基于平面折梁单元的可开启结构平衡矩阵分析方法  

EQUILIBRIUM MATRIX ANALYSIS OF RETRACTABLE STRUCTURE FORMED BY PLANAR MULTI-ANGULATED BEAM

作　　者：陆金钰[1] 罗尧治[1] 

机构地区：[1]浙江大学空间结构研究中心,浙江杭州310027

出　　处：《工程力学》2009年第2期148-157,共10页Engineering Mechanics

基　　金：国家自然科学基金重大项目(50638050);新世纪优秀人才支持计划项目(NCET-06-0517)

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。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.

关 键 词：可开启结构 超级单元 机动分析 平衡矩阵 矩阵缩聚 运动路径跟踪 

分 类 号：TU393.3[建筑科学—结构工程]