Abstract
Stability constitutes one of the basic demands that must be satisfied in designing elastic structures. It is particularly important in designs of slender structures or structures made of high-strength materials.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References for Chapter 8
Abramov, IU.Sh., Variational Methods in the Theory of Operator Bundles. Spectral Optimization, Leningrad, Leningrad State University, 1983, 180 pp.
Adali, S., Optimal shape and nonhomogenuity of nonuniformly compressed column, Intern. J. Solids Struct.,1979, 15, pp. 935–949.
Albul, A.V., Banichuk, N.V., and Barsuk, A.A., Optimization of stability for elastic rods with thermal loads, Izv. Akad. Nauk S.S.S.R., M.T.T., 1980, No. 3, pp. 127–133.
Alfumov, N.A., Foundations for Computation of Stability of Elastic Systems,Moscow, Mashinostroienie, 1978, 312 pp.
Alfumov, N.A., and Balabukh, L.I., Energy criteria for stability of elastic bodies which do not require determination of the initial stressed state, Prikl. Mat. Mekh.,1972, 32, No. 1, pp. 703–770.
Andreev, L.V., Mossakovskii, V.I., and Obodan, N.I., On optimal thickness of a cylindrical shell loaded by external pressure, Prikl. Mat. Mekh., 1972, 36, No. 4, pp. 717–726.
Arnol’d, V.I., Modes and quasi-modes, Functional Analysis and Its Applications, 1972, 6, No. 2, pp. 12–20.
Arnol’d, V.I., Mathematical Methods of Classical Mechanics (translated from Russian by K. Vogtman and A. Weinstein), 1978, Springer-Verlag, Berlin and Heidelberg, 464 pp.
Artunian, N.Kh., and Kolmanovskii, V.B., Theory of Creep for Inhomogeneous Bodies, Moscow, Nauka, 1983, 336 pp.
Ashley, H., and McIntosh, S.C., Application of aeroelastic constraints in Structural optimization. In: Proceedings 12th International Congress Applied Mechanics, Stanford University, 1969. Springer Verlag, Berlin, pp. 100–113.
Banichuk, N.V., Optimization of stability for elastically embedded rod, Izv. Akad. Nauk S.S.S.R., M.T.T., 1974, No. 4, pp. 150–154.
Banichuk, N.V., Minimization of the weight of a wing with bounded speed of divergence, Nauchn. Zap. TsAGI, 1978, 9, No. 5.
Banichuk, N.V., and Barsuk, A.A., On stability of torsioned elastic rods, Izv. Akad. Nauk S.S.S.R., M.T.T., 1982, No. 6, pp. 148–154.
Banichuk, N.V., and Barsuk, A.A., Optimization of stability of elastic beams against simultaneous compression and torsion. In: Applied Problems of Strength and Plasticity. Automation and algorithms for Solving Problems in Elastoplastic State (collection). Gorkii, Gorkii State University, 1982, pp. 122–126.
Banichuk, N.V., and Barsuk, A.A., Application of decomposition of the spectrum of eigenvalues to problems of optimal design. In: Problems of Stability and Critical Load Carrying Capacity of Structures,Leningrad, L.I.S.I., 1983, pp. 17–24.
Banichuk, N.V., and Gura, N.M., On a dynamic problem of optimal design. In: Mechanics of Deformable Solid Bodies, Novosibirsk, 1979, 41, pp. 20–24.
Banichuk, N.V., and Kobelev V.V., Optimization of structures made from chaotically reinforced composites, Mekh. komp. materialov,1981, No. 4, pp. 668–676.
Bochenek, B., and Gajewski, A., Certain problems of unimodal and bimodal optimal design of structures. In: Proceedings Euromech. In:Optimization Methods in Structural Design, H. Eschenauer and N. Olhoff (eds.), Mannheim, Bibl. Institute, 1983, pp. 204–209.
Bolotin, V.V., Dynamic Stability of Elastic Systems, Moscow, Gostekhizdat, 1956.
Bolotin, V.V., Non-conservative Problems in the Theory of Elastic Stability,Moscow, Fizmatgiz, 1961, 339 pp.
Bolotin, V.V., Variational Principles in Theory of Elastic Stability. In: Problems in Mechanics of Solid Deformable Bodies, Moscow, Subostroienie, 1973, pp. 83–88.
Budianski, B., Frauenthal, J.C., and Hutchinson, J.W., On optimal arches, J. Applied Mech., Trans. A.S.M.E.,1969, 36, No. 4, pp. 239–240.
Bushnell, D., Buckling of shells; Pitfall for Designers, A.I.A.A. J., 1981, 19, No. 9, pp. 1183–1226. (Russian translation in Raket. Tekh. Kosmon.).
Chentsov, P.G., Minimal weight supports, Trudy TsAGI, 1936, 265, pp. 1–48.
Choi, K.K., and Haug, E.J., Optimization of structures with repeated eigenvalues. In: Optimization of Distributed Parameter Structures, E.J. Haug and J. Cea (eds.), Alphen aan den Rijn, Sijthoff and Noordhoff, 1981, pp. 219–277.
Clausen, T., Uber die Formarchitektonischen Saulen, Bull. Phys. Math. Acad. St. Petersburg, 1851, 9, pp. 279–294.
Claudon J.-L., and Sunakawa M., Optimizing distributed structures for maximum flutter load, AIAA J., 1981, 19, No. 7, pp. 957–959.
Danielov, E.R., Girder with uniform strength against longitudinal-transverse bending, Tr. Khabar. Politechn. In. 1967, 8, pp. 26–34.
Fedoseev, V.I., Selected Problems and Exercises on Strength of Materials,Moscow, Nauka, 1973, 400 pp.
Frauenthal, J.C., Constrained optimal design of circular plates against buckling, J. Structural Mech.,1972, 1, pp. 159–186.
Gajewski, A., and Lyczkowski, M., Optimal design of elastic columns subject to general conservative behavior of loading, ZAMP, 1970, 21, No. 5, pp. 806–818.
Geniev, G.A., On the equigradient principle and its applications to problems of optimizing stability of systems of rods, Stroit. Mekh. i Raschet Sooruzhenii, 1979, No. 6, pp. 8–13.
Grinev, V.B., and Filippov, A.P., On optimal shape of beams in problems of stability, Stroit. Mekh. i Raschet Sooruzhenii, 1977, No. 2, pp. 21–27.
Grinev, V.B., and Filippov, A.P., Optimization of circular plates in problems of stability, Stroit. Mekh. i Raschet Sooruzhenii, 1977, No. 2, pp. 16–20.
Haug, E.J., Optimization of distributed parameter structures with repeated eigenvalues. In: New Approaches to Nonlinear Problems in Dynamics, P.J. Holmes (eds), Philadelphia, S.I.A.M., 1980, pp. 511–520.
Haug, E.J., and Rousselet, B., Design sensitivity analysis in structural mechanics II: Eigenvalues variations, J. Struct. Mech., 1980, 8.
Hu, K.K., and Kirmser, P.G., Numerical solution of a nonlinear differentialintegral equation for the optimal shape of the tallest column, Intern. J. Eng. Science, 1980, 18, pp. 333–339.
Iasinskii, F.S., Collected Works on Stability of Compressed Columns,Moscow and Leningrad, Gostekhizdat, 1952, 427 pp.
Karihaloo, B.L., and Parberry, R.D., Optimal design of beam-columns subjected to concentrated moments, Eng. Optim., 1980, 5, pp. 59–66.
Keller, J.B., The shape of the strongest column, Arch. Rational Mechanics and Analysis, 1960, 5, No. 4, pp. 275–285.
Keller, J.B., and Niordson, F.I., The tallest column. J. Math. and Mech.,1966, 16, No. 5, pp. 433–446.
Komkov, V., Application of invariant principles to the optimal design of a column, ZAMM, 1981, 61, pp. 75–80.
Komkov, V., and Haug, E.J., On the optimum shape of columns. In: Optimization of Distributed Parameter Structures, E.J. Haug and J. Cea (ed.), Alphen aan den Rijn, Sijthoff and Noordhoff, 1981, pp. 219–277.
Kruzelecki, J., Optimization of shells under combined loading via the concept of uniform stability. In: Optimization of Distributed Parameter Structures, E.J. Haug and J. Cea (eds.), Alphen aan den Rijn, Sijthoff and Noordhoff, 1981, pp. 929–950.
Lagrange, J.L., Sur la figure des colonnes, Miscellanea Taurinensia, 1770–1773, 5.
Kuznetsov, Iu.M., Compression and combined tension and bending of beams with minimal weight, Dopovidi Akad. Nauk Ukr.S.S.R., 1959, No. 14, pp. 372–378.
Larichev, A.D., Finding a minimum volume for a beam on an elastic foundation, for a given magnitude of a critical load. In: Applied and Theoretical Research into Building Structures, Moscow, Kucherenko TsNIINSK, 1981, pp. 19–25.
Leipholz, H.H.E., On conservative elastic systems of the first and second kind, Ing. Arch., 1974, 43, No. 5, pp. 255–271.
Litvinov, V.G., and Medvedev, N.G., Stability problem for shells of revolution and the Ritz-Galerkin techniques, Prikl. Mekhanika,1977, 13, No. 7, pp. 8–16.
Masur, E.F., Optimal design of symmetric structures against postbuckling collapse, Intern. J. Solids Struct., 1978, 14, pp. 319–326.
Masur, E.F., and Mrôz, Z., On nonstationary optimality conditions in structural design, Intern. J. Solids Struct., 1979, 15, pp. 503–512.
Masur, E.F., Optimal structural design under multiple eigenvalue constraint, Intern. J. Solids Struct.,1984, 20, No. 3, pp. 211–231.
McIntosh, S.C., and Ashley, H., On optimization of discrete structures with aeroelastic constraints, Comput. and Structures, 1978, 8, pp. 411–419.
Medvedev, N.G., Some spectral properties of optimal stability problems for shells with variable thickness, Dokl. Akad. Nauk U.S.S.R., Ser. A, No. 9, pp. 59–63.
Medvedev, N.G., and Totskii, N.P., Multiplicity of eigenvalues in the spectrum in optimal stability problems for cylindrical shells with variable thickness, Prikl. Mekhanika,1984, 20, No. 6, pp. 113–116.
Mikisheva, V.I., Optimal weaving of shells made of glassy plastics, subjected to loss of stability due to external pressure or to axial compression, Polymer Mechanics,1968, No. 5, pp. 864–875.
Naimark, M.A., Linear Differential Operators, Moscow, Nauka, 1969, 526 pp.
Nemirovskii, Iu.V., and Samsonov, V.I., On rational reinforcement of cylindrical shells compressed by an axial force, Izv. Akad. Nauk S.S.S.R., M.T.T., 1974, No. 1, pp. 103–112.
Nemirovskii, Iu.V., and Samsonov, V.I., Cylindrical reinforced shells most stable against external pressure, Polymers Mechanics,1974, No. 1, pp. 75–83.
Nicolai, E.L., Lagrange’s problem on the best shapes of columns, Izv. Peterburg. Polytekh. In., 1907, 5.
Nicolai, E.L., Research Works in Mechanics, Moscow, Gostekhizdat, 1955, 584 pp.
Olhoff, N., and Rasmussen, S.H., On single and bimodal optimum buckling loads of clamped columns, Intern. J. Solids Struct., 1977, 13, No. 7, pp. 605–614.
Olhoff, N., and Taylor, J.E., Designing continuous columns for minimum total cost of material and interior supports, J. Struct. Mech., 1978, 6, pp. 367–382.
Papkovich, P.F., Studies on Shipbuilding Structural Mechanics,vol. 4, Leningrad, (Sudostroienie), 1963, 552 pp.
Pedersen, P., and Seyranian, A.P., Sensitivity analysis for problems of dynamic stability, Intern. J. Solids Struct., 1983, 19, No. 4, pp. 315–335.
Pierson, B.L., Pannel flutter optimization by gradient projection, Intern. J. Numer. Meth Eng., 1975, 9, pp. 271–296.
Popelar, C.H., Optimal design of beams against buckling; a potential energy approach, J. Struct. Mech., 1976, 4, pp. 181–196.
Popelar, C.H., Optimal design of structures against buckling; a complementary energy approach, J. Struct. Mech., 1977, 5, pp. 45–66.
Prager, S., and Prager, W., A note on optimal designs of columns, Intern. J. Mech. Science, 1979, 21, pp. 249–251.
Prasad, S.N., and Herman, G., The usefulness of adjoint system in solving nonconservative problems of elastic continua, Intern. J. Solids Struct., 1969, 5.
Roorda, J., and Reiss A.J., Nonlinear interactive buckling; sensitivity and optimality, J. Struct. Mech.,1977, 5, pp. 207–232.
Rzhanitsyn, A.P., Stability of Equilibrium for Elastic Bodies, Moscow, Gostekhizdat, 1955, 476 pp.
Sandararaian, C., Optimization of a nonconservative elastic system with stability constraint, J. Optimiz. Theory Appl., 1975, 16, pp. 355–378.
Schmit, L.A., Jr., and Ramanathan, R., Multilevel approach to minimum weight design including buckling constraints, AIAA J., 1978, 16, No. 2, pp. 97–104.
Seyranian, A.P., Optimization of stability for a plate in a supersonic gas stream, Izv. Akad. Nauk S.S.S.R.,M.T.T., 1974, No. 1, pp. 103–112.
Seyranian, A.P., On a problem of Lagrange, Izv. Akad. Nauk S.S.S.R, M.T.T., 1974, No. 1, pp. 103–112.
Seyranian, A.P., and Sharaniuk, A.V., Seneitivity analysis for optimization of critical parameters in problems of dynamic stability, lzv. Akad. Nauk S.S.S.R., M.T.T., 1983, No. 5, pp. 173–182.
Seyranian, A.P., Sensitivity analysis and optimization of aeroelastic stability characteristics, Intern. J. Solids Struct., 1982, 18, No. 9, pp. 791–808.
Shanley, F.R., Optimum design for eccentrically loaded columns, J. Structural Division, Proc. Amer. Soc. Civ. Eng., 1967, 93, pp. 201–226.
Smirnov, A.F., Stability and Vibration of Reinforcements, Moscow, Transzheldorizdat, 1958, 572 pp.
Smirnov, A.F., Beams and arches of least weight in longitudinal bending, Tr. Mosk. In. Zheldor. Transp., 1950, 74, pp. 3–40.
Sofonov, Iu.D., Computation of the least weight of beams, with consideration of stability for a planar shape of deformed shape, Zap, Kazan’. Aviat. In., Kazan’, 1974, 168, pp. 3–43.
Solodovnikov, V.N., On techniques of optimization of shells for stability of the stressed state. In: Dynamics of Continuous Media,Novosibirsk, Institute of Hydrodynamics, 1976, 27, pp. 135–143.
Solodovnikov, V.N., Optimization of elastic shells of revolution, Prikl. Math. Mekh. 1978, 42, No. 3, pp. 511–520.
Stadler, W., Stability of the natural shapes of sinusoidally loaded uniform shallow arches, Quart. J. Mech. Appl. Math., 1983, 33, pt. 3, pp.
Swisterski, W., Wroblewski, W., and Zyczkowski, M., Geometrically nonlinear excentrically compressed columns of uniform creep strength vs optimal columns, Intern. J. Nonlinear Mechanics,1983, 18, No. 4, pp. 287–296.
Tadjbaksh, I., and Keller, J.B., Strongest columns and isoperimetric inequalities for eigenvalues, J. Appl. Mech., 1962, 29, No. 1, pp. 159–164.
Taylor, J.E., The strongest column; an energy approach. J. Appl. Mechanics, Trans. A.S.M.E., 1967, 34, No. 2, pp. 486–487.
Taylor, J.E., Optimal prestress against buckling; an energy approach, Intern. J. Solids Struct., 1971, 7, pp. 213–223.
Taylor, J.E., and Liu, C.Y., Optimal design of columns, A.I.A.A. J. 1968, 6, pp. 1496–1502.
Thomson, J.M.T., Optimization as a generator of structural instability, Intern. J. Mech. Science, 1972, 14, No. 9, pp. 627–630.
Thomson, J.M.T., and Hunt, G.W., Dangers of structural optimization Eng. Optim., 1974, 1, pp. 99–100.
Thomson, J.M.T., and Supple, W.D., Erosion of optimal design by compound branching phenomena, J. Mech. Phys. Solids, 1972, 21, No. 3, pp. 135–144.
Timoshenko, S.P., Stability of beams plates and shells. Selected Works,Moscow, Nauka, 1971, 808 pp.
Vol’mir, A.S., Stability of Deformed Systems, Moscow, Nauka, 1967, 984 pp.
Weisshaar, T.A., and Plaut, R.H., Structural optimization under nonconservative loading. In: Optimization of Distributed Parameter Structures, E.J. Haug and J. Cea (eds), Alphen aan den Rijn, Sijthoff and Noordhoff, 1981, pp. 843–864.
Ziegler, G., On stability of elastic systems. In: Problems of Mechanics, Moscow, Foreign Literature, 1959, pp. 116–160.
Ziegler, G., Foundations of the Theory of Structural Stability, Moscow, Mir, 1971, 192 pp.
Zyczkowski, M., Optimal design of shells with respect to their elastic stability. In: Stability of Elastic Structures, H.H.E. Leipholz (ed.), Wien, Springer-Verlag, 1978, pp. 268–291.
Zyczkowski, M., and Kruzelewski, J., Optimal design of shells with respect to their stability. In: Optimization in Structural Design, IUTAM, A. Sawczuk and Z. Mroz (eds.), Springer-Verlag, Berlin and New York, 1975, pp. 229–247.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1990 Springer-Verlag New York, Inc.
About this chapter
Cite this chapter
Banichuk, N.V. (1990). Application of the Stability and Weight Criteria. In: Introduction to Optimization of Structures. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-3376-3_8
Download citation
DOI: https://doi.org/10.1007/978-1-4612-3376-3_8
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-7988-4
Online ISBN: 978-1-4612-3376-3
eBook Packages: Springer Book Archive