DOI QR코드

DOI QR Code

Optimal Design of Composite Laminated Plates with the Discreteness in Ply Angles and Uncertainty in Material Properties Considered

섬유 배열각의 이산성과 물성치의 불확실성을 고려한 복합재료 적층 평판의 최적 설계

Kim, Tae-Uk;Sin, Hyo-Cheol
김태욱;신효철

  • Published : 2001.03.01

Abstract

Although extensive efforts have been devoted to the optimal design of composite laminated plates in recent years, some practical issues still need further research. Two of them are: the handling of the ply angle as either continuous or discrete; and that of the uncertainties in material properties, which were treated as continuous and ignored respectively in most researches in the past. In this paper, an algorithm for stacking sequence optimization which deals with discrete ply angles and that for thickness optimization which considers uncertainties in material properties are used for a two step optimization of composite laminated plates. In the stacking sequence optimization, the branch and bound method is modified to handle discrete variables; and in the thickness optimization, the convex modeling is used in calculating the failure criterion, given as constraint, to consider the uncertain material properties. Numerical results show that the optimal stacking sequence is found with fewer evaluations of objective function than expected with the size of feasible region taken into consideration; and the optimal thickness increases when the uncertainties of elastic moduli considered, which shows such uncertainties should not be ignored for safe and reliable designs.

Keywords

Stacking Sequence Optimization;Thickness Optimization;Branch and Bound Method;Convex Modeling

References

  1. Reddy, J. N., 1984, 'A Simple Higher-Order Theory for Laminated Composite Plates,' J. Appl. Mech., Vol. 51, pp. 745-752
  2. Elishakoff, I., 1994, 'A Deterministic Method to Predict the Effects of Unknown-but-Bounded Elastic Moduli on the Buckling of Composite Structures,' Comput. Methods Appl. Mech. Engng., Vol. 111, pp. 155-167 https://doi.org/10.1016/0045-7825(94)90043-4
  3. Jones, R. M., Mechanics of Composite Materials, McGraw-Hill, ToKyo, 1975
  4. Vanderplaats, G. N., Numerical Optimization Techniques for Engineering Design, McGraw-Hill, New York, 1984
  5. Givoli, D., and Elishakoff, I., 1992, 'Stress Concentration at a Nearly Circular Hole with Uncertain Irregularties,' J. Appl. Mech., Vol. 59, pp. 65-71
  6. Elishakoff, I., and Colombi, P., 1993, 'Combination of Probabilistic and Convex Models of Uncertainty When Scarce Knowledge Is Present an Acoustic Excitation Parameters,' Comput. Methods Appl. Mech. Engng., Vol. 104, pp. 187-209 https://doi.org/10.1016/0045-7825(93)90197-6
  7. Ben-Haim, 1993, 'Failure of an Axially Compressed Beam with Uncertain Initial Deflection of Bounded Strain Energy,' Int. J. Engng. Sci., Vol. 31, pp. 989-1001 https://doi.org/10.1016/0020-7225(93)90107-6
  8. Hajela P., and Shii, C. J., 1989, 'Optimal Design of Laminated Composites Using A Modified Mixed Integer and Discrete Programming Algorithm,' Comput. Struct., Vol. 32, pp. 213-221 https://doi.org/10.1016/0045-7949(89)90087-4
  9. Ben-Haim, Y. and Elishakoff, I., 1990, Convex Models of Uncertainty in Applied Mechanics, Elsevier, Amsterdam
  10. Sivakumar, K., Iyenger, N. G. R., and Kalyanmoy Deb, 1998, 'Optimum Design of Laminated Composite Plates with Cutouts Using a Genetic Algorithm,' Comput. Struct., Vol. 42, pp. 265-279 https://doi.org/10.1016/S0263-8223(98)00072-5
  11. Winston, W. L., Introduction to Mathematical Programming, Duxbury Press, California, 1995
  12. Franco Correia, V. M., Mota Soares, C. M., and Mota Soares, C. A., 1997, 'Higher Order Models on the Eigenfrequency Analysis and Optimal Design of Laminated Composite Structures,' Compos. Stuct., Vol. 39, pp. 237-253 https://doi.org/10.1016/S0263-8223(97)00118-9
  13. Mota Soares, C. M., Mota Soares, C. A., and Franco Correia, V. M., 1997, 'Optimization of Multilaminated Structures Using Higher-Order Deformation Models,' Comput. Methods Appl. Mech. Engng., Vol. 149, pp. 133-152 https://doi.org/10.1016/S0045-7825(97)00066-2
  14. Haftka, R. T., and Walsh, J. L., 1992, 'Stacking-Sequence Optimization for Bucking of Laminated Plates by Integer Programming,' AIAA J., Vol. 30, pp. 814-819
  15. Adali, S., Richter, A., and Verijenko, V. E., 1997, 'Optimization of Shear-Deformable Laminated Plates Under Bucking and Strength Criteria,' Compos. Struct., Vol. 39, pp. 167-178 https://doi.org/10.1016/S0263-8223(97)00111-6
  16. Riche, R. L., and Haftka, R. T., 1993, 'Optimization of Laminated Stacking Sequence for Bucking Load Maximization by Genetic Algorithm,' AIAA J., Vol. 31, pp. 951-956
  17. Tauchert, T. R., and Adibhatla, S., 1984, 'Design of Laminated Plates for Maximum Stiffness,' J. Compos. Mater., Vol. 18, pp. 58-69 https://doi.org/10.1177/002199838401800105
  18. Kam, T. Y., and Chang, R. R., 1992, 'Optimum Layup of Thick Laminated Composite Plates for Maximum Stiffness,' Eng. Opt., Vol. 19, pp. 237-249 https://doi.org/10.1080/03052159208941230
  19. Kam, T. Y., and Lai, M. D., 1989, 'Multilevel Optimal Design of Laminated Composite Plate Structures,' Comput. Struct., Vol. 31, pp. 197-202 https://doi.org/10.1016/0045-7949(89)90225-3
  20. Park, W. J., 1982, 'An Optimal Design of Simple Symmetric Laminates Under the First Ply Failure Criterion,' J. Compos. Mater., Vol. 16, pp. 341-355 https://doi.org/10.1177/002199838201600407
  21. Kim, C. W., Hwang, W., Park, H. C., and Han, K. S., 1997, 'Stacking Sequence Optimization of Laminated Plates,' Compos. Struct., Vol. 39, pp. 283-288 https://doi.org/10.1016/S0263-8223(97)00120-7