Uniqueness of Steady-state Paths and Symmetry Limit

本文的研究结果总结如下：1。对于完全反向循环弯曲的一维夹层梁柱连续体模型，导出了稳态增量变化惟一性的充分条件，即稳态路径惟一性的充分条件。由现任首席研究员等人证明的对称极限理论。是基于五个未经证明的假设。本文提出了一种新的涉及任何不确定假设的对称极限理论，其中预测了一个对称极限作为临界点，在该临界点上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。对于悬臂梁柱受幅值不断增加的完全相反的顶挠度循环程序（COIDA），新理论得到的对称极限解与以前的理论得到的解更加吻合。它甚至证明了悬臂梁柱受COIDA程序的影响，变形构型相对于跨中横向轴的对称性在对称极限振幅处被打破，而平衡路径的唯一性却没有丧失。这与希尔均衡路径的唯一性准则相矛盾。通过简单分析刚体-弹簧模型的滞回响应的封闭形式。通过COIDA程序，澄清了反对称挠度分量的出现机理，并对4.6中所述的矛盾给出了明确的解释。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。在包含初始构件轴和横断面对称轴的平面上，对经COIDA程序处理的悬臂梁柱，应用对称极限理论，阐明了其面外挠度的出现机理，并预测了其面内行为极限。平面内行为极限的存在已被实验证实。建立了一种预测悬臂梁柱在振幅不断增大的完全反向顶侧力作用下对称极限的理论。这些对称极限的存在性已被实验证实。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