HIERARCHICAL FINITE ELEMENT ANALYSES OF GEOMETRICALLY NON-LINEAR VIBRATION OF BEAMS AND PLANE FRAMES

Geometrically non-linear vibrations of beams and plane frameworks are analyzed by the hierarchical finite element method (HFEM). Two main points are of interest. The first is to compare polynomials, trigonometric functions and beam eigenfunctions as displacement shape functions for beam hierarchical finite elements. The second is to examine the suitability of the HFEM for time domain non-linear analyses.