Generalization of the super ellipsoid concept and its application in mechanics

B.Y. Ni; I. Elishakoff; C. Jiang; C.M. Fu; X. Han

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Generalization of the super ellipsoid concept and its application in mechanics

机译：超椭球概念的推广及其在力学中的应用

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In this paper, we generalize the concept of super ellipsoid that was proposed by the French mathematician and mechanician Gabriel Lame 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.

机译：在本文中，我们推广了法国数学家和力学家加布里埃尔·拉姆（Gabriel Lame）在1818年提出的超级椭球的概念。超级椭球本身代表了椭球的推广，即当超级椭球上出现的幂n等于2时，即传统的椭球。获得。在本文中，超级椭圆体的概念通过引入许多通常不同的幂而得到进一步扩展，这是由问题的维度和物理性质所决定的。具体而言，为广义超椭圆引入了两个不同的功率参数。同样，三维超级椭圆体等采用三种通常不同的幂。考虑一个应用力学问题，以证明广义超级椭圆体概念的效率，即研究发动机曲轴的静态行为。将指定曲轴的2到5个几何参数视为属于广义超椭圆体集。

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来源
《Applied Mathematical Modelling》 |2016年第22期|9427-9444|共18页
作者
B.Y. Ni; I. Elishakoff; C. Jiang; C.M. Fu; X. Han;
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作者单位

State Key laboratory of Advanced Design and Manufacturing for Vehicle Body, College of Mechanical and Vehicle Engineering, Hunan University, Changsha City 410082, PR China;

Department of Ocean and Mechanical Engineering, Florida Atlantic University, Boca Raton, FL 33431-0991, USA;

Department of Ocean and Mechanical Engineering, Florida Atlantic University, Boca Raton, FL 33431-0991, USA;

State Key laboratory of Advanced Design and Manufacturing for Vehicle Body, College of Mechanical and Vehicle Engineering, Hunan University, Changsha City 410082, PR China;

State Key laboratory of Advanced Design and Manufacturing for Vehicle Body, College of Mechanical and Vehicle Engineering, Hunan University, Changsha City 410082, PR China;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类
关键词
Super ellipsoid; Crankshaft; Different powers; Convex model;

机译：超级椭球;曲轴不同的权力;凸模型;

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Generalization of the super ellipsoid concept and its application in mechanics

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