基于无网格法的旋转运动功能梯度材料板刚-柔-热耦合动力学问题研究

The discretization method of the deformation field and the dynamic modeling theory of flexible plates are not perfect in the field of flexible multibody system dynamics. This project focuses on the research of rigid-flexible-thermal coupling dynamic problems for functionally graded material plates undergoing large overall motion by using meshless methods which is more suitable for high-speed rotating and large deformation cases to describe the deformation of flexible body. The research of the project will be done on the following respects:.1..The establishment of high-order rigid-flexible coupling dynamic model for a rotating flexible plate undergoing large overall motion based on meshless methods, in which the drawbacks of the assumed mode method and finite element method will be a serious consideration under the condition of high-speed rotation and large deformation. The simulation results will show that the meshless method is superior in high-speed rotating and large deformation cases..2..The establishment of high-order rigid-flexible coupling dynamic model for a functionally graded material plate undergoing large overall motion based on high-order shear deformation theory, in which considering the shear deformation and material nonlinearity and seeking the method to avoid shear locking phenomenon will be the key research points. The established dynamic model will be not only suitable for thin plate but also for thickness plate..3..The establishment of rigid-flexible-thermal coupling dynamic model for hub functionally graded material plate multibody system under thermal load, in which the heat conduction equation is strongly coupled with the rigid-flexible coupling dynamics equation, and the research will focus on the method of solving this strong coupling equation.

针对柔性多体系统动力学中柔性板的变形场描述方法及动力学建模理论存在的缺陷，本课题拟采用更适合高速旋转和大变形工况下的无网格法描述柔性体的变形，对作大范围旋转运动的功能梯度材料板的刚-柔-热耦合动力学问题进行研究。本课题的主要研究内容为:1、建立无网格法描述的作旋转运动的柔性板高次刚柔耦合动力学模型，重点研究高速转动及大变形工况下假设模态法和有限元法的不足，通过仿真对比，说明无网格法在计算上的优越性。2、建立高阶剪切变形理论下，作旋转运动的功能梯度材料板的高次刚柔耦合动力学模型，重点研究考虑板的剪切变形及材料非线性的动力学模型的建立和避免出现剪切闭锁的方法，使建立的动力学模型既适用于薄板，又适用于中厚板。3、考虑热效应，建立系统的刚-柔-热耦合动力学模型，重点研究热传导方程与刚-柔耦合动力学方程强耦合问题的求解方法。

工程中有很多柔性附件搭载于刚性主体的刚-柔耦合结构，如空间机械臂、人造卫星天线、直升机旋翼、太阳能帆板以及航空发动机叶片等。上述实际工程问题都可以简化为转动的中心刚体-柔性悬臂梁或悬臂板模型等典型的刚-柔耦合系统进行动力学分析，而能否正确合理的描述柔性体的变形场将对仿真结果的精度及计算效率产生重要的影响。因此，对变形场的离散方法研究一直是刚-柔耦合系统动力学领域的热点和难点，也是工程和科学领域的迫切需求。本项目对刚-柔耦合系统动力学的离散方法和建模理论进行研究，将近年来发展迅猛的无网格法和光滑有限元法引用到柔性多体系统动力学中，以期丰富柔性多体系统动力学的变形场离散方法和进一步完善其建模理论。. 基于浮动坐标系方法，采用假设模态法、有限元法、径向基点插值法和光滑有限元法描述板的变形场，考虑剪切变形、材料非均匀性、非线性耦合变形量和热效应的影响，建立了能处理不同厚长比的作大范围运动功能梯度材料矩形板的一次近似刚-柔-热耦合动力学模型和高次刚-柔-热耦合动力学模型。研究发现非线性耦合变形量的高阶项主要影响大变形工况；在同等计算条件下，无网格法具有更好的计算稳定性；给定沿厚度变化的功能梯度材料，功能梯度指数的增加会使系统柔性变大；温度场能引起系统轴向变形的高频振荡，对横向弯曲变形的影响相对偏弱，且该影响随着转速的增大逐渐减弱；绕定轴做匀速转动的中心刚体-悬臂板的相邻两阶自由振动固有频率会发生频率转向现象。