References
- Galin LA. Contact problems, solid mechanics and its applications. Vol. 155. Dordrecht: Springer; 1953.
- Signorini A. Questioni di elasticita non-linearizzata e semi-linearizzata. Rendiconti Di Matematica E Delle Sue Applicazioni. 1959;18:95–39.
- Fichera G. Problemi elastostatici con vincoli unilaterali:il problema di signorini con ambigue condizioni al contorno. Mem Accad Naz Lincei Ser. 1964;VIII(7):91–140.
- Duvaut G, Lions J-L. Les inéquations en mécanique et en physique. Paris: Dunod; 1972.
- Caffarelli LA, Friedman A. The obstacle problem for the biharmonic operator. Ann Scuola Norm Sup Pisa, Ser IV. 1979;6(1):151–184.
- Caffarelli LA, Friedman A, Torelli A. The two-obstacle problem for the biharmonic operator. Pacific J Math. 1982;103(3):325–335. doi: https://doi.org/10.2140/pjm.1982.103.325
- Dal Maso G, Paderni G. Variational inequalities for the biharmonic operator with varying obstacles. Ann J Mat Pura Appl. 1988;153:203–227. doi: https://doi.org/10.1007/BF01762393
- Paumier JC. Le problème de Signorini dans la théorie des plaques minces de Kirchhoff-Love. C R Acad Sci Ser. 2002;335:167–170. doi: https://doi.org/10.1016/S1631-073X(02)02422-6
- Chacha DA, Bensayah A. Asymptotic modeling of a coulomb frictional signorini problem for the von Kármán plates. CR Mecanique. 2008;336:846–850. doi: https://doi.org/10.1016/j.crme.2008.10.001
- Léger A, Miara B. Mathematical justification of the obstacle problem in the case of a shallow shell. J Elasticity. 2008;90:241–257. doi: https://doi.org/10.1007/s10659-007-9141-1
- Bensayah A, Chacha DA, Ghezal A. Asymptotic modeling of Signorini problem with Coulomb friction for a linearly elastostatic shallow shell. Math Meth Appl Sci. 2015. DOI: https://doi.org/10.1002/mma.3578.
- Guan Y. Mathematical justication of an obstacle problem in the case of a plate. September 2017, p. 1047–1058. (Chinese Annals of Mathematics Series B; 38(5)).
- Rodríguez-Arós Á. Mathematical justification of the obstacle problem for elastic elliptic membrane shells. Applicable Anal. 2018. DOI: https://doi.org/10.1080/00036811.2017.1337894.
- Léger A, Miara B. A linearly elastic shell over an Obstacle: the flexural case. J Elasticity. 2017. DOI https://doi.org/10.1007/s10659-017-9643-4.
- Rodríguez-Arós Á. Models of elastic shells in contact with a rigid foundation: an asymptotic approach. J Elast. 2018;130:211–237. doi: https://doi.org/10.1007/s10659-017-9638-1
- Ciarlet PG, Lods V. Asymptotic analysis of linearly elastic shells. I. justification of membrane shell equations. Arch Rational Mech Anal. 1996;136:119–161. doi: https://doi.org/10.1007/BF02316975
- Ciarlet PG, Mardare C, Piersanti P. An obstacle problem for elliptic membrane shells. Math Mech Solids. 2019;24(5):1503–1529. doi: https://doi.org/10.1177/1081286518800164
- Ciarlet PG, Mardare C, Piersanti P. Un problème de confinement pour une coque membranaire linéairement élastique de type elliptique. CR Acad Sci Paris, Sér I. 2018;356(10):1040–1051. doi: https://doi.org/10.1016/j.crma.2018.08.002
- Ciarlet PG, Piersanti P. An obstacle problem for Koiter's shells. Math Mech Solids. 2019;24(10):3061–3079. doi: https://doi.org/10.1177/1081286519825979
- Piersanti P. A time-dependent obstacle problem in linearised elasticity. Nonlinear Anal. 2020;192: 111660. 17 pages. doi: https://doi.org/10.1016/j.na.2019.111660
- Ciarlet PG, Piersanti P. A confinement problem for a linearly elastic Koiter's shell. CR Acad Sci Paris, Sér I. 2019;357:221–230. doi: https://doi.org/10.1016/j.crma.2019.01.004
- Ciarlet PG. Mathematical elasticity volume III: theory of shells. Springer: Noth Holland; 2005. (Studies in Mathematics and its Applications; 29).
- Kikuchi N, Oden JT. Contact problems in elasticity: A study of variational inequalities and finite element methods. Philadelphia: SIAM; 1988.
- Fichera G. Boundary value problems of elasticity with unilateral constrains. Handbuch der physik, Band 6a/2. Berlin: Springer-Verlag; 1972.
- Lions JL, Magenes E. Problèmes aux limites non Homogènes et applications I. Paris: Dunod; 1968.
- Mezabia ME, Ghezal A, Chacha DA. Asymptotic analysis of frictional contact problem for piezoelectric shallow shell. Q J Mech Appl Math. 2019;84:473–499. doi: https://doi.org/10.1093/qjmam/hbz014