Engineering Transactions, 43, 4, pp. 495-504, 1995

Optimization of the Structure of a Multilayer Cylindrical Shell Under Stability Loss Conditions

G. Mielczarek
Military University of Technology, Warszawa
Poland

The computer program presented here has been devised for minimizing the thickness of a thin cylindrical shell composed of linearly elastic, macro-homogeneous, orthotropic layers, resting on hinged supports and threatened with stability loss under the action of static compressive forces directed along the axis and uniformly distributed along the curvilinear edges of the shell. The optimization process is based on the method for determining the critical loads (Tcr), presented in [1] and on the kinematic broken line theory, and the static distribution theory of lateraI shear stresses.

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Copyright © Polish Academy of Sciences & Institute of Fundamental Technological Research (IPPT PAN).

References

G. MIELCZAREK, Determination of the critical load for a thin cylindrical multilayer shell resting on hinged supports and subjected to axial compression, [submitted for publication].

A.M. BRANDT, Optimization criteria and methods for structures [in Polish], Warszawa 1977.

A.M. BRANDT, Principles of optimization of elements of building structures [in Polish], Warszawa 1978.

A. GAJEWSKI and M. ŻYCZKOWSKI, Optimum formation of rod structures under conditions of stability [in Polish], Proc. of the Conference on "Present Problems of Structure Stability", Janowice 1985.

N. OLHOFF, Optimum design of structures [in Russian], Moscow 1981.

M. EPSTEIN and P.G. GLOCKNER, Nonlinear analysis of multilayered shells, Int. Solids Structures, 13, pp.1082-1089, 1977.

E.I. GRIGOLJUK and P.P. KULIKOV, The development of the general direction in the theory of multilayer shells [in Russian], Mechanics of Composite MateriaIs, 2, 287-298, 1988.

R.M. CHRISTENSEN, Mechanics of composite materials, New York 1979.

V.È. ČEPIGA, Linearization of the stability equation of thick multilayer shells [in Russian], Solid State Mech., 2, 33-41, 1975.

V.È. ČEPIGA, A tentative approach to the construction of mathematical models of layered shells [in Russian], Solid State Mech., 2, 190-191, 1975.

V.È. ČEPIGA, A contribution to the improved theory of layered shells [in Russian], Prikl. Mekh., 11, 45-49, 1976.

V.È. ČEPIGA, The construction of a theory of anisotropic multilayer shells with prescribed accuracy [in Russian], Solid State Mech., 4, 113-120, 1977.

È.I. GRIGOLJUK and P.P. KULIKOV, A contribution to the theory of anisotropic layered elastic shells [in Russian], Dokl. AN SSSR, 5, 1077-1079, 1984.

È.I. GRIGOLJUK and P.P. ČULKOV, Equations of three-layer shells with light filling material [in Russian], Izv. AN SSSR, 2, 77-84, 1950.

È.I. GRIGOLJUK and P.P. ČULKOV, Stability and vibrations of three-layer shells [in Russian], Moscow 1973.

È.I. GRIGOLJUK and V.V. KABANOV, Stability of shells [in Russian], Moscow 1978.

È.I. GRIGOLJUK and G.M. KULIKOV, Numerical solution of statical problems of geometrically nonlinear anisotropic multilayer shells of revolution [in Russian], Mechanics of Composite MateriaIs, 3, 853-860, 1981.

È.I. GRIGOLJUK and G.M. KULIKOV, Axially symmetric deformation of anisotropic layered shells of revolution of complex form [in Russian], Mechanics of Composite Materials, 4, 637-645, 1981.

È.I. GRIGOLJUK and G.M. KULIKOV, A variant of the nonlinear theory of shallow multilayer elastic shells [in Russian], Mechanics of Composite MateriaIs, 5, 853-860, 1985.

V.V. KABANOV, Stability of nonhomogeneous cylindrical shells [in Russian], Moscow 1982.

M.A. KANIDOLOTSKIĬ and JU.S. URŽUMCEV, Optimum design of layered structures [in Russian], Novosibirsk 1989.

I.F. OBRAZCOV and V.V. VASILEV, Optimum reinforcement of shells of revolution of composite materials [in Russian], Moscow 1977.

P.M. OGIBALOV and JU.V. SUVOROVA, Mechanics of reinforced plastics [in Rus­sian], Moscow 1965.

L. LIBRESCU, Nonlinear theory of anisotropic multilayer elastic shells [in Russian], Collection of Problems of Applied Mechanics, 453-466, 1974.

G.A. TETERS, R.B. RIKARDS and B.L. NARUSBERG, Optimization of layered composite shells [in Russian], Riga 1978.

G.A. VANIC, N.P. SEMENJUK and R.F. EMELJANOV, Stability of shells of reinforced materials [in Russian], Kiev 1978.

J.B. ROSEN, The gradient projection method for nonlinear programming, Part 1. Linear constraints, J. Soc. lndust. Appl. Math., 8, 703-712, 1960.

J.B. ROSEN, The gradient projection method for nonlinear programming, Part 2. Nonlinear constraints, J. Soc. lndust. Appl. Math., 9, 514-532, 1961.

W. FINDEISEN, J. SZYMANOWSKI and A. WIERZBICKI, Theory and computational methods in optimization [in Polish], Warszawa 1980.

J.H. WILKINSON, Handbook for automatic computation, vol. II, Linear Algebra, Berlin 1971.

R. CUPISZ and S. OCHELSKI, Creep of anisotropic polymer composites in plane state of stress, under non-stationary load [in Polish], Engng. Trans., 38, 11 57-72, 1990.