Generalization of the super ellipsoid concept and its application in mechanics
College
Engineering and Computer Science
Department
Ocean and Mechanical Engineering
Document Type
Article
Publication/Event/Conference Title
Applied Mathematical Modelling
Publication Status
Version of Record
Abstract
In this paper, we generalize the concept of super ellipsoid that was proposed by the French mathematician and mechanician Gabriel Lamé in 1818. Super ellipsoid itself represents a generalization of the ellipsoid, namely when the power n appearing in super ellipsoid equals 2, the conventional ellipsoid is obtained. In this paper the notion of super ellipsoid is further extended by introducing as many generally different powers, as is dictated by the dimensionality and the physics of the problem. Specifically, two different power parameters are introduced for the generalized super ellipse. Likewise, three generally different powers are adopted for the three-dimensional super ellipsoid etc. An applied mechanics problem is considered to demonstrate the efficiency of the notion of generalized super ellipsoids, namely we study the static behavior of an engine's crankshaft. Two to five geometric parameters specifying the crankshaft are treated as belonging to a generalized super ellipsoid set.
First Page
9427
Last Page
9444
DOI
10.1016/j.apm.2016.06.011
Publication Date
11-1-2016
Recommended Citation
Ni, B. Y.; Elishakoff, Isaac; Jiang, C.; Fu, C. M.; and Han, X., "Generalization of the super ellipsoid concept and its application in mechanics" (2016). Faculty Scholarship. 291.
https://digitalcommons.fau.edu/faculty_papers/291