DYNAMIC-RESPONSE OF AXISYMMETRIC SOLIDS SUBJECTED TO IMPACT AND SPIN

A numerical method is presented to obtain solutions for axisymmetric solids subjected to impact and spin. The method is based on a finite element formulation wherein the equations of motion are integrated directly rather than through the traditional stiffness matrix approach. The formulation is given for axisymmetric triangular elements which can experience large strains and displacements in the radial, axial, and angular directions. The effects of material strength and compressibility are included to account for elastic-plastic flow and wave propagation. The addition of angular displacements allows the effect of twisting to be included in the analysis. The radial and axial equations of motion are applied in the usual manner, whereas the angular (spin) equations of motion are obtained by conserving angular momentum; this allows the angular velocities of the nodes to be altered by a change in radial position and/or shear stress induced tangential forces acting on the concentrated masses. The numerical method can also be used to obtain steady-state solutions for spinning solids. © 1979 American Institute of Aeronautics and Astronautics, Inc., All rights reserved.