复合单元法动力分析初步研究

Preliminary study of composite element method for dynamic analysis

复合单元法是一种适用于不连续介质结构分析的数值计算方法,优点是建立网格时不用考虑结构中不连续面,计算时能离散模拟不连续面。在复合单元法静力计算模型的基础上,提出了复合单元的动力分析方法。给出了复合单元动力分析的质量矩阵和阻尼矩阵的具体表达式,通过质量矩阵、刚度矩阵和阻尼矩阵将分布于复合单元内部的惯性力和阻尼力分别转移到复合单元的广义节点上。建立了惯性力、阻尼力、动力荷载及弹性力作用下的复合单元动力系统的控制方程组。以一个基岩内含有两条断层的混凝土重力坝模型地震为例,采用复合单元法动力分析程序进行计算,其结果与有限单元法解吻合得较好,说明所提出方法的正确性和有效性。

Composite element method（CEM） is a numerical method suitable for discontinuous media structure.The main advantages of CEM are that the discontinuities can be ignored when creating grid,but the discontinuities can be explicitly simulated when calculating.Based on composite element model for static analysis,the composite element model for dynamic analysis is implemented.The formulas of mass matrix and damping matrix for dynamic analysis of CEM are presented.According to mass matrix,stiffness matrix and damping matrix,the inertial forces and the damping forces in composite element are converted to the generalized nodes.The control equations for dynamic system of CEM subjected to the inertia forces,the damping forces,the dynamic loads and the elastic forces are formulated.A seismic example of a concrete gravity dam on a rock base with two faults is computed by the CEM dynamic analysis program.The results meet well with the solution of finite element method（FEM）.It shows the validity and effectiveness of the new method.