Structural parameter optimization of linear elastic systems
Pages: 1517 - 1536, Volume 10, Issue 5, September 2011

doi:10.3934/cpaa.2011.10.1517      Abstract        References        Full text (548.9K)           Related Articles

David Russell - 418 McBryde Hall, Department of Mathematics, Virginia Tech, Blacksburg, VA 24061-0123, United States (email)

1	G. Allaire, "Shape Optimization by the Homogenization Method," Applied Mathematical Sciences, 146, Springer-Verlag, New York, 2002.
2	P. G. Ciarlet, "Mathematical Elasticity; Volume I: Three-Dimensional Elasticity," Studies in Mathematics and Its Applications, 20, Elsevier Inc., 1997.
3	M. C. Delfour and J.-P. Zolésio, Evolution equations for shapes and geometries, J. Evol. Equ., 6 (2006), 399-417.
4	M. C. Delfour and J.-P. Zolésio, Shape identification via metrics constructed from the oriented distance function, Control Cybernet, 34 (2005), 137-164.
5	M. C. Delfour and J.-P. Zolésio, "Shapes and Geometries; Analysis, Differential Calculus, and Optimization," Advances in Design and Control, 4, SIAM Publications, Philadelphia, PA, 2001.
6	N. Dunford and J. T. Schwartz, "Linear Operators, II Spectral Theory; Self Adjoint Operators in Hilbert Space," Interscience Pub., New York, 1963.
7	R. T. Haftka, Z. Gürdal and M. P. Kamat, "Elements of Structural Optimization," Kluwer Academic Publishers, Dordrecht, Boston, London, 1990.
8	J.-Y. Jaffray and J.-Ch. Pomerol, A direct proof of the Kuhn-Tucker necessary optimality theorem for convex and affine inequalities, SIAM Rev., 31 (1989), 671-674.
9	C. T. Kelley, "Iterative Methods for Optimization," SIAM Frontiers in Applied Mathematics, 18, 1999.
10	J.-L. Lions and E. Magenes, "Probl\`emes aux limites nonhomog\`enes," [Nonhomogeneous Boundary Value Problems], I, II, Dunod, Paris, 1968 (French).
11	J. E. Marsden and T. J. R. Hughes, "Mathematical Foundations of Elasticity," Dover Publications, Inc., New York, 1994.
12	M. Renardy and D. L. Russell, Formability of linear elastic structures with volume - type actuation, Arch. Rat. Mech. & Anal., 149 (1999), 97-122.
13	J. B. Rosen, The gradient projection method for nonlinear programming; I. Linear constraints, J. Soc. Indust. Appl. Math., 8 (1960), 181-217.
14	J. B. Rosen, The gradient projection method for nonlinear programming. II. Nonlinear constraints, J. Soc. Indust. Appl. Math., 9 (1961), 514-532.
15	D. L. Russell, The Betti reciprocity principle and the normal boundary component control problem for linear elastic systems, J. Global Optim., 40 (2008), 575-588.
16	P. Villagio, "Qualitative Methods in Elasticity," Noordhoff Intl. Pub., Leyden, 1977 (reprinted by Kluwer).
17	S. Wang, E. de Sturler and G. H. Paulino, Large-scale topology optimization using preconditioned Krylov 3 subspace methods with recycling, Internat. J. Numer. Methods Engrg., 69 (2007), 2441-2468.

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