@article{ff25a8f84134499fa28284964b66d66c, title = "On the generalized von Karman equations and their approximation", abstract = "We consider here the {"}generalized von K{\'a}rm{\'a}n equations{"}, which constitute a mathematical model for a nonlinearly elastic plate subjected to boundary conditions {"}of von K{\'a}rm{\'a}n type{"} only on a portion of its lateral face, the remaining portion being free. As already shown elsewhere, solving these equations amounts to solving a {"}cubic{"} operator equation, which generalizes an equation introduced by Berger and Fife. Two noticeable features of this equation, which are not encountered in the {"}classical{"} von K{\'a}rm{\'a}n equations are the lack of strict positivity of its cubic part and the lack of an associated functional. We establish here the convergence of a conforming finite element approximation to these equations. The proof relies in particular on a compactness method due to J. L. Lions and on Brouwer's fixed point theorem. This convergence proof provides in addition an existence proof for the original problem. {\textcopyright} World Scientific Publishing Company.", keywords = "Brouwer's theorem, Finite element method, Nonlinear plate theory", author = "Ciarlet, {Philippe G.} and Liliana Gratie and Srinivasan Kesavan", year = "2007", month = apr, doi = "10.1142/S0218202507002042", language = "English", volume = "17", pages = "617--633", journal = "Mathematical Models and Methods in Applied Sciences", issn = "0218-2025", publisher = "WORLD SCIENTIFIC PUBL CO PTE LTD", number = "4", }