Complexity control in the topology optimization of continuum structures

Journal of the Brazilian Society of Mechanical Sciences and Engineering

Volumn 25, Issue 3, 2003, Pages 293-301

  Cardoso, E L ^a   Fonseca, J S O ^a  

^a FEDERAL UNIVERSITY OF RIO GRANDE DO SUL   (Brazil)

Author keywords

Complexity control; Filtering; Gradient control; Topology optimization

Indexed keywords

ALGORITHMS; FINITE ELEMENT METHOD; GRADIENT METHODS; LINEAR PROGRAMMING; TENSORS; TOPOLOGY;

COMPLEXITY CONTROL; CONTINUUM STRUCTURES; GRADIENT CONTROL; TOPOLOGY OPTIMIZATION;

MECHANICS;

EID: 0141517405     PISSN: 16785878     EISSN: None     Source Type: Journal    
DOI: 10.1590/S1678-58782003000300012     Document Type: Article

References (30)

1. Ambrosio, L., Buttazzo, G., 1993, "An optimal design Problem with Perimeter Penalization", Calc. Var., 1, pp. 55-69.
2. Bathe, K., 1996, "Finite Element Procedures", Prentice-Hall.
3. Bazaraa, M. S., Shetty, C. M., 1979. "Nonlinear Programming - Theory and Algorithms", John Wiley & Sons, New York.
4. Beckers, M., 1997, "Optimisation de Structures en Variables Discretes", Universite de liege, Collection des Publications de la faculté des Science Appliquées, No. 181.
5. Bendsøe, M. P., 1995, "Optimization of Structural Topology, Shape and Material", Springer-Verlag, New York.
6. Bendsøe, M. P., Díaz, A. R., Lipton, R., Taylor, J. E., 1995, "Optimal Design of Material Properties and Material Distribution for Multiple Loading Conditions", International Journal of Numerical Methods in Engineering, Vol. 38, pp. 1149-1170.
7. Bendsøe, M. P., Kikuchi, N., 1988, "Generating Optimal Topologies in Structural Design Using Homogenization Method", Computer Methods in Applied Mechanics and Engineering, Vol. 71, No. 2, pp. 197-224.
8. Bendsøe, M. P., Sigmund, O., 1999, "Material Interpolation Schemes in Topology Optimization", Archive of Applied Mechanics, Vol. 69, pp. 635-654.
9. Bourdin, B., "Filters in topology optimization", In. J. Numer. Meth. Engng, 2001:50:2143-2158.
10. Bruns, T. E., Tortorelli, D. A., "Topology optimization of non-linear elastic structures and compliant mechanisms", Comput, Methods Appl. Mech. Engrg., 190 (2001) 3443-3459.
11. Cardoso, E. L., Fonseca, J., S., O., 1999c, "Spatial Gradient Control in the Structural Topology Optimization", First ASMO UK/ISSMO Conference on Engineering Design Optimization, Ilkley, West Yorkshire, UK.
12. Chen, T. 1993, "Calculation of the Move Limits for The Sequential Linear Programming Method", International Journal of Numerical Methods in Engineering, Vol. 36, pp. 2661-2679.
13. Cheng, K.T., 1981, "On Non-Smoothness in Optimal Design of Solid, Elastic Plates", Int. J. Solids Structures, Vol. 17, pp. 795-810.
14. Díaz, A., Sigmund, O., 1995, "Checkerboard Patterns in Layout Optimization", Structural Optimization, Vol. 10, No. 1, pp. 40-45.
15. Fernandes, P., Guedes, J., M., Rodrigues, H., 1999, "Topology Optimization of Three-Dimensional Linear Elastic Structures with a Constraint on Perimeter", Computers & Structures, Vol. 73, No. 6, pp. 583-594.
16. Fonseca, J. S. O., Kikuchi, N., 1998, "Digital Imaging Filtering in Topology Optimization", Computational Mechanics New Trends and Applications, CIMNE, Spain.
17. Hanson, R. J., Hirbert, K., L., 1981, "A sparse Linear Programming Subprogram", Report SAND81-0297, Sandia National Laboratories.
18. Hasani, B., Hinton, E., 1998a, "A Review of Homogenization and Topology I - Homogenization Theory for Media With Periodic Structure", Computer and Structures, Vol. 69, pp. 707-717.
19. Hassani, B., Hinton, E., 1998b, "A Review of Homogenization and Topology II- Analytical and Numerical Solution of Homogenization Equations", Computer and Structures, Vol. 69, pp. 719-738.
20. Jog, C., Haber, R. B., 1996, "Stability of Finite Element Models for Distributed-Parameter Optimization and Topology Design", Computer Methods in Applied Mechanics and Engineering, Vol. 130, pp. 203-226.
21. Kasper, E. P., Taylor, R. L., 2000a, "A mixed-enhanced strain method Part I: Geometrically linear problems", Computers & Structures, 75, pp. 237-250.
22. Kasper, E. P., Taylor, R. L., 2000b, "A mixed-enhanced strain method Part II: Geometrically nonlinear problems", Computers & Structures, 75, pp. 251-260.
23. Niordson, F. I., 1983, "Optimal Design of Plates with a Constraint on the Slope of the Thickness Function", Int. J. Solids Structures, Vol. 19, pp. 141-151.
24. Park, Y. K., 1995, "Extensions of Optimal Layout Design Using the Homogenization Method", PhD theses, University of Michigan.
25. Petersson, J., Sigmund, O., 1998, "Slope constrained Topology Optimization", International Journal of Numerical Methods in Engineering, Vol. 41, pp. 1171-1194.
26. Sigmund, O. 1997, "On the design of compliant mechanisms using topology optimization", Mechanics of Structures and Machines, 25(4), pp. 495-526, 1997.
27. Swan, C. C., Kosaka, I., 1997, "Voigt-Reuss Topology Optimization for Structures with Linear Elastic Material Behavior", International Journal of Numerical Methods in Engineering, Vol. 40, No. 1, pp. 3033-3057.
28. Wujek, B. A., Renaud, J., E., 1998a, "New Adaptive Move-Limit Management Strategy for Approximate Optimization, Part 1", AIAA Journal, Vol. 36, No. 10, pp. 1911-1921.
29. Wujek, B. A., Renaud, J., E., 1998b, New Adaptive Move-Limit Management Strategy for Approximate Optimization, Part 2, AIAA Journal, Vol. 36, No. 10, pp. 1922-1934.
30. Yuquin, L., Yin, X., 1994, "Generalized Conforming Triangular Membrane Element with Rigid Rotational Freedoms", Finite Elements in Analysis and Design, Vol. 17, pp. 259-271.