FEM modeling of infinite/semi-infinite domains by using slope constraint and drilling degrees of freedom (d.o.f.)

摘要

Infinite or semi-infinite domain problems occur frequently in the modeling of smart structures. Interaction of fields with 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 representations in the infinite/semi-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 reduce artificial reflection at the mathematical boundary. Of the different methods studied, it was found that a combination of slope constraint and drilling d.o.f. can reduce spurious reflections from the mathematical boundary. Examples involving elastic and acoustic wave scattering by a simple structure in a semi-infinite half space are considered. The method can also be easily applied to electromagnetic field problems.