Use of structural analogy in generation of smooth surfaces for engineering purposes
type: Item
instance of: scholarly article
title: Use of structural analogy in generation of smooth surfaces for engineering purposes
zbMATH Open document ID: 0655.65036
DOI: 10.1016/0010-4485(87)90285-5
published in: CAD. Computer-Aided Design
publication date: 1987-01-01T00:00:00Z
review text: The use of the minimization of surface integrals of functions of the mean and Gaussian curvature to obtain smooth surfaces that satisfy given boundary and other conditions is discussed. A structural analogy based on the bending theory of shells is introduced to enable the designer to predict the effect of changing parameters in the integrals to be minimized. Surfaces of zero mean curvature (minimal or soap film surfaces), surfaces of constant mean curvature (inflated soap films, including the sphere) and the elastica (in two dimensions) are all special cases of the theory.
Mathematics Subject Classification ID: 65D15
Mathematics Subject Classification ID: 51N05
Mathematics Subject Classification ID: 53A10
Mathematics Subject Classification ID: 53A04
zbMATH DE Number: 4070157
zbMATH Keywords: minimal surfaces
zbMATH Keywords: computer-aided geometric design
zbMATH Keywords: surface
zbMATH Keywords: finite element method
zbMATH Keywords: finite difference method
zbMATH Keywords: Gaussian curvature
zbMATH Keywords: bending theory of shells
zbMATH Keywords: zero mean curvature
zbMATH Keywords: soap film surfaces
author: Chris Williams
MaRDI profile type: Publication
full work available at URL: 0010-4485(87)90285-5
OpenAlex ID: W2075184248
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description: scientific article; zbMATH DE number 4070157