In this paper, structural topology optimization is extended to systems design. Locations and patterns of connections in a structural system that consists of multiple components strongly affect its performance. Topology of connections is defined, and a new classification for structural optimization is introduced that includes the topology optimization problem for connections. A mathematical programming problem is formulated that addresses this design problem. A convex approximation method using analytical gradients is used to solve the optimization problem. This solution method is readily applicable to large-scale problems. The design problem presented and solved here has a wide range of applications in all areas of structural design. The examples provided here are for spot-weld and adhesive bond joints. Numerous other potential applications are suggested.

1.
Anderson, K. S., 1990, “Recursive Derivation of Explicit Equations of Motion for Efficient Dynamic/Control Simulation of Large Multibody Systems,” Doctoral Dissertation, Department of Mechanical Engineering, The University of Stanford.
2.
Barthelemy
J.-F. M.
, and
Haftka
R. T.
,
1993
, “
Recent Advances in Approximation Concepts for Structural Optimization
,”
Structural Optimization
, Vol.
15
, No.
1
, pp.
1
15
.
3.
Barthelemy, J.-F. M., and Haftka, R. T., 1994, “Function Approximations,” In Structural Optimization: Status and Promise, edited by M. P. Kamat, AIAA, Washington, D.C., pp. 51–70.
4.
Bendso̸e
M. P.
,
1989
, “
Optimal Shape Design as a Material Distribution Problem
,”
Structural Optimization
, Vol.
1
, pp.
193
202
.
5.
Bendso̸e
M. P.
, and
Kikuchi
N.
,
1988
, “
Generating Optimal Topologies in Structural Design Using a Homogenization Method
,”
Computer Methods in Applied Mechanics and Engineering
, Vol.
71
, pp.
197
224
.
6.
Cai, W., Yuan, J., Hu, S. J., Infante, L., and Clemens, C., 1994, “Optimal Fixture Design for Sheet Metal Holding,” IBEC/94 Body Assembly & Manufacturing, Detroit, Michigan, pp. 123–128.
7.
Chirehdast, M., and Jiang, T., 1996, “Optimal Design of Spot-Weld and Adhesive Bond Pattern,” SAE congress, Detroit, No. 960812.
8.
Fleury
C.
,
1989
, “
Efficient Approximation Concepts Using Second Order Information
,”
International Journal for Numerical Methods in Engineering
, Vol.
28
, pp.
2041
2058
.
9.
Fleury
C.
, and
Breibant
V.
,
1986
, “
Structural Optimization: A New Dual Method Using Mixed Variables
,”
International Journal for Numerical Methods in Engineering
, Vol.
23
, pp.
409
428
.
10.
Gea, H. C., 1993, “Structural Optimization for Static and Dynamic Responses Using an Integrated System Approach,” Ph.D. Thesis, The University of Michigan, Ann Arbor.
11.
Haftka, R. T., and Gurdal, Z., 1993, Elements of Structural Optimization, Kluwer, Third Edition.
12.
Jiang, T., 1996, “Topology Optimization of Structural Systems Using Convex Approximation Methods,” Doctoral Dissertation, Department of Mechanical Engineering and Applied Mechanics, The University of Michigan, Ann Arbor.
13.
Jiang, T., and Papalambros, P. Y., 1995, “A First Order Method of Moving Asymptotes for Structural Optimization,” Proceedings of Fourth International Conference on Computer Aided Optimum Design of Structures, Computational Mechanics Publications, Southampton Boston, pp. 75–83.
14.
Jiang
T.
, and
Papalambros
P. Y.
,
1996
, “
Optimal Structural Topology Design Using the Homogenization Method With Multiple Constraints
,”
Engineering Optimization
, Vol.
27
, pp.
87
108
.
15.
Johanson, R. P., 1996, “Topology Optimization of Multicomponent Structures,” Doctoral Dissertation, The University of Michigan, Ann Arbor.
16.
Johanson, R. P., and Papalambros, P. Y., 1990, “A Knowledge-Based Method of Moving Asymptotes Algorithm for Structural Optimization,” Third NASA/Air Force Symposium on Recent Developments in Multidisciplinary Analysis and Optimization, San Francisco.
17.
Menassa
R. J.
, and
DeVries
W. R.
,
1991
, “
Optimization Methods Applied to Selecting Support Positions in Fixture Design
,”
ASME JOURNAL OF ENGINEERING FOR INDUSTRY
, Vol.
113
, November, pp.
412
418
.
18.
Mlejnek
H. P.
,
1992
, “
Some Aspects of The Genesis of Structures
,”
Structural Optimization
, Vol.
5
, pp.
64
69
.
19.
Mlejnek H. P., 1993, “Some Explorations in the Genesis of Structures,” In Topology Design of Structures, Proceedings of NATO ASI in Sesimbra, Portugal, Kluwer, Dordrecht, pp. 287–300.
20.
Rozvany
G. I. N.
,
Bendso̸e
M. P.
, and
Kirsch
U.
,
1995
, “
Layout Optimization of Structures
,”
Applied Mechanics Reviews
, Vol.
48
, No.
2
, pp.
41
19
.
21.
Rozvany
G. I. N.
,
Zhou
M.
, and
Birker
T.
,
1992
, “
Generalized Shape Optimization without Homogenization
,”
Structural Optimization
, Vol.
4
, pp.
250
252
.
22.
Svanberg
K.
,
1987
, “
The Method of Moving Asymptotes-A New Method for Structural Optimization
,”
International Journal for Numerical Methods in Engineering
, Vol.
24
, pp.
359
373
.
23.
Smaoui, H., Fleury, C., and Schmit, L. A., 1988, “Advances in Dual Algorithms and Convex Approximation Methods,” Proceeding of AIAA/ASME/ASCE/AHS 29th Structures, Structural Dynamics and Material Conference, Williamsburgh, VA, Part 3, pp. 1339–1347.
24.
Wehage, R. A., 1988, “Application of Matrix Partitioning and Recursive Projection to O(n) Solution of Constrained Equations of Motion,” In: Midha, A., ed., Trends and Developments in Mechanisms, Machines, and Robotics, ASME Design Technology Conference, 20th Biennial Mechanisms Conference, Kissimmee, Florida DE-Vol. 15-2, pp. 221–230.
25.
Yang
R. J.
, and
Chahande
A. I.
,
1995
, “
Automotive Applications of Topology Optimization
,”
Structural Optimization
, Vol.
9
, pp.
246
249
.
26.
Yang
R. J.
, and
Chuang
C. H.
,
1994
, “
Optimal Topology Design using Linear Programming
,”
Computers and Structures
, Vol.
52
, pp.
265
275
.
27.
Zhou
M.
, and
Rozvany
G. I. N.
,
1991
, “
The COC Algorithm, Part II: Topological, Geometrical and Generalized Shape Optimization
,”
Computer Methods in Applied Mechanics and Engineering
, Vol.
89
, pp.
309
336
.
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