Abstract
This study presents a unified reanalysis approach for structural analysis, design, and optimization that is based on the Combined Approximations (CA) method. The method is suitable for various analysis models (linear, nonlinear, elastic, plastic, static, dynamic), different types of structures (trusses, frames, grillages, continuum structures), and all types of design variables (cross-sectional, material, geometrical, topological). The calculations are based on results of a single exact analysis. The computational effort is usually much smaller than that needed to carry out a complete analysis of modified designs. Accurate results are achieved by low-order approximations for significant changes in the design. It is possible to improve the accuracy by considering higher-order terms, and exact solutions can be achieved in certain cases. The solution steps are straightforward, and the computational procedures presented can readily be used with general finite element systems. Typical results are demonstrated by numerical examples.
Similar content being viewed by others
References
Akgun, M.A.; Garcelon, J.H.; Haftka, R.T. 2001: Fast exact linear and nonlinear structural reanalysis and the Sherman–Morrison–Woodbury formulas. Int. J. Numer. Methods Eng. 50, 1587–1606
Aktas, A.; Moses, F. 1998: Reduced basis eigenvalue solutions for damaged structures. Mech. Struct. Mach. 26, 63–79
Bathe, K.J. 1996: Finite element procedures. Englewood Cliffs, NJ : Prentice Hall
Chen, S.H.; Yang, X.W. 2000: Extended Kirsch combined method for eigenvalue reanalysis. AIAA J. 38, 927–930
Chen, S.H.; Yang, X.W.; Lian, H.D. 2000: Comparison of several eigenvalue reanalysis methods for modified structures. Struct. Optim. 20, 253–259
Crisfield, M.A. 1997: Nonlinear finite element analysis of solids and structures. Vol. 1. Chichester: John Wiley & Sons
Fatemi, J.; Trompette, P. 2002: Optimal design of stiffened plate structures. 43rd Struct., Struct. Dyn. Mat. Conf. (held in Denver, Colorado)
Garcelon, J.H.; Haftka, R.T.; Scotti, S.J. 2000: Approximations in optimization of damage tolerant structures. AIAA J. 38, 517–524
Ghali, A.; Neville, A.M. 1997: Structural Analysis. London: E & FN SPON
Heiserer, D.; Baier, H. 2001: Applied reanalysis techniques for large scale structural mechanics multidisciplinary optimization in automotive industry. Proc. WCSMO – 4. (held in Dalian, China)
Kirsch, U. 1991: Reduced basis approximations of structural displacements for optimal design. AIAA J. 29, 1751–1758
Kirsch, U. 1993a: Structural optimization, fundamentals and applications. Berlin, Heidelberg, New York: Springer-Verlag
Kirsch, U. 1993b: Approximate reanalysis methods. Structural optimization: status and promise. Edited by Kamat, M.P., Washington D.C.: AIAA
Kirsch, U. 1993c: Efficient reanalysis for topological optimization. Struct. Optim. 6, 143–150
Kirsch, U. 1994: Effective sensitivity analysis for structural optimization. Comp. Methods Appl. Mech. Eng. 117, 143–156
Kirsch, U. 1995: Improved stiffness-based first-order approximations for structural optimization. AIAA J. 33, 143–150
Kirsch, U. 1999: Efficient-accurate reanalysis for structural optimization. AIAA J. 37, 1663–1669
Kirsch, U. 2000: Combined approximations – a general reanalysis approach for structural optimization. Struct. Optim. 20, 97–106
Kirsch, U. 2002: Design-oriented analysis of structures – A unified approach. Dordrecht: Kluwer Academic Publishers
Kirsch, U. 2003a: Design-oriented analysis of structures – a unified approach. ASCE Journal of Engineering Mech. 129, 264–272
Kirsch, U. 2003b: Approximate vibration reanalysis of structures. To be published, AIAA J.
Kirsch, U.; Frostig, Y. 2002: Nonlinear reanalysis of structures by combined approximations. Submitted
Kirsch, U.; Kocvara M.; Zowe J. 2002: Accurate reanalysis of structures by a preconditioned conjugate gradient method. Int. J. Numer. Methods Eng. 55, 233–251
Kirsch, U.; Liu, S. 1995: Exact structural reanalysis by a first-order reduced basis approach. Struct. Optim. 10, 153–158
Kirsch, U.; Liu, S. 1997: Structural reanalysis for general layout modifications. AIAA J. 35, 382–388
Kirsch, U.; Papalambros, P.Y. 2001a: Structural reanalysis for topological modifications. Struct. Optim. 21, 333–344
Kirsch, U.; Papalambros, P.Y. 2001b: Exact and accurate reanalysis of structures for geometrical changes. Eng. Comp. 17, 363–372
Kirsch, U.; Papalambros, P.Y. 2001c: Accurate displacement derivatives for structural optimization using approximate reanalysis. Comp. Methods Appl. Mech. Eng. 190, 3945–3956
Kirsch, U.; Papalambros, P.Y. 2001d: Exact and accurate solutions in the approximate reanalysis of structures. AIAA J. 39, 2198–2205
Leu, L.-J.; Huang, C.-W. 1998: A reduced basis method for geometric nonlinear analysis of structures. IASS J. 39, 71–75
Ramaswamy, B.; Nikolaidis, E.; Keerti, A.; Kirsch, U. 2001: Reliability analysis of systems with progressive failure modes using reduced basis approximations. Proc. 6th U.S. Nat. Congr. Comp. Mech. (held in Dearborn, Michigan)
Sherman, J.; Morrison, W.J. 1949: Adjustment of an inverse matrix corresponding to changes in the elements of a given column or a given row of the original matrix. Ann. Math. Statist. 20, 621
Woodbury, M. 1950: Inverting modified matrices. Memorandum Report 42 Statistical research group, Princeton University, Princeton, NJ
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Kirsch, U. A unified reanalysis approach for structural analysis, design, and optimization. Struct Multidisc Optim 25, 67–85 (2003). https://doi.org/10.1007/s00158-002-0269-0
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00158-002-0269-0