Abstract
An angle-ply laminated plate is optimized with the objective of minimizing the weight of the plate taking into account uncertainties in the multiple transverse loads. The weight is proportional to the laminate thickness which is minimized subject to deflection and buckling constraints under the least favourable loading with the ply angles taken as design variables. The convex modelling approach is employed to analyse the uncertain loading with the uncertain quantities allowed to vary arbitrarily around their average values subject to the requirements that these variations are bounded inL 2 norm and represented by a finite number of eigenmodes. The effect of uncertainty on the optimal design is investigated quantitatively. It is shown that the minimum weight increases with increasing level of uncertainty and the optimal ply angles also depend on the level of uncertainty.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Adali, S. 1992: Convex and fuzzy modelling of uncertainties in the optimal design of composite structures. In: Pedersen, P. (ed.)Optimal design with advanced materials. Amsterdam: Elsevier
Adali, S.; Richter, A.; Verijenko, V.E. 1994a: Non-probabilistic modelling and design of sandwich plates subject to uncertain loads and initial deflections.Int. J. Eng. Sci. (to appear)
Adali, S.; Richter, A.; Verijenko, V.E. 1994b: Optimal design of symmetric angle-ply laminates subject to uncertain loads and initial imperfections. In:Proc. 4-th Int. Conf. on Computer Aided Design in Composite Materials Technology (CADCOMP-94) (held in Southampton, England), pp. 39–48
Ben-Haim, Y. 1993: Failure of an axially compressed beam with uncertain initial deflection of bounded strain energy.Int. J. Eng. Sci. 31, 989–1001
Ben-Haim, Y.; Elishakoff, I. 1989: Non-probabilistic models of uncertainty in the non-linear buckling of shells with general imperfections: theoretical estimates of the knockdown factor.ASME J. Appl. Mech. 56, 403–410
Ben-Haim, Y.; Elishakoff, I. 1990:Convex models of uncertainty in applied mechanics. Amsterdam: Elsevier Science Publishers
Elishakoff, I.; Ben-Haim, Y. 1990: Dynamics of a thin cylindrical shell under impact with limited deterministic information on its initial imperfections.J. Struct. Safety 8, 103–112
Elishakoff, I.; Cai, G.Q.; Starnes, J.H. 1994: Non-linear buckling of a column with initial imperfection via stochastic and nonstochastic convex models.Int. J. Non-linear Mech. 29, 71–82
Elishakoff, I.; Colombi, P. 1993: Combination of probabilistic and convex models of uncertainty when scarce knowledge is present on acoustic excitation parameters.Comput. Meth. Appl. Mech. Eng. 104, 187–209
Elishakoff, I.; Li, Y.W.; Starnes, J.H. 1994: A deterministic method to predict the effect of unknown-but-bounded elastic moduli on the buckling of composite structures.Comput. Meth. Appl. Mech. Eng. 111, 155–167
Kam, T.Y.; Chang, R.R. 1992: Optimum layup of thick laminated composite plates for maximum stiffness.Eng. Optimiz. 19, 237–249
Kelly, P.J.; Weiss, M.L. 1979:Geometry and convexity: a study in mathematical methods. New York: John Wiley and Sons
Kengtung, C. 1986: Sensitivity analysis and a mixed approach to the optimization of symmetric layered composite plates.Eng. Optimiz. 9, 233–248
Khalil, M.; Ramahefarison, E. 1993: Optimum design of composite laminates subjected to multiple loads. In: Miravete, A. (ed.)Proc. 9-th Int. Conf. on Composite Materials, Composites Design (held in Madrid), pp. 643–650. University of Zaragoza: Woodhead Publishing Ltd.
Krikanov, A. 1985: Design of composite panels of minimum weight with several cases of loading.Mech. Composite Mater. 21, 599–602
Nemeth, M.P. 1986: Importance of anisotropy on buckling of compression-loaded symmetric composite plates.AIAA J. 24, 1831–1835
Quian, B.; Reiss, R.; Aung, W. 1990: The maximum stiffness design of rectangular symmetric angle-ply laminates. In: de Wilde, W.P.; Blain, W.R. (eds.)Proc. 2nd Int. Conf. on Computer Aided Design in Composite Material Technology (held in Southampton), pp. 451–464. Free University of Brussels and Wessex Institute of Technology: Computational Mechanics Publications
Sadek, I.S.; Sloss, J.M.; Adali, S.; Bruch, Jr., J.C. 1993: Nonprobabilistic modelling of dynamically loaded beams under uncertain excitations.Math. Comput. Modelling 18, 59–67
Tauchert, T.R.; Adibhatla, S. 1984: Design of laminated plates for maximum stiffness.J. Composite Mater. 18, 58–69
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Adali, S., Richter, A. & Verijenko, V.E. Minimum weight design of symmetric angle-ply laminates under multiple uncertain loads. Structural Optimization 9, 89–95 (1995). https://doi.org/10.1007/BF01758825
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01758825