Restrictions on Stress Components in the Top of Round Cone

Pestrenin, Valery Mikhaylovich; Pestrenina, I. V.; Landik, Lidiya Vladimirovna

doi:10.17223/19988621/52/9

Cited by 4 publications

(6 citation statements)

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“…In the process, not only first-order and second-order derivatives of displacements increase for small radii. The effect of forced deformations with a finite discontinuity along the contact line of the domain components extending into the cut-out apex at the boundary can result in an increase in first-order and second-order derivatives of displacements as the distance to the cut-out apex reduces along the radius, which is confirmed experimentally in [15,[20][21][22][23][24][25][26][27]29]. Therefore, taking into account the second-order displacement derivatives in such areas will result in a more accurate elasticity problem statement, which justifies the need to take finite deformations into account.…”

Section: Introductionmentioning

confidence: 81%

“…Values and gradients of stresses and deformations are great in a domain with geometrically non-linear shapes of the boundary (cut-outs, cuts) [1][2][3][4][7][8][9][10][11][12][13][14]. In such areas of the angular cut-out of the domain boundary, certain irregularities are experimentally identified in terms of the solution to the non-linear elasticity problem [15][16][17][18][19][20][21][22][23][24][25][26][27][28]. Displacements are continuous in the area of the boundary cut-out of the domain and in the cut-out apex itself [1][2][3][4][5][6][7][8][9][10][11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

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Geometrically Non-Linear Plane Elasticity Problem in the Area of an Angular Boundary Cut-Out

Frishter

2023

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A relevant problem in the development and improvement of numeric analytical methods for the research of structures, buildings and construction is studying the stress–strain state of structures and construction with boundaries that have complex shapes. Deformations and stresses arise in a domain with a geometrically non-linear shape of the boundary (cut-outs and cuts). These stresses and deformations have great values and gradients. Experiments carried out using the photoelasticity method show a change in the deformation order ratios for different subareas of the boundary cut-out area depending on proximity to the apex of the angular cut-out. Areas with minor deformations are observed, and areas where linear deformations and shears are more significant than rotations are also observed. In addition, areas where section rotations are more significant than linear and shear deformations are observed. According to the experimental data, the mathematical model of the SSS in the area of the apex of the cut-out of the domain boundary should take into account non-linear deformations. Hence, it is necessary to formulate the boundary value problem of the theory of elasticity, taking into account the geometrical non-linearity. The research aim of this paper is to formulate the problem of the elasticity theory taking into account the geometrical non-linearity in furtherance of the proposed mathematical model justified by the experimental data obtained using the photoelasticity method. The obtained formulation of the elasticity theory problem allows analyzing the form of the system of equations of the boundary value problem depending on the proximity of the considered area to the irregular point of the boundary, i.e., taking into account the difference in the effect of linear and shear deformations, rotations and forced deformations on the solution to the geometrically non-linear elastic problem dealing with forced deformations in the area of an angular cut-out of the boundary of the plane domain.

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Section: Introductionmentioning

confidence: 81%

Section: Introductionmentioning

confidence: 99%

Geometrically Non-Linear Plane Elasticity Problem in the Area of an Angular Boundary Cut-Out

Frishter

2023

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“…The method of composite disks calibration tests allows determining forced deformations and pressure acting in the model of the method of photoelasticity and defrosting of forced deformations. The obtained data of calibration tests are used for the experimental solution by the method of photoelasticity of elasticity problems with discontinuous forced deformations [10][11][12][13][14][15][16][17] and the simulation of composite structures with forced deformations. The accuracy of the obtained model parameters is determined by the accuracy of the experimental photoelasticity method.…”

Section: Discussionmentioning

confidence: 99%

Calibration testing of discs using photoelasticity method

Frishter

2018

MATEC Web Conf.

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Using of the photoelasticity method for determining the stresses under the action of specified forced deformations and, in particular, temperature deformations, which do not satisfy the compatibility conditions, is relevant in the study of composite structures. Photoelasticity method, which is a continual method, and the method of “defrosting” forced deformations, as its subsection, allow obtaining a stress-strain state in the composite area with forced deformations on models made of optically - responsive material. The method of defrosting forced deformations, using the procedure of preliminary freezing of model elements with subsequent defrosting of the entire model, is an effective, versatile and promising method for simulation of stresses as a result of specified forced deformations. In the study of composite structures by the method of photoelasticity and defrosting “defrosting” of forced deformations, a model composed of elements with previously created forced deformations is created. To determine the created forced deformations, calibration tests are performed, in which the following actual loads are determined: forced deformations, pressure, optical and mechanical characteristics of the model material: modulus of elasticity, material fringe value. Novelty of the calibration test method is the definition of “frozen” forced deformations in the blank of the photoelasticity model using a single composite disk model without testing additional models - beams [1, 2]. Taken into account the material parameters of model: Young's modulus, the price of a polymeric material strip, which are different for batches of initial components: epoxy resin and anhydrite. In order to approve the results of calibration tests, this paper considers the theoretical and experimental solution of the elasticity test problem for a composite disk, one of the areas of which is uniformly heated. The obtained data are used for calibration tests in determining the actual loads and mechanical characteristics in the model sections.

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“…This circumstance makes the problem of mechanics of a deformable solid with a non-classical singular point. Non-classical (in the indicated sense) problems were considered in the subsequent works of these authors such as (homogeneous flat wedges (Pestrenin et al, 2016), composite flat wedges (Pestrenin et al, 2015, composite spatial edges, internal singular points in flat and spatial structural elements (Pestrenin et al, 2018), three-dimensional composite edges , circular homogeneous and composite cones, regular polyhedral (Pestrenin et al, 2014). In the present article, a non-classical approach is used to study the state parameters at the edge of a homogeneous elastic body.…”

Section: Introductionmentioning

confidence: 99%

Restrictions on the stress components in the edge points of the homogeneous elastic body

Pestrenin¹,

Pestrenina²,

Landik³

2019

10.5267/j.esm

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The concept of a deformable body point is taken in the form of a continuum point and an elementary volume connected with it. The continuum point determines the spatial position of the deformable body point, and the elementary volume is the carrier of its material properties and stress-strain state characteristics. Based on this representation, restrictions on the state parameters at the edge points (singular points) of an isotropic body are constructed. These restrictions become preset conditions in singular points. The study covers possible interactions of the edge-forming surfaces with the external environment. It is shown that the restrictions formed at the edge points are usually more numerous than the restrictions at the regular point on the surface of a deformable body. This circumstance leads to a non-classical formulation of the mechanics problem for bodies with singular points. The combinations of geometric and material parameters of a structural component are discovered that determine the singular stresses behavior in elementary volumes with edge points. The load restrictions ensuring the compatibility of parameters defined at singular points are formulated. The attained results will apply to studying stress concentration in the vicinity of 3D-edges of structural components.

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Restrictions on Stress Components in the Top of Round Cone

Cited by 4 publications

References 0 publications

Geometrically Non-Linear Plane Elasticity Problem in the Area of an Angular Boundary Cut-Out

Geometrically Non-Linear Plane Elasticity Problem in the Area of an Angular Boundary Cut-Out

Calibration testing of discs using photoelasticity method

Restrictions on the stress components in the edge points of the homogeneous elastic body

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