铰接杆系机构运动分岔分析新方法——类刚度法  

A NEW APPROACH FOR KINEMATIC BIFURCATION ANALYSIS OF PIN-BAR MECHANISMS——ANALOGIOUS STIFFNESS METHOD

作　　者：周练[1] 袁行飞[1] 

机构地区：[1]浙江大学空间结构研究中心,浙江杭州310058

出　　处：《工程力学》2012年第10期199-204,共6页Engineering Mechanics

基　　金：国家自然科学基金项目(51278461);浙江省重点科技创新团队项目(2010R50034)

摘　　要：阐述了理想结构失稳时平衡路径出现分岔的本质是广义切线刚度为零,外荷载与结构位移之间失去可控性,结构出现奇异。基于机构运动分岔与结构平衡路径分岔的相似性,在机构中定义了类刚度为状态变量关于控制变量的导数。证明了当类刚度为零、无穷大或0/0型时,机构对应的控制变量与状态变量之间失去可控性,机构出现奇异;并对相应的奇异构型进行了归类。定义类刚度方程为类刚度等于零、无穷大或0/0型,提出了联立类刚度方程和协调方程求解机构运动分岔点的新方法——类刚度法。通过双自由度机构算例验证了此方法的可行性和优越性。The essence of equilibrium-path bifurcations in ideal structural instability was revealed.It was shown that when the generalized tangent stiffness becomes zero,the external forces and structural displacements lose control of each others,which leads to singularity of structures.Based on the analogy between equilibrium-path bifurcations of structures and kinematic bifurcations of mechanisms,the analogous stiffness in mechanisms was defined as the derivative of the state variable on the controlling variable.It was proved that when the analogous stiffness becomes zero,infinite or 0/0 type,the corresponding controlling and state variables lose control of each other and singularity of mechanisms emerges,whose corresponding singularity configurations were classified.After defining the analogous stiffness equations as the analogous stiffness being zero,infinite or 0/0,the analogous stiffness method was proposed to detect kinematic bifurcations of mechanisms by solving analogous stiffness equations and compatibility equations simultaneously.Finally,the validity and advantage of the present method were illustrated by a typical 2-DOF example,based on the method.

关 键 词：机构运动 运动分岔 奇异 广义切线刚度 类刚度 类刚度方程 

分 类 号：TU323[建筑科学—结构工程] TU311.2