Diseño óptimo y homogeneización
DOI:
https://doi.org/10.4067/S0716-09172000000300004Keywords:
Homogenization, homogenización, optimal design, difusion, lineal elasticity, diseño óptimo, difusión, elasticidad lineal.Abstract
Este artículo pretende dar una mayor difusión al uso de la teoría general de homogenización, desarrollada por F. Murat, L. Tartar y otros autores, en conexión con el diseño óptimo de materiales compuestos. El poder y la relativa simplicidad de la teoría son enfatizados mostrando varios resultados conocidos para los problemas de difusión y de elasticidad lineal.References
1. J. M. Ball: Constitutive Inequalities and Existence Theorems in Nonlinear Elastostatics. Nonlinear Analysis and Mechanics: Heriot-Watt Symposium, Vol. I. ed. R. J. Knops, Pitman Res. Notes Math. 17,187-241 (1977).
2. J. M. Ball: A Version of the Fundamental Theorem for Young Measures. PDEs and Continuum Models of Phase Transitions. Lecture Notes in Physics vol. 344, eds. M. Rascle et al. SpringerVerlag (1989).
3. G. Dal Maso: An Introduction to ?-Convergence. Progress in Nonlinear Differential Equations and their Applications, vol. 8, Birkhäuser, Boston (1993).
4. G. Francfort y G. Milton: Sets of Conductivity and Elasticity Tensors Stable under Lamination. Comm. Pure Appl. Math. XLVII, 257-279 (1994).
5. G. Francfort y F. Murat: Homogenization and Optimal Bounds in Linear Elasticity. Arch. Rat. Mech. Anal. 94, 307-334 (1986).
6. G. Geymonat, S. Müller y N. Triantafyllidis: Homogenization of Nonlinearly Elastic Materials, Mic roscopic Bifurcation and Macroscopic Loss of Rank-One Convexity. Arch. Rational Mech. Anal. 122, 231-290 (1993).
7. M. Gurtin: The Linear Theory of Elasticity. Handbuch der Physik Vol. VIa/2. Springer-Verlag (1972).
8. S. Gutiérrez: Laminations in Linearized Elasticity: The Isotropic Non-very Strongly Elliptic Case. J. Elasticity 53, 215-256 (1998).
9. Z. Hashin y S. Shtrikman: A variational approach to the theory of effective magnetic permeability of multiphase materials. J. Applied Physics 33, 3125-3131 (1962).
10. H. Le Dret: An Example of H1-unboundedness of Solutions to Strongly Elliptic Systems of Partial Differential Equations in a Laminated Geometry. Proc. Roy. Soc. Edinburgh 105A, 77-82 (1987).
11. F. Murat: H-convergence. Séminaire d’Analyse Fonctionnelle et Numérique de l’Université d’Alger (1977).
12. F. Murat y L. Tartar: Calculus of Variations and Homogenization. Collection d’Etudes de Electricité de France (1983).
13. P. Pedregal: Parametrized Measures and Variational Principles. Progress in Nonlinear Differential Equations and their Applications, vol. 30, Birkhäuser, Basel (1997).
14. S. Spagnolo: Sulla convergenza di soluzioni di equazioni paraboliche ed ellitiche. Ann. Sc. Norm. Sup. di Pisa Cl. di Scienze 22, 577-597 (1968).
15. L. Tartar: Cours Peccot, College de France (1977).
16. L. Tartar: Compensated Compactness and applications to Partial Differential Equations. Nonlinear Analysis and Mechanics: Heriot Watt Symposium, vol. IV, ed. R.J. Knops. Research Notes in Mathematics 39, Pitman 136-212 (1979).
17. L. Tartar: Homogenization, Compensated Compactness and HMeasures. CBMS-NSF Conference, Santa Cruz, June 1993. Notas en preparación.
2. J. M. Ball: A Version of the Fundamental Theorem for Young Measures. PDEs and Continuum Models of Phase Transitions. Lecture Notes in Physics vol. 344, eds. M. Rascle et al. SpringerVerlag (1989).
3. G. Dal Maso: An Introduction to ?-Convergence. Progress in Nonlinear Differential Equations and their Applications, vol. 8, Birkhäuser, Boston (1993).
4. G. Francfort y G. Milton: Sets of Conductivity and Elasticity Tensors Stable under Lamination. Comm. Pure Appl. Math. XLVII, 257-279 (1994).
5. G. Francfort y F. Murat: Homogenization and Optimal Bounds in Linear Elasticity. Arch. Rat. Mech. Anal. 94, 307-334 (1986).
6. G. Geymonat, S. Müller y N. Triantafyllidis: Homogenization of Nonlinearly Elastic Materials, Mic roscopic Bifurcation and Macroscopic Loss of Rank-One Convexity. Arch. Rational Mech. Anal. 122, 231-290 (1993).
7. M. Gurtin: The Linear Theory of Elasticity. Handbuch der Physik Vol. VIa/2. Springer-Verlag (1972).
8. S. Gutiérrez: Laminations in Linearized Elasticity: The Isotropic Non-very Strongly Elliptic Case. J. Elasticity 53, 215-256 (1998).
9. Z. Hashin y S. Shtrikman: A variational approach to the theory of effective magnetic permeability of multiphase materials. J. Applied Physics 33, 3125-3131 (1962).
10. H. Le Dret: An Example of H1-unboundedness of Solutions to Strongly Elliptic Systems of Partial Differential Equations in a Laminated Geometry. Proc. Roy. Soc. Edinburgh 105A, 77-82 (1987).
11. F. Murat: H-convergence. Séminaire d’Analyse Fonctionnelle et Numérique de l’Université d’Alger (1977).
12. F. Murat y L. Tartar: Calculus of Variations and Homogenization. Collection d’Etudes de Electricité de France (1983).
13. P. Pedregal: Parametrized Measures and Variational Principles. Progress in Nonlinear Differential Equations and their Applications, vol. 30, Birkhäuser, Basel (1997).
14. S. Spagnolo: Sulla convergenza di soluzioni di equazioni paraboliche ed ellitiche. Ann. Sc. Norm. Sup. di Pisa Cl. di Scienze 22, 577-597 (1968).
15. L. Tartar: Cours Peccot, College de France (1977).
16. L. Tartar: Compensated Compactness and applications to Partial Differential Equations. Nonlinear Analysis and Mechanics: Heriot Watt Symposium, vol. IV, ed. R.J. Knops. Research Notes in Mathematics 39, Pitman 136-212 (1979).
17. L. Tartar: Homogenization, Compensated Compactness and HMeasures. CBMS-NSF Conference, Santa Cruz, June 1993. Notas en preparación.
Published
2017-06-14
How to Cite
[1]
S. Gutiérrez, “Diseño óptimo y homogeneización”, Proyecciones (Antofagasta, On line), vol. 19, no. 3, pp. 271-289, Jun. 2017.
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