Abstract
This Section concentrates on two major objectives that are currently pursued at the research level, and that should soon be ready for implementation in practical Computer Aided Engineering systems. The first objective is to develop a general approach to shape optimal design of elastic structures discretized by the Finite Element Method (FEM). The key idea is to employ geometric modeling concepts typical of the Computer Aided Design (CAD) technology, in order to produce sensitivity analysis results. These sensitivity data can then be used by an optimizer to generate an improved design.
The second goal is to implement an interactive redesign system that integrates optimization methods within a flexible and efficient computational tool, easy to use by design engineers. This interactive module is intended to create the missing link between FEM and CAD technologies and therefore it should constitute one of the key elements in the complex chain needed to computerize the design cycle.
The approach followed can be summarized as follows. First the behavior of the structure is analyzed by using the finite element method. Subsequently a sensitivity analysis is performed to evaluate the first derivatives of the structural response quantities. These derivatives are used by an efficient optimizer, which selects an improved design. A reanalysis of the modified design is next performed after updating the finite element mesh. This iterative process is repeated until convergence to an acceptable optimum design has been achieved, which usually requires less than 10 FEM analyses.
The long term objective is to create a coherent interactive system that makes the best possible use of the respective capabilities of the engineer and the computer.
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References
L.A. Schmit and H. Miura, “A New Structural Analysis/Synthesis Capability — ACCESS 1”, AIAA Journal, Vol. 14, No. 1, pp. 661–671, 1976.
L.A. Schmit, “Structural Optimization — Some Key Ideas and Insights”, Chapter 1 of New Directions in Optimum Structural Design (E. Atrek et al. eds.), John Wiley & Sons, New York, 1984.
C. Fleury and L.A. Schmit, “Dual Methods and Approximation Concepts in Structural Synthesis”, NASA Contractor Report, NASA-CR-3226, 1980, 196 pages.
A.J. Morris (ed.), Foundations of Structural Optimization: A Unified Approach, John Wiley and Sons, New York, 1982.
O.C. Zienkiewicz and J.S. Campbell, “Shape optimalization and Sequential Linear Programming”, in Optimum Structural Design (Ed. R.H. Gallagher and O.C. Zienkiewicz ), Wiley, New York, 1973, pp. 109–126.
M.E. Botkin, “Shape Optimization of Plate and Shell Structures”, AIAA Journal, Vol. 20, No. 2, pp. 268–273, 1982.
V. Braibant and C. Fleury, “Shape Optimal Design using B-Splines”, Computer Methods in Applied Mechanics and Engineering, Vol. 44, pp. 247–267, 1984.
V. Braibant and C. Fleury, “Shape Optimal Design — A Performing C.A.D. Oriented Formulation”, Proc. AIAA/ASME/ASCE/AHS 25th Structures, Structural Dynamics and Materials Conference, Palm Springs, CA., 1984.
C. Fleury and D. Liefooghe, “Shape Optimal Design on an Engineering Workstation”, Paper presented at the MSC/NASTRAN Users Conference, Universal City, California, March 20–21, 1986.
D. Liefooghe, “An Interactive Graphics Capability for Shape Optimal Design”, Master Thesis, UCLA, 1986.
Muskhelishvili, N.I., “Some basic Problems of the Mathematical Theory of Elasticity”, Noordhoff, Groningen -Holland, pp. 320–372, 1953.
A.J Morris (ed.). Foundations of Structural Optimization: a Unified Approach, John Wiley and Sons, 1982.
C. Fleury and L.A. Schmit, “Dual Methods and Approximation Concepts in Structural Synthesis”, NASA Contractor Report, NASA-CR 3226, 1980.
V. Braibant and C. Fleury, “An Approximation Concepts Approach to Shape Optimal Design”, Computer Methods in Applied Mechanics and Engineering, Vol. 53, pp. 119–148, 1985.
V. Braibant and C. Fleury, “Aspect théoriques de l’optimisation de forme par variation de noeuds de controle”, Conception Optimale de Forme, INRIA, Rocquencourt (France), pp. 303–395, 1983.
C. Fleury, “Structural Weight Optimization by Dual Methods of Convex Programming”, International Journal for Numerical Methods in Engineering, Vol. 14, No. 12, pp. 1761–1783, 1979.
C. Fleury, “Reconciliation of Mathematical Programming and Optimality Criteria Approaches to Structural Optimization”, chapter 10 of Foundations of Structural Optimization: a Unified Approach (A.J. Morris, ed. ), John Wiley and Sons, 1982, pp. 363–404.
L. Berke and N.S. Khot, “Use of Optimality Criteria Methods for large Scale Systems”, AGARD Lecture Series LS-70, pp. 1–29, 1974.
C. Fleury, “A Unified Approach to Structural Weight Minimization”, Computer Methods in Applied Mechanics and Engineering, Vol. 20, No. 1, pp. 17–38, 1979.
C. Fleury and V. Braibant, “Prise en compte de contraintes lineaires dans les methodes duales d’optimisation structurale”, Rapport LTAS SF-107, University of Liege, 1982.
C. Fleury and V. Braibant, “Structural Optimization — A New Dual Method Using Mixed Variables”, International Journal for Numerical Methods in Engineering, Vol. 23, pp. 409–429, 1986.
J.H. Starnes and R.T. Haftka, “Preliminary Design of Composite Wings for Buckling, Stress and Displacement Constraints”, Journal of Aircraft, Vol. 16, pp. 564–570, 1979.
K. Svanberg, “Method of moving Asymptotes — A new Method for Structural Optimization”, International Journal for Numerical Methods in Engineering, to appear, 1987.
R. Schnabel, “Determining Feasibility of a Set of nonlinear Inequality Constraints”, Mathematical Programming Study, Vol. 16, No. 192, pp. 137–148, 1982.
SAMCEF, Systeme d’Analyse des Milieux Continus par Elements Finis, University of Liege, Belgium.
MSC/NASTRAN User’s and Application Manuals, The MacNeal-Schwendler Corporation, 1984.
G.K. Nagendra and C. Fleury, “Sensitivity and Optimization of Composite Structures Using MSC/NASTRAN,” paper presented at the NASA/VPI Symposium on “Sensitivity Analysis in Engineering,” NASA Langley Research Center, Hampton, VA, 1986.
V. Braibant, “Optimisation de forme des structures en vue de la conception assistée par ordinateur,” Doctoral Dissertation, University of Liege (Belgium), 1985.
S.P. Kuritz, “Configuration Optimization of Trusses using Convex Linearization Techniques,” Master Thesis, UCLA, 1986.
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Fleury, C. (1987). Computer Aided Optimal Design of Elastic Structures. In: Mota Soares, C.A. (eds) Computer Aided Optimal Design: Structural and Mechanical Systems. NATO ASI Series, vol 27. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-83051-8_25
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DOI: https://doi.org/10.1007/978-3-642-83051-8_25
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