Abstract
In the paper the uni- and multimodal optimization problems of elastic annular plates with respect to their stability under thermal loading are investigated. We look for such a distribution of a thickness of a plate (circularly symmetric), which leads to the maximum increment |ΔT| of temperature, causing buckling of the optimal structure under the equality constraint of a constant volume of the material and under inequality constraints imposed on the minimal and maximal values of a plate thickness. The optimal solutions for different modes of supports and different ratio of the inner and outer radius are looked for using the method of moving asymptotes and the simulated annealing.
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References
Albul AB, Banichuk NW, Barsuk AA (1980) Optimal design of elastic columns under thermal loadings. Mekh Tverdogo Tela 15(3):127–133 (in Russian)
Bochenek B (1999) Bimodal optimal design against instability and postbuckling behavior of thermally loaded columns. In: Skrzypek J, Hetnarski R (eds) Thermal Stresses ’99: Proceedings of the third international congress on thermal stresses, pp 471–474 (Bratni Zew 1999)
Bochenek B, Rasmussen J (1992) On implementation of equality constrains into the method of moving asymptotes. In: Hirsch C, Zienkiewicz O, Onate E (eds) Proceedings of the first European conference on numerical methods in engineering, Brussels. Elsevier, Amsterdam, pp 811–818
Gajewski A, Cupiał P (1992) Optimal structural design of an annular plate compressed by non-conservative forces. Int J Solids Struct 29(10):1283–1292
Griniev VB, Filippov AP (1977) Optimal design of circural plates in stability problems. Stroit Mech I Rozczot Sooruzeni 2:16–20 (in Russian)
Krużelecki J, Smaś P (2001) Optimal design of columns for buckling under loadings controlled by displacements and forces. In: Cheng G, Gu Y, Liu S, Wang Y (eds) Proceedings of the fourth world congress of structural and multidisciplinary optimization. Liaoning, Dalian
Krużelecki J, Smaś P (2003) Optimal design of annular plates against buckling under loadings controlled by displacements. Proceedings of the fifth world congress of structural and multidisciplinary optimization, Venice
Krużelecki J, Smaś P (2004) Optimal design of simply supported columns for buckling under loading controlled by displacements. Eng Optim 36(6):645–658
Masters T (1993) Practical neural network recipes in C++. Academic, Boston
Olhoff N (1988) Multicriterion structural optimization via bound formulation and mathematical programming. Struct Optim 1:11–17
Ozakca M, Taysi N, Kolcu F (2002) Buckling analysis and shape optimization of elastic variable thickness circular and annular plates-II. Shape optimization. Eng Struct 25:193–199
Rzegocińska-Pełech K, Waszczyszyn Z (1984) Numerical optimum design of elastic annular plate with respect to buckling. Comput Struct 18(2):369–378
Strzelczyk A, Drobniewicz M (1981) Elastic buckling of annular plates with variable thickness. Arch Bud Maszyn 28(2):91–103 (in Polish)
Svanberg K (1987) Method of moving asymptotes—a new method for structural optimization. Int J Numer Methods Eng 24:359–373
Życzkowski M, Krużelecki J, Trzeciak P (2001) Optimal design of rotationally symmetric shells for buckling under thermal loadings. J Theor Appl Mech 39(2):443–455
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A short version of the paper was presented at WCSMO-6
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Krużelecki, J., Smaś, P. Optimal annular plates with respect to their stability under thermal loadings. Struct Multidisc Optim 32, 111–120 (2006). https://doi.org/10.1007/s00158-006-0010-5
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DOI: https://doi.org/10.1007/s00158-006-0010-5