Two-level finite element method for thin plate vibration subject to concentrated harmonic loads

Abstract

A thin plate subject to concentrated harmonic loads (forces or moments) is customarily analyzed either by a fine finite element mesh or by singular elements. In this paper an alternative method is recommended in which conventional finite elements with a fine mesh are used and the number of unknowns is reduced by interpolating the nodal displacements by means of the shape functions associated with the previously mentioned singular elements. New element matrices need not be generated and integration is avoided completely. Accurate results under a point load, comparable to those of the full finite element analysis, are achieved with a substantially reduced number of unknowns. Both concentrated forces and moments are considered.