Concave finite elements for the cloning algorithm

Abstract

Analysis of wave propagation in unbounded media requires the analysis of an indented semi-infinite domain. The boundaries of the finite element mesh must be as parallel as possible to the indentation, to avoid interfering with the wave propagation. The wave propagation within the wave-absorbing boundary is central to the study of soil-structure interaction. For a building in unbounded media—such as the earth, such a boundary is necessarily concave. The concave elements are algebraically more complicated than their convex analog. Consequently, computational tools including computer algebra are indispensable to the creation of a generic formulation, which applies to any concave shape. Shape functions for concave elements require a higher order formulation than is required for convex shapes. Nevertheless, a smooth, integrable representation can be constructed.