极限荷载的突变模型研究

STUDY ON THE ULTIMATE LOAD WITH CATASTROPHE MODELS

结构的极限荷载是研究结构整体失效破坏和安全度的重要内容,该文以混凝土重力坝为对象,采用突变理论来研究混凝土重力坝的极限荷载,探讨重力坝沿建基面破坏时不同突变模型对极限荷载的影响。假定重力坝坝体和地基为刚性体,建基面存在一薄弱结合面,以建基面水平方向的位移为状态变量,施加的上游水压力为控制变量,分别建立反映此模型沿建基面失稳破坏的折迭突变模型和尖点突变模型,求出相应的极限荷载。研究表明,折迭突变模型得到的结果与力学系统稳定性理论解一致,而尖点突变模型给出的结果偏小。并指出,如果破坏面材料的本构关系为理想弹塑性或只考虑硬化阶段,确定重力坝整体稳定性的最大极限荷载宜采用折迭突变模型。如果需要研究破坏面材料进入软化阶段时的残余极限荷载,宜用尖点突变模型。

The determination of the ultimate load of structures is a key issue for the analysis of structural failure and safety index.In this paper,catastrophe theory is used to evaluate the ultimate load of a concrete gravity dam.Different catastrophe models of the ultimate load are discussed for the ultimate failure of the gravity dam along the base surface.In the analytical model,both the dam and the foundation are assumed as rigid bodies,and the base surface of the dam is considered sitting on a weak interface.With the horizontal displacement of the base surface regarded as a state variable and the applied upper water pressure as a control variable,the fold and cusp catastrophe models for the unstable failure of the above simple model are established,and the corresponding values of the ultimate load are obtained.It shows that the result by the fold catastrophe model is consistent with the available theoretical value,but the one by the cusp catastrophe model is smaller.It also demonstrates that the fold catastrophe model is capable of determining the maximal ultimate load against the ultimate failure of gravity dam when the material constitutive relationship of failure surface is elastic-perfectly plastic or only the hardening stage is considered.The cusp catastrophe model is suitable for obtaining the residual ultimate load when the material in failure surface goes in the softening stage.