Parametrization in laminate design for optimal compliance

International Journal of Solids and Structures

Volumn 34, Issue 4, 1997, Pages 415-434

  Hammer, V B ^a   Bendsoe M P ^a   Lipton, R ^b   Pedersen, P ^a  

^a TECHNICAL UNIVERSITY OF DENMARK   (Denmark)

^b Worcester Polytechnic Institute   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPOSITE STRUCTURES; LAMINATED COMPOSITES; LOADS (FORCES); OPTIMIZATION; STIFFNESS; STIFFNESS MATRIX; STRAIN;

LAMINATE DESIGN PARAMETRIZATION; LAMINATED PLATES; STIFFNESS DESIGN; TRIGONOMETRIC FUNCTIONS;

PLATES (STRUCTURAL COMPONENTS);

EID: 0031075686     PISSN: 00207683     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0020-7683(96)00023-6     Document Type: Article

References (37)

1. Allaire, G. and Kohn, R. V. (1993). Optimal design for minimum weight and compliance in plane stress using extremal microstructures. Eur. J. Mech. A. 12(6), 839-878.
2. Avallaneda, M. and Milton, G. W. (1989). Bounds on the effective elasticity tensor composites based on two-point correlation. In Composite Material Technology, (eds Hui, D. and Kozik, T. J.), ASME, New York, pp. 89-93.
3. Ball, J. M. (1989). A version of the fundamental theorem for young measures. In Partial Differential Equations and Continuum Models of Phase Transitions (eds Rascal, M., Serre, D. and Slemrod, M.), Springer, Berlin, pp. 207-215.
4. Bendsøe, M. P. (1995). Optimization of Structural Topology, Shape, and Material, Springer, Berlin, Heidelberg.
5. Bendsøe, M. P., Díaz, A. R., Lipton, R. and Taylor, J. E. (1995). Optimal design of material properties and material distribution of multiple loading conditions. Int. J. Num. Meth. Engng 38, 1149-1170.
6. Cea, J. and Malanovsky, K. (1970). An example of a max-min problem in partial differential equations. SIAM J. Control 8, 305-316.
7. Cherkaev, A. and Palais, R. (1996). Optimal design of three-dimensional axisymmetric elastic structures. Struct. Optim., to appear.
8. Diaz, A. R. and Bendsøe, M. P. (1992). Shape optimization of structures for multiple loading conditions using a homogenization method. Struct. Optim. 4, 17-22.
9. Díaz, A. R., Lipton, R. and Soto, C. A. (1995). A new formulation of the problem of optimum reinforcement of Reissner-Mindlin plates. Comp. Meth. Appl. Mech. Engng 123, 121-139.
10. Ekeland, I. and Temam, R. (1976). Convex Analysis and Variational Problems, North Holland, Amsterdam.
11. Fang, C. and Springer, G. S. (1993). Design of composite laminates by a Monte Carlo method. J. Comp. Mat. 27, 721-753.
12. Fedorov, A. V. and Cherkaev, A. V. (1983). Choice of optimal orientation of axes of elastic symmetry for an orthotropic plate. MTT 18, 135-142.
13. Fortin, M. and Glowinski, R. (1983). AugmentedLagrangian Methods, North-Holland, Amsterdam.
14. Fukunaga, H. and Vanderplaats, G. N. (1991). Stiffness optimization of orthotropic laminated composites using lamination parameters. AIAA J. 29, 641-646.
15. Fukunaga, H. and Sekine, H. (1992). Stiffness design method of symmetric laminates using lamination parameters. AIAA J. 30, 2791-2793.
16. Fukunaga, H. and Sekine, H. (1993). Optimum design of composite structures for shape, layer angle and layer thickness distributions. J. Comp. Mat. 27, 1479-1492.
17. Fukunaga, H., Sekine, H. and Sato, M. (1994). Optimal design of symmetric laminated plates for fundamental frequency. J. Sound Vibration 171, 219-229.
18. Fukunaga, H. and Sekine, H. (1994). A laminate design for elastic properties of symmetric laminates with extension-shear or bending-twisting coupling. J. Comp. Mat. 28, 708-731.
19. Grenestedt, J. L. (1991). Layup optimization against buckling of shear panels. Struct. Opt. 3, 115-120.
20. Grenestedt, J. L. and Gudmundson, P. (1993). Layup optimization of composite material structures. In Optimal Design with Advanced Materials (ed. Pedersen, P.), Elsevier Science, Amsterdam, 311-336.
21. Haftka, R. T., Gürdal, Z. and Kamat, M. P. (1990). Elements of Structural Optimization, Kluwer Academic Publishers, Dordrecht.
22. Jog, C., Haber, R. B. and Bendsøe, M. P. (1994). Topology design with optimized, self-adaptive materials. Int. J. Num. Meth. Engng 37, 1323-1350.
23. Krein, M. G. and Nudelman (1977). The Markov moment problem and extremal problems. In Translations of Mathematical Monographs, Vol. 50, American Mathematical Society, Providence, Rhode Island.
24. Lipton, R. (1994a). A saddle point theorem with application to structural optimization. JOTA 81, 549-568.
25. Lipton, R. (1994b). On optimal reinforcement of plates and choice of design parameters. Control Cybernetics 23, 481-493.
26. Lurie, K. A. (1993). Applied Optimal Control Theory of Distributed Systems, Plenum Press, New York.
27. Miki, M. (1982). Material design of composite laminates with required in-plane elastic properties. In Progress in Science and Engineering of Composites (eds Hayashi, T., Kawata, K. and Umekawa, S.), ICCM-IV, Tokyo, pp. 1725-1731.
28. Miki, M. and Sugiyama, Y. (1993). Optimum design of laminated composite plates using lamination parameters. AIAA J. 31, 921-922.
29. Pedersen, P. (1989). On optimal orientation of orthotropic materials. Struct. Opt. 1, 101-106.
30. Pedersen, P. (1990a). Bounds on elastic energy in solids of orthotropic materials. Struct. Opt. 2, 55-63.
31. Pedersen, P. (1990b). Combining material and element rotation in one formula. Comm. Appl. Num. Meth. 6, 549-555.
32. Pedersen, P. (1995). Simple transformations by proper contracted forms. Comm. Num. Meth. Engng 11, 821-829.
33. Pedersen, P. and Bendsøe, M. P. (1995). On strain-stress fields resulting from optimal orientation. In WCSMO-1 (eds Olhoff, N. and Rozvany, G. I. N.), Pergamon, Oxford, 243-250.
34. Petersson, J. (1996) On stiffness maximization of variable thickness sheet with unilateral constraints. Quart. Appl. Math., to appear.
35. Schittkowski, K. (1986). NLPQL: a Fortran subroutine solving constrained nonlinear programming problems. Ann. Operations Res. 5, 485-500.
36. Seregin, G. A. and Troitskii, V. A. (1982). On the best position of elastic symmetry planes in an orthotropic body. PMM USSR 45, 139-142.
37. Tsai, S. W. and Hahn, H. T. (1989). Introduction to Composite Materials, Technomic, Westport.