Uniqueness of Steady-state Paths and Symmetry Limit

本文的主要研究结果如下：1.对于完全反向循环弯曲的夹层梁柱的一维连续体模型，导出了稳态增量变化唯一性的充分条件，即稳态路径唯一性的充分条件。2.本文的主要研究者等人提出的对称极限理论是建立在五个未经证明的假设基础上的。本文提出了一种新的对称极限理论，该理论包含任何不确定性假设，并将对称极限作为临界点，在临界点处，基本稳态路径唯一性的充分条件首先被破坏。3.对于悬臂梁-柱，在连续增幅的完全反向挠度循环程序（COIDA）下，用新理论得到的对称极限解与 ...更多信息 4.对悬臂梁-柱进行COIDA程序计算，结果表明，在不损失平衡路径唯一性的前提下，变形构形关于跨中横轴线的对称性在极限振幅处被破坏。这与Hill的平衡路径唯一性准则相矛盾。5.通过对一个刚体-弹簧模型的滞回响应的解析分析，证明了该模型的正确性。支撑梁柱的COIDA程序，阐明了反对称挠度分量的出现机理，对4.6中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的根本区别。柱进行了COIDA程序在一个平面内包含初始成员轴和横截面对称轴线，平面外偏转的外观机制已被澄清和平面内的行为限制已被预测，通过应用弹性极限理论。通过试验验证了平面内行为极限的存在性。8.建立了悬臂梁-柱在连续增幅的完全反向端侧力作用下对称极限的理论。这些对称极限的存在已被实验所证实。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