Abstract
The numerical solution of shape optimization problems is considered. The algorithm of successive optimization based on finite element techniques and design sensitivity analysis is applied. Mesh refinement is used to improve the quality of finite element analysis and the computed numerical solution. The norm of the variation of the Lagrange augmented functional with respect to boundary variation (residuals in necessary optimality conditions) is taken as an a posteriori error estimator for optimality conditions and the Zienkiewicz—Zhu error estimator is used to improve the quality of structural analysis. The examples presented show meaningful effects obtained by means of mesh refinement with a new error estimator.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Babuška, I.; Miller, A. 1987: A feedback finite element method with a posteriori error estimation. Part I: The finite element method and some basic properties of the a posteriori error estimator.Comp. Meth. Appl. Mech. Engng. 61, 1–40
Babuška, I.; Rheinboldt, W. 1978: Error estimates for adaptive finite element computations.SIAM J. Num. Anal. 15, 736–756
Banichuk, N.V. 1990:Introduction to optimization of structures. Berlin, Heidelberg, New York: Springer
Barthold, F.-J. 1993: Theorie und Numerik zur Berechnung und Optimierung von Strukturen aus isotropen, hyperelastischen Materialien.Technical Report F 93/2, Forschungs- und Seminarberichte aus dem Bereich der Mechanik der Universität Hannover
Barthold, F.-J.; Becker, A.; Falk, A.; Rust, W. 1993: Zum Einfluß der Netzadaption bei der Formoptimierung.ZAMM 73, T680-T684
Becker, A. 1992: Strukturoptimierung stabilitätsgefährdeter Systeme mittels analytischer Gradientenermittlung.Technical Report F 92/1, Forschungs- und Seminarberichte aus dem Bereich der Mechanik der Universität Hannover
Falk, A. 1994: Adaptive Verfahren für die Formoptimierung flächiger Strukturen unter Berücksichtigung der CAD—FE—Kopplung.Technical Report F 94/2, Forschungs- und Seminarberichte aus dem Bereich der Mechanik der Universität Hannover (to appear)
Georges, M.K.; Shephard, M.S. 1991: Automated adaptive two dimensional system for the HP—version of the finite element method32, 867–893
Haug, E.J.; Arora, J.S. 1979:Applied optimal design. New York: Wiley
Johnson, C.; Hansbo, P. 1992: Adaptive finite element methods in computational mechanics.Comp. Meth. Appl. Mech. Engng. 101, 143–181
Plank, L.; Stein, E.; Bischoff, D. 1990: Accuracy and adaptivity in the numerical analysis of thin walled structures.Comp. Meth. Appl. Mech. Engng. 82, 223–256
Rank, E.; Babuška, I. 1987: An expert system for the optimal mesh design in the HP—version of the finite element method.Int. J. Num. Meth. Engng. 24, 2087–2106
Redanz, W.; Wunderlich, W. 1992: A local strategy for mesh refinement and adaptive control. In: Zienkiewicz, O.C.; Ladeveze, P. (eds.)New advances in computational mechanics, pp. 233–245. Amsterdam: Elsevier
Rust, W.; Stein, E. 1992: 2D—finite—element adaptations in structural mechanics, including shell analysis and non-linear calculations. In: Zienkiewicz, O.C.; Ladeveze, P. (eds.)New advances in computational mechanics, pp. 219–232. Amsterdam: Elsevier
Stein, E.; Rust, W.; Ohnimus, S. 1992: H— and d—adaptive finite element methods for two-dimensional structural problems including post—buckling of shells.Comp. Meth. Appl. Mech. Engng. 101, 315–354
Zienkiewicz, O.C.; Zhu, J.Z. 1987: A simple error estimator and adaptive procedure for practical engineering analysis.Int. J. Num. Meth. Engng. 24, 337–357
Zienkiewicz, O.C.; Zhu, J.Z. 1991: Adaptivity and mesh generation.Int. J. Num. Meth. Engng. 32, 783–810
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Banichuk, N.V., Barthold, F.J., Falk, A. et al. Mesh refinement for shape optimization. Structural Optimization 9, 46–51 (1995). https://doi.org/10.1007/BF01742644
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01742644