Influence of the order of polynomial on the convergence in ritz finite element formulation to nonlinear vibrations of beams

The influence of the order of inplane polynomial on the convergence of solution, when a Ritz finite element formulation is used to study nonlinear vibrations of beams, is investigated here. Three types of polynomial distributions for the inplane displacement "u" are considered while the polynomial distribution for transverse displacement "w" is retained as cubic always. A hinged-hinged beam on immovable ends with different discretization is chosen as an example for the convergence study on the nonlinear hardening parameter. From the results obtained, it has been concluded that for a chosen cubic polynomial distribution for transverse displacement, a cubic polynomial distribution for the inplane displacement will be a compatible mode shape satisfying the physical aspects of the convergence and nature of bound for the nonlinear hardening parameter. © 1984.