It is critical for the material to be of active supporting capacity before initial collapse ot mare root wltn supermgn water material backfill mining, and the maximum bending moment should be first calculated in order...It is critical for the material to be of active supporting capacity before initial collapse ot mare root wltn supermgn water material backfill mining, and the maximum bending moment should be first calculated in order to determine the initial collapse span. In the light of principal of virtual work, the simple expression of deflection, bending moment of elastic clamped plate were deduced under the condition of vertical uniform distributed load, horizontal pressure and supporting by elastic foundation, and then, the maximal bending moment expression was derived too. At the same time, the influence degree on square clamped plate by adding horizontal pressure and elastic foundation were analyzed. The results show that the effect of horizontal pressure on maximal bending moment can be ignored when the value of horizontal pressure is two orders of magni- tude less than that of coeificient of elastic stiffness existing elastic foundation.展开更多
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
基金Supported by the National Natural Science Foundation of China （41071273） the Special Research Fund for the Doctoral Program of Higher Education of China （200090095110002）
文摘It is critical for the material to be of active supporting capacity before initial collapse ot mare root wltn supermgn water material backfill mining, and the maximum bending moment should be first calculated in order to determine the initial collapse span. In the light of principal of virtual work, the simple expression of deflection, bending moment of elastic clamped plate were deduced under the condition of vertical uniform distributed load, horizontal pressure and supporting by elastic foundation, and then, the maximal bending moment expression was derived too. At the same time, the influence degree on square clamped plate by adding horizontal pressure and elastic foundation were analyzed. The results show that the effect of horizontal pressure on maximal bending moment can be ignored when the value of horizontal pressure is two orders of magni- tude less than that of coeificient of elastic stiffness existing elastic foundation.
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.
