微极饱和土波动分析中的变分原理

主要给出饱和多孔微极介质波动方程变分所对应的泛函表达式和有限元离散化方程。首先对u-U形式的饱和多孔微极介质波动方程和边界条件进行Laplace 变换,形成力学中的非齐次边值问题,然后构造变分后满足波动方程和边界条件的泛函,最后将有限元插值形式代入泛函表达式得到单元体的有限元离散方程。此方程对微极饱和多孔介质的动力固结问题数值分析具有重要意义。

VARIATIONAL PRINCIPLE FOR WAVE ANALYSIS OF SATURATED MICRO-POLAR SOIL

Functional representations corresponding to the variational principle for the elastic pragmatic wave equations of saturated porous micro-polar medium and their discretized equations obtained by the finite element method are presented here.Firstly,the dynamic consolidation equations of saturated micro-polar soil given by u-U format and the relevant boundary conditions are transformed by Laplace transformation,so the non-homogeneous boundary problems in mechanics are engendered.Next,the function which satisfy the wave equations and boundary conditions after variation are composed through mathematic theory.In the end,the interpolation forms of the finite element method are inserted into the functional representations and the discretized equations of an element are obtained.It is significant for the numerical analysis on dynamic consolidation problems of saturated porous micro-polar medium.