Mapped infinite p-element for two-dimensional problems of unbounded domains

A new mapped infinite p-element is formulated for two-dimensional problems of unbounded domains. The shape functions along the infinite direction are constructed from the shifted Legendre orthogonal polynomials. The element is characterized by the simplicity of the mapping and the retention of standard integration abscissas and weights. The performance of the proposed mapped infinite p-element is assessed by solving a problem of an infinite medium with a circular opening loaded by internal pressure, a problem of a uniformly loaded circular area on the surface of an elastic half-space, and a case of an infinitely extended medium loaded by uniform pressure. A version of the axisymmetric problem with uniform load applied to a circular slab resting on the surface of an elastic half-space is also shown. Furthermore, comparisons on a d.o.f. basis are made with solutions from truncated finite element meshes. The numerical results show the efficiency of the proposed mapped infinite p-element.