Solving the transverse bending problem of thin elastic orthotropic plates with form factor interpolation method

Korobko, V. I.; Коробко, А. В.; Savin, S.Y.; Chernyaev, A. L.

doi:10.5937/jsscm1602009k

Cited by 8 publications

(3 citation statements)

References 7 publications

(6 reference statements)

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“…In [7][8][9][10], a method of interpolation by the shape coefficient based on affine transformations was proposed for calculating triangular plates with a hinged or rigid support along their perimeter, a bending stress-strain state is considered, including with free vibrations. The plate material can be either isotropic or orthotropic.…”

Section: Introductionmentioning

confidence: 99%

Physical and Mechanical State of Cantilever Triangular Plates

Akhmediyev

Vatin

Yessenbayeva

et al. 2023

JMMCS

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In this paper, the bending of cantilever triangular plates at the same angles of inclination of the side edges to the base is investigated. Due to the complexity of the boundary conditions, a numerical finite difference method is applied using a grid of scalene triangles that fits well into the contour of the plate. To solve the problem of an acute angle at the top of the plate, the method of combining the results of calculating a cantilever bar of variable bending stiffness with similar results of calculating a triangular plate supported along the contour using a reduction factor is applied. The results of deflections of the cantilever triangular plate at different angles of inclination of the side edges to the base are given. The theoretical provisions and applied results of this study can be used both in scientific research and in engineering design.

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Section: Introductionmentioning

confidence: 99%

Physical and Mechanical State of Cantilever Triangular Plates

Akhmediyev

Vatin

Yessenbayeva

et al. 2023

JMMCS

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“…The method is based on the use of isoperimetric properties and patterns of change in the shape factor of the area under geometric transformations, which also allows calculating triangular plates. In [19,20], the possibility of applying the method of interpolation by the shape factor to the calculation of triangular plates from an orthotropic material is considered.…”

Section: Introductionmentioning

confidence: 99%

Studying Dynamics of a Cantilever Bar With Variable Bending Stiffness

Khabidolda

2023

JMMCS

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In this paper, there are studied the dynamic processes (free and forced oscillations) of isotropic cantilever plates in the form of an isosceles (wedge-shaped) triangle. In the study, the finite difference method has been applied using a regular one-dimensional (linear) grid. The finitedifference equations developed by the authors for point-distributed masses along the length of the wedge are presented, taking into account the linearly variable bending stiffness. On this basis, the results of studies in the form of amplitude-frequency characteristics (frequencies, dynamic forces and deflections) in the resonant and near-resonant regions have been obtained. The content of theoretical provisions and applied results can be widely used in the scientific and engineering fields and in the field of mechanics of structures.

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“…Over the last years in structural mechanics, the isoperimetric method of two-dimensional problems solution develops rapidly. Its geometric ground is based on isoperimetric properties of so-called form factor [8][9][10][11][12][13][14][15][16][17]. According to the carried out investigations, geometrical rigidity of sections with arbitrary convex contour functionally depends on this factor.…”

Section: Introductionmentioning

confidence: 99%

Estimation of Geometrical Torsion Rigidity of Triangular and Rectangular Sections Using Interpolation Method

Коробко

Savin

Balikhina

2018

Proceedings of the 4th International Conference on Industrial Engineering

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The article considers the problem on a pure torsion of elastic prismatic beam with arbitrary convex contour in the isoperimetric form. It is proved that for isometric sections with a convex contour, the normalized geometrical torsion rigidity depends on one parameter only-the form factor. The sections in the form of isosceles and rectangular triangles, rectangles, and parallelograms are considered. Graphical comparison of the given geometrical rigidity of the examined sections with the value reciprocal of the form factor displayed the real similarity of these graphs. Analysis of these graphs provides the conclusion that all the range of values of the normalized geometrical rigidity of parallelogram sections is limited from above with values i k for rectangular sections, and from below-for the rhombic sections. Applying the method of geometrical modeling rigidity of the sections by a section form, we suggest the interpolation method to determine the given geometrical rigidity of the sections by the form factor. The obtained results are otherwise satisfactory when performing engineering calculations.

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Solving the transverse bending problem of thin elastic orthotropic plates with form factor interpolation method

Cited by 8 publications

References 7 publications

Physical and Mechanical State of Cantilever Triangular Plates

Physical and Mechanical State of Cantilever Triangular Plates

Studying Dynamics of a Cantilever Bar With Variable Bending Stiffness

Estimation of Geometrical Torsion Rigidity of Triangular and Rectangular Sections Using Interpolation Method

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