Dynamics of Geometrically Nonlinear Rods: II. Numerical Methods and Computational Examples

The paper selects and develops appropriate numerical solutionmethods for initial boundary value problems of the equations of motionof geometrically nonlinear extensible Euler–Bernoulli-beams. A finiteelement method that uses first-order Hermitian polynomials as interpolationfunctions for the rod axis position vector is used as discretizationtechnique. An averaging method for the calculation of net forces andmoments is developed that achieves a better approximation than thedirect calculation from the strains. Time integration is done usingan energy and momentum conserving algorithm that is proposed in thispaper and Newmark type methods. The derived algorithms are used tosolve problems from space and marine engineering. The obtained simulationresults are compared with results which have been already publishedin the literature or were calculated by different methods.