In this paper, a new shape optimization approach, feature-based optimization of beam structures, is proposed to provide an efficient optimization solution of beam components in complex mechanical structures represented by polygonal meshes. Our approach consists of two main steps: 1) feature recognition of beam components: 2) gradient-based shape optimization of these components by reducing a weighted compliance among all load cases. The main contribution is to propose a new scheme to automate time-consuming shape optimization processes on polygonal meshes with beam components. Numerical experiments have been conducted and the results indicate the effectiveness of the approach.
Issue Section:
Technical Papers
1.
Bendsoe
, M. P.
, 1989
, “Optimal Shape Design as a Material Distribution Problem
,” Struct. Optim.
, 1
, pp. 193
–202
.2.
Suh, Y. S., and Wozny, M. J., 1997, “
Interactive Feature Extraction for a Form Feature Conversion System,” Solid Modeling, Proceedings of the Fourth ACM Symposium on Solid Modeling and Application, pp. 111–122.
3.
Iwata
, K.
, Onosato
, M.
, and Teramoto
, K.
, 1997
, “An Architecture for Form Feature Modeling for Concurrent, Cooperative and Consistent Product Design
,” JSME Int. J.
, 40
(3
), pp. 533
–539
.4.
Crawford
, R.
, 1993, “Integrating 3D Modeling and Process Planning by Features: A Case Study,” International Journal of Computer Integrated Manufacturing, 6, pp. 113–118.5.
Latif
, M. N.
, Boyd
, R. D.
, and Hannam
, R. G.
, 1993, “Integrating CAD and Manufacturing Intelligence Through Features and Objects,” International Journal of Computer Integrated Manufacturing 6, pp. 87–92.6.
Lenau
, T.
, and Mu
, L.
, 1993, “Features in Integrated Modeling of Products and Their Production,” International Journal of Computer Integrated Manufacturing, 6, pp. 65–73.7.
Cunningham, J. J., and Dixon, J. R., 1988, “Designing With Features: The Origin of Features,” Proc. of 1988 ASME International Computers in Engineering Conference and Exhibition, San Francisco, pp. 237–243.
8.
Shah
, J. J.
, 1991
, “Assessment of Features Technology
,” Comput.-Aided Des.
, 23
(5
), pp. 331
–343
.9.
Henderson
, M. R.
, and Taylor
, L. E.
, 1993, “A Meta-Model for Mechanical Products Based Upon the Mechanical Design Process,” Research in Engineering Design, Theory, Applications, and Concurrent Engineering, 5(3 & 4), pp. 140–160.10.
Rosen, D. W., and Peters, T. J., 1992, Topological Properties That Model Feature-Based Representation Conversions Within Concurrent Engineering. In: Springer-Verlag, New York, pp. 147–158.
11.
Rosen
, D. W.
, and Grosse
, I. R.
, 1992
, “A Feature Based Shape Optimization for the Configuration and Parametric Design of Flat Plates
,” Eng. Comput.
, 8
, pp. 81
–91
.12.
Dixon, J. R., Libradi, E. C., and Nielsen, E. H., 1990, Unsolved Research Issues in Development of Design With Features Systems. In: North-Holland, pp. 183–196.
13.
Perng
, D. B.
, and Chang
, C. F.
, 1997
, “Resolving Feature Interactions in 3D Part Editing
,” Comput.-Aided Des.
, 29
(10
), pp. 687
–699
.14.
Hoffman
, C. M.
, and Joan-Arinyo
, R.
, 1998
, “On User-Defined Features
,” Comput.-Aided Des.
, 30
(5
), pp. 321
–332
.15.
Gao, F., and Roller, D., 1998, “Modeling of Feature-Based Design Process,” Proceedings of 1998 ASME Design Engineering Technical Conference (DETC98/DTM-5644).
16.
Bardhan, T. K., Rajan, V. N., and Masud, A. S. M., 1999, “Methodology and Implementation of Dynamic Design Advisor (DDA) in a Feature-Based Design System,” Proceedings of 1999 ASME Design Engineering Technical Conference (DETC99/DAC-8563).
17.
Shapiro
, L.
, and Haralick
, R.
, 1979
, “Decomposition of Two-Dimensional Shapes by Graph-Theoretic Clustering
,” IEEE Trans. Pattern Anal. Mach. Intell.
, 1
, pp. 10
–20
.18.
Nevatia
, R.
, and Binford
, T. O.
, 1977
, “Description and Recognition of Curved Objects
,” Artif. Intel.
, 8
, pp. 77
–98
.19.
Pentland, A. P., 1987, “Recognition by Parts,” Proceedings of the 1st International Conference on Computer Vision, pp. 212–220.
20.
Blum
, H.
, 1978
, “Shape Description Using Weighted Symmetric Axis Features
,” Pattern Recogn.
, 10
, pp. 167
–180
.21.
Blum
, H.
, 1973
, “Biological Shape and Visual Science
,” J. Theor. Biol.
, 38
, pp. 205
–287
.22.
Freeman
, H.
, 1978
, “Shape Description via the Use of Critical Points
,” Comput. Graph. Image Process.
, 10
, pp. 159
–166
.23.
Siddiqi, K., 1992, “Parts of Visual Form: Ecological and Psychophysical Aspects,” Technical Report, LEMS, Brown University.
24.
Dill
, A. R.
, Levine
, M. D.
, and Noble
, P. B.
, 1987
, “Multiple Resolution Skeletons
,” IEEE Trans. Pattern Anal. Mach. Intell.
, 9
, pp. 495
–504
.25.
Guo
, Z.
, and Hall
, R. W.
, 1992
, “Fast Fully Parallel Thinning Algorithms
,” Comput. Vis. Graph. Image Process.
, 55
(3
), pp. 317
–328
.26.
Shapiro
, B.
, Pisa
, J.
, and Sklansky
, J.
, 1981
, “Skeleton Generation From x, y Boundary Sequences
,” Comput. Vis. Graph. Image Process.
, 15
, pp. 136
–153
.27.
Ogneiwicz, R., and Ilg, M., 1992, “Voronoi Skeletons: Theory and Applications,” Proceedings of the Conference on Computer Vision and Pattern Recognition., pp. 63–69.
28.
Gauch
, J.
, and Pizer
, S.
, 1992
, “The Intensity Axis of Symmetry and Its Application to Image Segmentation
,” IEEE Trans. Pattern Anal. Mach. Intell.
, 15
(8
), pp. 753
–770
.29.
Shen, J., and Yoon, D., 2003, “A New Scheme for Efficient and Direct Shape Optimization of Complex Structures Represented by Polygonal Meshes,” Int. J. Numer. Methods Eng. (accepted).
30.
Ding
, Y.
, 1986
, “Shape Optimization of Structures: A Literature Survey
,” Comput. Struct.
, 24
, pp. 985
–1004
.31.
Vigdergauz
, S.
, 1997
, “Two-Dimensional Grained Composites of Minimum Stress Concentration
,” J. Struct. Mech.
, 34
, pp. 661
–672
.32.
Xie, Y. M., and Steven, G. P., 1997, Evolutionary Structural Optimization, Springer, Berlin, Heidelberg, New York.
33.
Woon
, S. Y.
, Querin
, O. M.
, and Steven
, G. P.
, 2001, “Structural Application of a Shape Optimization Method Based on a Genetic Algorithm,” Structural and Multidisciplinary Optimization, 22, pp. 57–64.34.
Fourie
, P. C.
, and Groenwold
, A. A.
, 2002, “The Particle Swarm Optimization Algorithm in Size and Shape Optimization,” Structural and Multidisciplinary Optimization, 23, pp. 259–267.35.
Falk
, A.
, Barthold
, F. J.
, and Stein
, E.
, 1999
, “A Hierarchical Design Concept for Shape Optimization Based on the Interaction of CAGD and FEM
,” Struct. Optim.
, 18
, pp. 12
–23
.36.
Choi
, K. K.
, and Chang
, K. W.
, 1994
, “A Study of Design Velocity Field Computation for Shape Optimal Design
,” Finite Elem. Anal. Design
, 15
, pp. 317
–341
.37.
Botkin
, M. E.
, 1982
, “Shape Optimization of Plate and Shell Structures
,” AIAA J.
, 20
, pp. 268
–273
.38.
Yang
, R. J.
, and Botkin
, M. E.
, 1987
, “A Modular Approach for Three Dimensional Shape Optimization
,” AIAA J.
, 25
, pp. 492
–497
.39.
Botkin, M. E., 2000, “Structural Optimization of Automotive Body Components Based Upon Parametric Solid Modeling,” AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, Paper #2000–4707.
40.
Schumacher, A., and Hierold, R., 2002, “Parameterized CAD-Models for Multidisciplinary Optimization Process,” AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization., Paper #2000–4912.
41.
Belegundu
, A. D.
, and Rajan
, S. D.
, 1988
, “A Shape Optimization Approach Based on Natural Design Variables and Shape Function
,” Comput. Methods Appl. Mech. Eng.
, 66
, pp. 87
–106
.42.
Rajan, S. D., and Belegundu, A. D., 1989, “Shape Optimal Design Using Fictitious Loads,” AIAA Journal, 27, pp. 102–107.
43.
Tortorelli, D. A., 1990, “A Geometric Representation Scheme Suitable for Shape Optimization,” Proceedings of Second NASA/Air Force Symposium.
44.
Pickett
, R. M.
, Rubinstein
, M. F.
, and Nelson
, R. B.
, 1973
, “Automated Structural Synthesis Using a Reduced Number of Design Coordinates
,” AIAA J.
, 11
(4
), pp. 489
–494
.45.
Tvergaard, V., 1975, On the Optimum Shape of a Fillet in a Flat Bar with the Restrictions. In: Sawczuk A. and Mroz Z. (eds) Optimization in Structural Design, Springer-Verlag, New York, pp. 181–195.
46.
Pedersen
, P.
, and Laursen
, C. L.
, 1982
, “Design for Minimum Stress Concentration by Finite Elements and Linear Programming
,” J. Struct. Mech.
, 10
, pp. 375
–391
.47.
Dybbro
, J. D.
, and Holm
, N. C.
, 1986
, “On Minimization of Stress Concentration for Three-Dimensional Models
,” Computers & Structures
,24
, pp. 637
–643
.48.
Yang
, R. J.
, and McGeen
, D. T.
, 1992
, “Application of Basis Function Concept to Practical Shape Optimization Problems
,” Struct. Optim.
, 5
, pp. 55
–63
.49.
Dybbro
, J. D.
, and Holm
, N. C.
, 1986
, “On Minimization of Stress Concentration for Three-Dimensional Models
,” Computers & Structures
,24
, pp. 637
–643
.50.
Tvergaard, V., 1975, On the Optimum Shape of a Fillet in a Flat Bar With the Restrictions. In: Sawczuk A. and Mroz Z. (eds) Optimization in Structural Design, Springer-Verlag, New York, pp. 181–195.
51.
Pedersen
, P.
, and Laursen
, C. L.
, 1982
, “Design for Minimum Stress Concentration by Finite Elements and Linear Programming
,” Journal of Structural Mechanics
,10
, pp. 375
–391
.52.
Yang
, R. J.
, and McGeen
, D. T.
, 1992
, “Application of Basis Function Concept to Practical Shape Optimization Problems
,” Struct. Optim.
, 5
, pp. 55
–63
.53.
Meyer-Prubner, R., 1997, “Prozebkette Topologicoptimierung,” Beitrage zum NAFEMS Seminar zur Topologicoptimierung (in German), pp. 12.1–12.5.
Copyright © 2003
by ASME
You do not currently have access to this content.
