形状记忆合金数值模型的不确定性分析
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TU512.9.

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国家自然科学基金(51878390)


Probabilistic analysis of shape memory alloy modeling
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    摘要:

    形状记忆合金(shape memory alloy,简称为SMA)具有"超弹性",即在受到应力而发生较大变形并卸载后,可以恢复原始形状,并在这个过程中耗散能量,在建筑抗震和桥梁振动控制中具有广阔的应用前景。SMA的模型参数通常由优化方法来确定,然后用于装有SMA装置的结构地震时程响应分析中。利用Metropolis-Hasting算法(简称为MH算法)中的改进算法DRAM方法(延迟拒绝及自适应采样),基于经过"预拉伸"和热处理的SMA棒材循环拉伸试验结果,对SMA改进的Graesser&Cozzarelli模型参数进行采样,从SMA的本构模型参数和耗能能力两个方面分析了SMA材料的不确定性。建立了各参数的后验分布,并得到了参数两两之间的相关性,结果可用于概率模型的建立及基础模型数学形式的研究。研究表明,在累积概率密度为15%时,材料的能量耗散能力相对误差高达20%;累积概率密度为85%时,相对误差为10%。

    Abstract:

    Shape memory alloy(SMA) has "super elasticity", that is, it can recover original shape after deformation and unloading due to stress, and dissipate energy in this process. It has broad application prospect in seismic control of buildings and bridge vibration. The model parameters of SMA are often determined through optimization and treated as deterministic for dynamic analysis of structures with SMA based devices. In this study, the modified Metropolis-Hasting algorithm-DRAM algorithm, which is a combination of delay rejection and adaptive sampling, is utilized to characterize the uncertainties in modified Graesser & Cozzarelli SMA model parameters. A series of SMA bars with the same geometric size and heat treatment were tested under cyclic loads. The Markov Chain Monte Carlo (MCMC) method is applied to analyze the uncertainties of SMA in terms of model parameters and energy dissipation capacity. The analysis provide insight into the underlying mathematical form of a model, suggest simplifications or modifications and begin to indicate the relative significance of individual parameters, based on a limited set of experimental data. Besides, research shows thatthe energy dissipation of the SMA bar could have up to a relative error of 20% and 10% corresponding to the CDF of 15% and 85%.

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李金朋,陈城,侯和涛.形状记忆合金数值模型的不确定性分析[J].土木与环境工程学报(中英文),2020,42(6):112-118.

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  • 收稿日期:2020-03-20
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  • 在线发布日期: 2020-11-26
  • 出版日期: 2020-12-31