Basics of Shape Optimal Design
At present optimum structural design is understood as a synthesis of several disciplines which individually are to a large extend developed : (i) design modeling, (ii) structural analysis, (iii) behavior sensitivity analysis, (iv) mathematical programming, and (v) interactive computer graphics. Their interactions reflect the typical loop of each design process (Fig. 1). The art of structural optimization is to join the interdisciplinary dependencies in a clear, integrated overall model and to convert it into an efficient and practical computer code . Today, all the leading software packages offer optimization modules, although of different quality and still mainly restricted to sizing.
A lot of special software and procedures have been developed and presented in the literature which deal with shape optimal design [3–6]. The related process is reviewed and accompanied by a number of excellent papers [7–9], proceedings [10–12], and books [13–15] which clearly show the evolution from the first beginnings with sizing of structures to the latest developments in shape optimal design. Fields of applications are steadily increasing. Especially in automotive  and aircraft industries  the methods found wide-spread recognition as instruments of numerical simulation to improve structural quality. Civil engineering is yet behind to use structural optimization as a regular tool. But also here the methods can be used as an extra design aid; e.g. for the shape design of free formed shells [17–20]. It is the intention of this contribution to give some insight into the basic ideas of the methods and the underlying modeling; the application to general shells is described in .
KeywordsStructural Optimization Design Sensitivity Analysis Design Node Shape Optimal Design Continuity Patch
Unable to display preview. Download preview PDF.
- 2.Bletzinger, K.-U.; Kimmich, S. and Ramm, E.: Efficient modeling in shape optimal design, to appear in Computing Systems in Engineering, 1992.Google Scholar
- 3.Eschenauer, H.; Post, U. and Bremicker, M.: Einsatz der Optimierungsprozedur SAPOP zur Auslegung von Bauteilkomponenten, Bauingenieur, 63 (1989), 515–526.Google Scholar
- 4.Kimmich, S. and Ramm, E.: Structural optimization and analysis with program system CARAT, in:  1989, 186–193.Google Scholar
- 10.Bennett, J. A. and Botkin, M. E. (eds.): The Optimum Shape - Automated Structural Design, Plenum Press, New York, London, 1986.Google Scholar
- 11.Mota Soares, C. A. (ed.): Computer Aided Optimal Design - Structural and Mechanical Systems, NATO-ASI Series F: Computer and System Sciences, vol. 27, Springer, Berlin, Heidelberg, 1987.Google Scholar
- 12.Eschenauer, H. A. and Thierauf, G. (eds.): Discretization Methods and Structural Optimization - Procedures and Applications, Proc. GAMM-Seminar, Oct. 5–7, 1988, Siegen, Lecture Notes in Engineering, Springer, 1989.Google Scholar
- 14.Atrek, E.; Gallagher, R. H.;Ragsdell, K. M. and Zienkiewicz, O. C. (eds.): New Directions in Optimum structural Design, Wiley, Chichester, New York, 1984.Google Scholar
- 17.Bletzinger, K.-U.: Formoptimierung von Flächentragwerken, Ph. D. Dissertation, Institut für Baustatik, Universität Stuttgart, 1990.Google Scholar
- 18.Kimmich, S.: Strukturoptimierung und Sensibilitätsanalyse mit finiten Elementen, Ph.D. Dissertation, Institut für Baustatik, Universität Stuttgart, 1990.Google Scholar
- 20.Bletzinger, K.-U. and Ramm, E. Form finding of shells by structural optimization, to appear in Engng. with Comp., 1992.Google Scholar
- 21.Ramm, E.: Shape finding methods of shells, lecture notes CISM course NonlinearAnalysis of Shells by Finite Elements, Udine, June 24–28, 1991.Google Scholar
- 24.Andelfinger, U: Untersuchungen zur Zuverlässigkeit hybrid -gemischterfiniter Elemente für Flächentragwerke, Ph.D.-Dissertation, Institut für Baustatik, Universität Stuttgart, 1991.Google Scholar
- 25.Büchter, N. and Ramm, E.: Shell theory versus degeneration - a comparison in large rotation finite element analysis, submitted to Int. J. Num. Meth. Engng., 1990.Google Scholar
- 34.Berke, L. and Khot, N. S.: Structural optimization using optimality criteria, in:  1987, 271–311.Google Scholar
- 37.Gallagher, R.H.: Fully stressed design, in: Optimum Structural Design - Theory and Applications (Eds. R. H. Gallagher and O. C. Zienkiewicz ), J. Wiley, London, New York, 1973.Google Scholar
- 40.Ramm, E. and Schunck, E.: Heinz Isler - Schalen, Krämer, Stuttgart, 1986.Google Scholar
- 42.Schwefel, H. P.: Numerical Optimization of Computer Models, J. Wiley & sons, Chichester, 1981.Google Scholar
- 45.Adelman, H. M. and Haftka, R. T.: Sensitivity Analysis of discrete structural systems, AIM-Journal, 24 (1988), 823–832.Google Scholar