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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。
Based on the traditional proportional boundary finite element method, a new coordinate transformation relationship is proposed to solve the dynamic stiffness matrix of layered soils, that is, the modified proportional finite element method. A similar axis is substituted for a similar center of the traditional proportional boundary finite element method, and the layered ground displacement and dynamic stiffness matrix equation are deduced by the weighted residual method. The analytic properties are not only kept in the horizontal direction but also satisfied the radiation at the horizontal infinity Boundary conditions, and overcomes the incompatibility of traditional proportional boundary finite element method in solving the layered side-parallel problem. By solving the dynamic stiffness matrix of three typical layered soils, the efficiency of the improved method and its extensive adaptability to multi-layered soils are verified.