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On a symplectic analytical singular element for cracks under thermal shock considering heat flux singularity

机译：考虑热通量奇异性的热冲击裂纹的辛分析奇异单元

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摘要

In a precise numerical modelling of cracks under thermal shock, the singularity issue resulted from heat flux should also be considered in addition to the one resulted from stress. The assumptions of constant temperature distribution usually adopted in the existing studies may lead to significant error. The concerned problem involves the discretization in both space and time domains. Numerical error resulted from the singularity issues in the space domain may be accumulated in the time domain. Hence, a unified framework which integrates reliable methods for both space and time domains are desired. In the present contribution, the classic thermal stress problem is restudied under the Harniltonian system and the eigen functions are obtained analytically. A symplectic analytical singular element (SASE) for thermal stress analysis is reformulated based on the existing ones for thermal conduction and stress analyses. The singularity issues of both stress and heat flux are considered. A unified framework is formed with the precise time domain expanding algorithm (PTDEA) for the time domain and the formulated SASE for the space domain. A self-adaptive technique is used for the PTDEA to improve the numerical efficiency. The time dependent fracture parameters i.e., heat flux intensity factors (HFITs) and the mixed mode thermal stress intensity factors (TSIFs) can be solved accurately without any postprocessing. Numerical examples are given for verification and validation of the proposed method.
机译：在热冲击下的裂纹的精确数值模型中，除了应力引起的裂纹外，还应考虑由热通量引起的奇异性问题。现有研究中通常采用的恒定温度分布假设可能会导致重大误差。有关的问题涉及时域和离散的离散化。由时域中的奇异性问题引起的数值误差可能会在时域中累积。因此，需要一种集成了针对时域和时域的可靠方法的统一框架。在目前的贡献中，经典的热应力问题在Harniltonian系统下进行了重新研究，并且本征函数得到了解析。在现有的热传导和应力分析基础上，重新构造了用于热应力分析的辛分析奇异元素（SASE）。考虑了应力和热通量的奇异性问题。通过针对时域的精确时域扩展算法（PTDEA）和针对空间域的公式化SASE形成了一个统一的框架。 PTDEA使用自适应技术来提高数值效率。随时间变化的断裂参数，即热通量强度因子（HFIT）和混合模式热应力强度因子（TSIF）可以得到精确求解，而无需任何后处理。数值算例验证了该方法的有效性。

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  • 来源
    《Applied Mathematical Modelling》 |2020年第4期|1-16|共16页
  • 作者

  • 作者单位

    State Key Laboratory of Structural Analysis for Industrial Equipment International Research Center for Computational Mechanics Dalian University of Technology Dalian 116024 China;

    Shanghai Electro-Mechanical Engineering Institute Shanghai 201109 China;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    Symplectic approach; Thermal shock; Stress intensity factor; Heat flux intensity factor;

    机译：辛方法热冲击;应力强度因子;热通量强度因子;

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