Variation of shape operator under infinitesimal bending of surface

Velimirović, Ljubica S.; Cvetković, Milica; Najdanović, Marija S.; Velimirović, Nikola

doi:10.1016/j.amc.2013.09.033

Cited by 7 publications

(2 citation statements)

References 5 publications

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“…Moore and Healey [12] developed and applied numerical methods to construct and explore the stability of Möbius bands. Velimirović and coworkers [13,14] exposed connections between the literature inspired by Sadowsky's [1,2] work and mathematical investigations directed at minimizing the Willmore [15] functional.…”

Section: Introductionmentioning

confidence: 99%

Construction of Unknotted and Knotted Symmetric Developable Bands

2021

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We describe a method for constructing developable bands with N≥3 half twists. Each band is formed by threading a flat rectangular strip through a scaffold made from identical circular cylinders and smoothly connecting its short ends. The N cylinders in a scaffold are arranged with N-fold rotational symmetry. The number of half twists in a band is equal to the number N of cylinders in its scaffold and each band inherits the symmetry of its scaffold. Each scaffold admits a family of bands of the same length but variable width up to a maximum value determined by the features of the scaffold. Apart from orientable and nonorientable unknots, our method allows for the construction of bands with the topology of torus knots. We detail the geometric properties of the construction, discuss certain fundamental restrictions that must be met to ensure constructability, and calculate the elastic bending energy of each band. The rotational symmetry underlying the construction is essential for obtaining the presented bands, as the general non-symmetric problem is even more complex and has not yet been investigated. The bands and their corresponding scaffolds can be used as structural elements in practical applications, one of which we describe and analyze. The construction serves as a basis for a general framework for building a large variety of scaffolds and the corresponding unstretchable bands. Together, these assemblies can be used in architectural, interior, and machine design. They also open new avenues for the layout of conveyor belts in factories, airports, and other settings.

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Section: Introductionmentioning

confidence: 99%

Construction of Unknotted and Knotted Symmetric Developable Bands

2021

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“…The paper concerns with a study of infinitesimal rotary transformations [8], for other exmaples of infinitesimal transformations see also [2,12,[15][16][17][18][19][20]. The rotary diffeomorphism and rotary transformations of two-dimensional Riemannian spaces were first introduced by Leiko [4,5,7,11].…”

Section: Introductionmentioning

confidence: 99%

Infinitesimal rotary transformation

Rýparová

Mikeš

2019

Filomat

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The paper is devoted to further study of a certain type of infinitesimal transformations of twodimensional (pseudo-) Riemannian spaces, which are called rotary. An infinitesimal transformation is called rotary if it maps any geodesic on (pseudo-) Riemannian space onto an isoperimetric extremal of rotation in their principal parts on (pseudo-) Riemannian space. We study basic equations of the infinitesimal rotary transformations in detail and obtain the simpler fundamental equations of these transformations.

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Gaudi surfaces and curvature based functional variations

Velimirović

Cvetković

2014

Applied Mathematics and Computation

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Variation of shape operator under infinitesimal bending of surface

Cited by 7 publications

References 5 publications

Construction of Unknotted and Knotted Symmetric Developable Bands

Construction of Unknotted and Knotted Symmetric Developable Bands

Infinitesimal rotary transformation

Gaudi surfaces and curvature based functional variations

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