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Anti-optimization technique for structural design under load uncertainties. (English) Zbl 0954.74044
Summary: We describe a technique for design under uncertainty based on the worst-case-scenario technique of anti-optimization. When anti-optimization is integrated with structural optimization, we create a nested optimization problem, which can be very expensive to solve. The paper demonstrates the use of a technique alternating between optimization and anti-optimization which alleviates the computational burden. The method is applied to the optimization of a simply supported laminate composite, to the optimization of a simple beam problem with nonlinear objective function, and finally to the optimization of a more complex real-life composite sandwich structure.

74P05Compliance or weight optimization (solid mechanics)
74E30Composite and mixture properties
74K20Plates (solid mechanics)
74K10Rods (beams, columns, shafts, arches, rings, etc.) in solid mechanics
Full Text: DOI
[1] Adali, S.; Richter, A.; Verijenko, V. E.: Minimum weight design of symmetric angle-ply laminates under multiple uncertain loads. Struct. opt. 9, 89-95 (1995)
[2] Ben-Haim, Y.: A non-probabilistic concept of reliability. Struct. safety 14, 227-245 (1994)
[3] Ben-Haim, Y.; Elishakoff, I. E.: Convex models of uncertainties in applied mechanics. Studies in applied mechanics (1990) · Zbl 0703.73100
[4] Elishakoff, I. E.: An idea on the uncertainty triangle. Shock vib. Dig. 22, 1 (1990)
[5] Elishakoff, I. E.: Essay on uncertainties in elastic and viscoelastic structures: from A.M. Freudental’s criticisms to modern convex modeling. Comput. struct. 56, 871-895 (1995) · Zbl 0921.73004
[6] Elishakoff, I. E.; Cai, G. Q.; Jr., J. H. Starnes: Non-linear buckling of a column with initial imperfection via stochastic and non-stochastic convex models. Int. J. Non-linear mech. 29, 71-82 (1994) · Zbl 0796.73020
[7] Elishakoff, I. E.; Li, Y. W.; Jr., J. H. Starnes: A deterministic method to predict the effect of unknown-but-bounded elastic moduli on the buckling of composite structures. Comput. methods appl. Mech. engrg. 111, 155-167 (1994) · Zbl 0845.73031
[8] Elishakoff, I. E.; Haftka, R. T.; Fang, J.: Structural design under hounded uncertainty--optimization with anti-optimization. Comput. struct. 53, 1401-1405 (1994) · Zbl 0878.73041
[9] Fong, K. W.; Jefferson, T. H.; Suyehiro, T.; Walton, L.: Guide to the SLATEC common mathematical library. (1992)
[10] Gangadharan, S.; Nikolaidis, E.; Lee, K.; Haftka, R. T.: The use of anti-optimization to compare alternative structural models. Proc. 34th AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics and materials conference, 534-543 (1993)
[11] Lee, J.; Haftka, R. T.; Jr., O. H. Griffin; Watson, L. T.; Sensmeier, M. D.: Detecting delamination in a composite beam using anti-optimization. Struct. opt. 8, 93-100 (1994)
[12] Lomhardi, M.: Ottimizzazione strutturale: metodo a due passi e applicazioni a strutture in materiale composito. Doctorate thesis (1995)
[13] Lombardi, M.: Design and optimization of mechanical component using sandwich structures. Sandwich construction 3, 149-158 (1996)
[14] Metropolis, N.; Rosenbluth, A.; Rosenbluth, M.; Teller, E.: Equation of state calculation by fast computing machines. J. chem. Phys. 21, 1087-1092 (1953)
[15] Thompson, J. M. T.; Supple, W. J.: Erosion of optimal design by compound branching phenomena. J. mech. Phys. solids 21, 135-144 (1973)
[16] Vanderplaatz, G. N.: An efficient feasible direction algorithm for design synthesis. Aiaa J. 22 (1984)
[17] Van Wamelen, A.; Johnson, E. R.; Haftka, R. T.: Optimal design of laminated specimens to evaluate composite failure criteria. Presented al ASC 8th technical conference on composite materials (1993)
[18] Venter, G.; Haftka, R. T.; Jr., J. H. Starnes: Construction of response surfaces for design optimization applications. AIAA paper 96-4001 (1996)