Frishter, L. Minor and Major Strain: Equations of Equilibrium of a Plane Domain with an Angular Cutout in the Boundary. Axioms2023, 12, 893.
Frishter, L. Minor and Major Strain: Equations of Equilibrium of a Plane Domain with an Angular Cutout in the Boundary. Axioms 2023, 12, 893.
Frishter, L. Minor and Major Strain: Equations of Equilibrium of a Plane Domain with an Angular Cutout in the Boundary. Axioms2023, 12, 893.
Frishter, L. Minor and Major Strain: Equations of Equilibrium of a Plane Domain with an Angular Cutout in the Boundary. Axioms 2023, 12, 893.
Abstract
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.
Keywords
elastic boundary value problem; finite deformations; temperature deformations; polar coordinate system; angular cutout in the boundary of a planar domain; relations of deformation orders; equations of equilibrium
Subject
Computer Science and Mathematics, Applied Mathematics
Copyright:
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