Ellipticity of koiter's and naghdi's models for nonhomogeneous anisotropic shells

Abstract

We show that the bilinear forms associated to the linear thin shell models of Koiter and Naghdi, for a nonhomogeneous and anisotropic material are elliptic. Essentially we use the fact that these bilinear forms are deduced from the three dimensional elasticity tensor, which is positive defined and also the techniques introduced by M. Bernadou, P.G. Ciarlet and B. Miara for homogeneous and isotropic shells (cf. [1], [2], [3], [4]). The ellipticity assures the existence and uniqueness of solution for these models. For Koiter's model, a similar problem was considered by D. Caillerie and E. Sanchez-Palencia [5]

Keywords:

• Shells
• elasticity
• anisotropy
• ellipticity

^∗Departamento de MatemAtica, Universidade de Coimbra, Apartado 3008, 3000 Coimbra, Portugal. [email protected] and [email protected]

^∗Departamento de MatemAtica, Universidade de Coimbra, Apartado 3008, 3000 Coimbra, Portugal. [email protected] and [email protected]

Notes

^∗Departamento de MatemAtica, Universidade de Coimbra, Apartado 3008, 3000 Coimbra, Portugal. [email protected] and [email protected]