【作者】 马超；

【导师】 赵阳；

【作者基本信息】 哈尔滨工业大学 ， 航空宇航科学与技术， 2017， 博士

【摘要】 随着我国航天事业的发展和空间任务复杂程度的提高,一些搭载有大柔性、高速、轻质部件的新型机构以及具备高运载、长寿命的大型充液航天器逐渐提上研制计划。然而由这些柔性部件和液体燃料组成的多体系统在工作时,系统大范围刚体运动将会与柔体变形运动产生强烈的耦合效应,对航天器结构的稳定性和控制系统的控制精度产生显著影响,因此在航天器总体设计和控制系统设计过程中必须充分考虑柔性体的动力学建模问题。本文针对传统动力学建模方法中存在的不足,以航天工程中常见的大变形、大转动柔性部件及可等效为柔性部件的液体燃料为研究对象,提出了绝对节点坐标列式单元动力学建模方法,建立了包括实体单元、流体单元、非有理/有理样条函数单元在内的新型绝对节点坐标列式单元,并就相关动力学问题展开了研究。针对传统单元及绝对节点坐标列式梁板类单元在截面描述及变形处理上的不足,提出了基于幂基函数描述的绝对节点坐标列式三维八节点实体单元,对实体单元建模方法及在多体动力学中的应用进行了研究。实体单元模型采用不完备插值函数描述单元位移场,在保留绝对节点坐标列式单元优点的同时,通过节点坐标直接描述截面变形,无需引入局部坐标,能够准确描述截面变形及大变形、大转动运动。使用实体单元实现了对多体系统的建模,研究了不同柔性下的旋转梁算例,将所得结果进行对比,表明实体单元在处理大变形、大转动问题上能够精确的表征柔体系统,验证了单元建模方法及使用实体单元求解柔性多体问题的可行性,为绝对节点坐标列式实体单元的发展提供参考依据。实体单元是流体单元、非有理及有理样条函数单元建立的基础。针对贮箱内液体燃料的大幅晃动问题,在绝对节点坐标列式实体单元模型基础上,提出了基于完全拉格朗日描述的绝对节点坐标列式三维八节点流体单元,对流体单元建模方法及在液体晃动问题中的应用进行了研究。与欧拉描述不同,流体单元模型采用完全拉格朗日描述,能够直接跟踪流体物质点,同时保留了绝对节点坐标列式单元的特性,能够以较少的节点坐标描述流体大范围、大变形运动。使用流体单元实现了对流体系统的建模,研究了流体在自由流动、自由晃动和受迫晃动下的动力学特性,将所得结果进行对比,表明流体单元在处理流体大范围、大变形晃动问题上能够精确的描述流体系统,验证了流体建模理论及使用流体单元求解晃动问题的可行性,为绝对节点坐标列式流体单元的发展和应用提供参考依据。针对绝对节点坐标列式单元建模方法在场函数描述方式上的不足,提出了基于非有理样条函数描述的绝对节点坐标列式单元,对样条函数单元建模方法及其相关特性进行了研究。样条函数单元模型采用非有理样条函数描述单元位移场,对于复杂构型体不再需要通过提升单元数量或插值多项式阶次等方式近似表征,而是利用样条函数的特性根据结构的几何特征在样条曲线、曲面或实体上直接划分连续体,在保证模型精度的同时简化网格划分过程。根据新旧场函数描述方式的不同,讨论了样条函数和幂函数构建的两类插值多项式之间的关系以及样条函数单元的连续性条件,解决了由样条函数分段连续性导致的高阶连续不一致的问题,保证了样条函数单元的建模精度。非有理样条函数单元作为有理单元建立的基础,为绝对节点坐标列式单元的发展提供了新方向。针对传统单元及非有理绝对节点坐标列式单元在圆锥曲线、曲面及实体构型表征上的不足,在非有理样条函数单元基础上,提出了基于有理样条函数描述的绝对节点坐标列式有理单元,对有理单元建模方法及其应用进行了研究。有理单元模型的位移场由有理样条函数描述,而有理样条函数的优点是能够精确描述各类圆锥曲线、曲面及实体,使得有理单元建立的有限元模型可以准确保留结构形状和几何特征,实现对复杂构型尤其是圆锥曲线类构型的精确表示。使用有理样条函数单元实现了对多体系统的建模,研究了柔性体大变形、大转动问题,并将所得结果进行对比,表明有理单元能够准确的表征和求解柔性多体系统,验证了有理单元建模方法及使用有理单元求解复杂构型问题的可行性,为有理绝对节点坐标列式单元的发展提供依据。更多还原

【Abstract】 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.更多还原