Generating smooth curves in 3 dimensions by minimizing higher order strain energy measures

Sigrid M. Adriaenssens; Samar Malek; Masaaki Miki; Chris J.K. Williams

doi:10.1260/0266-3511.28.3-4.119

Generating smooth curves in 3 dimensions by minimizing higher order strain energy measures

Sigrid M. Adriaenssens, Samar Malek, Masaaki Miki, Chris J.K. Williams

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

Elastic beams or rods in two and three dimensions produce smooth curves by minimizing the strain energy due to classical Euler-Bernoulli bending and Saint-Venant torsion subject to constraints on the arc length and end positions and orientations.However it is possible to postulate other strain energy measures. In this paper we describe a strain energy measure which is the sum of the square of the rate of change of curvature and the square of the product of the curvature and the Frenet torsion.

Original language	English (US)
Pages (from-to)	119-126
Number of pages	8
Journal	International Journal of Space Structures
Volume	28
Issue number	3-4
DOIs	https://doi.org/10.1260/0266-3511.28.3-4.119
State	Published - Sep 1 2013

All Science Journal Classification (ASJC) codes

Conservation
Civil and Structural Engineering
Architecture
Building and Construction

Keywords

clothoid
cornu spiral
curvature
elastica
euler spiral
railway transition curve
torsion

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10.1260/0266-3511.28.3-4.119

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abstract = "Elastic beams or rods in two and three dimensions produce smooth curves by minimizing the strain energy due to classical Euler-Bernoulli bending and Saint-Venant torsion subject to constraints on the arc length and end positions and orientations.However it is possible to postulate other strain energy measures. In this paper we describe a strain energy measure which is the sum of the square of the rate of change of curvature and the square of the product of the curvature and the Frenet torsion.",

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AU - Malek, Samar

AU - Miki, Masaaki

AU - Williams, Chris J.K.

PY - 2013/9/1

Y1 - 2013/9/1

N2 - Elastic beams or rods in two and three dimensions produce smooth curves by minimizing the strain energy due to classical Euler-Bernoulli bending and Saint-Venant torsion subject to constraints on the arc length and end positions and orientations.However it is possible to postulate other strain energy measures. In this paper we describe a strain energy measure which is the sum of the square of the rate of change of curvature and the square of the product of the curvature and the Frenet torsion.

AB - Elastic beams or rods in two and three dimensions produce smooth curves by minimizing the strain energy due to classical Euler-Bernoulli bending and Saint-Venant torsion subject to constraints on the arc length and end positions and orientations.However it is possible to postulate other strain energy measures. In this paper we describe a strain energy measure which is the sum of the square of the rate of change of curvature and the square of the product of the curvature and the Frenet torsion.

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KW - elastica

KW - euler spiral

KW - railway transition curve

KW - torsion

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ER -

Generating smooth curves in 3 dimensions by minimizing higher order strain energy measures

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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