动力失稳的拟静力刚度准则与能量判别准则

以可模拟非线性保守结构体系的一个计算模型为例,重点分析、对比了判别结构动力稳定性的拟静力刚度准则和能量判别准则。拟静力刚度准则依靠切线刚度非正定判定结构发生动力失稳可能导致误判。能量判别准则适用于具有屈曲后不稳定平衡路径的结构,利用屈曲后不稳定平衡路径上鞍点处的总势能作为动力失稳临界能量,结构总能量超越临界能量则判定为动力失稳。振动极值位移随荷载变化的曲线可以作为一种动力平衡路径,在接近临界荷载时,荷载的微小增量会导致结构振动极大位移显著增大,最终在临界点发生跃越失稳。

Pseudo-static stiffness criterion and energy discriminant criterion for dynamic instability

A model suitable for simulating nonlinear conservative structural system being taken as an example, the pseudo-static stiffness criterion and the energy discriminant criterion for dynamic iAbnstability are analyzed and compared. The pseudo-static stiffness criterion may misjudge the structural dynamic instability according to the non-positive definiteness of the tangent stiffness. The energy discriminant criterion is applicable to structures with unstable postbuckling equilibrium paths. The total potential energy at the saddle point on the unstable postbuckling equilibrium path is taken as the critical energy, and dynamic instability is discriminated if the total energy exceeds the critical energy. Extremum dynamic displacement vs. load curve is taken as a dynamic equilibrium path. It is observed that small load increment near the critical load leads to significant increase of the maximum dynamic displacement and finally snaps-through at the critical point.