中文摘要：

提出了基于积分变换、对偶方程与精细积分算法求解多层地基任意形状刚性基础的动力刚度问题．首先在频率波数域内圆柱坐标体系中利用圆形微元的对称与反对称特性建立多层地基中格林影响函数的波动方程，然后将应力和位移关系表示成对偶形式进行精细积分求解以提高计算精度和稳定性．再将任意形状刚性基础与地基的交界面离散化为一系列圆形微元，利用格林影响函数建立其平动与转动动力刚度的矩阵方程．该求解方法高效、准确并且计算稳定，适于任意复杂多层地基任意形状基础动力刚度的计算．

英文摘要：

An approach based on integral transformation, dual form of wave motion equation and precise integration method is proposed for the solution of the dynamic stiffness matrices of rigid foundation of ar- bitrary shape on multi-layered half-space. Firstly, to take advantage of the axisymmetric property of the load-displacement field of subdisk-element in cylindrical coordinates, the equation of Green＇s influence function for multi-layered half-space is formulated. Then the dual form of the uncoupled wave motion equation in the frequency-wave number domain for in-plane motion and out-of-plane motion is established. It can be solved quite accurately by the precise integration method. Finally, the contact interface between the rigid foundation and the multi-layered half-space is discretized into a number of subdisk-elements, and the matrix-equation of translational and rotational dynamic stiffnesses of the foundation is evaluated. The proposed method is efficient, accurate and computationally stable. It is well suited to the dynamic interaction analysis of rigid foundation of arbitrary shape on complex multi-layered half-space. Numerical examples clearly demonstrate the superiority of the proposed approach.