## 1 Introduction
A nonlinear aeroelastic simulation toolbox named UM/NAST (The University of Michigan's Nonlinear Aeroelastic Simulation Toolbox) was developed by [PERSON] [18] and perfected by [PERSON] [19; 20] and [PERSON] [13], aimed at the investigations of dynamic aeroelastic responses coupled with flight dynamics of highly flexible aircrafts. Their analyses are based on the strain-based nonlinear beams and [PERSON] 2D aerodynamic model. Two simplified models that can take the effects of skin wrinkling and aerodynamic stall into consideration are added into their framework. A simulation framework called SHARP (Simulation of High-Aspect-Ratio Planes) was developed by [PERSON] and co-workers [21; 22] to study the dynamic characteristics of highly flexible aircraft with large deformations. The displacement-based nonlinear dynamic formulations coupled with an unsteady vortex lattice aerodynamic model are employed to capture the large deformations and nonlinear responses of the flexible aircraft. With the computation of nonlinear static trim parameters and dynamic responses to maneuver and gust loads, this framework can be used to conduct stability analyses, dynamic response simulations, flutter suppressions, and gust load alleviations. In addition, there are several more powerful nonlinear aeroelastic computer codes on the subject of computational aeroelasticity with high fidelity models and fluid structure interaction with reduced order models (ROMs) such as ARMA-ROM, Volterra-ROM, and POD-ROM. Many important works on this subject were done by [PERSON] et al. [23; 24; 25; 26] at Stanford University (Mech and Aerospace Engr Dept). A linearized synchronous and staggered fluid-structure time-integration interaction algorithms [27; 28; 29] were introduced and applied to predict the transient aeroelastic response of a reduced-order model of a complete F-16 aircraft configuration at a given Mach number. A rather comprehensive review, in which the up-to-date models, methodologies, applications, important observations and current challenges in the research of nonlinear aeroelasticity and flight dynamics of highly flexible aircraft are presented and discussed in detail, was recently carried out by [PERSON] et al. [30]. Readers are referred to this review for the state-of-the-art and further details on the design, analysis and performance predictions of this kind of highly flexible aircraft. The geometrically exact intrinsic beam proposed by [PERSON] and strain-based nonlinear beam proposed by [PERSON] are frequently used in the modeling of highly flexible wings. However, the displacement-based models, which are more intuitive and can be easily transported to the existing finite element programs, have rarely been utilized. As for the coupling between flight dynamics and aeroelasticity, many studies adopt the mean axes or its ramifications [31; 32], which assume that the elastic deformations are small, and essentially still being the 6-DOF formulation. Even in those approaches in which large deformations are considered, the Euler angles and airflow angles are not defined locally, resulting in the costs of coordinate transformations of displacements and velocities between global and local frames. The main contribution of this paper, which perfects the foundational work of forerunners, is to propose a new and more comprehensive framework to model and analyze the coupled nonlinear aeroelasticity and flight dynamics of highly flexible aircrafts, aimed at the requirements of time-domain simulations and performance evaluations in the preliminary design phase of HALE aircraft. The starting point of this framework is the dynamics of 3D co-rotational nonlinear beam model, which is low-order and capable of capturing the nonlinear elastic deformations and rigid-body motions in a computationally effective formulation, targeted for the low computational costs and quick analyses in the preliminary design. The original equations of nodal inertial force vector of the element modified to enhance its versatility.