ISSN:
0029-5981
Keywords:
Engineering
;
Engineering General
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Mathematics
,
Technology
Notes:
In many practical applications it is desired to describe a surface enclosing a given volume which has to possess a minimum area. Moreover, there are engineering criteria, e.g. the requirement of minimum resistance, which cannot be involved in the present interpolation algorithms of the existing CAD systems. The present paper describes an approach where the surface creation task is formulated as a constrained minimization problem. The pointwise specified co-ordinates are used as boundary conditions. The volume enclosed is a constraint, and the functional under minimization is the surface area. Thus, as the viscous resistance is roughly proportional to the area of the wetted surface, the result approximates the form having minimum viscous resistance. The finite element method is employed and the elements used are C1 continuous isoparametric elements to be able to represent infinite slopes. In the light of applications studied thus far it can be said that the method converges and is thus capable of creating surfaces of minimum area enclosing a given volume.
Additional Material:
5 Ill.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1002/nme.1620230907
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