The method of LargE Admissible Perturbations (LEAP) solves redesign problems of complex structures without trial and error or repetitive finite element analyses. Code RESTRUCT (Redesign of STRUCTures) produces an optimal redesign of minimum structural change or minimum weight with modal dynamics and/or static displacement specifications. LEAP allows for large structural changes. First, the general perturbation equations are derived relating the original structure S1 (known) to the objective structure S2 (unknown) which is to satisfy the designer’s specifications. Next, the redesign problem is solved using an incremental prediction-correction scheme. In the past, LEAP produced accurate results even for 100–300 percent changes in redesign for modal objectives without any intermediate FEAs. Accuracy in static redesign, however, was limited to about 50 percent changes in static objectives. In this work, a new static general perturbation equation and the corresponding LEAP algorithm are developed to achieve accuracy for 100–300 percent changes in static performance as well. The new formulation includes the static deflection shape as the zeroth mode in the expansion of static properties in terms of dynamic modes. Systematic numerical applications show that high accuracy is achieved by fewer extracted modes.

Issue Section:
Research Papers
Topics:
Algorithms, Deflection, Displacement, Dynamics (Mechanics), Errors, Finite element analysis, Perturbation theory, Shapes, Structures, Weight (Mass)
1.
Stetson
K. A.
, “
Perturbation Method of Structural Design Relevant to Holographic Vibration Analysis
,”
AIAA Journal
, Vol.
13
, No.
4
, April
1975
, pp.
457
–
459
.
2.
Hoff
C. J.
,
Bernitsas
M. M.
,
Sandstrom
R. E.
, and
Anderson
W. J.
, “
Nonlinear Incremental Inverse Perturbation Method for Structural Redesign
,”
AIAA Journal.
Vol.
22
, No.
9
, September
1984
, pp.
1304
–
1309
.
3.
Hoff
C. J.
, and
Bernitsas
M. M.
, “
Dynamic Redesign of Marine Structures
,”
Journal of Ship Research
, Vol.
29
, No.
4
, December
1985
, pp.
285
–
295
.
4.
Kim
J. H.
, and
Bernitsas
M. M.
, “
Redesign of Marine Structures
,”
Marine Structures
, Vol.
1
, No.
2
, September
1988
, pp.
139
–
183
.
5.
Bernitsas
M. M.
, and
Kang
B.
, “
Admissible Large Perturbation in Structural Redesign
,”
AIAA Journal
, Vol.
29
, No.
1
, January
1991
, pp.
104
–
113
.
6.
Tawekal
R. L.
, and
Bernitsas
M. M.
, “
Finite Element Model Correlation for Offshore Structures
,”
ASME JOURNAL OF OFFSHORE MECHANICS AND ARCTIC ENGINEERING
, Vol.
114
, August
1992
, pp.
154
–
164
.
7.
Twomey, W. J., Chen, T. L. C., Ojalvo, I. U., and Ting, T., “A General Method for Modifying a Finite Element Model to Correlate with Modal Test Data,” Journal of the American Helicopter Society, July, 1991.
8.
Haug, E. J., Choi, K. K., and Komkov, V., Design Sensitivity Analysis of Structural Systems, Academic Press, 1986.
9.
Vanderplaats, G. N., Miura, M., Nagendra, G., and Wallerstein, D., “Structural Synthesis Using MSC/NASTRAN,” Computers in Engineering, Proceedings of the International Computers in Engineering Conference and Exhibit, 1989, pp. 211–218.
10.
Haftka, R. T., Gurdal, Z., and Kamat, M. P., Elements of Structural Optimization, 2nd Edition, Kluwer Academic Publishers, 1990.
11.
Natake, H. G., “Minimum Modifications due to Dynamic Requirements; Comparison and Application,” Computer Aided Optimum Design of Structure: Recent Advances, Proceedings of the First International Conference, Southampton, UK, editors, Brebbia, C. A., and Hernandez, S., June 1989, pp. 31–40.
12.
Tits, A. L., and Zhou, J. L., “User’s Guide for FSQP Version 3.3b: A FORTRAN Code for Solving Constrained Nonlinear (Minimax) Optimization Problems, Generating Iterates Satisfying All Inequality and Linear Constraints,” Electrical Engineering Department and Institute for Systems Research, Univ. of Maryland, College Park, MD 20742, 1993.
13.
Bernitsas
M. M.
, and
Rim
C. H.
, “
Redesign of Plates by Large Admissible Perturbations
,”
AIAA Journal
, Vol.
32
, No.
5
, May
1994
, pp.
1021
–
1028
.
14.
Kang, B., and Bernitsas, M. M., “Stress Redesign by Large Admissible Perturbations,” Proceedings of BOSS’94 Conference, Cambridge, MA, July 1994, Vol. 3, pp. 201–212.
15.
Alzahabi, B., and Bernitsas, M. M., “Cylindrical Shell Redesign by Large Admissible Perturbations,” Proceedings of ASCE Engineering Mechanics Conference, College Station, Texas, May 24–27, 1992.
16.
Bernitsas, M. M., Suryatama, D., Kang, B., and Karl, D. G., “Shape and Topology Structural Redesign by Large Admissible Perturbations,” Proceedings of Solid Freeform Fabrication Symposium, Austin, Texas, August 1994, pp. 285–292.
17.
Gill, P. E., Murray, W., Saunders, M. A., and Wright, M. H., “User’s Guide for SOL/QPSOL: A FORTRAN Package for Quadratic Programming,” Department of Operation Research, Stanford University, 1983.
18.
Gill, P. E., Murray, W., Saunders, M. A., and Wright, M. H., “User’s Guide for SOL/NPSOL: A FORTRAN Package for Nonlinear Programming,” Department of Operation Research, Stanford University, 1983.
19.
Kang
B.
,
Beyko
E.
, and
Bernitsas
M. M.
, “
Invariant and Consistent Redundancy by Large Admissible Perturbations
,”
Marine Structures
, Vol.
5
, No.
1
,
1992
, pp.
23
–
70
.
20.
Beyko
E.
, and
Bernitsas
M. M.
, “
Reliability of Large Scale Structures by Large Admissible Perturbations
,”
ASME JOURNAL OF OFFSHORE MECHANICS AND ARCTIC ENGINEERING
, Vol.
115
,
1993
, pp.
167
–
178
.
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