论对称与非对称的Biot固结有限元方程组的一致性

A STUDY OF THE CONFORMABILITY OF FINITE ELEMENT EQUATIONS FOR SYMMETRIC AND NON-SYMMETRIC BIOT'S CONSOLIDATION

论述了对称与非对称的Biot固结有限元方程组间的一致性,发现Biot固结有限元方程组系数矩阵是否对称是与平衡方程中与孔隙水压力有关的项是否进行分部积分有关。如果不对其进行分部积分,则得到非对称的系数矩阵;如果对其进行了分部积分,则得到对称的系数矩阵,此时两种情况下与之对应的结点力的意义也不相同。如果把结点力的意义处理成一种情况,则会发现这两种情况下的Biot固结有限元方程组是一致的。

The conformability of finite element equations for symmetric and non-symmetric Biot抯 consolidation is discussed in this paper. It is found that the symmetry of the coefficient matrix of finite element equations for Biot抯 consolidation is dependent on the integration by part to the pore pressure item in Biot抯 equilibrium equations. When integration by part is not performed to the pore pressure item in Biot抯 equilibrium equations, non-symmetrical coefficient matrix results. When integration by part is performed to the pore pressure item in Biot抯 equilibrium equations, symmetrical coefficient matrix is produced, and the corresponding nodal load has different meaning. If the nodal load is handled in the same way, conformability of the finite element equations for Biot抯 consolidation will be reached.