The Steady Loops of Sdof Perfectly Elastoplastic Structures Under Sinusoidal Loadings
The Steady Loops of Sdof Perfectly Elastoplastic Structures Under Sinusoidal Loadings
复制标题
正弦载荷作用下Sdof完美弹塑性结构的稳定环
DOI：
10.51400/2709-6998.2453
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发表时间：
2000
影响因子：
2.6
通讯作者：
Chein
中科院分区：
文献类型：
--
作者：
Chein
本文讨论了单自由度理想弹塑性结构在外荷载作用下的模型。分析指出，对于理想弹塑性结构，其运动方程只是一个带有开关的两相线性系统。在此基础上，导出了正弦载荷作用下动力响应的精确解。对于这样的加载，我们证明，无论多么大的振幅是，结构是不可能经历一个永久的塑性运动，相反，长期的行为表现出稳定的滞后环和极限环，或弹性安定。提出了稳态响应的相平面估计方法，包括位移幅值和两个时滞的计算公式，以及弹性安定参数和耗散环最大尺寸的确定。通过与精确解的比较，证实了公式的准确性。然而，平均位移取决于初始条件，瞬态响应，不由稳态估计确定。
The model of single degree of freedom perfectly elastoplastic structures under external loading is treated in this paper. It is analyzed and pointed out that for the perfectly elastoplastic structure the equation of motion is nothing but a two-phase linear system with an on-off switch. Then the exact solutions of the dynamic responses are derived for sinusoidal loadings. For such loading we prove that no matter how large the amplitude is, the structure is impossible undergoing a permanent plastic motion; conversely, the long term behavior exhibits either stable hysteresis loop and limit cycle, or elastic shakedown. A phase plane estimation method of the steady response is developed, which includes not only the formulae for calculating the amplitude of displacement and two time lags, but also the identification of the parameters’ values for elastic shakedown and the maximum size of dissipation loop. The accuracy of the formulae is confirmed by comparing with the exact solutions. The mean displacement however depends on the initial conditions, a transient response, not being determined by the steady state estimation.