To analyze the time history response of flexible structures (membranes, cables), it’s required an algorithm with high accuracy to reproduce the geometrical nonlinear behavior. In order to check the accuracy of dynamic analyses, the conservation of energy or momentum under undamped conditions may be an important indicator. On the other hand, for ultra-large deformation analysis, the tangent stiffness method (TSM) has already enough achievement with strict evaluation of the rigid body displacement. As a time-integration algorithm applied to dynamic analysis is used Newmark β, which is unconditionally stable over time in the case of linear analysis under the condition of β=1/4. In this study, the combination of TSM and Newmark β is examined, and the conservation of energy through some numerical examples is verified.
As shown in Figure1, a cantilever with a moment acting on the free edge and deforming to a circular shape is adopted as a primary shape of a numerical example of free vibration without damping. It is detected that energy conservation can be observed by applying mode constraints focused in the beginning of increase of acceleration. In Figure2 is shown the energy response without mode constraining, and Figure3 shows the extension of energy conservation for 0.4 more seconds by constraining a number of modes at a specific time before the increase of those mode accelerations.

As future outlook, exploring if these results have general application in other models is important. Also using different value for Newmark beta, better results can be expected.