Development of axisymmetric dynamic infinite elements based on multiple wave functions and its application to solid-structure interaction analysis

Abstract

This dissertation presents a soil-structure interaction analysis method based on finite element method incorporating an infinite element formulation for axisymmetric bodies subject to three-dimensional dynamic loadings. In order to model exterior unbounded region corresponding to cylindrical near field in wave radiation problems, three kind of axisymmetric elastodynamic infinite elements were developed. They are horizontal, vertical, and corner infinite elements. Then an earthquake analysis method is presented, in which the proposed infinite elements are used in calculating equivalent earthquake forces along the interface between the near and far fields. The shape functions of the proposed infinite elements were derived from the approximate expressions for analytical solutions. An efficient integration scheme was also developed to calculate the mass and stiffness matrices of the infinite elements involving multi-wave components. To verify the proposed infinite elements, impedances of rigid disks on a homogeneous half space and on a layered half space were calculated. Numerical results compared with those obtained by other methods indicated that the method using the proposed infinite elements offers good solutions. Soil-structure interaction analyses were also carried out for a disk on a flexible caisson embedded in a homogeneous half space and for a containment structure on a multi-layered half space. Making use of the proposed vertical and corner infinite elements, the total number of degrees of freedom and CPU time for numerical analysis could be significantly reduced. The present earthquake analysis method was verified utilizing a site response problem. The free-field responses were obtained by assuming the input earthquake to be vertically incident SV-waves. Comparison of the result with free-field solution showed that the present method offers accurate solutions. To demonstrate the proposed techniques, a series of dynamic analyses was carried out in con...