Steffen's Flexible Polyhedron

Keyword(s):  

1975 ◽  
Vol 97 (4) ◽  
pp. 1291-1294 ◽  
Author(s):  
M. A. Townsend ◽  
F. Y. Lam

A direct search algorithm based upon the flexible tolerance method developed by Paviani and Himmelblau [1] for minimization of a functional subject to nonlinear equality and inequality constraints is proposed and evaluated. The modification incorporates a weighting on the direction of search in which the flexible polyhedron formed orients itself toward the gradient of the objective function (and clings to all active constraints). This is accomplished by weighting the centroid, in the sense of minimization, of the polyhedron with respect to the objective function. A number of problems have been solved satisfactorily by this algorithm, generally with more rapid convergence.





1988 ◽  
Vol 41 (4) ◽  
pp. 1106-1110
Author(s):  
Yu. D. Elizarov ◽  
E. L. Stolov


1988 ◽  
Vol 110 (4) ◽  
pp. 718-726 ◽  
Author(s):  
Z. P. Mourelatos

A theoretical model is presented to solve the transient, two-dimensional, compressible Reynolds equation for a gas bearing. The Newton-Raphson method is used on the governing nonlinear Reynolds equaion while the Galerkin’s method is employed to solve the resulting linear equations for the correction term. The numerical solution of the pressure distribution of an infinitely long, plane-wedge, slider bearing compares very well with the analytical (exact) solution. This theoretical model is then used to calculate the trajectory of a ringless piston within the cylinder of an I. C. engine under a given dynamic loading. The flexible polyhedron unconstrained minimization method is used to find the equilibrium position of the piston within the cylinder for each crankangle. It was found that a 40 mm long ringless piston can support a uniform side load of about 50 Newtons at 2000 r/min running on a gas film. However, the same piston can sustain a nonuniform side load with a much higher peak value (three to five times the uniform load) which lasts approximately 20 to 30 degrees of crankangle only. The sustainable side load by gas lubrication is much lower than the peak piston side load of conventional internal combustion engines.



2011 ◽  
Vol 66-68 ◽  
pp. 626-630
Author(s):  
Yong Qi Chen

The support vector interval regression model is an effective method to estimate imprecise data. Parameters of this model is very important in order to obtain the excellent regression result. The flexible polyhedron search algorithm is a fast optimization algorithm. Based on the flexible polyhedron search algorithm, this paper proposes an automatic parameters selection method for the support vector interval regression model. Experiments illustrate the validity and applicability of the support vector interval regression model based on the flexible polyhedron search algorithm.





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