Structural optimization - The interaction between form and mechanics

ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik

Volumn 79, Issue 10, 1999, Pages 651-673

  Maute, K ^a   Schwarz, St ^a   Ramm, E ^a  

^a UNIVERSITY OF STUTTGART   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 22844455857     PISSN: 00442267     EISSN: 15214001     Source Type: Journal    
DOI: 10.1002/(SICI)1521-4001(199910)79:10<651::AID-ZAMM651>3.0.CO;2-O     Document Type: Article

References (83)

1. ALLAIRE, G.; KOHN, R. V.: Explicit optimal bounds on the elastic energy of a two-phase composite in two space dimensions. Quart. Appl. Math. 60 (1993), 675-699.
2. ARMAND, J.-L.; LODIER, B.: Optimal design of bending element. Internat. J. Numer. Mech. Engin. 13 (1978), 373-384.
3. ARORA, J. S.: Introduction to optimum design. McGraw-Hill, New York 1989.
4. BANICHUK, N. V.; BARTHOLD, F.-J.; FALK, A.; STEIN, E.: Mesh refinement for shape optimization. Struct. Optimiz. 9 (1995), 46-51.
5. BENDSØE, M. P.; KIKUCHI, N.: Generating optimal topologies in structural design using a homogenization method. Comput. Meth. Appl. Mech. Engin. 71 (1988), 197-224.
6. BENDSØE, M. P.: Optimal shape design as a material distribution problem. Struct. Optimiz. 1 (1989), 193-202.
7. BENDSØE, M. P.; MOTA SOARES, C. A. (eds.): Topology design of structures. Kluwer Academic Publishers, Dordrecht 1993.
8. BENDSØE, M. P.; HABER, R. B.: The Michell layout problem as a low volume fraction limit of the perforated plate topology optimization problem. Struct. Optimiz. 6 (1993), 263-267.
9. BENDSØE, M. P.; GUEDES, J. M.; HABER, R. B.; PEDERSEN, P.; TAYLOR, J. E.: An analytical model to predict optimal material properties in the context of optimal structural design. J. Appl. Mech. 61 (1994), 930-937.
10. BENDSØE, M. P.: Optimization of structural topology, shape, and material. Springer-Verlag, Berlin 1995.
11. BENNET, J. A.; BOTKIN, M. E.: Structural shape optimization with geometric description and adaptive mesh refinement. AIAA J. 23 (1985), 458-464.
12. BENSOUSSAN, A.; LIONS, J.-L.; PAPANICOLAOU, G.: Asymptotic analysis for periodic structures. North-Holland, Amsterdam 1978.
13. BLETZINGER, K.-U.; KIMMICH, S.; RAMM, E.: Efficient modeling in shape optimal design. Comput. Syst. Engin. 2 (1991), 483-495.
14. BÖHM, W.; FARIN, G. E.; KAHMANN, J.: A survey of curve and surface methods in CAGD. Computer Aided Design 1 (1984), 1-60.
15. CHENG, H. C.; KIKUCHI, N.; MA, Z. D.: An improved approach for determining the optimal orientation of orthotropic material. Struct. Optimiz. 8 (1994), 101-112.
16. CHENG, K.T.; OLHOFF, N.: An investigation concerning optimal design of solid elastic plates. Internat. J. Solids Struct. 17 (1981), 305-323.
17. DAL MASO, G.: An introduction to G-convergence. Birkhäuser, Boston 1993.
18. DIAZ, A.; KIKUCHI, N.: Solutions to shape and topology eigenvalue optimization problems using a homogenization method. Internat. J. Numer. Meth. Engin. 35 (1992), 1487-1502.
19. DIAZ, A.; BENDSØE, M. P.: Shape optimization of structures for multiple loading conditions using a homogenization method. Struct. Optimiz. 4 (1992), 17-22.
20. DIAZ, A.; LIPTON, R.; SOTO, C.: A new formulation of the problem of optimum reinforcement of Reissner-Mindlin plates. Comput. Meth. Appl. Mech. Engin. 123 (1995), 121-139.
21. DORN, W. S.; GOMORY, R. E.; GREENBERG, H. J.: Automatic design of optimal structures. J. Méc. 3 (1964), 25-52.
22. ESCHENAUER, H. A.; KOBELEV, V. V.; SCHUMACHER, A.: Bubble method for topology and shape optimization of structures. Struct. Optimiz. 8 (1994), 42-51.
23. FALK, A.; BARTHOLD, F.-J.; STEIN, E.: Hierarchical modelling in shape optimization. In: [59], pp. 371-376.
24. FALK, A.: Adaptive Verfahren für die Formoptimierung von Flächentragwerken unter Berücksichtigung der CAD-FEM-Kopplung. Ph.D. dissertation, University of Hanover, Hanover, Germany, 1995.
25. FRANCFORT, G. A.; MURAT, F.: Homogenization and optimal bounds in linear elasticity. Arch. Rat. Mech. Anal. 94 (1986), 307-334.
26. FRECKER, M.; KIKUCHI, N.; KOTA, S.: Optimal design of compliance mechanism. In: GUTKOWSKI, W.; MRÓZ, Z. (eds.): Proceedings of the Second World Congress of Structural and Multidisciplinary Optimization, May 26-30 1997, Zakopane, Poland, pp. 345-350.
27. GRABOVSKY, Y.: Bounds and extremal microstructures for two-component composites: A unified treatment based on the translation method. Proc. Roy. Soc. London A 452 (1996), 919-944.
28. GUEDES, J. M.; KIKUCHI, N.: Pre- and post-processing for materials based on the homogenization method with adaptive finite element methods. Comput. Meth. Appl. Mech. Engin. 83 (1990), 143-198.
29. HABER, R. B.; JOG, C. S.; BENDSØE, M. P.: A new approach to variable-topology shape design using a constraint on perimeter. Struct. Optimiz. 11 (1996), 1-12.
30. HASHIN, Z.; SHTRIKMAN, S.: A variational approach to the theory of the elastic behavior of multiphase materials. J. Mech. Phys. Solids 11 (1963), 127-140.
31. HAUG, E. J.; CHOI, K. K.; KOMKOV, V.: Design sensitivity analysis of structural systems. Academic Press, Orlando 1986.
32. HEMP, W. S.: Optimum structures. Clarendon Press, Oxford 1973.
33. JOG, C. S.; HABER, R. B.; BENDSØE, M. P.: Topology design with optimized, self-adaptive materials. Internat. J. Numer. Meth. Engin. 37 (1994), 1323-1350.
34. KIKUCHI, N.; CHUNG, K. Y.; TORIGAKI, T.; TAYLOR, J. E.: Adaptive finite element methods for shape optimization of linearly elastic structures. Comput. Meth. Appl. Mech. Engin. 57 (1986), 67-89.
35. KIRSCH, U.: Optimal topology of structures. Appl. Mech. Rev. 42 (1989), 223-239.
36. KIRSCH, U.: Structural optimization: fundamentals and applications. Springer-Verlag, Berlin 1993.
37. KLEIBER, M.; ANTÚNEZ, H.; HIEN, T. D.; KOWALCZYK, P.: Parameter sensitivity in nonlinear mechanics. Wiley, Chichester 1997.
38. KOHN, R. V.; STRANG, G.: Optimal design for torsional rigidity. In: ATLURI, S. N.; GALLAGHER, R. H.; ZIENKIEWICZ, O. C. (eds.): Hybrid and mixed finite element methods. Wiley, Chichester 1983, pp. 281-288.
39. KOHN, R. V.; STRANG, G.: Optimal design and relaxation of variational problems. I-III. Comm. Pure Appl. Math. 39 (1986), 113-137, 139-182, 353-377.
40. LURIE, K. A.: On the optimal distribution of the resistivity tensor of the working substance in a magnetohydrodynamic channel. J. Appl. Math. Mech. 34 (1970), 255-274.
41. MA, Z.-D.; KIKUCHI, N.; CHENG, H.-C.; HAGIWARA, I.: Topological optimization technique for free vibration problems. ASME J. Appl. Mech. 62 (1995), 200-207.
42. MATHIAK, G.; SCHNACK, E.: An adaptive composition of unknown boundaries for shape optimization of three-dimensional elastic structures. In: [59], pp. 365-370.
43. MAUTE, K.; RAMM, E.: Topology optimization of plate and shell structures. In: ABEL, J. F.; LEONHARD, J. W.; PENALBA, C. U. (eds.): Spatial, lattice and tension structures - Proceedings of the IASS-ASCE International Symposium, Atlanta, April 1994. American Society of Civil Engineering, New York 1994, pp. 946-955.
44. MAUTE, K.; RAMM, E.: Adaptive topology optimization. Struct. Optimiz. 10 (1995), 100-112.
45. MAUTE, K.; RAMM, E.: General shape optimization - an integrated model for topology and shape optimization. In: [59], pp. 299-306.
46. MAUTE, K.; RAMM, E.: Adaptivity in structural optimization. In: TOPPING, B. H. V. (eds.): Advances in structural engineering optimization. Civil-Comp. Press, Edinburgh 1996, pp. 227-237.
47. MAUTE, K.; RAMM, E.: Adaptive topology optimization of shell structures. AIAA J. 35 (1997), 1767-1773.
48. MAUTE, K.; SCHWARZ, S.; RAMM, E.: Adaptive topology optimization of elastoplastic structures. Struct. Optimiz. 15 (1998), 81-91.
49. MAUTE, K.: Topologie- und Formoptimierung von dünnwandigen Tragwerken. Ph.D. dissertation. University of Stuttgart, Stuttgart, Germany, 1998.
50. MAXWELL, C.: Scientific papers. II. Cambridge Univ. Press, Cambridge 1869.
51. MAYER, R. R.; KIKUCHI, N.; SCOTT, R. A.: Application of topology optimization techniques to structural crashworthiness. Internat. J. Numer. Meth. Engin. 39 (1996), 1383-1403.
52. MICHELL, A. G. M.: The limits of economy of material in frame structures. Philos. Mag. Ser. 6, 8 (1904), 589-597.
53. MILTON, G.: Modelling the properties of composites by laminates. In: ERICKSON, J. L.; KINDERLEHRER, D.; KOHN, R. V.; LIONS, J. L. (eds.): Homogenization and effective moduli of materials and media. Springer-Verlag, Berlin 1986, pp. 150-175.
54. MLEJNEK, H. P.: Some aspects of the genesis of structures. Struct. Optimiz. 5 (1993), 64-69.
55. MURAT, F.: Centre-examples pour divers problèmes ou le contrôle intervient dans les coefficients. Ann. Mat. Pur. Appl. 112 (1977), 49-68.
56. NEVES, M. M.; RODRIGUES, H.; GUEDES, J. M.: Generalized topology design of structures with a buckling load criterion. Struct. Optimiz. 10 (1995), 71-78.
57. OLHOFF, N.: Optimal design of vibrating rectangular plates. Internat. J. Solids Struct. 10 (1974), 93-109.
58. OLHOFF, N.; BENDSØE, M. P.; RASMUSSEN, J.: On CAD-integrated structural topology and design optimization. Comput. Meth. Appl. Mech. Engin. 89 (1991), 259-279.
59. OLHOFF, N.; ROZVANY, G. I. N. (eds.): Proceedings of the first world congress of structural and multidisciplinary optimization, May 28-June 2, 1995, Goslar, Germany. Elsevier, Oxford 1995.
60. PAPALAMBROS, P. Y.; CHIREHDAST, M.: Integrated structural optimization systems. In: [7], pp. 501-514.
61. PATNAIK, S. N.; GUPTILL, D. J.; BERKE, L.: Merits and limitations of optimality criteria method for structural optimization. Internat. J. Numer. Meth. Engin. 38 (1995), 3087-3120.
62. PRAGER, W.; ROZVANY, G. I. N.: Optimization of structural geometry, In: BEDNAREK, A. R.; CESARI, L. (eds.): Dynamical systems. Academic Press, New York 1977, pp. 265-293.
63. RAMM, E.; BLETZINGER, K.-U.; REITINGER, R.; MAUTE, K.: The challenge of structural optimization. In: TOPPING, B. H. V.; PAPADRAKAKIS, M. (eds.): Advances in structural optimization. Civil-Comp Press, Edinburgh 1994, pp. 27-52.
64. RINGERTZ, U. T.: On finding the optimal distribution of material properties. Struct. Optimiz. 5 (1993), 265-267.
65. ROSEN, D. W.; GROSSE, I. R.: A feature based shape optimization technique for the configuration and parametric design of flat plates. Engin, with Comp. 8 (1992), 81-91.
66. ROZVANY, G. I. N.; ZHOU, M.; BIRKER, T.: Generalized shape optimization without homogenization. Struct. Optimiz. 4 (1992), 250-252.
67. ROZVANY, G. I. N.; BENDSØE, M. P.; KIRSCH, U.: Layout optimization of structures. Appl. Mech. Rev. 48 (1995), 41-119.
68. SANCHEZ-PALENCIA, E.: Non-homogeneous media and vibration theory. (Lecture Notes in Physics, 127.) Springer, Berlin 1980.
69. SCHITTKOWSKI, K.: NLPQL: A FORTRAN subroutine for solving constrained nonlinear programming problems. Anal. Oper. Res. 5 (1985), 485-500.
70. SCHUMACHER, A.: Topologieoptimierung von Bauteilstrukturen unter Verwendung von Lochpositionierungskriterien. Ph.D. dissertation. University of Siegen, Siegen, Germany, 1996.
71. SCHWARZ, S.; MAUTE, K.; RAMM, E.: Topology and shape optimization including elastoplastic behavior. Proceedings of the 7-th AIAA/USAF/NASA ISSMO Symposium on Multidisciplinary Analysis and Optimization, St. Louis, USA, September 1998, pp. 1911-1921.
72. SIGMUND, O.: Design of material structures using topology optimization. Dissertation. Report S 69. Danish Center for Applied Mathematics and Mechanics, Technical University of Denmark, 1994.
73. SIGMUND, O.: Materials with prescribed constitutive parameters: an inverse homogenization problem. Internat. J. Solids Struct. 31 (1994), 2313-2329.
74. SWAN, C. C.; ARORA, J. S.: Topology design of material layout in structured composites of high stiffness and strength. Struct. Optimiz. 13 (1997), 45-59.
75. SZABO, I.: Geschichte der mechanischen Prinzipien. Birkhäuser, Basel 1979.
76. TARTAR, L.: Problèmes de contrôle des coefficients dans les équations aux dérivées partielles. In: BENSOUSSAN, A.; LIONS, J. L. (eds.): Control theory, numerical methods, and computer system modelling. (Lecture notes in economics and mathematical systems, 107.) Springer, New York 1975, pp. 420-426.
77. TAYLOR, J. E.: Truss topology design for elastic/softening materials. In: [7], pp. 451-467.
78. TAYLOR, J. E.; WASHABAUGH, P. D.: Analysis and design of trussed structures made of elastic/stiffening materials. Struct. Optimiz. 8 (1994), 1-8.
79. TENEK, L. H.; HAGIWARA, I.: Static and vibrational shape and topology optimization using homogenization and mathematical programming. Comput. Meth. Appl. Mech. Engin. 109 (1993), 143-154.
80. VANDERPLAATS, G. N.: Numerical optimization techniques for engineering design: with applications. McGraw-Hill, New York 1984.
81. WILLIS, J. R.: Bounds and self-consistent estimates for the overall properties of anisotropic composites. J. Mech. Phys. Solids 25 (1977), 185-202.
82. YANG, R. J.; CHEN, C. J.: Stress-based topology optimization. Struct. Optimiz. 12 (1996), 98-105.
83. YUGE, K.; KIKUCHI, N.: Optimization of a frame structure subjected to a plastic deformation. Struct. Optimiz. 10 (1995), 197-208.