Ашық рұқсат
Рұқсат берілді
Тек жазылушылар үшін
Том 228, № 2 (2018)
- Жылы: 2018
- Мақалалар: 7
- URL: https://journals.rcsi.science/1072-3374/issue/view/14877
Article
Influence of a Stationary Heat Source on the Stress State of a Half Space with Rigidly, Smoothly, or Flexibly Fastened Boundary
Аннотация
By using the thermoelastic potential of displacements and the Love biharmonic function, we determine the temperature, displacements, and stresses caused by a stationary heat source in a semiinfinite body whose boundary is rigidly, smoothly, or flexibly fastened either under the conditions of zero temperature kept on it or under the conditions of heat insulation. The plots of the dependences of axial, radial, circular, and tangential stresses on the boundary of the body on the distance between the heat source and this boundary are presented.
91-104
Two-Dimensional Mixed Problem of Thermoelasticity for a Semistrip
Аннотация
We study the stress state of a semistrip with conditions of smooth contact imposed on one of its lateral surfaces and coupling conditions given on the other surface under the action of normal loading and temperature on the end face. The original problem is reduced to a one-dimensional vector boundary-value problem by the method of integral transformations. By using the tools of matrix differential calculus and Green matrix function, we reduce the obtained problem to a singular integral equation for the derivative of displacements on the end face of the semistrip and solve this equation by the method of orthogonal polynomials. We perform the numerical analysis of fields of displacements and stresses inside the semistrip and establish the zones of tensile stresses on the lateral face of the semistrip and the conditions of their formation.
105-121
On One Numerical-Analytic Method for the Solution of One-Dimensional Quasistatic Problems of Thermoelasticity for Thermosensitive Bodies of Simple Geometry
Аннотация
We propose a procedure for the numerical-analytic solution of one-dimensional problems of thermoelasticity for bodies of simple geometry based on the representation of temperature dependences of the physicomechanical characteristics of materials in the form of piecewise constant functions of temperature and the application of the Kirchhoff substitution and the methods of generalized functions. This procedure enables us to study one-dimensional nonstationary thermal and quasistatic stress-strain states under the combined thermal and force action with controlled reliability.
122-132
Approximate Solution of the One-Dimensional Problem of the Theory of Elasticity for an Inhomogeneous Solid Cylinder
Аннотация
For the solution of the one-dimensional problem of the theory of elasticity for a radially inhomogeneous solid cylinder, we use the method of reduction to a Volterra integral equation. By estimating the error of satisfying the governing integral equation, we establish a criterion of accuracy of the approximate solution of the problem.
133-141
Plastic Deformation of Materials Under Loading Along Piecewise Smooth Trajectories with Areas of Unloading by the Elastic Law
Аннотация
Within the framework of a version of plasticity theory based on the concept of slip, we propose a method for the determination of plastic strains in materials with regard for the strain anisotropy in the case of loading applied along piecewise smooth trajectories (with areas of unloading according to the elastic law). The material function of plasticity Π used in this theory is determined, for a given function of hardening F , either from the tension–compression tests or from the tests with alternating torsion of thin-walled pipes.
142-161
Biaxial Bending of an Isotropic Plate with Through Rectilinear Crack with Regard for the Width of the Contact Zone of its Edges and in the Presence of Plastic Zones Near its Tips
Аннотация
We pose and solve the problem of the biaxial bending of an isotropic plate with through rectilinear crack by distributed bending moments applied at infinity. The edges of the crack are in contact over the zone of constant width and plastic zones are formed near the crack tips. By using the Tresca plasticity conditions in the form of a surface layer and a plastic hinge, we determine the length of the plastic zone and the crack opening displacements near the tips. The numerical analysis of the problem is performed.
162-172
Contact Problem of Wear of the Elastic Half Plane with Winkler’s Coating Caused by Punches of Canonical Shapes
Аннотация
The problem of contact interaction of punches of canonical shapes (cylindrical, elliptic, and hyperbolic) with elastic half planes covered with protective coatings is solved with regard for the wear of the material. We propose a method for the solution of the singular integrodifferential equation of the problem. The numerical analysis of contact pressure is performed for different times, and some specific features of wear of the material by the punches of different shapes are discovered. The time for which the coating is totally worn out at a given point of the contact zone is determined.
173-179