FEATURES OF STRESSES AT THE APEX OF AN ELASTIC WEDGE, SUPPORTED BY A THIN FLEXIBLE COATING ON THE SIDES
| Autor: | G. M. Murtazaliev, M. M. Payzulaev, B. V. Sobol, E. V. Rashidova, A. N. Soloviev |
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| Rok vydání: | 2019 |
| Předmět: |
Technology
business.product_category Transcendental equation Base (geometry) 02 engineering and technology Edge (geometry) engineering.material 01 natural sciences Stress (mechanics) 0203 mechanical engineering Coating wedge-shaped area boundary conditions Boundary value problem 0101 mathematics Physics Cauchy stress tensor Mathematical analysis General Medicine flexible coating Wedge (mechanical device) 010101 applied mathematics 020303 mechanical engineering & transports stress singularity engineering solution angle business |
| Zdroj: | Vestnik Dagestanskogo Gosudarstvennogo Tehničeskogo Universiteta: Tehničeskie Nauki, Vol 46, Iss 3, Pp 59-166 (2019) |
| ISSN: | 2542-095X 2073-6185 |
| DOI: | 10.21822/2073-6185-2019-46-3-159-166 |
| Popis: | ObjectivesTo study the problem of determining the degree of stress at the apex of a wedge-shaped area in cases where the sides (or one of them) are covered with a thin flexible coating.MethodIt is assumed that the coating is not stretchable. On the other side of the wedge-shaped area, the same coating is assumed to be present; it is either fixed, stress-free or in smooth contact with a rigid base. Mathematically, the problem is reduced to the task of determining the roots of characteristic transcendental equations arising from the existence of a nontrivial solution to the system of linear homogeneous equations.ResultsValues for the specific characteristics of the radial component of a stress tensor are determined for different combinations of boundary conditions and solution angles. In particular, the angles at which the singular behaviour of stresses occurs are determined. The case is considered when a special boundary condition is given on the edge surface, simulating the overlay. Characteristic equations are obtained to determine the index of the degree dependency of the asymptotic solution in its vicinity for four variants of boundary conditions. In two cases, transcendental equations are obtained, which are solved numerically.ConclusionCalculations of the first positive roots of the equations depending on the angle of the edge solution and Poisson's ratio are presented. The values of the angles, at which the singular behaviour of stresses occurs, are determined. In the case of a combination of boundary conditions (III – IV), the singular stress behaviour is observed for the angle ???? = ????/8, while in the case of (III – III) this value is equal to ????/4. |
| Databáze: | OpenAIRE |
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