Advantages of Infinite Elements over Prespecified Boundary Conditions in Unbounded Problems

Abstract

This paper promotes the further development and adoption of infinite elements for unbounded problems. This is done by demonstrating the ease of application and computational efficiency of infinite elements. Specifically, this paper introduces a comprehensive set of coordinate and field variable mapping functions for one-dimensional and two-dimensional infinite elements and the computational steps for the solution of the affiliated combined finite-infinite element models. Performance is then benchmarked against various parametric models for deflections and stresses in two examples of solid, unbounded problems: (1) a circular, uniformly-distributed load, and (2) a point load on a semiinfinite, axisymmetrical medium. The results are compared with those from the respective closed-form solution. As an example, when the vertical deflections in Example 2 are compared with the closed form solution, the 45% error level generated with fixed boundaries and 14% generated with spring-supported boundaries is reduced to only 1% with infinite elements, even with a coarse mesh. Furthermore, this increased accuracy is achieved with lower computational costs.