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考虑非局部效应和记忆依赖微分的广义热弹问题

张培 何天虎

张培, 何天虎. 考虑非局部效应和记忆依赖微分的广义热弹问题[J]. 力学学报, 2018, 50(3): 508-516. doi: 10.6052/0459-1879-18-079
引用本文: 张培, 何天虎. 考虑非局部效应和记忆依赖微分的广义热弹问题[J]. 力学学报, 2018, 50(3): 508-516. doi: 10.6052/0459-1879-18-079
Zhang Pei, He Tianhu. A GENERALIZED THERMOELASTIC PROBLEM WITH NONLOCAL EFFECT AND MEMORY- DEPENDENT DERIVATIVE[J]. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(3): 508-516. doi: 10.6052/0459-1879-18-079
Citation: Zhang Pei, He Tianhu. A GENERALIZED THERMOELASTIC PROBLEM WITH NONLOCAL EFFECT AND MEMORY- DEPENDENT DERIVATIVE[J]. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(3): 508-516. doi: 10.6052/0459-1879-18-079

考虑非局部效应和记忆依赖微分的广义热弹问题

doi: 10.6052/0459-1879-18-079
基金项目: 国家自然科学基金资助项目(11372123).
详细信息
    作者简介:

    通讯作者:何天虎,教授,主要研究方向:多场耦合及电磁固体力学. E-mail:heth@lut.edu.cn

    通讯作者:

    何天虎

  • 中图分类号: O343.6;

A GENERALIZED THERMOELASTIC PROBLEM WITH NONLOCAL EFFECT AND MEMORY- DEPENDENT DERIVATIVE

  • 摘要: 现有的广义热弹理论主要适用于求解时间尺度极短但空间尺度仍属宏观尺度的广义热弹问题的动态响应,而当所研究的弹性体的特征几何尺寸也属微尺度时,弹性体的力学响应将呈现出强烈的尺寸相关性,现有的广义热弹理论不再适用. 本文基于通过非局部效应和记记依赖微分修正的广义热弹性理论,研究了两端固定、受移动热源作用的有限长热弹杆的动态响应. 建立了问题的控制方程,给出了问题的初始条件及边界条件,运用拉普拉斯变换及其数值反变换,对方程进行了求解. 数值计算中,首先考察了时间延迟因子对模型所预测各物理量分布的影响;然后对比了模型中的时间延迟因子在两种不同类别核函数下(通过归一化条件修正和未修正形式)对各物理量分布的影响效应;最后考察了考虑新的可以描述尺寸效应的非局部因子对无量纲温度、位移及应力的影响,并用图形进行了示例. 结果表明, 时间延迟因子增大,各物理量的峰值变大,传播距离变小,且时间延迟因子在归一化条件修正过的核函数下影响更加显著;非局部参数几乎不影响无量纲温度的分布,轻微影响无量纲位移的分布,但对无量纲应力的峰值的影响显著.

     

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出版历程
  • 收稿日期:  2018-03-19
  • 刊出日期:  2018-05-18

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