Stress-Strain State in Structure Angular Zone Taking into Account Differences Between Intensity Factors

Frishter, Lyudmila

doi:10.1007/978-3-030-57453-6_31

Cited by 3 publications

(6 citation statements)

References 3 publications

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“…An experimental solution to the elastic problem of strain is illustrated for the plane domain through the case of a composite plane model that is 180 mm long and 24 mm wide. Deformation defrosting and photo-elasticity methods are employed to obtain the experimental solution [15][16][17][18][19][20]. An experimental solution to the elastic problem of strain is illust domain through the case of a composite plane model that is 180 mm wide.…”

Section: Introductionmentioning

confidence: 99%

“…An experimental solution to the elastic problem of strain is illust domain through the case of a composite plane model that is 180 mm wide. Deformation defrosting and photo-elasticity methods are empl experimental solution [15][16][17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

“…It has been experimentally proven [15][16][17][18][19][20] that substantial strain and rotations are observed in the area close to the vertex of the angular cutout in the boundary area, which corresponds to higher values of the first and second derivatives of displacements along the radius if the radii in the neighborhood of the irregular boundary point are small enough. The plane problem of elasticity theory must be considered for such areas, taking into account geometric nonlinearity under the action of strain.…”

Section: Introductionmentioning

confidence: 99%

“…The experimental data, obtained using the photo-elasticity method [15][16][17][18][19], show that areas with small strain and areas with large stress and strain gradients are identified in the area of an angular cutout in the boundary.…”

Section: Introductionmentioning

confidence: 99%

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Minor and Major Strain: Equations of Equilibrium of a Plane Domain with an Angular Cutout in the Boundary

Frishter

2023

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Large values and gradients of stress and strain, triggering concentrated stress and strain, arise in angular areas of a structure. The strain action, leading to the finite loss of contact between structural elements, also triggers concentrated stress. The loss of contact reaches an irregular point and a line on the boundary. The theoretical analysis of the stress–strain state (SSS) of areas with angular cutouts in the boundary under the action of discontinuous strain is reduced to the study of singular solutions to the homogeneous problem of elasticity theory with power-related features. The calculation of stress concentration coefficients in the domain of a singular solution to the elastic problem makes no sense. It is experimentally proven that the area located near the vertex of an angular cutout in the boundary features substantial strain and rotations, and it corresponds to higher values of the first and second derivatives of displacements along the radius in cases of sufficiently small radii in the neighborhood of an irregular boundary point. As far as these areas are concerned, it is necessary to consider the plane problem of the elasticity theory, taking into account the geometric nonlinearity under the action of strain, to analyze the effect of relationships between strain orders, rotations, and strain on the form of the equation of equilibrium. The purpose of this work is to analyze the effect of relationships between strain orders, rotations, and strain on the form of the equilibrium equation in the polar system of coordinates for a V-shaped area under the action of temperature-induced strain, taking into account geometric non-linearity and physical linearity.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Minor and Major Strain: Equations of Equilibrium of a Plane Domain with an Angular Cutout in the Boundary

Frishter

2023

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“…They are reviewed in classical papers [1][2][3][4][5][6][7][8][9][10], and the stress-strain concentration factors are no longer relevant. The stress-strain intensity factors are determined more accurately the more detailed the stress-strain state is modeled in a certain approximate neighborhood of the domain boundary cut-out excluding the apex [3,[11][12][13][14][15][16][17][18][19]. Therefore, the mathematical formulation of the elasticity problem in the domain of the boundary cut-out apex becomes relevant from the standpoint of practice if its geometrical non-linearity in the case of forced deformations is taken into account.…”

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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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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Minor and Major Deformations. Equations of Equilibrium of a Planar Domain with an Angular Cutout of the Boundary

Frishter¹

2023

Preprint

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Large values and gradients of stresses and deformations, triggering concentrations of stresses and deformations, arise in the corner areas of a structure. The action of forced deformations, leading to the finite rupture of the contact between the elements of a structure, also triggers the concentration of stresses, while the rupture reaches an irregular point, a line on the area boundary. The theoretical analysis of the stress-strain state (SSS) of areas with angular cutouts in the boundary under the action of discontinuous forced deformations is reduced to the study of singular solutions to the homogeneous problem of the elasticity theory that has power-related features. The calculation of stress concentration coefficients in the domain of a singular solution to the elastic problem makes no sense. It is experimentally proven that the zone, that is close to the vertex of the angular cutout in the area boundary, has substantial deformations, rotations, and it corresponds to rising values of the first and second derivatives of displacements along the radius in cases of sufficiently small radii in the neighbourhood of the irregular point of the boundary. For such areas, it is necessary to consider the plane problem of the elasticity theory, taking into account the geometric nonlinearity under the action of forced deformations. This will allow analyzing the effect of relations between orders of values of deformations, rotations, and forced deformations on the form of the equation of equilibrium. The purpose of this work is to analyze the effect of relations of deformation orders, rotations, forced deformations on the form of the equilibrium equation in the polar coordinate system for a V-shaped area under the action of forced temperature-induced deformations with regard for the geometrical non-linearity and physical linearity.

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Stress-Strain State in Structure Angular Zone Taking into Account Differences Between Intensity Factors

Cited by 3 publications

References 3 publications

Minor and Major Strain: Equations of Equilibrium of a Plane Domain with an Angular Cutout in the Boundary

Minor and Major Strain: Equations of Equilibrium of a Plane Domain with an Angular Cutout in the Boundary

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

Minor and Major Deformations. Equations of Equilibrium of a Planar Domain with an Angular Cutout of the Boundary

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