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Optimality conditions in the problem of seeking the hole shapes in elastic bodies. (English. Russian original) Zbl 0401.73030

J. Appl. Math. Mech. 41, 946-951 (1979); translation from Prikl. Mat. Mekh. 41, 920-925 (1977).

MSC:

74G70 Stress concentrations, singularities in solid mechanics
74K20 Plates
74C99 Plastic materials, materials of stress-rate and internal-variable type
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References:

[1] Banichuk, N. V., On a variational problem with unknown boundaries and determination of the optimal shapes of elastic bodies, PMM, Vol. 39, No. 6 (1975) · Zbl 0336.49009
[2] Kurshin, L. M., On the problem of determining the shape of a rod section of maximum torsional stiffness, Dokl. Akad. Nauk, SSSR, Vol. 223, No. 3 (1975)
[3] Banichuk, N. V.; Karihaloo, B. L., Minimum-weight design of multi-purpose cylindrical bars, (Internat.J. Solids and Struc., Vol. 12 (1976), Pergamon Press), No. 4 · Zbl 0319.73028
[4] Banichuk, N. V., On a two-dimensional optimization problem in the theory of torsion of elastic rods, (Mekah. Tverd. Tela No. 5 (1976), Izv. Akad. Nauk. SSSR) · Zbl 0319.73029
[5] Cherepanov, G. P., Some problems of the theory of elasticity and plasticity with unknown boundaries, (Application of Function Theory in the Mechanics of a Continuous Medium, Vol. 1 (1965), Nauka: Nauka Moscow) · Zbl 0137.19702
[6] Cherepanov, G. P., Inverse problems of a plane theory of elasticity, PMM, Vol. 38, No. 6 (1974) · Zbl 0315.73106
[7] Ivanov, G. M.; Kosmodamianskii, O. S., Inverse doubly-periodic problem of plane elasticity theory, Dopov. Akad. Nauk. USSR, No. 9 (1972)
[8] Kosmodamianskii, A. S., Stress Distribution in Isotropic Multiply-connected Media (1972), Donetsk Univ. Press
[9] Vladimirov, V. S., Equations of Mathematical Physics (1976), Nauka: Nauka Moscow · Zbl 0353.32004
[10] Muskhelishvili, N. I., Some Fundamental Problems of the Mathematical Theory of Elasticity (1966), Nauka: Nauka Moscow · Zbl 0151.36201
[11] Hutchinson, J. W.; Niordson, F. I., Designing vibrating membranes, (Mechanics of a Continuous Medium and Kindred Problems of Analysis (1972), Nauka: Nauka Moscow) · Zbl 0255.73074
[12] Neuber, H., Der zugbeanspruchte Flachstab mit optimalem Querschnittsübergang, Forsch. Geb. Ingenieurwesens, Vol. 35 (1969)
[13] Neuber, H., Zur Optimierung der Spannungskonzentration, (Mechanics of a Continuous Medium and Kindred Problems of Analysis (1972), Nauka: Nauka Moscow) · Zbl 0271.73020
[14] Tvergaard, V., (IUTAM Sympos.. IUTAM Sympos., Warsaw, Poland (1973), Springer-Verlag: Springer-Verlag Berlin-Heidelberg-New York) · Zbl 0336.73020
[15] Aleksandrov, A. Ia., Some solutions of problems about the equivalent and equistrength reinforcements of holes in plates, (Selected Problems of Applied Mechanics (1974), VINITI: VINITI Moscow)
[16] Wheeler, L., On the role of constant -stress surfaces in the problem of minimizing elastic stress concentration, (Internat. J. Solids and Struc., Vol. 12 (1976), Pergamon Press), No.11 · Zbl 0367.73025
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