非均质材料有限变形下的热弹性随机均化方法

发布时间：2018-02-07 15:19

本文关键词： 热弹性随机均化非均质材料随机有效性质数字特征值　出处：《西安电子科技大学学报》2017年03期 　论文类型：期刊论文

【摘要】：在有限变形条件下,充分考虑微观结构具有不确定性时对二相非均质材料进行热弹性随机均化分析.将蒙特卡洛方法和多尺度有限元方法相结合,构建了有限变形下的热弹性随机均化框架.采用两步法分别对有限变形下非均质材料的宏观随机有效力学和有效热学性质进行了求解,并进一步对随机有效性质的数字特征值进行了推导,得到了应力张量、热流量张量、变形梯度张量等随机有效量.最后通过算例对所提方法进行了验证,得出了不同相关条件及边界条件下随机有效量的均值和变异系数.讨论了不同相关条件及边界条件下随机有效量在表征体积单元中的分布.结果表明,有限变形下微观结构中客观存在的随机性和相关性在热弹性的随机均化分析中不能忽略.
[Abstract]:Under the condition of finite deformation, considering the uncertainty of microstructure, the thermoelastic random homogenization analysis of two-phase heterogeneous materials is carried out. The Monte Carlo method is combined with the multi-scale finite element method. The thermoelastic random homogenization frame under finite deformation is constructed, and the macroscopic stochastic effective mechanics and effective thermal properties of heterogeneous materials under finite deformation are solved by two-step method, respectively. Furthermore, the numerical eigenvalues of stochastic effective properties are derived, and the random effective quantities such as stress Zhang Liang, heat flux Zhang Liang and deformation gradient Zhang Liang are obtained. Finally, the proposed method is verified by a numerical example. The mean value and coefficient of variation of the random effective quantity under different correlation conditions and boundary conditions are obtained. The distribution of the random effective quantity in the characterizing volume unit under different correlation conditions and boundary conditions is discussed. The randomness and correlation of the microstructure under finite deformation can not be ignored in the stochastic homogenization analysis of thermoelasticity.
【作者单位】：西安电子科技大学机电工程学院;
【基金】：国家自然科学基金资助项目(11572233);国家自然科学基金青年基金资助项目(11102143) 中央高校基本科研业务费专项资金资助项目(JBG150405)
【分类号】：TB30

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