The static analysis of an annular disc with a clamped inner boundary and a concentrated, in-plane load at the outer boundary is presented. The singularity associated with the concentrated load is isolated and the resulting non-singular problem is solved by the method of complex potentials. The superposition of these two solutions gives the desired solution. Results are presented for various radius ratios.
Get full access to this article
View all access options for this article.
References
1.
GurkinG. S.‘Stresses resulting from cutting forces in circular saws of constant thickness’, Lesnol Zhurnal1961, 102–111 (in Russian).
2.
DugdaleD. S.SquiresB. A.‘Effect of radial load on the flexural stiffness of a thin disc’, J. mech. Phys. Solids196513, 237–245.
3.
CarlinJ. F.ApplF. C.BridwellH. C.DuboisR. P.‘Effects of tensioning on buckling and vibration of circular saw blades’, Trans. ASME197597B (No. 1), 37–48.
4.
LiuG.‘Stress analysis and buckling of circular plates with a concentrated edge load’, Univ. Calif., For. Prod. Lab., Richmond, Calif., Tech. Rep. 4, File No. 35.01.130, 1975.
5.
MuskhelishviliN. I.Some basic problems of the mathematical theory of elasticity1953 (P. Noordhoff Ltd, Groningen, Holland).
6.
EnglandA. H.Complex variable methods in elasticity1971 (Wiley Interscience, London).
7.
DugdaleD. S.RueC.Elasticity for engineers1971 (McGraw-Hill, London).
8.
St CyrW. W.Vibration and stability of circular plates subjected to concentrated, in-plane forces Unpublished Ph.D. Dissertation, Kansas State University, 1965.
9.
DuboisR. P.Buckling loads of tensioned circular plates subject to concentrated in-plane loading Unpublished Master's Report, Kansas State University, 1970.
10.
TimoshenkoS. P.GoodierJ. N.Theory of elasticity1951 (McGraw-Hill, New York).
11.
ZienkiewiczO. C.‘Two-dimensional stress analysis and plate flexure by finite differences’, in ZienkiewiczO. C.HolisterG. S. (Eds) Stress Analysis1965 (John Wiley and Sons Ltd, London).
12.
YamamotoY.‘Finite element approaches with the aid of analytical solutions’, in GallagherR. H.YamadaY.OdenJ. T. (Eds) Recent advances in matrix methods of structural analysis and design1971, 85–103 (Univ. Alabama Press).
