Efficient computational approaches for analysis of thin and flexible multibody structures

A large group of real mechanical problems can be modeled and analyzed using the approaches of flexible multibody dynamics. The computational models in the form of differential–algebraic equations can be quite complex, and therefore, it is suitable to develop efficient approaches for the analysis of such models. This paper deals with the development of fast and efficient computational techniques for the analysis of flexible and thin mechanical structures modeled using the absolute nodal coordinate formulation (ANCF). The first original contribution of this paper is the introduction of fast evaluation of nonlinear elastic forces of the ANCF cable element based on the pre-computation of various terms that are constant when evaluated numerically at Gaussian points. The second part of the paper is aimed at the usage of quasi-Newton methods, which led to the reduction in iteration matrix re-evaluations in case of Newmark type of numerical integration methods for equations of motion. Proposed improvements are implemented in an in-house software in MATLAB environment, and their effects are tested on the cable-mass system considered as a flexible multibody system. The numerical results shown in the paper have proven the efficiency of the proposed algorithms. Real behavior of testing mechanical systems was supported by presented experimental results.