The finite-element floating frame of reference (FFR) formulation is used, for the most part, in the small deformation analysis of flexible bodies that undergo large reference displacements. This formulation allows for filtering out systematically complex shapes associated with high frequencies that have no significant effect on the solution in the case of small deformations. The resulting low-order FFR models have been widely used to obtain efficient and accurate solutions for many engineering and physics applications. In this investigation, the use of the FFR formulation in the large deformation analysis is examined, and it is demonstrated that large deformation FFR models can be accurate in applications, where the deformation can be described using simple shapes as it is the case in robot system manipulators. In these cases, the standard finite-element FFR formulation must be used with non-linear strain—displacement relationships that account for the geometric non-linearities. The results obtained using the large deformation FFR models are compared with the results obtained using the large deformation absolute nodal coordinate formulation (ANCF), which does not allow for the use of linear modes. The ANCF models are developed using two different methods for formulating the elastic forces: the basic continuum mechanics approach (ANCF-BC) and the elastic line method (ANCF-EL). While the explicit Adams method can be used to obtain the numerical solution of the FFR model, two implicit integration methods are implemented in order to be able to obtain an efficient solution of the FFR and ANCF models. These implicit integration methods are the RADAU5 method and the Hilber—Hughes—Taylor (HHT) method. In the case of simple large deformation shapes, the simulation results obtained in this study show a good agreement between the FFR and the ANCF solutions. The results also show that, in the case of thin and stiff beams, the coupled deformation modes that result from the use of the ANCF-BC can be a source of numerical and locking problems, as reported in the literature. These ANCF-BC numerical problems can be circumvented using the implicit HHT integration method. Nonetheless, the HHT integrator does not capture high-frequency FFR axial modes which are necessary in order to obtain accurate solutions for high-speed rotating beams. In addition to the comparison with the ANCF solutions, experimental results of a forward dynamics model are used in this study to validate the large deformation FFR numerical solutions. The experimental set-up used in the validation of the numerical solutions is also described in this investigation.

Soft continuum robots, inspired by the adaptability and agility of natural soft-bodied organisms like octopuses and elephant trunks, present a frontier in robotics research. However, exploiting their full potential necessitates precise modeling and control for specific motion and manipulation tasks. This study introduces an innovative approach using Deep Convolutional Neural Networks (CNN) for the inverse quasi-static modeling of these robots within the Absolute Nodal Coordinate Formulation (ANCF) framework. The ANCF effectively represents the complex non-linear behavior of soft continuum robots, while the CNN-based models are optimized for computational efficiency and precision. This combination is crucial for addressing the complex inverse statics problems associated with ANCF-modeled robots. Extensive numerical experiments were conducted to assess the performance of these Deep CNN-based models, demonstrating their suitability for real-time simulation and control in statics modeling. Additionally, this study includes a detailed cross-validation experiment to identify the most effective model architecture, taking into account factors such as the number of layers, activation functions, and unit configurations. The results highlight the significant benefits of integrating Deep CNN with ANCF models, paving the way for advanced statics modeling in soft continuum robotics.

Accurate modeling of large wind turbine blades is an extremely challenging problem. This is due to their tremendous geometric complexity and the turbulent and unpredictable conditions in which they operate. In this paper, a continuum based three dimensional finite element model of an elastic wind turbine blade is derived using the absolute nodal coordinates formulation (ANCF). This formulation is very suitable for modeling of large-deformation, large-rotation structures like wind turbine blades. An efficient model of six thin plate elements is proposed for such blades with non-uniform, and twisted nature. Furthermore, a mapping procedure to construct the ANCF model of NACA (National Advisory Committee for Aeronautics) wind turbine blades airfoils is established to mesh the geometry of a real turbine blade. The complex shape of such blades is approximated using an absolute nodal coordinate thin plate element, to take the blades tapering and twist into account. Three numerical examples are presented to show the transient response of the wind turbine blades due to gravitational/aerodynamics forces. The simulation results are compared with those obtained using ANSYS code with a good agreement.