The formal asymptotic analysis of D. Fox, A. Raoult & J.C. Simo[10] has justified the twodimensional nonlinear "membrane" equations for a plate made of a Saint Venant-Kirchhoff material.This model, which...The formal asymptotic analysis of D. Fox, A. Raoult & J.C. Simo[10] has justified the twodimensional nonlinear "membrane" equations for a plate made of a Saint Venant-Kirchhoff material.This model, which retains the material-frame indifference of the original three dimensional problem in the sense that its energy density is invariant under the rotations of R3, is equivalent to finding the critical points of a functional whose nonlinear part depends on the first fundamental form of the unknown deformed surface.The author establishes here, by the inverse function theorem, the existence of an injective solution to the clamped membrane problem around particular forces corresponding physically to an "extension" of the membrane. Furthermore, it is proved that the solution found in this fashion is also the unique minimizer to the nonlinear membrane functional, which is not sequentially weakly lower semi-continuous.展开更多
文摘The formal asymptotic analysis of D. Fox, A. Raoult & J.C. Simo[10] has justified the twodimensional nonlinear "membrane" equations for a plate made of a Saint Venant-Kirchhoff material.This model, which retains the material-frame indifference of the original three dimensional problem in the sense that its energy density is invariant under the rotations of R3, is equivalent to finding the critical points of a functional whose nonlinear part depends on the first fundamental form of the unknown deformed surface.The author establishes here, by the inverse function theorem, the existence of an injective solution to the clamped membrane problem around particular forces corresponding physically to an "extension" of the membrane. Furthermore, it is proved that the solution found in this fashion is also the unique minimizer to the nonlinear membrane functional, which is not sequentially weakly lower semi-continuous.
