Abstract
We review our work on the development of efficient algorithms for sensitivity analysis of contact problems with application to the solution of multi-body contact shape optimization problems solved by the gradient methods. The methods presented exploit a special structure of quadratic programming problems arising in dual formulation of the state problem to efficient implementation of semi-analytic sensitivity analysis. The results of numerical experiments are reported that illustrate the efficiency of the algorithms presented.
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References
J. Haslinger and P. NeittaanmäkiFinite element approximation for optimal shape, material and topology designJohn Wiley and Sons, London, 1996.
A. R. Conn, N. I. M. Gould, and Ph. L. TointA globally convergent augmented Lagrangian algorithm for optimization with general constraints and simple boundsSIAM J. Numer. Anal.28 (1991), p. 545–572.
Z. DostálDuality based domain decomposition with proportioning for the solution of free boundary problemsJ. Comput. Appl. Math.63 (1995), pp. 203–208.
Z. DostálBox constrained quadratic programming with proportioning and projectionsSIAM J. Optim.7 (1997), pp. 871–887.
Z. Dostál, A. Friedlander, and S. A. SantosAugmented Lagrangians with adaptive precision control for quadratic programming with simple bounds and equality constraintsto appear in SIAM J. Optim.
Z. Dostál, A. Friedlander, and S. A. SantosSolution of coercive and semicoercive contact problems by FETI domain decompositionContemporary Math.218 (1998), pp. 82–93.
ODESSY System for Optimization, IME Aalborg Universityhttp://www.ime.auc.dk/afd3/odessy/manuals/index.htm
V. Vondrák, Z. Dostál, and J. RasmussenFETI domain decomposition algorithms for sensitivity analysis in contact shape optimizationProceedings of 11th International Conference Domain Decomposition in Science and Engineering, Choi-Hong Lai, P. E. Bjorstad, M. Cross, and 0. B.Widlund, eds., Domain Decomposition Press, Bergen, 1999, pp. 561–567.
Z. Dostál, F. A. M. Gomes, and S. A.Santos, Solution of contact problems by FETI domain decomposition with natural coarse-space projectionsto appear in Comput. Methods Appl. Mech. Engrg.
E. A. Fancello and R. FeijóoShape optimization in frictionless contact problemsInternat. J. Numer. Methods Engrg.37 (1997), pp. 2311–2335.
C. Farhat and M. GérardinOn the general solution by a direct method of a large scale singular system of linear equations: application to the analysis of floating structuresInternat. J. Numer. Methods Engrg.41 (1997), pp. 675–696.
C. Farhat, J. Mandel, and F.-X. RouxOptimal convergence properties of the FETI domain decomposition methodComput. Methods Appl. Mech. Engrg.115 (1994), pp. 365–385.
U. KirschEfficient sensitivity analysis for structural optimizationComput. Methods Appl. Mech. Engrg.117 (1994), pp. 143–156.
V. Vondrák, Ph.D. Thesis, VSB-Technical University Ostrava, in preparation.
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Dostál, Z., Vondrák, V., Rasmussen, J. (2001). Efficient Algorithms for Contact Shape Optimization. In: Hoffmann, KH., Hoppe, R.H.W., Schulz, V. (eds) Fast Solution of Discretized Optimization Problems. ISNM International Series of Numerical Mathematics, vol 138. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8233-0_8
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DOI: https://doi.org/10.1007/978-3-0348-8233-0_8
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