Abstract
Strength criteria constitute the fundamental constraints that must be taken into account in any optimal design. Such constraints are local in nature and are stated in terms of the components of the stress tensor. At the present time various theories of strength have been investigated and some of them have been extensively applied in optimal design research. The choice of any specific strength criteria, or the use of such approximate criteria, depends on the structural materials, the type of loads, the use of a specific computational scheme, and on other factors.
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References for Chapter 6
Aleksandrov, M.A., Korshinin, M.S., and Smoliarov, N.N., Computation of elastic plates and shells that are close to uniform strength, Prikl. Mekh., 1978, 14, No. 10, pp. 41–46.
Banichuk, N.V., On a game theoretic approach to optimization problems for elastic bodies, Prikl. Mat. Mekh., 1973, 37, No. 6, pp. 1098–1108.
Banichuk, N.V., Optimal design for a one-dimensional bending problem for fixed and moving loads, Izv. Akad. Nauk SSSR. MTT, 1974, No. 5, pp. 113–123.
Banichuk, N.V., The problem of optimizing the shape of a hole in a plate subjected to bending, Izv. Akad. Nauk SSSR. MTT, 1977, No. 3, pp. 81–88.
Banichuk, N.V., Conditions for optimality in problem of finding the shapes of holes in elastic bodies, Prikl. Mat. Mekh., 1977, 41, No. 5, pp. 920–925.
Banichuk, N.V., Designing of plates for minimum stress and deflection, In: Optimization of Distributed Parameter Structures, Iowa, 1980, E.J. Haug and J.J. Cea (eds.), Alphen aan den Rijn, Sijthoff-Noordhoff, 1981, pp. 333–361.
Banichuk, N.V., and Kobelev, V.V., Some problems of optimal design of shells of revolution, lzv. Arm. SSR, Mekhanika, 1983, No. 2, pp. 10–17.
Banichuk, N.V., and Kobelev, V.V., On optimal but not uniformly strong shapes of cross-sections of beams, Izv. Akad. Nauk SSSR. MTT, 1983, No. 5, pp. 162–167.
Barnett, R.L., Survey of optimum structural design, Exp. Mech., 1966, 6, No. 12, pp. 19–26.
Beliaev, N.V., Strength of Materials, Gostekhizdat., Moscow-Leningrad 1951, 856 pp.
Cherepanov, G.P., Inverse problems in the two-dimensional theory of elasticity, Prikl. Mat. Mekhanika, 1974, 38, No. 6, pp. 963–979.
Chiras, A.A., Barkauskas, A.E., and Karkauskas, R.P., Theory and Technique in Optimizing Elastoplastic Systems, Leningrad, Stroiizdat., 1974.
Cinquini, C., and Sacchi, G., Problems of optimal design for elastic and plastic structures, J. Mech. Appl., 1980, 4, No. 1, pp. 1–29.
Cinquini, C, Limit analysis and optimal plastic design of circular cylindrical shells. In: Optimization Methods in Structural Design, H. Eschenauer and N. Olhoff (eds.), Mannheim Bibliogr. Institute, 1983, pp. 309–318.
Cinquini, C., Structural optimization of plates of general shape by finite elements, J. Structural Mechanics, 1981, 9, No. 4, pp. 465–481.
Dorn, W.S., Gomory, R.E., and Greenberg, H.G., Automatic design of optimal structures, J. Mech., 3, No. 1, 1964.
Drucker, D.C., and Shields, R.T., Design for minimum weight. In: Proc. 9th International Congr. Applied Mechanics, Brussels, 1957, Vol. 5, pp. 212–222.
Drucker, D.C., and Shields, R.T., Bounds on minimum weight design. Quart. Appl. Math., 1957, 15, No. 3, pp. 269–281.
Erkhov, M.I., On the theory of optimal design for dynamically loaded rigid-plastic bodies. In: Mechanics of deformable solid bodies, Novosibirsk, Institute of Hydrodynamics, 1979, pp. 44–47.
Flügge, W., Statics and Dynamics of Shells, Moscow, Gostekhizdat., 1961, 306 pp.
Francavilla, A., Ramakrishnan, C.V., and Zienkiewicz, O.C., Optimization of shape to minimize stress concentration, J. Strain Analysis, 1975, 10, pp. 6370.
Galilei, Galileo, Discorsus et demonstrationes mathematicae, circa duas novas scientias, Leyden, 1699, a Latin translation from the 1638 edition by Mathias Bernegger, including Galileo’s direction to Elzeviers. New translation into English with introduction and notes by Stillman Drake, University of Wisconsin Press, Madison, 1974.
Ganeeva, M.S., Kornishin, M.S., and Malakhov, V.G., Uniformly stressed elastic shells of revolution. In: Seminar on Theory of Shells, Kazan’, Phys: Tekh. In., 1975, Vol. 3, pp. 92–106.
Gol’denblat, I.I., and Kozhnov, V.A., Strength and Plasticity Criteria for Structural Materials, Moscow, Mashinostroenie, 1968, 192 pp.
Haug, E.J., and Kwak, B.M., Contact stress minimization by contour design, Intern. J. Numer. Meth. Eng., 1978, 12, pp. 917–930.
Hegemeier, G.A., and Prager W., On Michell trusses, Intern. J. Mech. Science, 1969, 11, p. 209.
Hemp, W., On Michell framework for uniform load between fixed supports, Eng. Optim., 1974, 1, No. 1, pp. 61–69.
Hodge, F.G., Computation of Structures with Plastic Deformations, Moscow GNTI, 1963, 380 pp.
Hopkins, H.G., and Prager, W., Limits on economy of material in plates, J. Appl. Mech. 1955, 22, pp. 372–374.
Ivanov, G.B., Computation of an optimal variable thickness of a shell. In: Problems of Mekhanics of a Solid Deformable Body, Leningrad, Sudpromgiz, 1970, pp. 171–177.
Ivanov, G.B., and Kosmodem’ianskii, A.S., Inverse problem of bending for thin isotropic plates, Izv. Akad. Nauk SSSR. MTT, 1974, No. 5, pp. 53–56.
Il’iushin, A.A., A theory of elastoplastic strains, Prikl. Mat. Mekh., 1946, 10, No 3, pp. 347–356.
Il’iushin, A.A., Plasticity, Moscow and Leningrad, Gostekhizdat., 1948, 308 pp.
Ishlinskii, A.Iu., Mechanics, Ideas, Problems and Applications, Moscow, Nauka, 1985, 624 pp.
Ishlinskii, A.Iu., On a uniformly stressed cross-section of a beam, Nauchn. Zap, Mekh. Moscow State University, 1940, 39, pp. 87–90.
Ishlinskii, A.Iu., Strength hypothesis for a change of shape, Nauchn. Zap. Mekh. Moscow State University Scientific Notes (Mechanics) Moscow State University 1940, 16, pp. 111–124.
Khuberian, K.M., Rational Shapes of Pipes, Reservoirs, and Pressure Vessels, Moscow, Gosstroiizdat, 1956.
Khutorianskii, N.M., Certain inverse and optimization problems in a two-dimensional theory of elasticity. In: Applied Problems of Strength and Plasticity, Gorkii, Gorkii University, 1978, 6, pp. 81–87.
Khutorianskii, N.M., On solution of certain two-dimensional and three-dimensional shape optimization problems in elastic bodies. In: Applied Problems of Strength and Plasticity, Gorkii, Gorkii University, 1978, 8, pp. 66–74.
Koiter, V.T., A General Theory of Elastoplastic Media, Moscow, Innostr. Liter. ( Russian translation ) 1961, 80 pp.
Komarov, V.A., On a rational distribution of material in structures, Izv. Akad. Nauk SSSR (Mekhanika), 1965, No. 5, pp. 85–87.
Konig, J.A., On optimum shakedown design. In: Proc. I UTAM Symposium on Optimal Design, Warsaw, 1973, Springer-Verlag, Berlin, 1975, pp. 405–414.
Kornishin, M.S., Aleksandrov, M.A., and Smoliarov, N.N., Computation of close to uniformly stressed deformable plates and shallow shells using numerical techniques. In: Proc. All-Union Conf. on Numerical Solutions of Problems in Elasticity and Plasticity; Part II, Novosibirsk, V.Ts. SO Akad. Nauk SSSR, 1976, pp. 69–76.
Kristenson, E.S., and Madson, N.F., On optimum shape of a fillet in plates subjected to multiple in-plane loading cases, Intern. J. Numer. Meth. Eng., 1976, 10, pp. 1007–1019.
Kurshin, L.M., and Rastorguyev, G.I., On the problem of reinforcing the boundary of a hole in a plate, Izv. Akad. Nauk SSSR. MTT, 1979, No. 6, pp. 94–102.
Kurshin, L.M., and Rastorguyev, G.I., On the problem of reinforcing the boundary of a hole in a plate, using a moment-free, elastic rod, Prikl. Mat. Mekh., 1980, 44, No. 5, pp. 905–915.
Lepik, Iu.R., Application of Pontryagin’s maximality principle for an optimal design of cylindrical shells made from rigid-plastic materials. In: Advances in Mechanics of Deformable Media, Moscow, Nauka, 1975, pp. 340–349.
Lepik, U. [Iu.], Application of Pontryagin’s maximum principle for minimum weight design of rigid-plastic circular plates. Intern. J. Solids Structures, 1973, 9, pp. 615–624.
Litvinov, V.G., and Panteleev, A.D., The problem of optimization of plates with variable thickness, Izv. Akad. Nauk SSSR. MTT, 1980, No. 2, pp. 174–181.
Maier, G., Zavelani-Rossi, A., and Benedetti, D., A finite element approach to optimal design of plastic structures in plane stress, Intern. J. Numer. Meth. Eng., 1972, 4, pp. 455–473.
Malkov, V.P., and Strongin, R.G., Optimization of structures with respect to weight and strength criteria. In: Solution techniques for problems in elasticity and plasticity. Gorkii, Gorkii University, 1971, 4, pp. 138–149.
Malkov, V.P., and Salganskaya, E.A., Optimal distribution of material in rotat- ing discs from a strength criterion, Izv. Vuzov, Aviats. Tekhnika,1976, No. 3.
Malkov, V.P., Equivalent reinforcement for a boundary of a cutout in a thin-walled member. In: Applied Problems of Strength and Plasticity. Gorkii, Gorkii University, 1979, 10, pp. 96–113.
Mansfield, E.H., An optimum surface of revolution for pressured shells, Intern. J. Mech. Science, 1981, 23, pp. 57–62.
Mansfield, E.H., Neutral holes in plane sheet-reinforced plates which are elastically equivalent to the uncut sheet, Quart. J. Mech. Appl. Math., 1953, 6, Part 3, pp. 370–378.
Maxwell, C., Scientific Papers, Cambridge University Press, 1880, Vol. 2, pp. 175–177.
Mazzarella, C., and Polizzotto C., Optimum design of rigid-workhardening structures with constraints on deformation, Eng. Struct. 1980, 2, No. 3, pp. 138–146.
Medvedev, N.G., and Totskii, N.P., Optimization of cylindrical shells with variable thickness and axially symmetric loads, Prikl. Mat. Mekh. 1984, 20,No. pp. 53–57.
Michell, A.G., and Melbourne, M.C.S., The limits of economy of material, Phil. Mag., Series 6, 1904, 8, pp. 589–597.
Mikhailovskii, E.I., Optimal reinforcement for the edges of a shell, Izv. Akad. Nauk SSSR-MTT, 1975, No. 1, pp. 42–51.
Mushtari, Kh.A., On the bending theory for a rectangular plate with variable thickness, Inzh. Zh., 1964, 4, No. 1, pp. 45–49.
Mushtari, Kh.A., On the bending theory for a plate with minimal weight and made of a composite material, Prikl. Mekh., 1967, 3, No. 4, pp. 1–7.
Nemirovskii, Iu.V., Estimates of the weight of optimal plastic structures, Inzh. Zhurnal, Mekh. Tve. Tela, 1968, No. 4, pp. 159–162.
Nemirovskii, Iu.V., and Reznikov, B.S., Uniform strength in conditions of creep for beams and plates, Mashinovedenie, 1969, No. 2, pp. 58–64.
Neuber, H., Der Zugbeanspruchte Flachstab mit optimalen Querschnittsubergang, Forsch. Ingenieurwiss. 1969, 35, pp. 29–30.
Neuber, H., Zur Optimierung der Spannungskonzentration. In: Mechanics of Continuous Media and Related Problems of Analysis, Moscow, Nauka, 1972, pp. 375–380.
Oda, J., On a technique to obtain an optimum strength shape by the finite element method, Bull. JSME, 1977, 20, pp. 160–167.
Onat, E.T., and Prager, W, Limit of economy of material in shells, Ingenieur, 1955, 67, pp. 46–49.
Onat, E.T., Shumann, W., and Shield, R.T., Design of circular plates for minimum weight, ZAMP, 1957, 8, No. 6, pp. 485–499.
Pisarenko, G.S., and Lebedev, A.A., Deformation and Strength of Materials in a Complex Stressed State. Kiev, Naukova Dumka, 1976, 415 pp.
Pochtman, Iu.M., and Piatigorskii, Z.I., Computation and Optimal Design of a Structure with Consideration of Adaptability. Moscow, Nauka, 1978, 208 pp.
Polizzotto, C., Optimal design for multiple sets of loads, Meccanica, 1974, 9, pp. 206–219.
Polizzotto, C., Mazzarella, C., and Panzeca, T., Optimal design for work-hardening adaptation, Comp. Meth. Appl. Mech. Eng., 1977, 12, No. 2, pp. 129–144.
Polizzotto, C., and Panzeca, T., Optimal design of beams for workhardening adaptation. In: Optimization of Distributed Parameter Structures, Iowa, 1980, E.J. Haug and J. Cea (eds.), Alphen aan den Rijn, Sijthoff-Noordhoff, 1981, pp. 910–927.
Prandtl, L., Anwendungsbeispiele zu einem Henkyschen Satz über das plastische Gleichgewicht, Ztschrft angew. Math. Mech., 1923, 3, No. 6.
Rabinovich, I.M., Beam systems of minimal weight. In: Proc. II-nd All-Union Conf. Theoretical and Applied Mechanics, Moscow, Nauka, 1966, Vol. 3, pp. 265–275.
Runge, C., and Konig, H., Vorlesungen uber numerischen Rechnen, Berlin, 1924.
Save, M.A., Some aspects of minimum weight design. In: Engineering Plasticity, J. Heymann and F.A. Leckie (eds.), Cambridge Univ. Press, 1968, pp. 611–6626.
Save, M.A., A unified formulation of the theory of optimal plastic design with convex cost functions, J. Struct. Mech., 1972, 1, No. 2, pp. 257–276.
Savin, G.N., Stress Distribution around Openings, Kiev, Naukova Dumka, 1968, 887 pp.
Savin, G.N., Stress Concentration around Openings, Moscow and Leningrad, Gostekhizdat, 1951, 496 pp.
Schnack, E., An optimization procedure for stress concentrations by the finite element technique, Intern. J. Numer. Meth. Eng., 1979, 14, pp. 115–124.
Shamiev, F.G., On designing ring-shaped plates of minimal weight, Izv. Akad. Nauk. Az. SSR, Fiz-Mat. Tekh. Nauk, 1963, No. 3, pp. 13–20.
Shamiev, F.G., On designing elliptically shaped plates of minimal weight, lzv. Akad. Nauk, Az. SSR, Fiz-Mat Tekh. Nauk, 1966, No. 4, pp. 23–27.
Shefer, G., and Demkowicz, L., Optimal design of elastic nonlinear plates by means of the mini-max theory. In: Optimization Methods in Structural Design, H. Eschenauer and N. Olhoff (eds.), Mannheim Bibliogr. Institute, 1983, pp. 409–414.
Shirko, I.V., Axially symmetric bending of a cylindrical shell with uniform strength. Prikl. Mekh., 1969, 5, No. 4, pp. 45–53.
Shirko, I.V., The shape of a plate with uniform strength, Inzhin. Zh., 1965, 5, No. 2, pp. 293–298.
Sirazutdinov, Iu.K., Beam cross-sections of uniform strength, Proc. Kazan Aviation Institute, 1974, No. 168, pp. 11–18.
Strang, G., and Kohn, R.V., Hencky-Prandtl nets and constrained Michell trusses. In: Proc. Intern. Symp. Optimum Structural Design, University of Arizona, Tucson, Arizona, 1981, pp. 4. 17–4. 22.
Sirazutdinov, Iu.K., Designs of optimal systems of beams, Archivum Inzynierji Lgdowej, 1979, 25, No. 2, pp. 245–264.
Sofronov, Iu.D., Designs of uniformly stressed and of uniform strength trusses, beams and frames subjected to cyclic loads, with consideration of hysteresis losses in materials. In: Loss of Energy in Vibrations of Mechanical Systems. Kiev, Naukova Dumka, 1968, pp. 76–82.
Timoshenko, S.P., Strength of Materials, Moscow, Fizmatgiz, 1960, Vol. 1, 380 pp.
Timoshenko, S.P., and Voinovski-Krieger, S., Plates and Shells, Moscow, Nauka, 1966, 636 pp.
Tveergand, V., On the optimum shape of a fillet bar with restrictions. In: IUTAM Symposium on Optimal Design, Warsaw, 1973. Springer Verlag, Berlin, 1975, pp. 181–195.
Vigderhauz, S.B., An integral equation for a problem in two-dimensional theory of elasticity, Prikl. Mat. Mekh., 1976, 40, No. 3, pp. 566–569.
Vigderhauz, S.B., On a case of the inverse problem of two-dimensional theory of elasticity, Prikl. Mat. Mekh., 1977, 41, No. 5, pp. 902–908.
Vigderhauz, S.B., Optimality conditions in axially symmetric problems of the theory of elasticity, Prikl. Mat. Mekh., 1982, 46, No. 2, pp. 278–282.
Vigderhauz, S.B., An inverse problem in a three-dimensional theory of elasticity, Izv. Akad. Nauk SSSR. MTT, 1983, No. 2, pp. 90–93.
Wheeler, L., On the role of constant stress surfaces in the problem of minimizing elastic stress concentrations, Intern. J. Solids Structures, 1976, 12, No. 11, pp. 779–789.
Zavelani, A., Maier, G., and Binda, L., Shape optimization of plastic structures. In: IUTAM Symposium on Optimal Design, Warsaw, 1973. Springer Verlag, Berlin, 1975, pp. 181–195.
Zienkiewicz, O.C., and Campbell, J.S., Shape optimization and sequential linear programming. In: Optimum Structural Design, R.H. Gallagher and O.C. Zienkiewicz (eds.), Wiley, New York, 1973, pp. 109–126.
Ziegler, N., Dome with uniform strength, Mechanika, 1952, pp. 127–132.
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Banichuk, N.V. (1990). Application of Strength and Weight Criteria. In: Introduction to Optimization of Structures. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-3376-3_6
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