摘要
对热载荷作用下中心刚体与大变形薄板多体系统的动力学建模问题进行研究.基于Kirchhoff假设,从格林应变和曲率与绝对位移的非线性关系式出发,推导了非线性广义弹性力阵,用绝对节点坐标法建立了大变形矩形薄板的有限元离散的动力学变分方程.为了考虑刚体姿态运动、弹性变形和温度变化的相互耦合作用,推导了热流密度与绝对节点坐标之间的关系式.引入系统的运动学约束方程,建立了中心刚体-矩形板多体系统的考虑刚-柔-热耦合的热传导方程和带拉格朗日乘子的第一类拉格朗日动力学方程.为了有效地提高计算效率,将改进的中心差分法和广义-α法相结合,求解热传导方程和动力学方程,差分后的方程通过牛顿迭代法耦合求解.对刚-柔耦合和刚-柔-热三者耦合两种模型的仿真结果进行比较表明,刚体运动对温度梯度和热变形的影响显著.此外,本文建模方法考虑了几何非线性项,因此也考虑了热膨胀引起的轴向变形对横向变形的影响.
In this paper, rigid-flexible-thermal coupling dynamic formulation for hub rectangular plate muhibody system with large deformation under thermal load is investigated. Based on Kirchhoff assumption, and the nonlin- ear relationships among the Green strain, the curvature and the absolute coordinates, the nonlinear elastic force is derived. Additionally, the finite element discretized dynamic variational equations of the rectangular plate are de- rived using absolute nodal coordinate formulation. In order to investigate the rigid-flexible-thermal coupling effect, the relationship between the heat flux and the absolute coordinates is also obtained. And through the con- strained equations of the muhibody system, the rigid-flexible-thermal coupling equations are derived, which in- clude the heat conduction equations and the Lagrange dynamic equations of the first kind. Moreover, in order to improve the simulation efficiency, modified central difference method and generalized-a method are combined to solve the heat conduction equations and the dynamic equations. And the discretized equations are solved by using Newton-Raphson method. Satellite and plate multibody system applied with solar heat flux is taken as examples to verify the effectiveness of the formulation. Comparison of the results obtained by non-coupling method and rigid- flexible-thermal coupling method shows that the effect of the rigid body motion on the temperature gradient in the thickness direction and thermally induced deformation is significant, which should be taken into account. Fur- thermore, due to the inclusion of the geometric nonlinear terms, the influence of the axial deformation caused by the temperature increase on the transverse deformation is also taken into consideration.
出处
《动力学与控制学报》
2016年第5期438-447,共10页
Journal of Dynamics and Control
基金
国家自然科学基金资助项目(11272203
11132007)~~
关键词
大变形薄板多体系统
刚-柔-热耦合
改进的中心差分法
hub-plate multibody system
rigid-flexible-thermal coupling
modified central difference method
