Kurshin, L. M.; Rastorguev, G. I. On the problem of reinforcement of the hole outline in a plate by a momentless elastic rod. (English. Russian original) Zbl 0498.73070 J. Appl. Math. Mech. 44, 638-645 (1981); translation from Prikl. Mat. Mekh. 44, 905-915 (1980). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 3 Documents MSC: 74E30 Composite and mixture properties 74K20 Plates 74K10 Rods (beams, columns, shafts, arches, rings, etc.) 74S30 Other numerical methods in solid mechanics (MSC2010) Keywords:shape of hole outline; law of stiffness variation; reinforcing momentless rod; condition of minimum total elastic strain energy; boundary conditions; varying functional related to elastic strain energy; domains with moving boundaries; expansion in terms of small parameter; parameter of nonsymmetry of load PDF BibTeX XML Cite \textit{L. M. Kurshin} and \textit{G. I. Rastorguev}, J. Appl. Math. Mech. 44, 638--645 (1980; Zbl 0498.73070); translation from Prikl. Mat. Mekh. 44, 905--915 (1980) Full Text: DOI OpenURL References: [1] Mansfield, E.H., Neutral holes in plane sheet: reinforced holes which are elastically equivalent of the uncut sheet, Aeronaut. res. council repts. and mem. no. 2815, (1950) · Zbl 0051.16201 [2] Sheremet’ev, M.P., Plate state of stress of a plate with reinforced circular hole, Inzh. sb., Vol. 14, (1953) [3] Savin, G.N.; Tul’chii, V.I., Plates reinforced by composite rings and elastic cover-plate, (1971), Naukova Dumka Kiev [4] Radok, J.R.M., Problems of plane elasticity for reinforced boundaries, Trans. ASME, J. appl. mech., Vol. 22, No. 2, (1955) · Zbl 0066.18505 [5] Wells, A.A., On the plane stress-distribution in an infinite plate with a rim-stiffened elliptical opening, Quart. J. mech. and appl. math., Vol. 3, (1950), Pt. 1 · Zbl 0040.26701 [6] Mansfield, E.H., Optimum design for reinforced circular holes, Aeronaut. res. council current papers no. 239, (1956) [7] Mansfield, E.H.; Hanson, C.J., Optimum reinforcement around a circular hole in a flat sheet under uniaxial tension, Aeronaut. res. council repts. and mem. no. 3723, (1973) [8] Hicks, R., Reinforced elliptical holes in stressed plates, J. roy. aeronaut. soc., Vol. 61, No. 562, (1957) [9] Hicks, R., Variably reinforced circular holes in stressed plates, Aeronaut. quart., Vol. 9, (1958), Pt. 3 [10] Savin, G.N.; Fleishman, N.P., Plates whose edges are reinforced by thin ribs, Prikl. mekhan., Vol. 7, No. 4, (1961) [11] Tul’chii, V.I., On the optimal reinforcement of holes in plates, Prikl. mekhan., Vol. 1, No. 3, (1965) [12] Kurshin, L.M., On the problem of determining the shape of a rod section by the maximal torsional stiffness, Dokl. akad. nauk SSSR, Vol. 223, No. 3, (1975) [13] Bolza, O., Vorlesungen über variationsrechnung, (1949), Kochler Leipzig · JFM 61.0546.04 [14] Banichuk, N.V., Optimality conditions in the problem of seeking the hole shape in elastic bodies, Pmm, Vol. 41, No. 5, (1977) [15] Wheeler, L., On the role of constant-stress surface in the problem of minimizing elastic stress concentration, Intern. J. solids and struct., Vol. 12, No. 11, (1976) · Zbl 0367.73025 [16] Cherepanov, G.P., Some problems of elasticity and plasticity theory with unknown boundary, () · Zbl 0137.19702 [17] Mikhailovskii, E.I., On the optimal reinforcement of shell edge, () · Zbl 1291.74132 [18] Mikhailovskii, E.I.; Chaunin, M.P., Rational reinforcement of a circular hole in a plane plate being stretched, Problemy prochnosci, No. 1, (1978) [19] Muskhelishvili, N.I., Some fundamental problems of mathematical elasticity theory, (1966), Nauka Mosow · Zbl 0151.36201 [20] Aleksandrov, A.Ia.; Gorbatyi, A.V.; Kurshin, L.M., On the solution of the problem of the equivalent hole reinforcement, () [21] Banichuk, N.V., On a variational problem with unknown boundaries and the determination of optimal shapes of elastic solids, Pmm, Vol. 39, No. 6, (1975) · Zbl 0336.49009 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.