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Surfaces of minimum area by FEM
Author(s) -
Pramila A.,
Virtanen S.
Publication year - 1986
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620230907
Subject(s) - pointwise , surface (topology) , interpolation (computer graphics) , minification , finite element method , constraint (computer aided design) , boundary (topology) , volume (thermodynamics) , mathematics , geometry , mathematical optimization , mathematical analysis , mechanical engineering , engineering , structural engineering , physics , frame (networking) , quantum mechanics
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 C 1 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.