The classical inverse problem of the plane theory of elasticity, in which the stress along the boundary contour is rendered uniform, is considered. The exact solution to the problem delivering symmetrical optimum shapes with four infinite branches along the axes of symmetry is constructed. The method enables one to find many other optimum shapes with two, three, four, five, etc., infinite branches.
Issue Section:
Technical Papers
1.
Bienzeno, C. B., and Grammel, R., 1956, Engineering Dynamics, Vol. II (Elastic Problems of Single Machine Elements), Blackie & Son Ltd., Glasgow, pp. 267–290 (English translation of 1939 edition in German).
2.
Cherepanov, G. P., 1963, “An Inverse Elastic-Plastic Problem Under Plane Strain,” Notices of the USSR Academy of Sciences, Mekhanika i Mashinostroenie, No. 1, pp. 63–71, in Russian.
3.
Cherepanov, G. P., 1966a, “Equistrong Mine in a Rock,” Problems of Rock Mechanics, A. Erzhanov, ed., Nauka, Alma-Ata, pp. 166–178, in Russian.
4.
Cherepanov, G. P., 1966b, “One Inverse Problem of the Theory of Elasticity,” Engineering Journal (Solid Mechanics), No. 3, pp. 518–525, in Russian.
5.
Cherepanov, G. P., and Liberman, L. K., 1971, “Mathematical Method of Optimal Design in Mining,” Mining Journal, No. 9, pp. 987–992, in Russian.
6.
Cherepanov
G. P.
1974
, “Inverse Problems of the Plane Theory of Elasticity
,” Applied Mathematics and Mechanics (PMM)
, Vol. 38
, pp. 963
–979
.7.
Cherepanov, G. P., and Tagizade, A. G., 1975a, “Extension of Plates and Shells of Uniform Strength,” Letters to Applied and Engineering Science, No. 3, pp. 64–69.
8.
Cherepanov, G. P., and Tagizade, A. G., 1975b, “Bending of Plates and Shells of Uniform Strength,” Letters to Applied and Engineering Science, No. 2, pp. 38–43.
9.
Cherepanov, G. P., and Yershov, L. V., 1977, Fracture Mechanics, Moscow, Mashinostroenie Press, pp. 1–240, in Russian.
10.
Cherepanov, G. P., ed., 1995, Fracture: A Topical Encyclopedia Dedicated to A. A. Griffith, Krieger Publ., Melbourne, FL.
11.
Wheeler
L. T.
1976
, “On the Role of Constant-Stress Surfaces in the Problem of Minimizing Elastic Stress Concentration
,” J. Solids and Structures
, Vol. 12
, pp. 779
–789
.12.
Wheeler, L. T., 1978, “On Optimum Profiles for the Minimization of Elastic Stress Concentration,” ZAMM, pp. 235–236.
13.
Wheeler
L. T.
Kunin
I. A.
1982
, “On Voids of Minimum Stress Concentration
,” J. Solids and Structures
, Vol. 18
, pp. 85
–89
.14.
Wheeler
L. T
1992
, “Stress Minimum Forms for Elastic Solids
,” ASME Applied Mechanics Reviews
, Vol. 45
, pp. 110
–125
.
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