Finite element modeling of scattering problems involving infinite domains using drilling degrees of freedom

Abstract

Scattering of waves involving complex geometries in conjunction with infinite or semi-infinite domains is modeled by introducing a mathematical boundary within which the finite element representation is employed. On the mathematical boundary, the finite element representation is matched with analytical representation in the infinite/sem-infinite domain. The matching has been done with and without slope constraints on the boundary. Drilling degrees of freedom at each of the nodes of the finite element model are introduced to take into account the transverse component of the elastodynamic field more precisely. Use of the slope constraint makes the eigenvalues of the mathematical domain complex and hence reduces the error at those frequencies compared to the use of field continuity only, which would result in real eigenvalues. Use of drilling degrees of freedom improves accuracy. Examples involving elastic and acoustic wave scattering at the interface of fluid-solid half spaces are considered. In the examples involving a fluid-solid interface, a method for using displacement formulation in the irrotational fluid region is also presented. The approach presented here can be applied to acoustic and electromagnetic field problems also.