A NEW MAPPED INFINITE ELEMENT FOR DYNAMIC ANALYSIS OF SOIL-STRUCTURE INTERACTION PROBLEMS

Abstract

In numerical calculations, only a finite region of the foundation radian is analyzed. Unless something is done to prevent the outwardly radiating waves from reflecting from the region's boundaries, errors are introduced into the results. The present work studies such effects, using the finite element method with two types of transmitting boundaries at the edge of the computational grid. The first type is by using mapped infinite element and the second is by using viscous boundaries.

Two types of mapped infinite elements are derived.  These types are the 8-noded infinite element extended from that of Zienkiewicz mapped infinite element and the 5-noded coding of mapped infinite element extended from that presented by Selvadurai and Karpurapu in 1988.

The mapping functions and their derivatives of the infinite elements are presented for two cases; the first when the infinite element extending to infinity in the negative ξ direction and in the second case, the infinite element is extending to infinity in the negative η direction.

A dynamic finite-element analysis is carried out for soil-structure interaction problems  considering transmitting boundaries. Two types of boundaries are considered: viscous boundaries and mapped infinite elements. The results are compared for three cases; the first one using finite elements only, the second using 5-node and 8-node mapped infinite elements which were added to the finite element code MIXDYN and the third one using viscous boundaries.

In order to check the validity and accuracy of the derived infinite elements in analyzing soil-structure interaction problems considering infinite boundaries, two verification examples are considered for this purpose. The results of the modified program are compared with the results of other program software called ANSYS representing other types of elements modeling infinite boundaries using viscous boundary method.

It was found that the viscous boundaries are more effective in absorbing the waves resulting from dynamic loads than mapped infinite elements. This is clear when comparing the results of both types with those of transient infinite elements.