### Analysis of stress-strain state on top of a rectangular wedge

Pages 57-62

Modeling singular solutions of the elasticity theory problems, which are determined by geometric factor - bird's mouth of the edge, make it necessary to analyze the solutions with some peculiarity, which are obtained experimentally with the help of photoelasticity method. In this article the peculiar stress-strain state is analyzed on the example of the known experimental solutions for a wedge under a concentrated force obtained by M. Frocht. Solution analysis for a wedge with a power-type peculiarity obtained experimentally by photoelasticity method, helps to detach a singular solution field, where fringe contour is not visible. Due to idealization of the boundary shape and loading technique, infinitely large stresses arise, which are obtained as a singular solution of the boundary problem in a planar domain. Comparison of theoretical and experimental solutions obtained for a wedge shows areas of overlap and areas of significant and insignificant differences as a result of the inability to experimentally apply the force to a single point.

DOI: 10.22227/1997-0935.2014.5.57-62

- Kondrat'ev V.A. Asimptotika resheniya uravneniya Nov'e — Stoksa v okrestnosti uglovoy tochki granitsy [Asymptotics of Navier — Stokes Equations Solutions in the Area of Angular Edge Point]. Prikladnaya matematika i mekhanika [Applied Mathematics and Mechanics]. 1967, no. 1, pp. 119—123.
- Kuliev V.D. Singulyarnye kraevye zadachi [Singular Boundary Problems]. Moscow, Nauka Publ., 2005, 719 p.
- Parton V.Z., Perlin P.I. Metody matematicheskoy uprugosti [Methods of Mathematical Elasticity]. Moscow, Nauka Publ., 1981, pp. 305—325.
- Timoshenko S.P., Gud'er Dzh. Teoriya uprugosti [Elasticity Theory]. Moscow, Nauka Publ., 1975, 576 p.
- Aksentyan O.K. Osobennosti napryazhenno-deformirovannogo sostoyaniya plity v okrestnosti rebra [Peculiarities of Stress-Strain State of a Slab near Arris]. Prikladnaya matematika i mekhanika [Applied Mathematics and Mechanics]. 1967, vol. 31, no. 1, pp. 178—186.
- Vardanyan G.S., Savost'yanov V.N., Mozgaleva M.L., Frishter L.Yu. O sobstvennykh znacheniyakh v reshenii zadach dlya oblastey, soderzhashchikh neregulyarnye tochki [On Characteristic Values in Problems Solution for the Areas Containing Irregular Points]. Izvestiya vuzov. Stroitel'stvo [News of Higher Educational Institutions. Construction]. 2003, no. 3, pp. 28—31.
- Williams M.L. Stress Singularities Resulting from Various Boundary Conditions in Angular Corners of Plates in Extension. J. Appl. Mech. 1952, vol. 19, no. 4, p. 526.
- Williams M.L. The Complex Variable Approach to Stress Singularities. J. Appl. Mech. 1956, vol. 23, no. 3, p. 477.
- Frocht M.M. Photoelasticity. J. Wiley and Sons, London, 1965.
- Khesin G.L. Metod fotouprugosti [Photoelasticity Method]. In 3 volumes. Moscow, Stroyizdat Publ., 1975, vol. 3, pp. 311.
- Frishter L.Yu. O vozmozhnostyakh polucheniya metodom fotouprugosti napryazhennogo sostoyaniya v oblasti kontsentratsii napryazheniy [On the Possibilities to Obtain Stress State in the Area of Stress Concentration by the Photoelasticity Method]. Vestnik MGSU [Proceedings of Moscow State University of Civil Engineering]. 2008, no. 1, pp. 165—168.
- Krasnov L.A. Tsvetnost' izokhrom v fotouprugosti. Eksperimental'naya mekhanika i raschet sooruzheniy [Isochrome Firmness in Photoelasticity]. Moscow, MGSU Publ., 2004, pp. 49—62.