Uniqueness of Steady-state Paths and Symmetry Limit

本文的研究结果概括如下：1.对于受完全反向循环弯曲的一维连续介质夹层梁柱模型，给出了稳态增量变化唯一的充分条件，即稳态路径唯一的充分条件。2.前人提出的先验对称极限理论。是基于在没有证明的情况下提出的五个假设。本文发展了一种新的对称极限理论，该理论涉及任何不确定假设，其中对称极限被预测为临界点，在该临界点，稳态路径唯一性的充分条件首先在基本稳态路径上被打破。3.对于受完全可逆的端部挠度循环程序作用的悬臂梁柱，证明了新理论得到的对称极限解与…一致4.对于受COIDA程序约束的悬臂梁柱，证明了变形构型相对于跨中横轴的对称性在对称极限幅值下被破坏，而平衡路径的唯一性不受损失。这与Hill的平衡路径唯一性准则相矛盾。5.对模型刚体-弹簧的滞回响应进行了闭合形式的分析。将支承梁柱转化为COIDA程序，阐明了反对称挠度分量的出现机理，并对4.6中提出的矛盾作了明确的解释。指出了稳态路径唯一性的充分条件与平衡路径唯一性的充分条件之间的基本区别。7.对于具有初始杆件轴线和对称截面轴的悬臂梁柱，应用对称极限理论，阐明了面外挠度的出现机理，并预测了面内行为极限。通过试验验证了平面内行为极限的存在。8.建立了预测端部横向力完全相反且幅值不断增大的悬臂梁柱对称极限的理论。这些对称性极限的存在已被实验所证实。较少

The results obtained in the present investigations are summarized as follows:1.A sufficient condition for uniqueness of the incremental variation of steadystate, namely that for uniqueness of steady-state path, has been derived for a one-dimensional continuum model of sandwich beam-column subjected to completely reversed cyclic bending.2.The provious symmetry limit theory due to the present head investigator et.al. is based upon five hypotheses introduced without proves. Developed in the present study is a new symmetry limit theory involving any uncertain assumption, where a symmetry limit is predicted as the critical point, at which the sufficient condition for uniqueness of steady-state paths is first broken on the fundamental steady-state path.3.For cantilever beam-columns subjected to a completely reversed tip-deflection cycling program with continuously increasing amplitude, which is named COIDA, the symmetry limit solutions obtained by the new theory have been shown to coincide w … More ith those obtained by the previous theory.4.It has veen shown for a cantilever beam-column subjected to a COIDA program that the symmetry of deformed configurations with respect to the mid-span lateral axis is broken at the symmetry-limit amplitude without loss of uniqueness of equilibrium paths. This contradicts Hill's uniqueness criterion of equilibrium paths.5.By a closed-form analysis of the hysteretic response of a rigid body-spring of model smiply. supported beam-column to a COIDA program, the appearance mechanism of the anti-symmetric deflection component has been clarified and a clear explanation has been given to the contradiction stated in 4.6.Basic differences between a sufficient condition for uniqueness of steady-state paths and that for uniqueness of equilibrium paths have been pointed out.7.For cantilever beam-columns subjected to a COIDA program in a plane containing the initial member axis and a cross-sectional axis of symmetry, the appearance mechanisms of out-of-plane deflection have been clarified and in-plane behavior limits have been predicted by applying the symmetry-limit theory. The existence of in-plane behavior limits has been verified by experiments.8.A theory has been established for predicting the symmetry limits of cantilever beam-columns subjected to completely reversed tip lateral force with continuously increasing amplitude. The existence of these symmetry limits has been verified by experiments. Less