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Structural parameter optimization of linear elastic systems
1. | 418 McBryde Hall, Department of Mathematics, Virginia Tech, Blacksburg, VA 24061-0123 |
References:
[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.
doi: 10.1007/s00028-006-0257-8. |
[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.
doi: 10.1137/1031131. |
[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.
doi: 10.1007/s002050050169. |
[13] |
J. B. Rosen, The gradient projection method for nonlinear programming; I. Linear constraints, J. Soc. Indust. Appl. Math., 8 (1960), 181-217.
doi: 10.1137/0108011. |
[14] |
J. B. Rosen, The gradient projection method for nonlinear programming. II. Nonlinear constraints, J. Soc. Indust. Appl. Math., 9 (1961), 514-532.
doi: 10.1137/0109044. |
[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.
doi: 10.1007/s10898-006-9116-y. |
[16] |
P. Villagio, "Qualitative Methods in Elasticity," Noordhoff Intl. Pub., Leyden, 1977 (reprinted by Kluwer).
doi: 10.1002/zamm.19790590921. |
[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.
doi: 10.1002/nme.1798. |
show all references
References:
[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.
doi: 10.1007/s00028-006-0257-8. |
[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.
doi: 10.1137/1031131. |
[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.
doi: 10.1007/s002050050169. |
[13] |
J. B. Rosen, The gradient projection method for nonlinear programming; I. Linear constraints, J. Soc. Indust. Appl. Math., 8 (1960), 181-217.
doi: 10.1137/0108011. |
[14] |
J. B. Rosen, The gradient projection method for nonlinear programming. II. Nonlinear constraints, J. Soc. Indust. Appl. Math., 9 (1961), 514-532.
doi: 10.1137/0109044. |
[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.
doi: 10.1007/s10898-006-9116-y. |
[16] |
P. Villagio, "Qualitative Methods in Elasticity," Noordhoff Intl. Pub., Leyden, 1977 (reprinted by Kluwer).
doi: 10.1002/zamm.19790590921. |
[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.
doi: 10.1002/nme.1798. |
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