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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 the bifurcation of the balanced path when the ideal structure is destabilized is that the generalized tangent stiffness is zero, and the controllability between the external load and the structure displacement is lost and the structure is singular. Based on the similarity between the bifurcation of the mechanism motion and the bifurcation of the structure equilibrium path, the derivative of the state variable about the control variable is defined in the mechanism. It is proved that when the stiffness is zero, infinity or 0/0 type, the controllable variables corresponding to the mechanism lose controllability with the state variables, and the bodies appear singular. The corresponding singular configurations are classified. Defining the stiffness of a class as a class of stiffness equal to zero, an infinite or a 0/0 type, a new method called class-stiffness method is proposed to solve simultaneous equations of stiffness and to solve the bifurcation of the mechanism. The feasibility and superiority of this method are verified by an example of a two-degree-of-freedom mechanism.