卸荷裂隙岩体线弹性阶段的广义变分问题  

Generalized variational problem about unloading fractured rock mass on linear elastic stage

作　　者：余丽[1] 扶名福[1,2] 谢志龙[1] 

机构地区：[1]南昌大学建筑工程学院,江西南昌330031 [2]南昌工程学院,江西南昌330099

出　　处：《南昌大学学报（理科版）》2012年第2期184-186,191,共4页Journal of Nanchang University(Natural Science)

基　　金：教育部博士点基金资助项目(20050403002)

摘　　要：阐述了卸荷裂隙岩体线弹性阶段本构关系及弹性问题的基本方程,运用弹性问题基本方程中的控制方程和边界条件构造卸荷裂隙岩体线弹性阶段的变分问题。构造卸荷裂隙岩体线弹性阶段的变分问题事先构造了一个适当的最小位能泛函,在最小位能泛函中引入两个待定的拉氏乘子λij和λi,把变分约束条件吸收到泛函中去,从而建立卸荷裂隙岩体线弹性阶段的新泛函。然后将新泛函中的εij、ui、λij、λi作为独立变量,同时考虑新泛函的变分驻值条件识别待定拉氏乘子λij、λi,最后证明卸荷裂隙岩体线弹性阶段双变量的广义变分原理。First the constitutive equations about the unloading fractured rock mass on the linear elastic stage and the basic equations of elasticity problems were described, then using the basic equations of elasticity problems and the boundary conditions, the variational problem of the unloading fractured rock mass on the linear elastic stage was constructure. Before constructing the variational problem,the appropriate minimum potential energy functional should prior to construct. In the process of constructing the appropriate minimum potential energy functional the new functional in which the two Lagrange multipliers λij -λi were intro- duced and the variational constraints were absorbedas established. Then let λij. ui. λij, as the independent variables and considering the variational stationary value conditions of the new functional can identify the Lagrange multipliers λij .λi which to be determined. At last, the generalized variational principle of dual variables of the unloading crack rock mass on the linear elastic stage was simply proved.

关 键 词：卸荷裂隙岩体 拉氏乘子 广义变分原理 泛函 

分 类 号：TU458[建筑科学—岩土工程]