@article{220ee20239d54e73b6e681eacfb024b9, title = "An existence theorem for a two-dimensional nonlinear shell model of Koiter's type", abstract = "We propose a minimization problem with a stored energy function that is polyconvex and satisfies all the other assumptions of John Ball's theorem, while being at the same time well adapted for modeling a nonlinearly elastic shell. By restricting the admissible deformations to be specific quadratic polynomials with respect to the transverse variable, we are able to define a new nonlinear shell model for which a satisfactory existence theory is available and that is still two-dimensional, in the sense that minimizing the corresponding total energy amounts to finding three vector fields defined on the closure of a bounded open subset of R2.The most noteworthy feature of our nonlinear shell model is that the {"}lowest order part{"} of its stored energy function coincides, at least formally, with the stored energy function found in Koiter's model for a specific class of deformations that are to within the first-order identical to the Kirchhoff-Love deformations considered by W. T. Koiter.", keywords = "Nonlinear elasticity, John Ball's theorem, nonlinearly elastic shells, Koiter's equations, existence theory", author = "Ciarlet, {Philippe G.} and Cristinel Mardare", year = "2018", month = dec, day = "30", doi = "10.1142/S0218202518500628", language = "English", volume = "28", pages = "2833--2861", journal = "Mathematical Models and Methods in Applied Sciences", issn = "0218-2025", publisher = "WORLD SCIENTIFIC PUBL CO PTE LTD", number = "14", }