On optimum design of structures and materials

Meccanica

Volumn 31, Issue 2, 1996, Pages 143-161

  Olhoff, Niels ^a  

^a AALBORG UNIVERSITY   (Denmark)

Author keywords

Mathematical programming; Mechanics of materials; Optimization; Structural mechanics

Indexed keywords

FINITE ELEMENT METHOD; INTEGRATION; ITERATIVE METHODS; MATERIALS; MATHEMATICAL PROGRAMMING; MECHANICS; SENSITIVITY ANALYSIS; STRUCTURAL DESIGN; TOPOLOGY;

DESIGN PROCESS; ENGINEERING DESIGN; MECHANICS OF MATERIALS; OPTIMUM DESIGN; SHAPE OPTIMIZATION; STRUCTURAL MECHANICS;

OPTIMIZATION;

EID: 0030123282     PISSN: 00256455     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF00426257     Document Type: Article

References (70)

1. Almgren, R.F., 'An isotropic three-dimensional structure with Poisson's ratio = -1', J. Elasticity, 15 (1985), 427-430.
2. Atrek, E. R., Gallagher, R.H., Ragsdell, K.M. and Zienkiewicz, O.C., (eds.), New Directions in Optimum Structural design, John Wiley and Sons, New York, 1984.
3. Barthelemy, B., Haftka, R.T., 'Accuracy analysis of the semi-analytical method for shape sensitivity analysis', AIAA Paper 88-2284, Proc. AIAA/ASME/ASCE/ASC 29th Structures, Structural Dynamics and Materials Conference, Part 1, 1988, pp. 562-581, Also
4. Mechanics of Structures and Machines, 18 (1990), 407-432.
5. Bendsøe, M.P., Optimization of Structural Topology, Shape, and Material. Springer-Verlag, Berlin, 1995.
6. Bendsøe, M.P., Díaz, A.R., Lipton, R. and Taylor, I.E. 'Optimal design of material properties and material distribution for multiple loading conditions, To appear in Int. J. Num. Meth. Engng.
7. Bendsøe, M.P. and Mota Soares, C.A., (eds.), Topology Design of Structures, Kluwer, Dordrecht, The Netherlands, 1993.
8. Bendsøe, M.P., 'Optimal shape as a material distribution problem', Structural Optimization, 1 (1989), 193-202.
9. Bendsøe, M.P. and Kikuchi, N., 'General optimal topologies in structural design using a homogenization method', Comp. Meth. in Appl. Mech. and Engrg., 71 (1988), 197-224.
10. Bendsøe, M.P., Olhoff, N. and Taylor, I.E., 'A variational formulation for multicriteria structural optimization', J. Struct. Mech., 11 (1983), 523-544.
11. Bennett, J.A. and Botkin, M.E., The Optimum Shape. Automated Structural Design. Plenum Press, New York, 1986.
12. Braibant, V. and Fleury, C., 'Shape optimal design using B-splines', Computer Methods in Applied Mechanics and Engineering, 44 (1984), 247-267.
13. Cheng, G. and Liu, Y., 'A new computational scheme for sensitivity analysis', Engineering Optimization, 12 (1987), 219-235.
14. Cinquini, C. and Rovati, M., 'Problems and methods of structural optimization', In: Rovati, M. and Contro, R. (eds), Lecture notes for COMETT Course 'Computer Aided Optimal Design of Structures - Advanced Materials and Shape Optimization', September 1991, University of Trento, Italy.
15. Ding, Y, 'Shape optimization of structures: a literature survey', Computers and Structures, 24(6) (1986), 985-1004.
16. Eschenauer, H.A. and Olhoff, N., (eds.), Optimization Methods in Structural Design, B.I.-Wissenschaftsverlag, Mannheim, 1983.
17. Eschenauer, H.A., Mattheck, C. and Olhoff, N., (eds.), Engineering Optimization in Design Processes. Springer-Verlag, Berlin, 1991.
18. Esping, B.J.D., Minimum Weight Design of Membrane Structures, Ph.D. Thesis, Dept. Aeronautical Structures and Materials, The Royal Institute of Technology, Stockholm, Report 83-1, 1983.
19. Esping, B.J.D., 'Minimum weight design of membrane structures using eight node isoparametric elements and numerical derivatives', Computers and Structures, 19(4) (1984), 591-604.
20. Fleury, C., 'CONLIN: an efficient dual optimizer based on convex approximation concepts', Structural Optimization, 1 (1989), 81-89.
21. Fleury, C. and Braibant, V., 'Structural optimization: a new dual method using mixed variables', International Journal for Numerical Methods in Engineering, 23 (1986), 409-428.
22. Gilmore, B.J., Hoeltzel, D.A., Azram, S. and Eschenauer, H.A., 'Advances in design automation', Proc. 1993 ASSME Design Technical Conferences - 19th Design Automation Conference, Albuquerque, New Mexico, The American Society of Mechanical Engineers, New York, 1993.
23. Haftka, R.T. and Grandhi, R.U., 'Structural shape optimization - a survey, Computer Methods in Applied Mechanics and Engineering, 57 (1986), 91-106.
24. Haug, E.J., (ed.), Concurrent Engineering: Tools and Technologies for Mechanical System Design, Springer-Verlag, Berlin, 1993, pp. 998.
25. Haug, E.J. and Cea, J., (eds.), Optimization of Distributed Parameter Structures, Sijthoff and Nordhoff. The Netherlands, 1981, vol. 1, pp. 1-842, vol 2, pp. 843-1609.
26. Haug, E.J., 'A review of distributed parameter structural optimization literature', In: Hang, E.J. and Cea, J. (eds), Optimization of Distributed Parameter Structures, vol. 1, Sijthoff and Nordhoff. The Netherlands, 1981, pp. 3-74.
27. Herskovits, J., (ed.), Proc. Structural Optimization '93 - The World Congress on Optimal Design of Structural Systems 1 - 2. Federal University of Rio de Janeiro, Brazil, 1993.
28. Lakes, R., 'Design considerations for materials with negative Poisson's ratio', J. Mech Design, 115 (1993), 696-700.
29. Larsen, U.D., Sigmund, O. and Bouwstra, S., Fabrication of Compliant Micromechanisms and Materials with Negative Poisson's Ratio. Manuscript, 1995.
30. Lund, E., Finite Element Based Design Sensitivity Analysis and Optimization, Ph.D. Thesis, Special Report No. 23, Institute of Mechanical Engineering, Aalborg University, Denmark, 1994, p. 240.
31. Lund, E. and Olhoff, N., 'Shape design sensitivity analysis of eigenvalues using 'exact' numerical differentiation of finite element matrices', Structural Optimization, 8 (1994), 52-59.
32. Milton, G.V., 'Composite materials with Poisson's ratio close to -1', J. Mech. Phys Solids, 40(5) (1992), 1105-1137.
33. Milton, G.V. and Cherkaev, A.V., 'Materials with elastic tensors that range over the entire set compatible with thermodynamics', Presented at the joint ASCE-ASME-SES MettN, June 1993, University of Virginia, Charlottesville, Virginia, USA.
34. Morris, A.J., (ed.), Foundations of Structural Optimization: A Unified Approach. Chichester, England, 1982.
35. Mota Soares, C.A., (ed.), Computer Aided Optimal Design: Structural and Mechanical Systems. Springer-Verlag, Berlin, 1987.
36. Olhoff, N., 'Multicriterion structural optimization via bound formulation and mathematical programming', Structural Optimization, 1 (1989), 11-17.
37. Olhoff, N., Bendsøe, M.P. and Rasmussen, J., 'On CAD-integrated structural topology and design optimization', Computer Methods in Applied Mechanics and Engineering, 89 (1991), 259-279.
38. Olhoff, N. and Lund, E., 'Finite element based engineering design sensitivity analysis and optimization', In: Herskovits, J. (ed.) Advances in Structural Optimization, Kluwer, The Netherlands, 1995, pp. 1-45.
39. Olhoff, N., Lund, E. and Rasmussen, J., 'Concurrent engineering design optimization in a CAD environment', In: E.J. Hang (ed), Concurrent Engineering: Tools and Technologies for Mechanical System Design, Springer-Verlag, Berlin, 1993, pp. 523-586.
40. Olhoff, N., Rasmussen, J. and Lund, E., 'A method of 'Exact' numerical differentiation for error elimination in finite element based semi-analytical shape sensitivity analysis', Mechanics of Structures and Machines, 21 (1993), 1-66.
41. Olhoff, N. and Rozvany, G.I.N., Structural and Multidisciplinary Optimization, Pergamon, Oxford, 1995.
42. Olhoff, N. and Taylor, J.E., 'On structural optimization', Journal of Applied Mechanics, 50 (1983), 1139-1151.
43. Papalambros, P.Y. and Chirehdast, M., 'An integrated environment for structural configuration design', J. Engrg. Design. 1 (1990), 73-76.
44. Pedersen, P., 'On the minimum mass layout of trusses', Proc. AGARD Symposium 1970, Istanbul, AGARD-CP-36-7., 1970.
45. Pedersen, P., 'On the optimal layout of multi-purpose trusses', Computers and Structures. 2 (1972), 695-712.
46. Pedersen, P., 'Optimal joint positions for space trusses', J. Struct. Div., ASCE 99 (1973), 2459-2476.
47. Pedersen, P., (ed.), Optimal Design with Advanced Materials. Elsevier, The Netherlands, 1993.
48. Pedersen, P., 'Concurrent engineering design with and of advanced materials', In: E.J. Hang (ed.), Concurrent Engineering: Tools and Technologies for Mechanical System Design, Springer-Verlag, Berlin, 1993, pp. 627-670.
49. Pedersen, P., 'Bounds on elastic energy in solids of orthotropic materials', Structural Optimization, 1 (1990), 55-63.
50. Pedersen, P., 'On optimal orientation of orthotropic materials', Structural Optimization, 1 (1989), 101-106.
51. Pedersen, P., Cheng, G. and Rasmussen, J., 'On accuracy problems for semi-analytical sensitivity analysis', Mechanics of Structures and Machines, 17(3) (1989), 373-384.
52. Pedersen, P., 'Design with several eigenvalue constraints by finite elements and linear programming', Journal of Structural Mechanics, 10(3) (1981), 243-271.
53. Rasmussen, J., Development of the Interactive Structural Shape Optimization System CAOS (in Danish), Ph.D. thesis, Institute of Mechanical Engineering, Aalborg University, Denmark, Special Report No. 1a, 1989.
54. Rasmussen, J., 'The structural optimization system CAOS', Structural Optimization 2 (1990), 109-115.
55. Rasmussen, J., Lund, E., Birker, T. and Olhoff, N., 'The CAOS system', International Series of Numerical Mathematics, 110 (1993), 75-96, Birkhäuser Verlag, Basel.
56. Rasmussen, J., Lund, E. and Olhoff, N., 'Integration of parametric modeling and structural analysis for optimum design', Gilmore et al. (eds), Proc. Advances in Design Automation, The American Society of Mechanical Engineers, Albuquerque, New Mexico, USA, 1993.
57. Rasmussen, J., Olhoff, N. and Lund, E., 'Foundations for optimum design system development', In: Lecture Notes for: Advanced TEMPUS Course on Numerical Methods in Computer Optimal Design, 11-15 mai 1992, Zakopane, Poland, 1992.
58. Rozvany, G.I.N. and Karihaloo, B.L., (eds.), Structural Optimization, Kluwer, Dordrecht, The Netherlands, 1988.
59. Rozvany, G.I.N., (ed.), Optimization of Large Structural Systems, Kluwer, Dordrecht, The Netherlands, 1993, vol. 1, pp. 1-622, vol. 2, pp. 623-1198.
60. Rozvany, G.I.N., Bendsøe, M.P. and Kirch, U., 'Layout optimization of structures', Applied Mechanics Reviews. 48 (1995), 41-119.
61. Sacchi Landriani, G. and Rovati, M., 'Optimal design for two-dimensional structures made of composite materials', J. Engineering Materials and Technology, 113 (1991), 88-92.
62. Schmit, L.A., 'Structural synthesis - its genesis and development', AIAA Journal, 20 (1982), 992-1000.
63. Sergeyev, O. and Pedersen, P., On design of joint positions for minimum mass 3D frames, Manuscript, 1995 p. 21.
64. Sigmund, O., 'Design of Material Structures Using Topology Optimization', DCAMM Special Report No. 69, Ph.D. Thesis, Technical University of Denmark, 95 p. +22 p. (appendix), December 1994.
65. Sigmund, O., 'Materials with prescribed constitutive parameters: an inverse homogenization problem', Int. J. Solids Structures, 31(17) (1994), 2313-2329.
66. Sigmund, O., 'Tailoring materials with prescribed elastic properties', Mech. Materials, 20 (1995), 351-368.
67. Sigmund, O., 'Design of material structures using topology optimization', In: Olhoff, N. and Rozvany, G. (eds.) Structural and Multidisciplinary Optimization, Pergamon, Oxford, 1995.
68. Svanberg, K., 'The method of moving asymptotes - a new method for structural optimization', International Journal for Numerical Methods in Engineering, 24 (1987), 359-373.
69. Thomsen, J. and Olhoff, N., 'Optimization of fiber orientation and concentration in composites', Control and Cybernetics, 19 (1990), 327-341.
70. Zienkiewicz, O.C. and Campbell, J.S., 'Shape optimization and sequential linear programming', In: Gallagher, R.H. and Zienkiewicz (eds.), Optimum Structural Design, Theory and Applications, Wiley and Sons, London, 1973, pp. 109-126.