Abstract
In this paper, the solutions of two contact problems for a wedge with a symmetric cut on the edge are presented. First, special approximation methods and orthogonal polynomials are used to solve the auxiliary problem on the action of a lumped force on the cut edge. The obtained solutions are compared with known solutions in some special cases.
Similar content being viewed by others
References
E. M. Nekislykh and V. I. Ostrik, “Problems on Elastic Equilibrium of a Wedge with Cracks on the Axis of Symmetry, ” Izv. Ross. Akad. Nauk. Mekh. Tverd. Tela, No. 5, 111–129 (2010) [Mech. Solids (Engl. Transl.) 45 (5), 743–756 (2010)].
R. D. Bantsuri, “The Solution of the First Fundamental Problem in the Theory of Elasticity for a Wedge Having a Finite Slot, ” Dokl. Akad. Nauk SSSR 167 (6), 1256–1259 (1966) [Sov. Math. Dokl. (Engl. Transl.) 11 (4), 359–361 (1966)].
B. I. Smetanin, “On aMixed Problem of Elasticity Theory for aWedge, ” Prikl. Mat. Mekh. 32 (4), 708–714 (1968) [J. Appl. Math. Mech. (Engl. Transl.) 32 (4), 732–739 (1968)].
B. I. Smetanin, “Certain Problems of Cracks in Elastic Wedge and Plate, ” Inzh. Zh. MTT, No. 2, 115–122 (1968) [Mech. Solids (Engl. Transl.)].
H. E. Doran, “TheWedge with a Symmetric Crack at the Vertex in Plane Electostatics, ” J. Inst. Math. Appl. 5 (4), 363–372 (1969).
A. A. Khrapkov, “An Infinite TriangularWedge with a Cut on the Bisectrix under the Action of Concentrated Forces Applied to the Cut Shores, ” Izv. Akad. Nauk SSSR. Mekh. Tverd. Tela, No. 5, 88–97 (1972) [Mech. Solids (Engl. Transl.)].
F. Quchterlony, “Symmetric Cracking of aWedge by Concentrated Load, ” Int. J. Engng Sci. 15 (2), 109–116 (1977).
G. R. Irwin, The Crack-Extension Force fora Crack at a Free SurfaceBoundary, Report No. 5120 (Naval Research Lab., 1958).
O. L. Bowie and D. M. Neal, “Single Edge Cracks in Rectangular Tensile Sheet, ” Trans. ASME. Ser. E. J. Appl. Mech. 32 (3), 708–709 (1965).
A. M. P. Stallybrass, “A Crack Perpendicular to an Elastic Half-Plane, ” Int. J. Engng Sci. 8 (5), 351–362 (1970).
R. J. Hartranft and G. C. Sih, “Alternating Method Applied to Edge and Surface Crack Problems [A], ” in Mechanics of Fracture, Ed. by G. C. Sih, Vol. 1 (Nordhoff, Leyden, 1973), pp. 179–238.
N. Hasebe and Y. Chen, “An Edge Crack Problem in a Semi-Infinite Plane Subjected to Concentrated Forces, ” Appl. Math. Mech. 22 (1), 1279–1290 (2001).
S. V. Bosakov, “Bending of aWall in an Elastic Half-Plane, ” Prikl. Mekh. 18 (10), 45–50 (1982) [Int. Appl. Mech. (Engl. Transl.) 18 (10), 895–900 (1982)].
V. M. Alexandrov, “Contact Problems for ElasticWedge, ” Inzh. Zh. MTT, No. 2, 120–131 (1967).
L. A. Galin (Editor), The Development of Theory of Contact Problems in USSR (Nauka, Moscow, 1976) [in Russian].
I. I. Vorovich, V. M. Alexandrov, and V. A. Babeshko, Nonclassical Mixed Problems of Elasticity (Nauka, Moscow, 1974) [in Russian].
Ya. S. Ufland, Integral Transforms in Elasticity Problems (Nauka, Leningrad, 1967) [in Russian].
I. S. Gradshtein and I. M. Ryzhik, Tables of Integrals, Sums, Series, and Products (Fizmatgiz, Moscow, 1963) [in Russian].
H. B. Dwight, Tables of Integrals and Other Mathematical Formulas (Macmillan, New York, 1957; Nauka, Moscow, 1982).
G. Ya. Popov, Elastic Stress Concentration near Punches, Cuts, Thin Inclusions, and Stiffeners (Nauka, Moscow, 1982) [in Russian].
M. P. Savruk, Two-Dimensional Elasticity Problems for Bodies with Cracks (Naukova Dumka, Kiev, 1981) [in Russian].
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © S. V. Bosakov, A. V. Krupoderov, 2016, published in Izvestiya Akademii Nauk, Mekhanika Tverdogo Tela, 2016, No. 1, pp. 19–29.
Deceased.
About this article
Cite this article
Bosakov, S.V., Krupoderov, A.V. Two contact problems for a wedge with a symmetric cut on the edge. Mech. Solids 51, 12–21 (2016). https://doi.org/10.3103/S0025654416010027
Received:
Published:
Issue Date:
DOI: https://doi.org/10.3103/S0025654416010027