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References
This problem was investigated by E. Reissner, Note on the theorem of the symmetry of the stress tensor, J.Math.Phys. Vol. 23 (1944), 192. See also D.B.Bogy and E.Sternberg, The effect of couplestresses on the corner singularity due to an asymmetric shear loading, Int. J.Solids Structures, Vol. 4 (1968), 159–174.
M.L. Williams, Stress singularities resulting from various boundary conditions in angular corners of plates in extension, ASME J.Appl.Mech., Vol. 19 (1952), 526–528.
D.B. Bogy, Two edge-bonded elastic wedges of different materials and wedge angles under surface tractions, ASME J.Appl.Mech., Vol. 38 (1971), 377–386.
A problem of this kind was solved by G.G. Adams, A semi-infinite elastic strip bonded to an infinite strip, ASME J.Appl.Mech., Vol. 47 (1980), 789–794.
J. Dundurs and M.S. Lee, Stress concentration at a sharp edge in contact problems, J.Elasticity, Vol. 2 (1972), 109–112; M.Comninou, Stress singularities at a sharp edge in contact problems with friction, Z.angew.Math.Phyz., Vol. 27 (1976), 493–499.
I.N. Sneddon, Fourier Transforms, McGraw-Hill, New York, 1951.
The basic theory of the Mellin transform and its relation to the Fourier transform is explained by I.N. Sneddon, loc. cit.. For applications to elasticity problems for the wedge, see E.Sternberg and W.T.Koiter, The wedge under a concentrated couple: A paradox in the two-dimensional theory of elasticity, ASME J.Appl.Mech., Vol. 25 (1958), 575–581, W.J.Harrington and T.W.Ting, Stress boundary-value problems for infinite wedges, J.Elasticity, Vol. 1 (1971), 65–81.
A problem of this kind was considered by G. Tsamasphyros and P.S. Theocaris, On the solution of the sector problem, J.Elasticity, Vol. 9 (1979), 271–281.
This requires that the eigenfunction series is complete for this problem. The proof is given by R.D. Gregory, Green’s functions, bi-linear forms and completeness of the eigenfunctions for the elastostatic strip and wedge, J.Elasticity, Vol. 9 (1979), 283–309.
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© 2004 Kluwer Academic Publishers
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(2004). Wedge Problems. In: Elasticity. Solid Mechanics and Its Applications, vol 107. Springer, Dordrecht. https://doi.org/10.1007/0-306-48395-5_11
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