An alternative derivation of Marguerre’s solution for displacements in plane isotropic elasticity is provided. It is shown that the present approach, which is based on Green’s theorem and parallel to the Airy stress function approach, is straightforward. Also, the current derivation establishes the completeness of the Marguerre solution. [S0021-8936(00)00302-0]
Issue Section:
Brief Notes
1.
Muskhelishvili, N. I., 1953, Some Basic Problems of the Mathematical Theory of Elasticity, Noordhoff, Groningen, The Netherlands.
2.
Teodorescu
, P. P.
, 1964
, “One Hundred Years of Investigations in the Plane Problem of the Theory of Elasticity
,” Appl. Mech. Rev.
, 17
, pp. 175
–186
.3.
Gao
, X.-L.
, 1996
, “A General Solution of an Infinite Elastic Plate With an Elliptic Hole Under Biaxial Loading
,” Int. J. Pressure Vessels Piping
, 67
, pp. 95
–104
.4.
Marguerre
, V. K.
, 1933
, “Ebenes und achsensymmetrisches Problem der Elastizita¨tstheorie
,” Z. Angew. Math. Mech.
, 13
, pp. 437
–438
.5.
Little, R. W., 1973, Elasticity, Prentice-Hall, Englewood Cliffs, NJ.
6.
Barber, J. R., 1992, Elasticity, Kluwer Academic, Dordrecht, The Netherlands.
7.
Marguerre
, V. K.
, 1955
, “Ansa¨tze zur Lo¨sung der Grundgleichungen der Elastizita¨tstheorie
,” Z. Angew. Math. Mech.
, 35
, pp. 242
–263
.8.
Chou, P. C., and Pagano, N. J., 1967, Elasticity: Tensor, Dyadic, and Engineering Approaches, Van Nostrand, Princeton, NJ.
9.
Gao
, X.-L.
, 1998
, “A Mathematical Analysis of the Elasto-Plastic Plane Stress Problem of a Power-Law Material
,” IMA J. Appl. Math.
, 60
, pp. 139
–149
.10.
Gao
, X.-L.
, 1999
, “An Exact Elasto-Plastic Solution for the Plane Wedge Problem of an Elastic Linear-Hardening Material
,” Math. Mech. Solids
, 4
, 289
–306
.11.
Gao. X.-L., 2000, “Two Displacement Methods for In-Plane Deformations of Orthotropic Linear Elastic Materials,” submitted for publication.
12.
Wang
, L.
, 1985
, “On General Solution of Problem of Elastic Shallow Thin Shells
,” Acta Mech. Sin.
, 17
, pp. 64
–71
.13.
Gurtin, M. E., 1972, “The Linear Theory of Elasticity,” Handbuch der Physik, Vol VIa/2, C. Truesdell, ed., Springer-Verlag, Berlin, pp. 1–295.
14.
Truesdell
, C.
, 1959
, “Invariant and Complete Stress Functions for General Continua
,” Arch. Ration. Mech. Anal.
, 4
, pp. 1
–29
.15.
Raack, W., 1989, Ebene Fla¨chentragwerke, Scheiben, Schriftenreihe Ebene Fla¨chentragwerke, Band 2, Technische Universita¨t Berlin Press, Berlin, Germany.
16.
Lurie, S. A., and Vasiliev, V. V., 1995, The Biharmonic Problem in the Theory of Elasticity, Gordon and Breach, Luxembourg.
Copyright © 2000
by ASME
You do not currently have access to this content.