A justification of the Marguerre-von K�rm�n equations

Justification of the two‐dimensional equations of a linearly elastic shallow shell

“…Theorem 1). This is an improvement over the nonlinear case, where, as of now, the justification is only formal: Ciarlet and Paumier have shown in 1986 (see [ 191) that the leading term of a formal expansion of the three-dimensional solution is indeed the solution of two-dimensional nonlinear shallow shell equations, but no proof of convergence is as yet available. The situation is analogous for nonlinearly elastic plates (cf.…”

A new class of variational problems arising in the modeling of elastic multi-structures

“…That such "asymptotic assumptions on the data as e-~O" are unavoidable in order that a limit problem exist, has already been observed by Caillerie [1980] and Ciarlet [1980] in the case of a "single" plate. The reader is referred to Ciarlet [1980Ciarlet [ , 1990Ciarlet [ , 1991 for more detailed discussions on the meaning of such asymptotic orders.…”

“…The reader is referred to Ciarlet [1980Ciarlet [ , 1990Ciarlet [ , 1991 for more detailed discussions on the meaning of such asymptotic orders.…”

Mathematical justification of a one-dimensional model for general elastic shallow arches

“…In fact, in Figueiredo and Trabucho [35] the same change of variable is used to study a Galerkin approximation of the solution of the tridimensional linearized elasticity problem posed in a curved rod, in Ciarlet and Paumier [26] the same technique is applied to the formal asymptotic obtention of the Marguere-von Ka´rma´n equations of a shallow shell from the three-dimensional non-linear elasticity problem posed in the tridimensional shell, and in Ciarlet and Miara [25] this method leads to the mathematical justification of the two-dimensional equations of a linear elastic shallow shell.…”