Elastodynamic infinite elements with united shape functions for soil–structure interaction

Abstract

In this paper, new formulations of 2D four and five node elastodynamic infinite elements with united shape functions ( EIEUSF) are proposed. Such elements can be treated as family elastodynamic infinite elements, appropriate for dynamic soil–structure interaction (SSI) problems and can be used directly as finite elements. The common characteristic of the proposed infinite elements is the so-called united shape function, which is based on a finite number of wave shape functions. The idea of the united shape function is presented and discussed in details. It is demonstrated that if only one wave function is used (only one wave frequency) these elements are transformed to single-wave elastodynamic infinite elements. The basic difference between the four and five node formulations is the number of nodes for interpolation of the displacement field in the finite direction of the element. The EIEUSF elements are given in decay and mapped form. Fundamental advantage of the proposed infinite elements is that such elements can directly be used in the FEM concept. Once generated the EIEUSF mass and stiffness matrices can be addressed, introduced appropriately in the FEM equation of motion. After the mapping such elements can be recognized and treated, in the FEM technology, as finite elements. The elements are tested for multi-wave soil–structure interaction problems. The results give the guarantee for adequate numerical simulation.