Abstract
Part one consists of seven chapters corresponding to seven lectures delivered. The first chapter gives general introduction to structural optimization, discusses typical objectives, design variables, constraints and equations of state. Chapter 2 applies the concept of local shell buckling to optimization of elastic shells under stability constraints. The remaining chapters are devoted to optimization with respect to plastic or creep buckling: trusses, columns, arches, plates and shells are optimized, in most cases with rheological properties of the material allowed for. The last chapter gives a short survey of recent results, obtained within the years 1984 – 1988.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Prager, W.: Optimality criteria in structural design, Proc. Nat- Acad. Sci. USA 61 (1968), 3, 794 – 796.
Prager, W.: Conditions for structural optimality, Computers and Structures 2 (1972), 5, 833 – 840.
Prager, W. and J-E- Taylor: Problems of optimal structural design, Trans. ASME, J. Appl. Mech. 35 (1968), 1, 102 – 106.
Berke, L. and V.B. Venkayyas Reviev of optimality criteria approaches in structural optimization, Proc. Struct. Optimiz. Symp, ASME, AMD 7 (1974), 23 – 34.
Save, H.A.: A general criterion for optimal structural design, J. Optimiz. Theory and Appl. 15 (1975), 1, 119 – 129.
Fleury, C. and M. Geradin: Optimality criteria and mathematical programming in structural weight optimization, Comput. and Struct. 8 (1978), 7 – 17.
Mróz, Z. and A. Mironov: Optimal design for global mechanical constraints, Arch. Mech. Stos. 32 (1980), 4, 505 – 516.
Galileo Galilei Linceo: Discorsi e dimostrazioni maternatiche, Leiden 1638.
Gajewski, A. and M. Życzkowski: Optimal structural design under stability constraints, Kluwer — Nijhoff, Dordrecht 1988.
Krzyś, W. and M. Życzkowski: Klasyfikaeja problemów kształtowania wytrzymałościowego, Czasopismo Techniczne 68 (1963), 2, 1 – 4.
Życzkowski, M.: Optimal structural design in rheology, J. Appl. Mech. 38 (1971), 1, 39 – 46.
Życzkowski, M. and A. Gajewski: Optimal structural design under stability constraints, Proc. IUTAM Symp. Collapse — the Buckling of Structures, London 1982, Cambridge Univ. Press 1983, 299 – 332.
Razani, R.: The behavior of the fully stressed design of structures and its relationship to minimum weight design, AIAA Journal 3 (1965), 12, 2262 – 2268.
Kicher, T.P.: Optimum design — minimum weight versus fully stressed, Proc. ASCE, J. Struct. Div. 92 (1966), 6, 265 – 279.
Reinschmidt, K., C.A. Cornell and J.F. Brotchie: Iterative design and structural optimization, Proc. ASCE, J. Struct. Div. 92 (1966), ST6, 281 – 318.
Malkov, V.P. and R.G. Strongin: Minimum weight design based on strength constraints (in Russian), Mietody Reshenya Zadach Uprugosti i Plastichnosti 4, Gorky 1971, 138 – 149.
Gallagher, R.H.: Fully stressed design, Optimum structural design: theory and applications, Wiley, New York 1973, 19 – 32.
Nemirovsky, Yu.V. and B.S. Reznikov: Beams and plates of uniform strength in creep conditions (in Russian), Mashinovedenye (1969), 2, 58 – 64.
Życzkowski, M. and W. Swisterski: Optimal structural design of flexible beams with respect to creep rupture time, Proc. IUTAM Symp. Structural Control, Waterloo 1979, North — Holland 1980, 795 – 810.
Drucker, D.C. and R.T. Shields Design for minimum weight, Proc. 9th Int. Congr. Appl. Mech., Brussels 1956, vol. 5 (1957), 212 – 222.
Drucker, D.C. and R.T. Shield: Bounds on minimum weight design, Quart. Appl. Math. 15 (1957), 269 – 281.
Zavelani-Rossi, A.: Minimum — weight design for two -dimensional bodies, Meccanica 4 (1969), 4, 445 – 452.
Kordas, Z. and M. Życzkowski: Investigations of the shape of thick-walled non-circular cylinders showing full plasticization at the collapse, Bull. Acad. Pol., Ser. Sci. Techn. 18 (1970), 10, 839 – 847 (English extensive summary);
Kordas, Z. and M. Życzkowski: Investigations of the shape of thick-walled non-circular cylinders showing full plasticization at the collapse, Rozpr. Inż. 18 (1970), 3, 371 – 390 (Polish full text).
Kordas, Z.: Problematyka określania ksztaltów ciał wykazujacych całkowite uplastycznienie w stadium zniszczenia, Zeszyty Naukowe Politechniki Krakowskiej, Podstawowe Nauki Techniczne 15 (1977).
Bochenek, B., Z. Kordas and M. Życzkowski: Optimal plastic design of a cross section under torsion with small bending, J. Struct. Mech. 11 (1983), 3, 383 – 400.
Skrzypek, J. and M. Życzkowski: Termination of processes of finite plastic deformations of incomplete toroidal shells, Solid Mech. Arch. 8 (1983), 1, 39 – 98.
Szuwalski, K. and M. Życzkowski: On the phenomenon of decohesion in perfect plasticity, Int. J. Solid Struct. 9 (1973), 1, 85 – 98.
Wasiutyński, Z.: O kształtowaniu wytrzymałościowym, Akademia Nauk Technicznych, Warszawa 1939.
Prager, W.: Optimal structural design for given stiffness in stationary creep, Z. angew Math. Physik 19 (1968), 252 – 256.
Niordson, F.: On the optimal design of a vibrating beam, Quart. Appl. Math. 23 (1965), 1, 47 – 53.
Olhoff, N.: A survey of the optimal design of vibrating structural elements. Shock and Vibration Digest 8 (1976), 8, 3 – 10; 9, 3 – 10.
Troitsky, V.A.: Optimization of elastic bars in the presence of free vibrations (in Russian), Izv. AN SSSR, Mekh. Tverd. Tela (1976), 3, 145 – 152.
Shanley, F.R.: Principles of structural design for minimum weight, J. Aero. Sci. 16 (1949), 3.
Shanley, F.R.: Weight — strength analysis of aircraft structures, McGraw-Hill, New York — Toronto — London 1952.
Spunt, L.: Optimum structural design, Prentice — Hall, Englewood Cliffs, N.J., 1971.
Neut, A., van der: The interaction of local buckling and column failure of thin-walled compression members, Proc. 12th Int. Congr. Appl. Mech. Stanford 1968, Springer 1969, 389 – 399.
Thompson, J.M.T.: Optimization as a generator of structural instability, Int. J. Mech. Sci. 14 (1972), 9, 627 – 629.
Thompson, J.M.T. and W.J. Supple: Erosion of optimum designs by compound branching phenomena, J. Mech. Phys. Solids 21 (1973), 3, 135 – 144.
Volmir, A.S.: Stability of elastic systems (in Russian), Fizmatgiz, Moskva 1963; Stability of deformable systems (in Russian), Nauka, Moskva 1967.
Życzkowski, M. and J. Kruzelecki: Optimal design of shells with respect to their stability, Proc. IUTAM Symp. Optimization in Structural Design, Warsaw 1973, Springer 1975, 229 – 247.
Prager, W.: Introduction to structural optimization, CISM Courses 212, Springer, Wien — New York 1974.
Markiewicz, M.: Kształtowanie prostych ustrojów kratowych przy warunkach stateczności sprężysto — -plastycznej metodą wyznaczania konturu całkowitej niejednoznaczności, Rozpr. Inż. 28 (1980), 4, 569 – 584.
Markiewicz, M. and M. Życzkowski: Contour of complete non-uniqueness as a method of structural optimization with stability constraints, J. Optimiz. Theory Appl. 35 (1981), 1, 23 – 30.
Bürgermeister, G. and H. Steup: Stabilitätstheorie, Teil 1, Akademie — Verlag, Berlin 1957; Teil 2 (with H. Kretzschmar), Berlin 1963.
Wojdanowska, R. and M. Życzkowski: Optimal trusses transmitting a force to a given contour in creep conditions, Int. J. Mech. Sci. 26 (1984), 1, 21 – 28.
Shtaerman, I.Ya.: Stability of shells (in Russian), Trudy Kievsk. Aviats. Instituta 1 (1936).
Rabotnov, Yu.N.: Local stability of shells (in Russian), Dokl. AN SSSR, Novaya Seria 52 (1946), 2, 111 – 112.
Shirshov, V.P.: Local stability of shells (in Russian), Trudy II Vsesoy. Konf. po Teorii Plastin i Obolochek, Lvov 1961, Kiev 1962, 314 – 317.
Axelrad, E.L: On local buckling of thin shells, Int. J. Non-Linear Mech. 20 (1985), 4, 249 – 259.
Krużelecki, J.: Optimal design of a cylindrical shell under overall bending with axial force, Bull. Acad. Pol., Ser- Sci. Techn- 35 (1987) (English extensive summary); Rozpr. Inż. 33 (1985), 1/2, 135 – 149, (Polish full text).
Krużelecki, J.: Optimization of shells under combined loadings via the concept of uniform stability, Optimization of distributed parameter structures, Ed. by E.J. Haug and J. Cea, Nijhoff, Vol. II, 929 – 950 (1981).
Krużelecki, J. and M. Życzkowski: Optimal design of an elastic cylindrical shell under overal bending with torsion, Solid Mechanics Archives 9 (1984), 3, 269 – 306.
Krużelecki, J. and M. Życzkowski: Optimal structural design of shells — a survey, Solid Mechanics Archives 10 (1985), 2, 101 – 170.
Pflüger, A.: Stabilitätsprobleme der Elastostatik, Springer, Berlin — Göttingen — Heidelberg 1950 (1964, 1975).
Laasonen, P.: Nurjahdustuen edul1isimmasta poikipin-nanvalinnasta, Tekn- Aikakauslehti 38 (1948), 2, 49.
Krzyś, W.: Optimale Formen Bedrückter dünnwandiger Stützen im elastisch-plastischen Bereich, Wiss. Z. TU Dresden 17 (1968), 2, 407 – 410.
Krzyś, W.: Optimum design of thin — walled closed cross — section columns, Bull. Acad. Pol., Ser. Sci. Techn. 21 (1973), 8, 409 – 420.
Bleich, F.: Buckling strength of metal structures, McGraw-Hill, New York 1952.
Siegfried, W.: Failure from creep as influenced by the state of stress, J. Appl. Mech. 10 (1943), 4, 202 – 212.
Freudenthal, A.M.: Some time effects in structural analysis, Rep. 6th Int. Congr. Appl. Mech., Paris 1946.
Rzhanitsyn, A.R.: Deformation processes of structures consisting of viscoelastic elements, (in Russian), Dokl. AN SSSR 52 (1946), 25, 1.
Ross, A.D.: The effect of creep on instability and indeterminacy investigated by plastic models, Struct. Eng. 24 (1946), 413.
Wojdanowska, R.: Optimal design of weakly curved compressed bars with Maxwell type creep effects, Arch. Mech. Stos. 30 (1978), 6, 845 – 851.
Wojdanowska, R. and M. Życzkowski: On optimal imperfect columns subject to linear creep buckling, J. Appl. Mech. 47 (1980), 2, 438 – 439.
Kempner, J.: Creep bending and buckling of non-linearly viscoelastic columns, PIBAL Rep. No. 200, Brooklyn 1952; NACA TN 3137, Jan. 1954.
Hoff, N.J.: Buckling and stability, J. Roy. Aero. Sci. 58 (1954), 3 – 52.
Gerard, G.: A creep buckling hypothesis, J. Aero. Sci. 23 (1956), 9, 879 – 882.
Rabotnov, Yu.N. (G.N.) and S.A. Shesterikovs Creep stability of columns and plates, Prikl. Mat. Mekh. 21 (1957), 3, 406 – 412 (Russian version);
Rabotnov, Yu.N. (G.N.) and S.A. Shesterikovs Creep stability of columns and plates, Prikl. Mat. Mekh. J. Mech. Phys. Solids 6 (1957), 1, 27 – 34 (English version).
Życzkowski, M. and R. Wojdanowska-Zając: Optimal structural design with respect to creep buckling, Proc. IUTAM Symp. Creep in Structures 2, Göteborg 1970, Springer 1972, 371 – 387.
Błachut, J. and M. Życzkowski: Bimodal optimal design of clamped-clamped columns under creep conditions, Int. J. Solids Struct. 20 (1984), 6, 571 – 577.
Wróblewski, A.: Parametryczna optymalizacja prętów mimośrodowo ściskanych w nawiązaniu do teorii wyboczenia pełzającego Kempnera — Hoffa (in print).
Ṡwisterski, W., A. Wróblewski and M. Życzkowskis Geometrically non-linear eccentrically compressed columns of uniform creep strength vs. optimal columns, Int. J. Non-Linear Mech. 18 (1983), 4, 287 – 296.
Życzkowski, M. Recent results on optimal design in creep conditions, Euromech Coll. 164 on Optimization Methods in Structural Design, Siegen 1982, Bibliograph. Inst. Zürich 1983, 444 – 449.
Wróblewski, A. and M. Życzkowski: On multimodal optimization of circular arches against plane and spatial creep buckling, Structural Optimization 1 (1989), 2.
Kordas, Z.: Stability of the elastically clamped compressed bar in the general case of behaviour of the loading, Bull. Acad. Pol., Ser. Sci. Techn. 11 (1963), 419 – 428 (English extensive summary);
Kordas, Z.: Stability of the elastically clamped compressed bar in the general case of behaviour of the loading, Rozpr. Inż. 11 (1963), 3, 435 – 448 (Polish full text).
Bochenek, B. and A. Gajewski: Multimodal optimal design of a circular funicular arch with respect to in-plane and out-of-plane buckling, J. Struct. Mech. 14 (1986), 3, 257 – 274.
Wróblewski, A.: Optimal design of a circular plate with respect to creep buckling (in print).
Rysz, M. and M. Życzkowski: Optimal design of a cylindrical shell under overall bending and axial force with respect to creep stability. Structural Optimization 1 (1989), 1.
Haftka, R.T. and R.V. Grandhi: Structural shape optimization — a survey, 26th Struct. Dyn. and Mat. Conf., Part I, New York 1985, 617 – 628.
Levy, R. and O.E. Lev: Recent developments in structural optimization, Proc. ASCE, J. Struct. Engng. 113 (1987), 9, 1939 – 1962.
Życzkowski, M.: Optimal structural design under creep conditions, Mech. Teor. Stos. 24 (1986), 3, 243 – 258 (Polish version), Appl. Mech. Rev., 41 (1988), 12, 453 – 461 (English extended version).
Haftka, R.T. and M.P. Kamat: Elements of structural optimization, Nijhoff, Dordrecht 1985.
Haug, E.J., K.K. Choi and V. Komkov: Design sensitivity analysis of structural systems, Academic Press, Orlando — San Diego — New York 1986.
Save, M. and W. Prager: Structural optimization, Vol.1, Optimality criteria, Plenum Press, New York 1985.
Banichuk, N.V.: Introduction to structural optimization (in Russian), Nauka, Moskva 1986.
Banichuk, N.V. and A.A. Barsuk: Application of spectral decomposition of eigenvalues in structural optimization under stability constraints (in Russian), Problemy Ustoych. i Pred. Nes. Sposobn. Konstruktsiy, Leningrad 1983, 17 – 24.
Bratus, A.S. and A.P. Seyranian: Bimodal solutions in optimization of eigenvalues (in Russian), Prikl. Mat. Mekh. 47 (1983), 4, 546 – 554.
Shin, Y.S., R.H. Plaut and R.T. Haftka: Simultaneous analysis and design for eigenvalue maximization, AIAA/ASME/ASCE/AHS 28th Struct., Struct. Dyn. and Mat. Conf., Monterey, 1987, New York 1987, 334 – 342.
Antman, S.S. and C.L. Adler: Design of material properties that yield a prescribed global buckling response, Trans. ASME, J. Appl. Mech. 54 (1987), 2, 263 – 266.
Bushnell, D.: PANDA 2 — program for minimum weight design of stiffened, composite, locally buckled panels, Comp. and Struct. 25 (1987), 4, 469 – 605.
Seyranian, A.P.: On a certain problem of Lagrange (in Russian), Izv. AN SSSR, Mekh. Tverd. Tela (1984), 2, 101 – 111.
Madsen, N.: Analytical determination of higher buckling modes for unimodal optimal columns, J. Struct. Mech. 11 (1984), 4, 545 – 560.
Olhoff, N.: Structural optimization by variational methods, Computer Aided Optimal Design, Proc. NATO Adv. Study Institute, Tróia 1986, Springer 1987, 87 – 164.
Efremov, A.Yu. and K.A. Matveev: Shape optimization of bars in stability problems (in Russian), Dinam. i Prochnost Aviats. Konstr., Novosibirsk 1986, 89 – 92.
Pfefferkorn, W.: Der dünnwandige Knickstab mit minimierter Masse, IfL — Mitteilungen 25 (1986), 3, 65 – 67.
Larichev, A.D.: Optimization of stability of thin-walled bars of open cross-section, (in Russian), Prikl. Probl. Prochn. Plastichn. (Gorky), 1986, No. 34, 97 – 103.
Mikulski, T. and C. Szymczak: Optymalne kształtowanie przekroju poprzecznego ściskanych pretów cienkościennych o przekroju otwartym, Zesz. Nauk. Polit. Gdańskiej 42 (1987), 73 – 92.
Hasegawa, A-, H. Abo, M. Mauroof and F. Nishino: A simplifiield analysis and optimality on the steel column behavior with local buckling, Proc. Jap. Soc. Eng. 1986, No. 374, 195 – 204.
Kartvelishvili, V.M.: On optimal solutions to a Prandtl’s problem (in Russian), Issled. po stroit. mekh. i nadezhn. konstr., Moskva 1986, 81 – 89.
Wang, C.M., V. Thevendran, K.L. Tea and S. Kitipornchai: Optimal design of tapered beams for maximum buckling strength, Eng. Struct. 8 (1986), 4, 276 – 284.
Vison, J.R.: Optimum design of composite honeycomb sandwich panels subjected to uniaxial compression, AIAA Journal 24 (1986), 10, 1690 – 1696.
Vinson, J.R.: Minimum weight web-core sandwich panels subjected to combined uniaxial compression and in-plane shear loads, AIAA/ASME/ASCE/AHS 28th Struct., Struct. Dyn. and Mat. Conf., Monterey 1987, New York 1987, 282 – 288.
Nakagiri, S. and H. Takabatake: Optimum design of FRP laminated plates under axial compression by use of the Hessian matrix, Proc. Int. Conf. Computer Mechanics ’86, Tokyo, Vol. 2, Tokyo 1986, X/71 – X/76.
Mróz, Z.: Sensitivity analysis and optimal design with account for varying shape and support conditions. Computer Aided Optimal Design, Proc. NATO Adv. Study Institute, Tróia 1986, Springer 1987, 407 – 438.
McGrattan, R.J.: Weight optimization of stiffened cylindrical panels, Trans. ASME, J. Pressure Vessel Techn. 109 (1987), 1, 1 – 9.
Błachut, J.: Optimal barrel — shaped shells under buckling constraints, AIAA Journal 25 (1987), 1, 186 – 188.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1989 Springer-Verlag Wien
About this chapter
Cite this chapter
Zyczkowski, M. (1989). Part I. In: Zyczkowski, M. (eds) Structural Optimization under Stability and Vibration Constraints. International Centre for Mechanical Sciences, vol 308. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2969-2_1
Download citation
DOI: https://doi.org/10.1007/978-3-7091-2969-2_1
Publisher Name: Springer, Vienna
Print ISBN: 978-3-211-82173-2
Online ISBN: 978-3-7091-2969-2
eBook Packages: Springer Book Archive