Abstract
In this paper, a mathematical programming formulation is presented for the structural optimization with respect to the shakedown analysis of 3-D perfectly plastic structures on basis of a finite element discretization. A new direct algorithm using plastic sensitivities is employed in solving this optimization formulation. The numerical procedure has been applied to carry out the shakedown analysis of pipe junctions under multi-loading systems. The computational effort of the new approach is much lower compared to so called derivative- free search methods.
Chapter PDF
Similar content being viewed by others
Keywords
- Direct Search Method
- Line Search Method
- Mathematical Programming Formulation
- Pattern Search Method
- Good Vertex
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Charbonneau, P.: Genetic Algorithms in Astronomy and Astrophysics, The Astro-physical Journal (Supplements), 101 (1995) 309–334
Corana A., Marchesi M., Martini C., Ridella S.,: Minimizing Multimodal Functions of Continuous Variables with the ”Simulated Annealing” Algorithm, ACM Transactions on Mathematical Software 13 (1987) 262–280
Dennis, J.E., Schnabel, R.B.: Numerical methods for unconstrained optimization, Engelwood Cliffs, N.J., Prentice Hall (1983)
Fiacco, A.: Introduction to Sensitivity and Stability Analysis in Nonlinear Programming, New York, Academic Press (1983)
Goffe, W.L., Ferrier, G., Rogers, J.: Global Optimization of Statistical Functions with Simulated Annealing, Journal of Econometrics 60 (1994) 65–99
Goldberg, D.E.: Genetic Algorithms in Search, Optimization, and Machine Learning Addison Wesley (1989)
Heitzer, M.: Traglast-und Einspielanalyse zur Bewertung der Sicherheit passiver Komponenten, Berichte des Forschungszentrums Jülich Jül—3704 (1999)
Heitzer, M.: Structural optimization with FEM-based shakedown analyses Journal of Global Optimization (to appear).
Heyman, J.: Minimum weight of frames under shakedown loading. Journal of Engineering Mechanics, ASCE 84 (1958) 1–25
Hooke, R., Jeeves, T.A.: Direct search solution of numerical and statistical problems. J. Assoc. Comput. Mach. 8 (1961) 212–229
IMSL: Fortran Subroutines for Mathematical Application, Math/Library Vol. 1 & 2 Visual Numerics, Inc. (1997)
Kleiber, M., Antuneź, H., Hien, T.D., Kowalczyk, P.: Parameter Sensitivity in Nonlinear Mechanics: Theory and Finite Element Computations, New York, J. Wiley & Sons (1997)
König, J. A.: Shakedown of Elastic-Plastic Structures, Amsterdam and Warsaw, Elsevier and PWN (1987)
Lewis, R.M., Torczon, V., Trosset, M.W.: Direct search methods: then and now, Journal of Computational and Applied Mathematics 124 (2000) 191–207
PERMAS: User’s Reference Manuals, Stuttgart, INTES Publications No. 202, 207, 208, 302, UM 404, UM 405 (1988)
Schwabe, F.: Einspieluntersuchungen von Verbundwerkstoffen mit periodischer Mikrostruktur, Phd-Thesis, RWTH-Aachen (2000)
Staat, M., Heitzer M.: LISA a European Project for FEM-based Limit and Shakedown Analysis, Nuclear Engineering and Design 206 (2001) 151–166
Stein, E., Zhang, G., and Mahnken, R.: Shakedown analysis for perfectly plastic and kinematic hardening materials, in Stein, E. (ed.): Progress in computational analysis of inelastic structures, Wien, Springer, 175–244 (1993)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Heitzer, M. (2002). FEM-based Structural Optimization with Respect to Shakedown Constraints. In: Sloot, P.M.A., Hoekstra, A.G., Tan, C.J.K., Dongarra, J.J. (eds) Computational Science — ICCS 2002. ICCS 2002. Lecture Notes in Computer Science, vol 2329. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46043-8_84
Download citation
DOI: https://doi.org/10.1007/3-540-46043-8_84
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-43591-4
Online ISBN: 978-3-540-46043-5
eBook Packages: Springer Book Archive