A Sierpiński triangle geometric algorithm for generating stronger structures

Zhikharev, L.

doi:10.1088/1742-6596/1901/1/012066

Cited by 12 publications

(10 citation statements)

References 12 publications

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“…These new elements allow one to create models of geometric transformations and to apply these models in solutions to various problems. The geometric transformations and correspondences can find application in solutions to the problems of modeling in engineering [6,7], architecture [4], geometric fractals [8], design, etc. Any geometric construction or correspondence that can be defined constructively can be implemented through the GC language.…”

Section: Discussionmentioning

confidence: 99%

Modeling of geometric correspondences and transformations via geometry constructions language

Boykov

2022

J. Phys.: Conf. Ser.

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Geometric correspondences and transformations can be applied in solutions to numerous problems of geometric modeling, mainly in order to create models of curves and surfaces. Among the tools of CAD systems, the geometric transformations are presented in the form of a limited set of editing tools, array tools, tools providing formation of 3D solids and surfaces through motion. In practice, this set of tools restricts application of the wide capabilities of geometric transformations and correspondences. In this regard, it is proposed to model the geometric transformations and correspondences via the geometry construction language. The elements of the geometric transformation theory are analyzed. The geometric transformations are proposed to be created on par with other objects of the geometric model. The commands of the geometry constructions language enabling construction of the transformation objects are considered, their application is discussed. Solutions to practical problems of surface modeling via the geometry constructions language with the use of geometric transformation are demonstrated on examples. The proposed approach allows us to facilitate modeling of curves and surfaces in CAD systems, if said curves and surfaces can be acquired through geometric transformation or correspondence that can be defined via a certain constructive algorithm.

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Section: Discussionmentioning

confidence: 99%

Modeling of geometric correspondences and transformations via geometry constructions language

Boykov

2022

J. Phys.: Conf. Ser.

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“…In addition to the use of rational cross-sections, truss, lattice structures and topology optimization [7], the use of fractal structures [8,9] belongs to the geometric method. In the article [10], the effectiveness of increasing the strength of light structures using fractal geometry created on the basis of the Sierpinski triangle was theoretically confirmed.…”

Section: Introductionmentioning

confidence: 94%

“…"The base part" of such an element is a triangle assembled from plates of constant thickness. These plates perceive the main part of the compressive load, which is the reason for this name [10]. A fractal grid of thinner plates is placed inside the base triangle, which prevents the loss of stability of the basic elements.…”

Section: The Experimentalmentioning

confidence: 99%

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Grid Based on the Sierpinski Fractal and an Assessment of the Prospects for its Application in Aircraft Parts

Zhikharev

2021

Proceedings of the 31th International Conference on Computer Graphics and Vision. Volume 2

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Modern geometric methods open up prospects for improving the shape and structure of parts. Such improvement can pursue the goals of increasing the strength with constant material consumption, or reducing the mass when it is not necessary to increase the strength. The meaning of geometric methods is to create a part shape the stresses arising in the part material under the action of applied loads are distributed most evenly. Such methods include the use of fractal geometry. This article presents the results of a study of a fractal lattice created on the basis of the Sierpinski triangle. Computer simulation in the SolidWorks, as well as strength studies of parts produced using additive technologies, allowed us to confirm a multiple increase in the strength of the fractal lattice with an increase in the number of fractal iterations. One of the most promising areas of application of fractal structures may be aviation technology. In this area, weight reduction is needful, and the complex shape of the parts is realized with the help of expensive production methods. For this reason, a number of experiments were conducted within the framework of the study, the purpose of which was to test the feasibility of using fractal gratings to reduce the weight of aircraft parts, using the example of the fork of the front landing gear of the combat training aircraft Yak-130.

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“…Surfaces generated as geometric locus of points equidistant to various geometric shapes offer practical value in architecture, industrial construction and cosmonautics [5]. A frame designed of GLP surfaces can be optimized with methods documented in paper [6]. At the moment, various studies on modeling and application of complex surfaces are being held [7,8].…”

Section: Introductionmentioning

confidence: 99%

Modeling and study of properties of surfaces equidistant to a sphere and a plane

Vyshnepolsky

Efremov

Заварихина

2022

J. Phys.: Conf. Ser.

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In the present paper geometric locus of points (GLP) equidistant to a sphere and a plane is considered; the properties of the acquired surfaces are studied. Four possible cases of mutual location of a sphere and a plane are considered: the plane passing through the center of the sphere, the plane intersecting the sphere, the plane tangent to the sphere and the plane passing outside the sphere. GLP equidistant to a sphere and a plane constitutes two co-axial co-focused paraboloids of revolution. General properties of the acquired paraboloids were studied: the location of foci, vertices, axis and directing planes, distance between the sphere center and the vertices, the distance between the vertices. GLP for each case of mutual location of a plane and a sphere constitutes: in case one passes through the center of other, two co-axial co-focused oppositely directed paraboloids of revolution symmetrical with respect to the given plane; in case they intersect each other, two co-axial co-focused oppositely directed non-symmetrical paraboloids; in case they are tangent to each other, a paraboloid and a straight line passing through the tangency point; in case they have no common points, a pair of co-axial co-focused mutually directed paraboloids of revolution.

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A Sierpiński triangle geometric algorithm for generating stronger structures

Cited by 12 publications

References 12 publications

Modeling of geometric correspondences and transformations via geometry constructions language

Modeling of geometric correspondences and transformations via geometry constructions language

Grid Based on the Sierpinski Fractal and an Assessment of the Prospects for its Application in Aircraft Parts

Modeling and study of properties of surfaces equidistant to a sphere and a plane

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