可变杆系结构展开过程的数值模拟

NUMERICAL SIMULATION FOR THE DEPLOYMENT OF VARIABLE MEMBER STRUCTURES

可变结构的应用范围很广,如建筑和航空领域中的折叠帐篷、可展天线等。采用了以自然坐标描述的多体系统动力学的有限元方法,根据基于刚体假设的最小应变能原理与拉格朗日乘子法给出了多体系统运动学基本方程的建立方法,并结合Hamilton原理建立了约束多体系统动力学基本方程,并讨论了数值模拟的收敛准则。最后基于MATLAB软件平台编制了多体系统动力学的有限元分析程序,通过对平面双摆机构的数值模拟,表明需要考虑数值阻尼以保证数值稳定及精度。最后对一四连杆机构的运动过程进行了数值模拟,验证了该文方法适用于可变杆系结构展开过程分析的可行性。

Variable structures are widely used in civil and aeronautic engineering, such as the deployable shelter and foldable antenna, etc. The mutibody dynamics of the finite element method with natural coordinates is used in this analysis. Based on the minimum strain energy method with the rigid body hypothesis and the Lagrangian multiplier method, the fundamental equations construction of multibody kinematics is given. And based on Hamiltonian theory, the fundamental equations construction of multibody dynamics is illustrated. The convergence principle of numerical simulations is also investigated. An analysis program is written with MATLAB software. By simulating a planar double pendulum, the results indicate that the numerical damper should be considered to ensure numerical stability and precision. Finally, the motion analysis of a four-bar linkage is carried out to verify that the proposed method can be used to simulate the deployment of variable member structures.