Isogeometric Analysis for Nonlinear Dynamics of Timoshenko Beams

Dr. Clemens Hofreither

Oct. 21, 2014, 3:30 p.m. S2 059

We analyze the dynamics of beams that undergo large displacements using
an isogeometric discretization. As the underlying mathematical model, we
assume the nonlinear Timoshenko theory for bending of beams. We obtain a
nonlinear system of second order ordinary differential equations. Since
periodic responses are of interest, we apply the harmonic balance
method. The nonlinear algebraic system is then solved by an arc-length
continuation method in frequency domain.

We present numerical experiments and give a comparison between results
obtained by isogeometric analysis and a p-FEM. It is shown that IGA
gives better approximations than the p-FEM using the same number of
degrees of freedom.