改进的比例边界有限元法求解层状地基动力刚度矩阵

Modified Scaled Boundary Finite Element Method Solution for Dynamic Stiffness Matrix of Laminar Foundation

在传统比例边界有限元法基础上,提出了一种新的坐标变换关系来求解层状地基动力刚度矩阵即改进的比例有限元法。以一条相似轴代替传统比例边界有限元法的相似中心,并利用加权余量法推导得到层状地基位移及动力刚度矩阵方程,不仅在水平向保持了解析特性、满足了水平无穷远处的辐射边界条件,且克服了传统比例边界有限元法在求解侧边平行的层状问题时的不适应性。通过求解3个典型层状地基的动力刚度矩阵,验证了改进方法的求解效率及其对多层地基的广泛适应性。

A new scaled boundary transformation is proposed to solve the dynamic stiffness matrix of laminar founda- tion based on the traditional scaled boundary finite element method （SBFEM）. A scaling line is used to instead of the scal- ing center in traditional SBFEM. Then the scaled boundary finite element equations in displacement and stiffness are ob- tained based on the weighted residual method. Analytic solution in the horizontal direction is available and the radiant con- dition at horizontal infinity is satisfied accurately. Parallel layers in unbounded foundation can be modeled exactly in this way. In three numerical examples, the dynamic stiffness matrix of laminar foundation is solved, which demonstrates the adaptability and efficiency of the proposed method for multilayer foundations.