Forced oscillations of an axisymmetric structure in contact with an elastic half-space by a version of global local finite elements

Abstract

A version of the global local finite element method (GLFEM) is presented for determining the steady state forced response of an axisymmetric structure in contact with an elastic, homogeneous, isotropic half-space. In this GLFEM version, conventional finite elements are used to model the structure and some portion of the sorrounding medium, and global functions in the form of a complete set of outgoing spherical harmonic waves for the entire space are used to capture the behavior in the half-space region beyond the finite element mesh. An arbitrary distribution of steady state normal loads may be applied to the structure. Full traction and displacement continuity are enforced at the finite element mesh interface with the outer region. On the half-space surface of the outer region, traction-free surface conditions are met by requiring a sequence of weighted-average integrals of the tractions to vanish. Comparison of the present results for the problem of a rigid plate in frictionless contact with the half-space with those obtained by krenk and Schmidt [1] show excellent agreement over a wide frequency range. Other examples on circular plates under various contact conditions with the half-space are presented as illustrations of the forced response.