基于机构位移模态的受荷可展结构平衡状态找形方法

Form-finding approach for equilibrium configuration of deployable structure subjected to external loads based on internal mechanism

基于欠约束机构和过约束机构的共性,提出了一种运用内部机构位移分析受荷可展结构平衡状态的找形方法.通过建立体系的势能函数,利用最速下降原理,推导了机构位移模态的组合系数,以确定荷载作用下可展结构的运动方向.机构位移模态可由可展结构的平衡矩阵经奇异值分解求得.给出了非线性找形算法的详细流程,并推导了平衡状态判定公式.最后,以空间铰接杆系机构与径向可开启结构为数值算例,实现了找形过程的运动模拟及平衡状态的确定,并探讨了可开启结构在不同荷载模式下的展开率.研究表明,基于机构位移模态的找形算法具有很好的准确性及稳定性.

Based on the common characteristics of under-constraint and over-constraint mechanism,a form-finding approach for equilibrium configuration of deployable structure subjected to external loads is proposed.The potential energy equation of system is established.Utilizing the rapid convergence theory of the steepest descent method,the combination coefficient of mechanism modes is deduced,which can be used for the determination of the movement direction under different load patterns.The inextensional mechanism mode is generated by the singular value decomposition of equilibrium matrix for deployable structure.The detailed algorithm procedure for the form-finding approach is conducted and the criterion of equilibrium configuration is also presented in the paper.Finally,the numerical simulation of a three-dimensional pin-jointed mechanism and a radial retractable structure are illustrated.Furthermore,the expansion ratio of the retractable structure under different load patterns is discussed.The analysis shows that the unified form-finding approach based on internal mechanism had good accuracy and robustness.