Two-dimensional problems of the calculus of variations in nonparametric form, transformed into parametric form

1958 ◽  
pp. 319-339 ◽  
Author(s):  
A. G. Sigalov
Keyword(s):  
Calculus Of Variations ◽  
Parametric Form ◽  
Two Dimensional

Optimization of Self-Acting Gas Bearings for Maximum Static Stiffness

1990 ◽  
Vol 57 (3) ◽  
pp. 758-761 ◽  
Author(s):  
Michel P. Robert
Keyword(s):  
Finite Element ◽  
Film Thickness ◽  
Calculus Of Variations ◽  
Two Dimensional ◽  
Final Solution ◽  
Static Stiffness ◽  
Finite Element Technique ◽  
Minimum Film Thickness ◽  
Element Technique ◽  
Gas Bearing

The gap profile of a two-dimensional self-acting gas bearing is determined such that the static stiffness it can achieve is maximum. Three fundamental profiles are obtained according to the stiffness mode to be considered: normal, pitch, or roll. The optimization process takes place within the framework of the compressible lubrication theory among all the profiles having a given minimum film thickness. The method proposed here is based on the calculus of variations and uses a finite element technique coupled with an iterative mapping to converge to the final solution. As an example, the case of a square bearing is treated and the three fundamental gap profiles, along with their optimum characteristics, are plotted to illustrate the solutions.

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