Spinning finite elements

Abstract

By means of Lagrangian equations, the finite element method is extended to spinning structures. Skeletal structures consisting of straight beam members are taken as examples. Explicit element matrices are given. Numerical solution procedures based on the Newtonian algorithm are suggested. The orientation of a beam member is arbitrary with reference to a rotating frame, so that general spinning space structures can be considered. Numerical examples show the well known fact that the axial force in a beam induced by the centrifugal force has destabilizing effects while gyroscopic motion has stabilizing effects. The combined effect may be either stabilizing or destabilizing depending on the boundary conditions.