A variational approach to asynchronous time-integration of structural dynamics problems in the context of feti and spurious oscillations on the interfaces

In this contribution we derive a nonlinear version of the BGC-macro asynchronous time-integration method and investigate the resulting spurious oscillations on the interface, resulting from the coupling on a course time-grid. The main difference to the nonlinear PH-method lies in a different coupling condition, which is only based on the coupling of velocities by Lagrange-Multipliers. We give a brief introduction to our implementation in our in-house developed open-source software AMfe and PyFETI. Afterwards we address the possibility of wave-reflections on the interfaces in certain cases. In the last part of the paper we derive a different asynchronous coupling-method from the variational principle utilizing a generalized midpoint-rule. Due to weak instabilities, when the constraint is formulated on displacmentlevel, we modify the arising condition such that it is enforced on velocity-level but still represents an energy with the interface-forces. As a prove of concept and for comparability to the BGC-macro method we only use a coarse discretization of the Lagrange-Multiplier-field. Then we show that spurious oscillations couldn’t be eliminated in our special test-case, due to that coarse discretization, but incompatibilities in the displacements-filed were smoothed. The amplitude of energy-oscillations is kept similar compared to the BGC-macro method.