This study presents an approach based on the floating frame of reference method to model complex three-dimensional bodies in a multibody system. Unlike most of the formulations based on the floating frame of reference method, which assume small or moderate deformations, the present formulation allows large elastic deformations within each frame by using the co-rotational form of the updated Lagrangian description of motion. The implicit integration scheme is based on the Generalized-alpha method, and kinematic joints are invoked in the formulation through the coordinate partitioning method. The resulting numerical scheme permits the usage of relatively large time steps even though the flexible bodies may experience large elastic deformations. A triangular element, based on the first order shear deformable theory, has been developed specifically for folded plate and shell structures. The plate element does not suffer from either shear or aspect-ratio locking under transverse and membrane bending, respectively. A stiffened plate element has been developed that combines a shear deformable plate with a Timoshenko beam. A solid element, that utilized the isoparametric formulation along with incompatible modes, and one-dimensional elements are also included in the element library. The tools developed in the present work are then utilized for detailed rotorcraft applications. As opposed to the conventional approach of using beam elements to represent the rotor blade, the current approach focuses on detailed modeling of the blade using plate and solid elements. A quasi-steady model based on lifting line theory is utilized to compute the aerodynamic loads on the rotor blade in order to demonstrate the capabilities of the proposed tool to model rotorcraft aeroelasticity.

In this study, a new vector form intrinsic finite element (VFIFE) for the plate is developed and applied to study the responses of a traditional plate member applied to engineering structures. The VFIFE method is a solution procedure for the mechanic problems by adopting the traditional co-rotational explicit finite element method developed by Belyschko and Hsieh (1973). Three different shape-functions including the simplest polynomial form shape-function (Poly), non-conforming area coordinate shape-function (BCIZ) and the conforming area coordinate shape-function (BCIZC) are utilized to simulate the displacement field of the plate. For a system with nonzero rigid-body displacement, the equilibrium will be difficult to achieve in the global coordinate system when the traditional finite element method is applied. By separating the rigid-body motions from the deformed motions, this problem can be easily taken care. In numerical examples, the accuracy and efficiency of this new developed vector form intrinsic finite element for plate simulation are also examined. It is found that compared to the analytical solution, the accuracy is excellent, while compared to traditional finite element method, the efficiency is also encouraging. This new VIFIFE plate element was also applied to the analysis for the sheet plate members in the harbor structures such as the sheep-pile wharf structural system. It was found that not only can the global behaviors of the pile be clearly observed but also local variations in deformations of the steel sheet are clearly shown.