In this paper, a rational absolute nodal coordinate formulation (RANCF) thin plate element is developed and its use in the analysis of curved geometry is demonstrated. RANCF finite elements are the rational counterpart of the nonrational absolute nodal coordinate formulation (ANCF) finite elements which employ rational polynomials as basis or blending functions. RANCF finite elements can be used in the accurate geometric modeling and analysis of flexible continuum bodies with complex geometrical shapes that cannot be correctly described using nonrational finite elements. In this investigation, the weights, which enter into the formulation of the RANCF finite element and form an additional set of geometric parameters, are assumed to be nonzero constants in order to accurately represent the initial geometry and at the same time preserve the desirable ANCF features, including a constant mass matrix and zero centrifugal and Coriolis generalized inertia forces. A procedure for defining the control points and weights of a Bezier surface defined in a parametric form is used in order to be able to efficiently create RANCF/ANCF FE meshes in a straightforward manner. This procedure leads to a set of linear algebraic equations whose solution defines the RANCF coordinates and weights without the need for an iterative procedure. In order to be able to correctly describe the ANCF and RANCF gradient deficient FE geometry, a square matrix of position vector gradients is formulated and used to calculate the FE elastic forces. As discussed in this paper, the proposed finite element allows for describing exactly circular and conic sections and can be effectively used in the geometry and analysis modeling of multibody system (MBS) components including tires. The proposed RANCF finite element is compared with other nonrational ANCF plate elements. Several numerical examples are presented in order to demonstrate the use of the proposed RANCF thin plate element. In particular, the FE models of a set of rational surfaces, which include conic sections and tires, are developed

The development of new and complex vehicle models using the absolute nodal coordinate formulation (ANCF) and multibody systems (MBS) algorithms is discussed in this paper. It is shown how a continuum-based finite element (FE) leaf spring and tire assembly can be developed at a preprocessing stage and integrated with MBS algorithms, allowing for the elimination of dependent variables before the start of the dynamic simulations. Leaf springs, which are important elements in the suspension system of large vehicles, are discretized using ANCF FEs and are integrated with ANCF tire meshes to develop new models with significant details. To this end, the concept of the ANCF reference node (ANCF-RN) is used in order to systematically assemble the vehicle model using linear algebraic constraint equations that can be applied at a preprocessing stage. These algebraic constraint equations define new FE connectivity conditions that include the leaf spring shackle/chassis assembly, tire flexible tread/rigid rim assembly, tire/axle assembly, and revolute joints between different vehicle components. The approach presented in this paper allows for using both gradient deficient and fully parameterized ANCF FEs to develop the new models. In order to develop accurate leaf spring models, the prestress of the leaves and the contact forces between leaves are taken into consideration in the ANCF models developed in this investigation. Numerical results are presented in order to demonstrate the use of the computational framework described in this paper to build continuum-based leaf spring/tire assembly that can be integrated with complex vehicle models. The results of this paper also demonstrate the feasibility of developing a CAD (computer-aided design)/analysis system in which the geometry and analysis mesh of a complete vehicle can be developed in one step, thereby avoiding the incompatibility and costly process of using different codes in the flexible MBS analysis.

Since the thermal load would adversely introduce degradation to the normal operation of spacecraft, resulting in unpredictable thermal-dynamic behavior, thermomechanical coupling problems are important and have been investigated extensively. Based on the absolute nodal coordinate formulation (ANCF), a thermal integrated ANCF thin plate element based on the unified description is constructed, which could depict the displacement and the temperature field integratedly. By means of the proposed element, the heat transfer and continuum mechanics are integrated in the unified finite element method (FEM) mesh of revolving paraboloid antenna. Additionally, the ANCF reference node is introduced for describing the rigid central hub where the antenna is mounted on to make the rigid-flexible-thermal coupled response being captured in a unified analysis procedure. The solar radiation input and the surface emitting radiation are included in the heat transfer equations. Furthermore, the influence of the rigid body motion and the deformation on the radiant absorption are also considered with the self-shadowing. The established rigid-flexible-thermal coupled simulation is performed on a modified generalized-α integrator which solves the set of multidisciplinary governing equations synchronously. For revealing the nonlinear behavior of the rigid-flexible-thermal coupled system, the observed thermally induced vibration and perturbation on the pointing accuracy of the spacecraft are given in the results, and the feasibility of the presented method is proved.

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