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中文摘要：
平面折梁单元是可开启结构中的常用单元类型。在平面梁单元基础上,构造平面多角折梁以及折梁单元组成的剪式铰两种超级单元,利用矩阵缩聚理论将内部自由度封装,推导超级单元平衡矩阵,组装可开启结构的整体平衡矩阵。通过矩阵奇异值分解,分离出自应力模态、机构位移模态、最小非零奇异值等信息,对可开启结构进行机动性能分析。运用基于平衡矩阵分解的非线性力法,提出主动与被动控制实现机构轨迹模拟。最后,基于该文给出的算法,从数值计算的角度寻找两类圆形径向可开启结构的拓扑形式,并模拟开启运动轨迹。
英文摘要：
Planar multi-angulated beams are commonly used in retractable structures. They are generated based on planar beam. The inner degree-of-freedoms （DOFs） of these macro-elements are packaged, and the equilibrium matrices are deduced by matrix reduction theory. The global equilibrium matrix is assembled by element equilibrium matrix. The characteristics of structural and kinematic properties, e.g. modes of independent states of self-stress and inextensional mechanisms, minimum non-zero singular values, etc., are achieved by equilibrium matrix SVD（Singular Value Decomposition）. The kinematic properties and mobility condition of retractable structures are analyzed. Then the geometrically nonlinear force method is introduced, and two kinds of trajectory tracking simulation methods, i.e. active and positive control, are proposed and the corresponding algorithm procedures are listed. Based on the equilibrium matrix analysis method this paper discussed, the topology of two types of circular radially retractable structure is found numerically. The trajectory tracking simulations of retractable structures are also illustrated.
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