Topology and geometry optimization of trusses and frames

Recent Advances in Optimal Structural Design

Volumn , Issue , 2002, Pages 97-123

  Ohsaki, M ^a   Swan, C C ^a  

^a KYOTO UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

GEOMETRY; STRUCTURAL ANALYSIS; STRUCTURAL FRAMES; STRUCTURAL LOADS; TOPOLOGY; TRUSSES;

LAYOUT; STRUCTURAL SYSTEMS;

STRUCTURAL OPTIMIZATION;

EID: 0036402787     PISSN: None     EISSN: None     Source Type: Book    
DOI: None     Document Type: Article

References (111)

1. Achtziger, W. (1996). "Truss topology optimization including bar properties different for tension and compression." Structural Optimization, 12, 63-74.
2. Achtziger, W. (1999a). "Local stability of trusses in the context of topology optimization Part I: Exact modelling." Structural Optimization, 17, 235-246.
3. Achtziger, W. (1999b). "Local stability of trusses in the context of topology optimization Part I: A numerical approach." Structural Optimization, 17, 247-258.
4. Allaire, G. and Kohn, R.V. (1993). "Topology optimal design and optimal shape design using ho-mogenization," in Topology Design of Structures, M.P. Bendsoe and C.A. Mota-Soares (Eds.), Kluwer Academic Publishers, Dordrecht/Boston, 207-218.
5. Bendsoe, M.P. and Kikuchi, N. (1988). "Generating optimal topology in structural design using a homogenization method," Computer Methods in Applied Mechanics and Engineering 71 197-224.
6. Bendsoe, M.P. (1989). "Optimal shape design as a material distribution problem," Structural Optimization 1 193-202.
7. Bendsoe, M.P., Diaz, A. and Kikuchi, N. (1993). "Topology and generalized layout optimization of elastic structures," in Topology Design of Structures, M.P. Bendsoe and C.A. Mota-Soares (Eds.), Kluwer Academic Publishers, Dordrecht/Boston 159-205.
8. Bendsoe, M.P., Diaz, A.R., Lipton, R., and Taylor, J.E. (1995). "Optimal design of material properties and material distribution for multiple loading conditions," International Journal for Numerical Methods in Engineering, 38 1149-1170
9. Beckers, M. and Fleury, C. (1997). "A primal-dual approach in truss topology optimization." Comp. Struct., 64, 77-88.
10. Bendsoe, M.P., Ben-Tal, A. and Zowe, J. (1994). "Optimization method for truss geometry and topology design." Structural Optimization, 7, 141-159.
11. Bennage, W.A. and Dhingra, A.K. (1995). "Optimization of truss topology using tabu search." Int. J. Numer. Meth. Engng., 38, 4035-4052.
12. Ben-tal, A. and Bendsoe, M.P. (1993). "A new method for optimal truss topology design." SIAM J. Opt., 3(2), 322-358.
13. Ben-tal, A. and Nemirovski, A. (1994). "Potential reduction polynomial time method for truss topology design." SIAM J. Opt., 4(3), 596-612.
14. Ben-Tal, A. and Nemirovski, A. (1996). "Robust truss topology optimization via semidefinite programming." Working Paper, Faculty of Industrial Engineering and Management, Technion, Haifa, Israel.
15. Bojczuk D. and Mróz, Z. (1999). "Optimal topology and configuration design of trusses with stress and buckling constraints." Structural Optimization, 17, 25-35.
16. Buhl, T. Pedersen, W., and Sigmund, O. (2000). "Stiffness design of geometrically nonlinear structures using topology optimization," Struct. Multidisc. Optim., Vol. 19, 2000, pp. 93-104.
17. Cheng, G. (1995). "Some aspects of truss topology optimization." Structural Optimization, 10, 173-179.
18. Cheng, G. and Guo, X. (1997). "ε-relaxed approach in structural topology optimization." Structural Optimization, 13, 258-266.
19. Cheng, G. and Jiang, Z. (1992). "Study on topology optimization with stress constraints." Eng. Opt., 20, 129-148.
20. Cheng, K.T., and Olhoff, N. (1981). "An investigation concerning optimal design of solid elastic plates," International Journal of Solids & Structures, 17 305-323.
21. Choi, K.K., Haug, E.J. and Lam, H.L., (1982). "A numerical method for distributed parameter structural optimization problems with repeated eigenvalues." Journal of Structural Mechanics, 10 (2) 191-207.
22. Choi, K.K., Haug, E.J., and Seong, H.G., (1983). "An iterative method for finite dimensional structural optimization problems with repeated eigenvalues," International Journal for Numerical Method in Engineering, 19 93-112.
23. Dems, K. and Gatkowski, W. (1995). "Optimal design of a truss configuration under multiloading conditions." Structural Optimization, 9, 262-265.
24. Diaz, A.R. and Bendsøe, M.P. (1992). "Shape optimization of structures for multiple loading conditions using a homogenization method." Structural Optimization, 4, 17-22.
25. Diaz, A. and Sigmund, O. (1995). "Checkerboard patterns in layout optimization," Structural Optimization 10 40-45.
26. Dobbs, W. and Felton, L.P. (1969). "Optimization of truss geometry." Proc. ASCE, 95 (ST10), 2105-2119.
27. Dorn, W., Gomory, R. and Greenberg, H. (1964). "Automatic design of optimal structures." J. de Mecanique, 3, 25-52.
28. Gea, H. C., and Luo, J. (2001). "Topology optimization of structures with geometrical nonlinearities," Computers & Structures, Vol. 79, 2001, pp. 1977-1985.
29. Grierson, D.E. and Pak, W.H. (1993). "Optimal sizing, geometrical and topological design using a genetic algorithm." Structural Optimization, 6, 151-159.
30. Haber, R.B. and Bendsoe, M.P. (1994). "Topology design with optimized, self-adaptive materials," International Journal for Numerical Methods in Engineering 37 1323-1350.
31. Haber, R.B. Jog, C.S. and Bendsoe, M.P. (1996). "A new approach to variable-topology shape design using a constraint on perimeter," Structural Optimization 11 1-12.
32. Hajela, P. and Lee, E. (1995). "Genetic algorithms in truss topological optimization." Int. J. Solids Struct., 32(22), 3341-3357.
33. Hajela, P. and Sangameshwaran, N. (1990). "A coupled algorithmic and heuristic approach for optimal structural topology generation." Comp. Struct., 36(5), 971-977.
34. Haug, E.J. and Cea, J. eds., (1981). Optimization of Distributed Parameter Structures, Sijthoff Noordhoff.
35. Haug, E.J. and Choi, K.K. (1982). "Systematic occurrence of repeated eigenvalues in structural optimization." J. Optimiz. Theory and Appl., 38, 251-274.
36. Hemp, W.S. (1973). Optimum Structures, Oxford University Press.
37. Imai, K. and Schmit, L.A. (1982). "Configuration optimization of trusses." Proc. ASCE, 107(ST5), 745-756.
38. Jenkins, W.M. (1991). "Towards structural optimization via the genetic algorithm." Comp. Struct, 40, 1321-1327.
39. Jog, C.S. and Haber, R.B. (1996). "Stability of finite element models for distributed-parameter optimization and topology design," Computer Methods in Applied Mechanics and Engineering, 130, 203-226.
40. Kirsch, U. (1989a). "Optimal topologies of truss structures." Comput. Meth. Appl. Mech. Engng., 72, 15-28.
41. Kirsch, U. (1989b). "Optimal topologies of truss structures." Appl. Mech. Rev., 42, 223-239.
42. Kirsch, U. (1990). "On singular topologies in optimum structural design." Structural Optimization., 2, 133-142.
43. Kirsch, U. (1993). "Efficient reanalysis for topological optimization." Structural Optimization, 6, 143-150.
44. Kirsch, U. (1995). "Improved stiffness-based first-order approximations for structural optimization." AIAA J., 33(1), 1995.
45. Kirsch, U. (1996). "Integration of reduction and expansion process in layout optimization." Structural Optimization, 11, 13-18.
46. Kirsch, U. and Liu, S. (1995). "Exact structural reanalysis by a first-order reduced basis." Structural Optimization, 10, 153-158.
47. Kocvara, M. (1997). "Topology optimization with displacement constraints: a bilevel programming approach." Structural Optimization, 14, 256-263.
48. Kohn, R.V. and Strang, G. (1986). "Optimal design and relaxation of variational problems," Communications on Pure and Applied Mathematics 39 Part I 113-137; Part II 139-182; Part III 353-377.
49. Kojima, M., Shindoh, S. and Hara, S. (1997). "Interior-point methods for the monotone semidefinite linear complementarity problems." SIAM J. Opt., 7, 86-125.
50. Kosaka, I. and Swan, C.C. (1999). "A symmetry reduction method for continuum structural topology optimization," Computers & Structures, 70, No. 1, 47-61.
51. Kwan, A.S. (1998). "An evolutionary approach for layout optimization of truss structures." Int. J. Space Struct., 13(3), 145-155.
52. Lin, J.H., Che, W.Y. and Yu, Y.S. (1982). "Structural optimization on geometrical configuration and element sizing with statical and dynamical constraints." Comp. Struct., 15, 507-515.
53. Ma, Z.-D., Kikuchi, N., Cheng, H.-C. and Hagiwara, I., (1995). Topological optimization technique for free vibration problems. Journal of Applied Mechanics, 62 200-207.
54. Maxwell, J.C. (1890). "On reciprocal figures, frames and diagrams of forces." Scientific Papers, Cambridge Univ. Press, 2, 175-177.
55. McKeown, J.J. (1998). "Growing optimal pin-jointed frames." Structural Optimization, 15, 92-100.
56. Michell, A.G.M. (1904). "The limits of economy in frame structures." Philosophical Magazine Sect. 6, 8(47), 589-597.
57. Mijar, A.R., Swan, C.C., Arora, J.S., and Kosaka, I. (1998). "Continuum topology optimization for concept design of frame bracing systems," Journal of Structural Engineering, 124, No. 5, 541-550.
58. Mlejnek, H.P. and Schirrmacher, R., (1993). "An engineer's approach to optimal material distribution and shape finding," Computer Methods in Applied Mechanics and Engineering, 106 1-26.
59. Nakamura, T. and Ohsaki, M. (1992). "A natural generator of optimum topology of plane trusses for specified fundamental frequency." Comp. Meth. Appl. Mech. Engng., 94, 113-129.
60. Nakanishi, Y. and Nakagiri, S. (1996). "Optimization of frame topology using boundary cycle and genetic algorithm." JSME Int. J., A., 39(2), 279-285.
61. Nakanishi, Y. and Nakagiri, S. (1997). "Structural optimization under topological constraint represented by homology groups." JSME Int. J., A., 40(3), 219-227.
62. Neves, M.M., Rogrigues, H. and Guedes, J.M. (1995). "Generalized topology design of structures with a buckling criterion," Structural Optimization, 10, No. 2, 71-78.
63. Oberndorfer, J.M., Achtziger, W. and Hörnlein, H.R.E.M. (1996). "Two approaches for truss topology optimization: a comparison for practical use." Structural Optimization, 11, 137-144.
64. Ohkubo, S. and Asai, K. (1992). "A hybrid optimal synthesis method for truss structures considering shape, material and sizing variables." Int. J. Numer. Meth. Engng., 34, 839-851.
65. Ohsaki, M. (1995). "Genetic algorithm for topology optimization of trusses." Comp. Struct., 57, 219-225.
66. Ohsaki, M. (1997). "Simultaneous optimization of topology and geometry of a regular plane truss." Comp. Struct., 66(1), 69-77.
67. Ohsaki, M. Kato, Y. (1999). "Simultaneous optimization of topology and nodal locations of a plane truss associated with a Bézier curve." in: Struct. Engng. in the 21st Century, Proc. Structures Congress, ASCE, 582-585.
68. Ohsaki, M., Fujisawa, K., Katoh, N. and Kanno, Y. (1999). "Semi-definite programming for topology optimization of trusses under multiple eigenvalue constraints," Comp. Meth. Appl. Mech. Engng., 80, 203-217.
69. Ohsaki, M. and Nakamura, T. (1993). "A natural generator of optimum topology of a space frame for specified fundamental frequency." In: Space Structures 4, Proc. 4th Int. Conf. on Space Structures, Surrey, UK, Parke, G. and Howard, C. (eds.), Thomas Telford, 1221-1229.
70. Ohsaki, M. Nakamura, T. and Isshiki, Y. (1998). "Shape-size optimization of plane trusses with designer's preference." J. Struct. Engng., ASCE, 124(11), 1323-1330.
71. Ohsaki, M. Nakamura, T. and Kohiyama, M. (1997). "Shape optimization of a double-layer space truss described by a parametric surface." Int. J. Space Structures, 12(2), 109-119.
72. Pedersen, N.L. (2000). "Maximization of eigenvalues using topology optimization," Struct. Multidisc. Optim. 20 2-11.
73. Pedersen, P. (1990). "Bounds on elastic energy in solids of orthotropic materials," Structural Optimization 2 55-63.
74. Petersson, J. (1999). "Some convergence results in perimeter-controlled topology optimization," Computer Methods in Applied Mechanics and Engineering 171 123-140.
75. Rahmatalla, S. and Swan, C.C. (2001). "Continuum topology optimization of buckling-sensitive structures, in review for publication in AIAA Journal.
76. Rajeev, S. and Krishnamoorthy, C.S. (1997). "Genetic algorithms-based methodologies for design optimization of trusses." J. Struct. Engng., ASCE, 123, 350-358.
77. Ramm, E. Bletzinger, K.-U. Reitinger, R. and Maute, K. (1994). "The challenge of structural optimization," in Advances in Structural Optimization, B.H.V. Topping and M. Papadrakakis (Eds.), Civil-Comp Press, Edinburgh, UK, pp. 27-53.
78. Rasmussen, J. Thomsen, J. and Olhoff, N. (1993). "Integrating topology and boundary variation design methods in a CAD system," in Topology Design of Structures, M.P. Bendsoe and C.A. Mota Soares (Eds.), Kluwer Academic Publishers, Dordrecht/Boston 483-499.
79. Reddy, G.M. and Cagan, J. (1995a). "Optimally directed truss topology generation using shape annealing." J. Mech. Engng., ASME, 117, 206-209.
80. Reuss, A. (1929). Z. Angew. Math. Mech., 9.
81. Ringertz, U.T. (1985). "On topology optimization of trusses." Eng. Opt., 9, 209-218.
82. Ringertz, U.T. (1986). "A branch and bound algorithm for topology optimization of truss structures." Eng. Opt., 10, 111-124.
83. Rozvany, G.I.N. (1976). Optimal Design of Flexural Systems, Pergamon Press.
84. Rozvany, G.I.N. (1989). Structural Design via optimality Criteria, Kluwer Academic Publishers.
85. Rozvany, G.I.N. (1996). "Difficulties in truss topology optimization with stress, local buckling and system stability constraints." Structural Optimization, 11, 213-217.
86. Rozvany, G.I.N. (ed.) (1997). Topology Optimization in Structural Mechanics, CISM Courses and Lectures 374, Springer.
87. Rule, W.K. (1994). "Automatic truss design by optimized growth." J. Struct. Engng., ASCE, 120(10), 3063-3070.
88. Sadek, E. (1986). "Dynamic optimization of framed structures with variable layout." Int. J. Numer. Meth. Engng., 23, 1273-1294.
89. Sadek, E. (1989). "An optimality criterion method for dynamic optimization of structures." Int. J. Numer. Meth. Engng., 28, 579-592.
90. Saka, M.P. (1980). "Shape optimization of trusses." Proc. ASCE, 106(ST5), 1155-1174.
91. Seyranian, A.P. Lund, E. and Olhoff, N. (1994). "Multiple eigenvalues in structural optimization problem." Structural Optimization, 8, 207-227.
92. Shea, K., Cagan, J. and Fenves, S.J. (1997). "A Shape annealing approach to optimal truss design with dynamic grouping of members." J. Mech. Engng., ASME, 118, 388-394.
93. Sheu, C.Y. and Schmit, L.A. (1972). "Minimum weight design of elastic redundant trusses under multiple static loading conditions." AIAA J., 10(2), 155-162.
94. Shiraishi, N., Furuta, H. and Ikejima, K. (1981). "Configurational optimization of framed structural systems." Theoretical and Appl. Mech., 29, 85-91.
95. Sigmund, O. (1994). "Design of material structures using topology optimization," Report S69, Danish Center for Applied Mathematics and Mechanics, Technical University of Denmark, Lyngby, Denmark.
96. Smith, O.S. (1996). "An interactive system for truss topology design." Advances in Engng. Software, 27, 167-178.
97. Smith, O.S. (1997). "Topology optimization of trusses with local stability constraints and multiple loading conditions - a heuristic approach." Structural Optimization, 13, 155-166.
98. Sved, G. and Ginos, Z. (1968). "Structural optimization under multiple loading." Int. J. Mech. Sci., 10, 803-805.
99. Swan, C.C. and Kosaka, I. (1997a). "Voigt-Reuss topology optimization for structures with linear elastic material behaviors," International Journal for Numerical Methods in Engineering, 40 3033-3057.
100. Swan, C.C. and Kosaka, I. (1997b). "Voigt-Reuss topology optimization for structures with nonlinear material behaviors," International Journal for Numerical Methods in Engineering, 40 3785-3814 (1997).
101. Swan, C.C. and Arora, J.S. (1997). "Topology design of material layout in structured composites of high stiffness and strength," Structural Optimization, 13 No. 1, 45-59.
102. Swan, C.C., Arora, J.S., Kosaka, I. and Mijar, A.R. (1998). "Concept design of bridge structures for stiffness and vibrations using continuum topology optimization," in Structural Engineering World Wide 1998, ed. Srivastava N.K., Paper t159-4.
103. Tagawa, H. and Ohsaki, M. (1999). "A continuous topology transition model for shape optimization of plane trusses with uniform cross-sectional area." Proc. 3rd WCSMO.
104. Topping, B.H.V. (1984). "Shape optimization of skeletal structures: a review." J. Struct. Engng., ASCE, 109(8), 1933-1951.
105. Topping, B.H.V. (1992). "Mathematical programming techniques for shape optimization of skeletal structures." In: Shape and Layout Optimization of Structural Systems and Optimality Criteria Methods, Rozvany, G.I.N. (Ed.), 349-375, Springer.
106. Topping, B.V.H, Khan, A.I. and Leite, J.P. (1996). "Topological design of truss structures using simulated annealing." Struct. Engng. Rev., 8, 301-314.
107. Venkayya, V.B. and Tishler, V.A. (1983). "Optimization of structures with frequency constraints," in: Computer Methods in Nonlinear Solids Structural Mechanics, ASME-AMD-54, ASME, New York, 239-259.
108. Voigt, W. (1889). Wied Ann., 38.
109. Yang, R.J. and Chuang, C.H. (1994). "Optimal topology design using linear programming," Computers & Structures, 52-2 265-275.
110. Zou, M. (1996). "Difficulties in truss topology optimization with stress and local buckling constraints." Structural Optimization, 11, 134-136.
111. Zou, M. and Rozvany, G.I.N. (1991). "The COC algorithm, Part II: Topological, geometrical and generalized shape optimization." Comp. Meth. Appl. Mech. Engng., 89, 309-336.