An iterative method to evaluate the impedance matrix of finite-size foundation

A new approach used in the finite element method to calculate the impedance matrix of rock (or soil) foundation, is presented. First, an iterative technique is developed to solve the complex-valued equations of motion for the foundation subjected to a harmonic surface force. The proposed technique can be used to calculate the complex-valued displacement response of the foundation in an adjacent area near a certain exciting frequency. Second, the complex-valued static substructure method is introduced to the procedure for solving the equations of motion. The method of combining the complex-valued static substructure method with the iterative technique is presented to reduce the computational effort needed in the procedure. The effectiveness of these new calculation techniques is demonstrated by numerical examples.