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首页> 外文期刊>Journal of Heat Transfer >A Symplectic Analytical Singular Element for Steady-State Thermal Conduction With Singularities in Anisotropic Material
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A Symplectic Analytical Singular Element for Steady-State Thermal Conduction With Singularities in Anisotropic Material

机译：各向异性材料中具有奇异性的稳态导热的辛分析奇异元

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摘要

Modeling of steady-state thermal conduction for crack and v-notch in anisotropic material remains challenging. Conventional numerical methods could bring significant error and the analytical solution should be used to improve the accuracy. In this study, crack and v-notch in anisotropic material are studied. The analytical symplectic eigen solutions are obtained for the first time and used to construct a new symplectic analytical singular element (SASE). The shape functions of the SASE are defined by the obtained eigen solutions (including higher order terms), hence the temperature as well as heat flux fields around the crackotch tip can be described accurately. The formulation of the stiffness matrix of the SASE is then derived based on a variational principle with two kinds of variables. The nodal variable is transformed into temperature such that the proposed SASE can be connected with conventional finite elements (FE) directly without transition element. Structures of complex geometries and complicated boundary conditions can be analyzed numerically. The generalized flux intensity factors (GFIFs) can be calculated directly without any postprocessing. A few numerical examples are worked out and it is proven that the proposed method is effective for the discussed problem, and the structure can be analyzed accurately and efficiently.
机译：各向异性材料中裂纹和V型缺口的稳态热传导建模仍然具有挑战性。常规数值方法可能会带来很大的误差，应使用解析解来提高精度。在这项研究中，研究了各向异性材料中的裂纹和V型缺口。首次获得了解析辛本征解，并将其用于构造新的辛解析奇异元（SASE）。 SASE的形状函数由获得的本征解（包括高阶项）定义，因此可以精确描述裂纹/缺口尖端周围的温度以及热通量场。然后，基于具有两种变量的变分原理，得出SASE刚度矩阵的公式。节点变量被转换为温度，从而使所提出的SASE可以直接与常规有限元（​​FE）连接，而无需过渡元件。复杂的几何结构和复杂的边界条件的结构可以进行数值分析。广义通量强度因子（GFIF）可以直接计算而无需任何后处理。数值算例表明，该方法对所讨论的问题是有效的，并且可以对结构进行准确，高效的分析。

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  • 来源
    《Journal of Heat Transfer》 |2018年第9期|091301.1-091301.13|共13页
  • 作者

    X. F. Hu; W. A. Yao; S. T. Yang;

  • 作者单位

    State Key Laboratory of Structural Analysis forIndustrial Equipment,Dalian University of Technology,International Center for ComputationalMechanics,Dalian University of Technology;

    State Key Laboratory of Structural Analysis forIndustrial Equipment,Dalian University of Technology,International Center for ComputationalMechanics,Dalian University of Technology;

    Department of Civil and EnvironmentalEngineering,University of Strathclyde;

  • 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

    Temperature; Anisotropy; Fracture (Materials); Eigenvalues; Heat flux; Heat conduction; Steady state; Boundary-value problems; Wedges;

    机译：温度;各向异性;断裂（材料）;特征值;热通量;热传导;稳态;边值问题;楔形;

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