A two-dimensional nonlinear shell model "of Koiter’s type" has recently been proposed by the first author. It is shown here that, according to two mutually exclusive sets of assumptions bearing on the assoc...A two-dimensional nonlinear shell model "of Koiter’s type" has recently been proposed by the first author. It is shown here that, according to two mutually exclusive sets of assumptions bearing on the associated manifold of admissible inextensional displacements, the leading term of a formal asymptotic expansion of the solution of this two-dimensional model, with the thickness as the "small’ parameter, satisfies either the two-dimensional equations of a nonlinearly elastic "membrane" shell or those of a nonlinearly elastic "flexural" shell. These conclusions being identical to those recently drawn by B. Miara, then by V. Lods and B. Miara, for the leading term of a formal asymptotic expansion of the solution of the equations of three-dimensional nonlinear elasticity, again with the thickness as the "small" parameter, the nonlinear shell model of Koiter’s type considered here is thus justified, at least formally.展开更多
This paper gives all the two-dimensional membrane models obtained from formal asymptotic analysis of the three-dimensional geometrically exact nonlinear model of a thin elastic shell made with a Saint Venant-Kirchhoff...This paper gives all the two-dimensional membrane models obtained from formal asymptotic analysis of the three-dimensional geometrically exact nonlinear model of a thin elastic shell made with a Saint Venant-Kirchhoff material. Therefore, the other models can be quoted as flexural nonlinear ones. The author also gives the formal equations solved by the associated stress tensor and points out that only one of those models leads, by linearization, to the "classical" linear limiting membrane model, whose justification has already been established by a convergence theorem.展开更多
文摘A two-dimensional nonlinear shell model "of Koiter’s type" has recently been proposed by the first author. It is shown here that, according to two mutually exclusive sets of assumptions bearing on the associated manifold of admissible inextensional displacements, the leading term of a formal asymptotic expansion of the solution of this two-dimensional model, with the thickness as the "small’ parameter, satisfies either the two-dimensional equations of a nonlinearly elastic "membrane" shell or those of a nonlinearly elastic "flexural" shell. These conclusions being identical to those recently drawn by B. Miara, then by V. Lods and B. Miara, for the leading term of a formal asymptotic expansion of the solution of the equations of three-dimensional nonlinear elasticity, again with the thickness as the "small" parameter, the nonlinear shell model of Koiter’s type considered here is thus justified, at least formally.
文摘This paper gives all the two-dimensional membrane models obtained from formal asymptotic analysis of the three-dimensional geometrically exact nonlinear model of a thin elastic shell made with a Saint Venant-Kirchhoff material. Therefore, the other models can be quoted as flexural nonlinear ones. The author also gives the formal equations solved by the associated stress tensor and points out that only one of those models leads, by linearization, to the "classical" linear limiting membrane model, whose justification has already been established by a convergence theorem.
