Rotation-free isogeometric dynamic analysis of an arbitrarily curved plane Bernoulli-Euler beam

A novel rotation-free isogeometric formulation of in-plane dynamic analysis of an arbitrarily curved Bernoulli-Euler beam in the convective frame of reference is presented. The driving force behind the present study has been the development of the NURBS-based element which enables an elegant framework of in-plane vibrations of arbitrarily curved Bernoulli-Euler beams, being a function only of the global Cartesian coordinates. Due to the fact that no additional simplifications are made, besides those related to the classic Bernoulli-Euler hypothesis and small strain theory, the formulation is particularly applicable for problems regarding the behavior of strongly curved beams.

An excellent agreement of the results is accomplished and efficiency for academic and practical use are shown. The influence of the product of the maximum curvature and the thickness of the beam on the accuracy of the solution is specially treated and debated. The effects of the hpk-refinements are thoroughly checked and a highly nonlinear convergence behavior under the h-refinement is noticed. The well-known fact that models with the highest interelement continuities return superior accuracy per degree of freedom is substantiated by an in-depth numerical analysis of order of convergence. Furthermore, the accuracy of the developed model is analyzed utilizing normalized numerical discrete spectrums. It is remarked that the accuracy per degree of freedom degrades with the complexity of reference geometry of the beam.