Abstract
Design optimization of multibody systems is usually established by a direct coupling of multibody system analysis and mathematical programming algorithms. However, a direct coupling is hindered by the transient and computationally complex behavior of many multibody systems. In structural optimization often approximation concepts are used instead to interface numerical analysis and optimization. This paper shows that such an approach is valuable for the optimization of multibody systems as well. A design optimization tool has been developed for multibody systems that generates a sequence of approximate optimization problems. The approach is illustrated by three examples: an impact absorber, a slider-crank mechanism, and a stress-constrained four-bar mechanism. Furthermore, the consequences for an accurate and efficient accompanying design sensitivity analysis are discussed.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Gabriele, G.A., 'Optimization in mechanisms', in Modern Kinematics: Developments in the Last Forty Years, A.G. Erdman (ed.), John Wiley & Sons, New York, 1993, Chapter 11, 471–519.
Sohoni, V.N. and Haug, E.J., 'A state space technique for optimal design of mechanisms', ASME Journal of Mechanical Design 104, 1982, 792–798.
Haug, E.J., Wehage, R.A. and Mani, N.K., 'Design sensitivity analysis of large-scale constrained dynamic mechanical systems', ASME Journal of Mechanisms, Transmissions, and Automation in Design 106, 1984, 156–162.
Ashrafiuon, H. and Mani, N.K., 'Analysis and optimal design of spatial mechanical systems', ASME Journal of Mechanical Design 112, 1990, 200–207.
Bestle, D., Analyse und Optimierung von Mehrkörpersystemen, Springer-Verlag, Berlin, 1994.
Schiehlen, W., 'Multibody system dynamics: roots and perspectives', Multibody System Dynamics 1, 1997, 149–188.
Haug, E.J., Choi, K.K. and Komkov, V., Design Sensitivity Analysis of Structural Systems, Academic Press, London, 1986.
Erdman, A.G., 'Computer-aided mechanism design: now and the future', ASME Special 50th Anniversary Design Issue 117(B), 1995, 93–100.
Barthelemy, J.-F.M. and Haftka, R.T., 'Approximation concepts for optimum structural design – A review', Structural Optimization 5, 1993, 129–144.
Haftka, R.T. and Gürdal, Z., Elements of Structural Optimization, Kluwer Academic Publishers, Dordrecht, 1992.
Hsieh, C.C. and Arora, J.S., 'Design sensitivity analysis and optimization of dynamic response', Computer Methods in Applied Mechanics and Engineering 43, 1984, 195–219.
Bestle, D., 'Zur Optimierung von Mehrkörpersystemen', Institutsbericht IB-14, Institut B für Mechanik, University of Stuttgart, 1989.
Grandhi, R.V., Haftka, R.T. and Watson, L.T., 'Design-oriented identification of critical times in transient response', AIAA Journal 24, 1986, 649–656.
Vanderplaats, G.N., 'Thirty years of modern structural optimization', Advances in Engineering Software 16, 1993, 81–88.
Etman, L.F.P., 'Optimization of multibody systems using approximation concepts', Ph.D. Thesis, Eindhoven University of Technology, 1997.
NAG FORTRAN Library Manual, Mark 15, Numerical Algorithms Group, Oxford, 1991.
Sepulveda, A.E. and Schmit, L.A., 'Approximation-based global optimization strategy for structural synthesis', AIAA Journal 31, 1993, 180–188.
Fleury, C. and Braibant, V., 'Structural optimization: A new dual method using mixed variables', International Journal for Numerical Methods in Engineering 23, 1986, 409–428.
Svanberg, K., 'The method of moving asymptotes – A new method for structural optimization', International Journal for Numerical Methods in Engineering 24, 1987, 359–373.
Svanberg, K., 'A globally convergent version of MMA without linesearch', in WCMSO-1 First World Congress of Structural and Multidisciplinary Optimization, N. Olhoff and G.I.N. Rozvany (eds), Pergamon, Oxford, 1996, 9–16.
Bestle, D. and Eberhard, P., 'Analyzing and optimizing multibody systems', Mechanics of Structures and Machines 20, 1992, 67–92.
Afimawala, K.A. and Mayne, R.W., 'Optimum design of an impact absorber', ASME Journal of Engineering for Industry 96, 1974, 124–130.
Paradis, M.J. and Willmert, K.D., 'Optimal mechanism design using the Gauss constrained method', ASME Journal of Mechanisms, Transmissions, and Automation in Design 105, 1983, 187–196.
{SAMCEF MECANO Manual, Version 5.1}, Samtech, Liège, 1994.
Etman, L.F.P., van Campen, D.H. and Schoofs. A.J.G., 'Optimization of multibody systems using approximation concepts', in IUTAM Symposium on Optimization of Mechanical Systems, D. Bestle and W. Schiehlen (eds), Kluwer Academic Publishers, Dordrecht, 1996, 81–88.
Etman, L.F.P., Thijssen, E.J.R.W., Schoofs, A.J.G. and van Campen, D.H., 'Optimization of multibody systems using sequential linear programming', in ASME Advances in Design Automation, Vol. DE 69-2, B.J. Gilmore, D.A. Hoeltzel, D. Dutta and H.A. Eschenauer (eds), American Society of Mechanical Engineers, New York, 1994, 525–530.
Bischof, C.H., 'On the automatic differentiation of computer programs and an application to multibody systems', in IUTAM Symposium on Optimization of Mechanical Systems, D. Bestle and W. Schiehlen (eds), Kluwer Academic Publishers, Dordrecht, 1996, 41–48.
Eberhard, P., Zur Mehrkriterienoptimierung von Mehrkörpersystemen, VDI Fortschritt-Berichte 11 (227), VDI Verlag, Düsseldorf, 1996.
Rights and permissions
About this article
Cite this article
Etman, L., van Campen, D. & Schoofs, A. Design Optimization of Multibody Systems by Sequential Approximation. Multibody System Dynamics 2, 393–415 (1998). https://doi.org/10.1023/A:1009780119839
Issue Date:
DOI: https://doi.org/10.1023/A:1009780119839