Quasi-Static Structural Optimization Technique Using Equivalent Static Loads Calculated at Every Time Step as a Multiple Loading Condition

매 시간단계의 등가정하중을 다중하중조건으로 이용한 준정적 구조최적화 방법

  • Published : 2000.10.01


This paper presents a quasi-static optimization technique for elastic structures under dynamic loads. An equivalent static load (ESL) set is defined as a static load set which generates the same displacement field as that from a dynamic load at a certain time. Multiple ESL sets calculated at every time step are employed to represent the various states of the structure under the dynamic load. They can cover every critical state that might happen at an arbitrary time. Continuous characteristics of dynamic load are simulated by multiple discontinuous ones of static loads. The calculated sets of ESLs are applied as a multiple loading condition in the optimization process. A design cycle is defined as a circulated process between an analysis domain and a design domain. Design cycles are repeated until a design converges. The analysis domain gives a loading condition necessary for the design domain. The design domain gives a new updated design to be verified by the analysis domain in the next design cycle. This iterative process is quite similar to that of the multidisciplinary optimization technique. Even though the global convergence cannot be guaranteed, the proposed technique makes it possible to optimize the structures under dynamic loads. It has also applicability, flexibility, and reliability.


Equivalent Static Load;Multiple Loading Condition;Design Cycle;Analysis Domain;Design Domain;Time Step


  1. GENESIS User Manual: version 3.0, 1996, VMA Engineering
  2. 최우석, 1999, '동하중의 등가정하중으로의 변환 및 이를 이용한 구조최적설계,' 박사학위논문, 한양대학교, 서울
  3. Grandhi, R.V., Haftka, R.T., and Watson, l.T., 1986, 'Design-Oriented Identification of Critical Times in Transient Response,' AIAA Journal, Vol. 24, No. 4, pp. 649-656
  4. CSA/NASTRAN Users Manual, 1994, CSAR
  5. Kang, B.S., Choi, W.S., and Park, G.J., 1999, 'Structural OptimizationUnder Equivalent Static Loads Transformed from Dynamic Loads Based on Displacement,' AIAA Conference, St. Louis, MO
  6. Shin, M.J., Choi, W.S., and Park, G.J., 1997, 'Transformation of Dynamic Loads into Equivalent Static Loads and Shape Optimization of the Road Arm,' RACAM V Conference, Puerto Rico
  7. Choi, W.S. and Park, G.J., 1999, 'Transformation of Dynamic Loads into Equivalent Static Loads Based on Modal Analysis,' Int.J. for Num. Engng., Vol. 46, pp.29-43<29::AID-NME661>3.0.CO;2-D
  8. Haftka R.T. and Gurdal Z., 1991, Elements of Structural Optimizaton, The Netherlands: Kluwer Academic Publishers
  9. Chahade, A.I. and Arora, J.S., 1994, 'Optimization of Large Structure Subjected to Dynamic Loads with Multiplier Method,' Int. J.for Engng., Vol. 37, pp. 413-430
  10. Feng, T.T., Arora, J.S., and Haug, E.J., 1977, 'Optical Structural Design under Dynamic Loads,' Int. J. for Num. Meth. in Engng., Vol. 11, pp. 39-62
  11. Paeng, J.K. and Arora, J.S., 1989, 'Dynamic Response Optimizaton of Mechanical Systems with Multiplier Methods,' ASME Journal of Mechanism ,Transmission and Automaton in Design, Vol. 111, pp. 73-80
  12. Schmit, L.A., 1960, 'Structural Design by SystematicSynthesis,' Proceedings of teh 2nd Conference on Electric Computation, ASCE, New York
  13. Friswell, M.I., and Moltershead, J.E., 1995, Finite Element Model Updating in Structural Dynamics, Kluwer Academic Publishers, Dordrecht, The Netherlands
  14. Imregun, M. and Visser, W.J., 1991, 'A Review of Model Updating Techniques,' Shock and Vibration Digest, Vol. 23, pp. 9-20
  15. Motlershead, J.E. and Friswell, M.I., 1993, 'Modal Updating in Structural Dynamcis: A Survey,' Journal of Sound and Vibration, Vol. 167, pp. 347-375
  16. Menke, W., 1989, Geophysical Data analysis: Discrete inverrse Theory, Academic Press, New York
  17. Tarantora, A., 1987, Inverse Problem Theory: Methods for Data Fitting and Model Parameter Estimation, Elsevier, Amsterdam
  18. Bui, H.D., 1994, Inverse Problems in the Mechanics of Materials : An Introduction, CRC Press, Boca Raton, FL
  19. Moller, P.W., 1999, 'Load Identification Through Structural Modification,' ASME Journal of Applied Mechanics, Vol. 66, pp. 236-241
  20. Austin, M.A., Lister, K.S., and Mahin, S.A., 1987a, 'Probabilistic Design of Moment-Resistant Structures,' ASCE Journal of Structural Engineering, Vol. 113(8), pp. 1642-1659
  21. Austin, M.A., Lister, K.S., Mahin, S.A., 1987b,'Probabilistic Design of Moment-Resistant Frame Under Seismic Loading,' ASCE Journal of Structural Engineering, Vol. 118, pp. 1660-1677
  22. Cheng F.Y. and Chang, C.C., 1988, Safety-Based Optimum Design of Nondeterministic Structures Subject to Various Types of Seismic Loads, NSF Report, U.S. Department of Commerce, VA, NTIS No. PB90-133489/AS p. 326
  23. Truman, K.Z. and Petruska, D.J., 1991, 'Optimum Design of Dynamically Excited Structural Systems Using Time History Analysis,' OPTl91-Internatioal Conference for Computer Aided Optimum Design of Structures, Boston, MA, June 25-27, 1991; Optimization of Structural Systems and Industrial Applications, S. Hernandez and C.A. Brebbia, eds. Elsevier Applied Science, London, 197-207
  24. Cheng F.Y. and Chang, C.C., 1985, 'Optimm Design of Steel Building with Consideration of Reliability,' Proceedings of 4th international Conference on Structural Safty and Reliability, Kobe, Japan, Vol. 3, pp. 81-88
  25. Cheng, F.Y. and Truman, K.Z., 1983, 'Optimization Design of 3-D Building Systems for Static and Seismic Loading,' Modeling and Simulation in Engineering , III, North-Holland Publishing Co., New York, pp. 315-326
  26. Truman, K.Z. and Jan, C.T., 1988, 'Optimal Bracing Schemes for Structural Systems Subject to the ATC 3-06, UBC, and BOCA Seismic Provisions,' Proceedings of the 9th World conference on Earthquake Engineering, Tokyo and Kyoto, Japan, August 2-9, 1998, Vol. V, pp. 1149-1155
  27. Truman, K.Z. and Cheng, F.Y., 1990, 'Optimum assessment of Irregular 3-D Buildings,' ASCE Journal of Structural Engineering, Vol. 116, pp. 3324-3337
  28. Cheng, F.Y. and Juang, D.S., 1988, 'Assessment of Various Code Provisions Based on Optimum Design of Steer Structures,' Journal of Earthquake Engineering and Structural Dynamics, Vol. 16, pp. 46-61
  29. Cheng, F.Y. and Juang, D.S., 1989 'Recursive Optimization for Seismic Steel Frames,' ASCE Journal of Structural Engineering, Vol. 115, pp. 445-466