Response on the "Extended Comment on the Article "Consistent Development of a Beam-To-Beam Contact Algorithm via the Curve to Solid Beam Contact - Analysis for the Non-Frictional Case"

Abstract

Summarizing our discussions, in the Extended Comment on the Article, that we received, we again did not find any general solution of CPP including any method of solution of inequalities either. This is rather a confirmation of the specific nature of the contact criterion and the corresponding solution plus algorithmic scheme. Surprisingly, the authors started to criticize our alternative Curve-To-Solid Beam formulation, which is based on the CPP for surfaces and not based neither on CPP for PTC, nor on CPP for CTC as a closer look should have revealed. While doing so, the aforementioned authors are apparently not fully following the logic in our paper. Thus, as an example, while criticizing our parallel curves, they claim in several places that it is not possible to construct any parallel curves with an arbitrary angle between tangent lines. However, one can easily wind a wire on a cylinder at any desired angle -- in this case the distance between the axis of a cylinder and the mid-curve of a wire will be constant -- solution is, of course, multiple excluding application of CTC algorithm. We are emphasizing in detail again the fact, that a very general criterion for the existence and uniqueness of the CPP procedure for Curve-To-Curve algorithm by no means can be derived by performing ad-hoc and not consistent mathematical operations.