach morphodynamic models. A special criterion taking into account a total volume of bed deformations per one hour was suggested to determine the conditions of profile stabilization. For both models the time scales of equilibrium profile formation were found to be the same. However, the deformation magnitudes differed significantly. Bed deformations were computed on the whole profile length over the 200-hours duration of wave impact. It was concluded that both models predict a trend of the bed slope toward a stable value. CROSS-P model shows the widening of accumulative terrace during the profile evolution. The mean slope of the equilibrium profile was found to depend on the initial bed slope.

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