AN ELASTICITY SOLUTION FOR AXISYMMETRIC PROBLEM OF FINITE CIRCULAR CYLINDER

Abstract

Abstract: In this paper the complete double-series in the closed region expressing the double-variable functions and their partial derivatives are derived by the H-transforniution and Stockes transformation. Using the double-series, a series solution for the axisyinmetric boundary value problem of the elastic circular cylinder with finite length is presented.In a numerical example, the cylinder subjected to the axisymmetric traellens with various loaded regions is investigated and the distributions of the displacement sand stresses are obtained.It is possible to solve the axisymmetric boundary value problems in the eylinderical coordinates for other scientific fields by use of the method presented in this paper.

Key words: circular cylinder, function of double-variables, elasticity solution, H-transformation, Stockes’ transformation

Hou Yu;He Fu-bao. AN ELASTICITY SOLUTION FOR AXISYMMETRIC PROBLEM OF FINITE CIRCULAR CYLINDER. Applied Mathematics and Mechanics (English Edition), 1991, 12(10): 967-976.

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References

[1] Little.R.W.and S.B.Childs.Elastostatic boundary region problem in solid cylinders.Quart.Appl.,Math.,25(1967).261-274.
[2] Flügge,W.and V.S.Kelkar,The problem of an elastic circular cylinder.Internat.J.Solids Structures,4(1968),397-420.
[3] Power,L.D.and S.B.Childs,Axisymmetric stresses and displacements in a finite circular bar Internat.J.Engrg.Sci.,9(1971),241-255.
[4] Duncan,M.E.and Q.J.Fama,Radial eigen function for the elastic circular cylinder.Quart.J.Mech.Appl.Math.,25(1972),479-495.
[5] Gregory,R.D.,A note on bi-orthogonality relations for elastic cylinders of general cross section,J.Elasticity,13(1983),351-355.
[6] Gerhardt.T.D.and S.Cheng,A diagonally dominant solution for the cylinder end problem,J.Appl.Mech.,48(1981),867-880.
[7] Mayes,P.J..End stress calculations on elastic cylinders.Internal,J.Solids Structures.19(1983).895-906.
[8] Benthem,J.P.and P.Minderhoud,The problem of the solid cylinder compressed between rough rigid stamps,Internat.J.Solids Structures.8(1972),1027-1042.
[9] Robert,M.and L.M.Keer,An elastic circular cylinder with displacement prescribed at the end.Quart.J.Mech.Appl.Math.,40(1987).339-381.
[10] Robert,M.and L.M.Keer,Stiffness of an elastic circular cylinder of finite length.J.Appl.Mech..55(1988),560-565.
[11] Pickett.G,.Application of the Fourier method to the solution of certain boundary problem in the theory of elasticity,J.Appl.Mech.,11(1944),176-182.
[12] Luo Zu-dao.On axisymmetric deformation of a finite hollow cylinder,Acta Mechanica Sinica,11,3(1979),219-228. (in Chinese).
[13] Luo Zu-dao and Shen Song-qi,An analysis of finite thick-walled circular cylindrical shells,Acta Mechanica Solida Sinica,1,2(1980),145-158. (in Chinese).
[14] Horvay,G.and J.A.Mirable,The end problem of cylinder,J.Appl.Mech.,25(1958), 561-571.
[15] Mendelson,A.and E.Roberts,The axisymmetric stress distribution in finite cylinders.Proceedings of 8th Midwestern Mechanics Conference(1963).40-58.
[16] Hou Yu and He Fu-bao,H-transformation and its application.Chinese Journal of Applied Mechanics(to be published),(in Chinese).
[17] La Bromwich,T.J.,An Introduction to the Theory of Infinite Series,MacMillan Publication,London(1955).
[18] Liu De-gui et al.,Algorithm Assembly in FORTRAN,Defence Industry Publishing House(1983).(in Chinsese).