铰接杆系机构稳定性条件分析

Analysis of stability conditions for pin-bar mechanisms

基于能量准则,讨论了铰接杆系机构的稳定性问题.通过分析体系切线刚度矩阵解析表达式的构成,阐明了机构的稳定仅来源于可行内力(预应力或外荷载效应)的强化,严格证明了经典预应力机构的稳定性判别准则,其等同于系统势能二阶变分的正定性条件,同时指出该准则的不完善性.针对荷载强化机构的稳定问题,提出了相应的稳定性判别准则并辅以算例说明.最后对几何稳定性问题的实质、结构和机构的定义以及机构稳定性的必要条件等问题进行了相关讨论.

Structural stability conditions for pin-bar mechanism system were investigated on the basis of energy criterion. From analytical expression of tangential stiffness matrix, the structural stability of mechanisms is expounded as resulting from reinforcement of feasible internal forces caused by prestress or loading. Classical stability criterion for prestressed mechanism was rigidly proved, and clarified to be equivalent to positive definitive second-order variation of potential energy. Imperfection of this criterion was also pointed out. Further investigations on the stability of mechanism stiffened by loading were carried out, and a corresponding stability criterion was developed and explained by means of an illustrative example. Some discussions on essential of geometrical stability issue, conventional definition of structures and mechanism, and necessary condition of mechanism stability were provided in the end to improve understanding of the structural stability of pin-bar mechanisms.