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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。
Planar Beam units are common unit types in openable structures. Based on the planar beam element, two kinds of super-elements of the planar hinge consisting of a planar polygonal folded beam and a folded beam element are constructed. The internal degree of freedom is encapsulated by using the matrix polycondensation theory to deduce the superunit balancing matrix and assemble the integral balance matrix of the openable structure . Through matrix singular value decomposition, the information of self-stress mode, displacement mode and minimum non-zero singular value are separated, and the maneuverability of the open structure is analyzed. Using the nonlinear force method based on equilibrium matrix decomposition, active and passive control is proposed to realize the mechanism trajectory simulation. Finally, based on the algorithm presented in this paper, two kinds of topological structures with circular and radially openable structures are searched from the numerical calculation point, and the trajectories are opened.