References
- Tartar L. The general theory of homogenization. Heidelberg: Springer; 2009.
- Allaire G, Kelly A. Optimal design of low-contrast two phase structures for the wave equation. Math Models Methods Appl Sci. 2011;21(7):1499–1538. doi: 10.1142/S0218202511005477
- Gutiérrez S, Mura J. Small amplitude homogenization applied to inverse problems. Comput Mech. 2008;41:699–706. doi: 10.1007/s00466-007-0225-3
- Allaire G, Gutiérrez S. Optimal design in small amplitude homogenization. ESAIM Math Model Numer Anal. 2007;41(3):543–574. doi: 10.1051/m2an:2007026
- Tartar L. H-measures and small amplitude homogenisation. In: Kohn R, Milton G, editors. Random media and composites. Philadelphia: SIAM; 1989. p. 89–99.
- Antonić N, Vrdoljak M. Parabolic H-convergence and small-amplitude homogenization. Appl Anal. 2009;88:1493–1508. doi: 10.1080/00036810903042158
- Tartar L. H-measures, a new approach for studying homogenisation, oscillations and concentration effects in partial differential equations. Proc Roy Soc Edinburgh. 1990;115A:193–230. doi: 10.1017/S0308210500020606
- Tartar L. Mathematical tools for studying oscillations and concentrations: from Young measures to H-measures and their variants. In: Antonić N, et al., editors. Multiscale problems in science and technology. Berlin: Springer; 2002. p. 1–84.
- Antonić N, Lazar M. Parabolic H-measures. J Funct Anal. 2013;265(7):1190–1239. doi: 10.1016/j.jfa.2013.06.006
- Antonić N, Vrdoljak M. Small-amplitude homogenisation of diffusion equation. Int J Pure Appl Math. 2009;50:233–238.
- Kohn RV, Vogelius M. A new model for thin plates with rapidly varying thickness. Int J Solids Struct. 1984;20(4):333–350. doi: 10.1016/0020-7683(84)90044-1
- Lurie KA, Cherkaev AV. G-closure of some particular sets of admissible material characteristics for the problem of bending of thin elastic plates. J Optim Theory Appl. 1984;42(2):305–316. doi: 10.1007/BF00934301
- Lurie KA, Cherkaev AV, Fedorov AV. Regularization of optimal design problems for bars and plates, I and II. J Optim Theory Appl. 1982;37(4):499–543. doi: 10.1007/BF00934953
- Muñoz J, Pedregal P. On the relaxation of an optimal design problem for plates. Asymptotic Anal. 1998;16:125–140.
- Damlamian A, Vogelius M. Homogenization limits of the equations of elasticity in thin domains. SIAM J Math Anal. 1987;18:435–451. doi: 10.1137/0518034
- Bukal M, Velčić I. On the simultaneous homogenization and dimension reduction in elasticity and locality of Γ-closure. Calc Var Partial Differ Equ. 2017;56:59. doi: 10.1007/s00526-017-1167-z
- Ciarlet PG. Mathematical elasticity, volume II: theory of plates. Amsterdam: Elsevier Science; 1997.
- Antonić N, Balenović N. Homogenisation and optimal design for plates. Z Angew Math Mech. 2000;80:757–758.
- Antonić N, Balenović N. Optimal design for plates and relaxation. Math Commun. 1999;4:111–119.
- Burazin K, Jankov J, Vrdoljak M. Homogenization of elastic plate equation. Math Model Anal. 2018;23(2):190–204. doi: 10.3846/mma.2018.012
- Zhikov VV, Kozlov SM, Oleinik OA, et al. Averaging and G-convergence of differential operators. Russian Math Surveys. 1979;34(5):69–147. doi: 10.1070/RM1979v034n05ABEH003898
- Bensoussan A, Lions JL, Papanicolaou G. Asymptotic analysis for periodic structures. Amsterdam: North-Holland; 1978.
- Allaire G. Shape optimization by the homogenization method. New York: Springer; 2001.