### On the Total Dynamic Response of Soil-Structure Interaction System in Time Domain Using Elastodynamic Infinite Elements with Scaling Modified Bessel Shape Functions

Konstantin Kazakov
2013 American Journal of Computational Mathematics
This paper is devoted to a new approach-the dynamic response of Soil-Structure System (SSS), the far field of which is discretized by decay or mapped elastodynamic infinite elements, based on scaling modified Bessel shape functions are to be calculated. These elements are appropriate for Soil-Structure Interaction problems, solved in time or frequency domain and can be treated as a new form of the recently proposed elastodynamic infinite elements with united shape functions (EIEUSF) infinite
more » ... EIEUSF) infinite elements. Here the time domain form of the equations of motion is demonstrated and used in the numerical example. In the paper only the formulation of 2D horizontal type infinite elements (HIE) is used, but by similar techniques 2D vertical (VIE) and 2D corner (CIE) infinite elements can also be added. Continuity along the artificial boundary (the line between finite and infinite elements) is discussed as well and the application of the proposed elastodynamical infinite elements in the Finite element method is explained in brief. A numerical example shows the computational efficiency and accuracy of the proposed infinite elements, based on scaling Bessel shape functions. The idea and concept of the elastodynamic infinite elements with united shape functions (for short EIEUSF class infinite elements) are presented in [20, 21] . Several EIEUSF formulations are discussed and have been demonstrated that the shape functions, related to nodes k and l (the nodes, situated in infinity, Figure 1 , are not necessary to be constructed, because corresponding to these shape functions generalized coordinates or weights, see Equation (1), are zeros). The displacements in infinity are vanished, and these shape functions must be omitted. The theory used for the formulation of the EIEUSF class infinite elements has been published in detail in  , and hence only summarize of the basic idea is demonstrated here. In  is mentioned why the EIEUSF class infinite elements are more general and powerful than the standard infinite elements. The displacement field in the elastodynamical infinite