Research On Dynamic Modeling Method Of Absolute Nodal Coordinate Formulation Finite Element

Along with the development of Astronautics,a series of large-flexible high-speed light-weight components with complicated configurations and long-life large-scale liquid-filled spacecrafts have been developed for the space missions.The rigid motion of the flexible components will have coupling effects with the flexible deformation during orbit maneuver,and affect the stability of the craft structure and the control precision.Therefore,it is necessary to fully consider the dynamics modelling of flexible components and liquid fuels during the design process.The conventional dynamic modelling methods based on small-deformation and small-rotation cannot get accurate results for large deformation analysis in flexible multibody problems.In this dissertation,accroding to the deficiency of conventional dynamic modeling methods,the modeling method of absolute nodal coordinate formulation finite element is provided,and some new elements included the solid element,fluid element,nonrational and rational finite elements are established for the modeling of large-deformation and large-rotation components and liquid fuels in aerospace engineering.The comprehensive investigations are carried out as follows:In the multibody system dynamics formulations,the modeling of classical non-isoparametric element cannot accurately describe the deformation and the cross section.Although the absolute node coordinate formulation beam-plate element is able to achieve section describe,it is necessary to introduce additional description frames and deal with series locking problems.Different from the elements mentioned above,the absolute nodal coordinate formulation solid element directly describes the section deformation through the node coordinates without the locking problems.Based on the absolute nodal coordinate solid element,the absolute nodal coordinate solid element approach considering the continuity condition and internal viscoelastic damping,has been provided and achieved.With the solid element,the modelling of a rotating flexible beam is realized.According to numerical simulations,solid element can get higher precision and better reflection for large deformations than traditional elements.It is shown that,the absolute nodal coordinate formulation solid element can fit the requirement of multibody system dynamics.Different from the most fluid dynamics methods based on Eulerian approach focus on fluid status by a certain spatial fixation point or a fixed control volume,the absolute nodal coordinate formulation fluid element adopts Lagrangian approach,which can follow fluid material points and establish an unified description of fluid and multi-body systems.In this dissertation,the absolute nodal coordinate formulation fluid element approach is derived,and used to model the fluid systems.In order to verify its correctness and feasibility,the absolute nodal coordinate formulation fluid element is applied to the analysis of liquid sloshing.Some simulations are provided and the result shows that the absolute nodal coordinate formulation fluid element can fit the requirement of large sloshing calculation.Accroding to the deficiency of conventional representation for the descriptions of the displacement field,the Bézier and B-spline representations are provided for the element modeling.Different from the representation mentioned previously in this dissertation,the relationships between the nonrational curve,surface and volume and the finite element are provided,and the generalized transformation matrices are established correspondingly.Using these transformation matrices,the elements based on nonrational Bézier and B-spline representations are established based on the absolute nodal coordinate formulation.As the foundations of rational element representation,the differences of the finite element based on conventional representation and the Bézier and B-spline representations are discussed.The selection of interpolation function and the element consistency are discussed either.Due to the effect of the piecewise continuous of spline geometry,the presence of higher-order continuous inconsistency at elements boundary is considered in order to guarantee the modelling accuracy when using multiple elements.However,the absolute nodal coordinate formulation,uses power functions and nonrational functions as interpolating polynomials to describe displacement field,can get accurate results for flexible bodies that undergo large-deformation and large-rotation.But these functions are nonrational representation which cannot describe the complex shapes precisely,especially for circular and conic sections.Different from the conventional representation,the rational absolute nodal coordinate formulation utilizes rational functions to describe geometric shapes,which allows representing complicated displacement and deformation accurately in dynamics modelling.In this dissertation,the relationships between the rational curve,surface and volume and the finite element are provided,and the generalized transformation matrices are established correspondingly.Using these transformation matrices,some new elements based on rational Bézier and NURBS representations are proposed based on the rational absolute nodal coordinate formulation.Numerical examples are given to demonstrate the applicability of the proposed elements.It is shown that,the rational elements can depict the geometric characteristics and structure configurations precisely,and lead to better convergence for the dynamic analysis of flexible bodies.