The Mathematical Basis of Finite Element Methods.

1986 ◽  
Vol 47 (175) ◽  
pp. 383
Author(s):  
W. G. ◽  
David F. Griffiths
Keyword(s):  
Finite Element ◽  
Finite Element Methods ◽  
Mathematical Basis

Mathematical Basis of G Spaces

2016 ◽  
Vol 13 (04) ◽  
pp. 1641007 ◽  
Author(s):  
Meng Chen ◽  
Ming Li ◽  
G. R. Liu
Keyword(s):  
Finite Element ◽  
Finite Element Methods ◽  
Weak Formulation ◽  
Mathematical Basis ◽  
Numerical Examples ◽  
Interpolation Methods ◽  
Point Interpolation ◽  
Theoretical Frame ◽  
Lower Boundedness ◽  
Numerical Approaches

This paper represents some basic mathematic theories for G[Formula: see text] spaces of functions that can be used for weakened weak (W2) formulations, upon which the smoothed finite element methods (S-FEMs) and the smoothed point interpolation methods (S-PIMs) are based for solving mechanics problems. We first introduce and prove properties of G[Formula: see text] spaces, such as the lower boundedness and convergence of the norms, which are in contrast with H1spaces. We then prove the equivalence of the Gsnorms and its corresponding semi-norms. These mathematic theories are important and essential for the establishment of theoretical frame and the development of relevant numerical approaches. Finally, numerical examples are presented by using typical S-FEM models known as the NS-FEM and [Formula: see text]S-FEM to examine the properties of a smoothed method based on Gsspaces, in comparison with the standard FEM with weak formulation.

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

Design and Research of Double-Drum Winch with Anti-Pressure Wheel

2012 ◽  
Vol 479-481 ◽  
pp. 1709-1713
Author(s):  
Kai An Yu ◽  
Tao Yang ◽  
Chang Zhi Gong
Keyword(s):  
Finite Element ◽  
Bearing Capacity ◽  
Finite Element Methods ◽  
Design Method ◽  
New Method

In view of the problems of large stress and severe bearing heating in double-drum winch at present, this paper adopted a new method to enhance bearing capacity for double-drum winch by adding anti-pressure wheels between two drums. Finite element methods were used to analyze the strength of 4000kN-traction double-drum winches with anti-pressure wheels and without anti-pressure wheels respectively. The results of the analysis revealed that the stress of the cylinder bearing decreased from 264MPa to 167MPa. The new method by adding anti-pressure wheels had remarkably improved the endurance of the bearing. Therefore, the design method can be widely used in large-traction double-drum winch.

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