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 crack/notch 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.
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September 2018
This article was originally published in
Journal of Heat Transfer
Research-Article
A Symplectic Analytical Singular Element for Steady-State Thermal Conduction With Singularities in Anisotropic Material
X. F. Hu,
X. F. Hu
State Key Laboratory of Structural Analysis for
Industrial Equipment,
Dalian University of Technology,
Dalian 116024, China;
International Center for Computational
Mechanics,
Dalian University of Technology,
Dalian 116024, China
e-mail: hxf@dlut.edu.cn
Industrial Equipment,
Dalian University of Technology,
Dalian 116024, China;
International Center for Computational
Mechanics,
Dalian University of Technology,
Dalian 116024, China
e-mail: hxf@dlut.edu.cn
Search for other works by this author on:
W. A. Yao,
W. A. Yao
State Key Laboratory of Structural Analysis for
Industrial Equipment,
Dalian University of Technology,
Dalian 116024, China;
International Center for Computational
Mechanics,
Dalian University of Technology,
Dalian 116024, China
Industrial Equipment,
Dalian University of Technology,
Dalian 116024, China;
International Center for Computational
Mechanics,
Dalian University of Technology,
Dalian 116024, China
Search for other works by this author on:
S. T. Yang
S. T. Yang
Department of Civil and Environmental
Engineering,
University of Strathclyde,
Glasgow G1 1XJ, UK
Engineering,
University of Strathclyde,
Glasgow G1 1XJ, UK
Search for other works by this author on:
X. F. Hu
State Key Laboratory of Structural Analysis for
Industrial Equipment,
Dalian University of Technology,
Dalian 116024, China;
International Center for Computational
Mechanics,
Dalian University of Technology,
Dalian 116024, China
e-mail: hxf@dlut.edu.cn
Industrial Equipment,
Dalian University of Technology,
Dalian 116024, China;
International Center for Computational
Mechanics,
Dalian University of Technology,
Dalian 116024, China
e-mail: hxf@dlut.edu.cn
W. A. Yao
State Key Laboratory of Structural Analysis for
Industrial Equipment,
Dalian University of Technology,
Dalian 116024, China;
International Center for Computational
Mechanics,
Dalian University of Technology,
Dalian 116024, China
Industrial Equipment,
Dalian University of Technology,
Dalian 116024, China;
International Center for Computational
Mechanics,
Dalian University of Technology,
Dalian 116024, China
S. T. Yang
Department of Civil and Environmental
Engineering,
University of Strathclyde,
Glasgow G1 1XJ, UK
Engineering,
University of Strathclyde,
Glasgow G1 1XJ, UK
1Corresponding author.
Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received October 24, 2017; final manuscript received April 20, 2018; published online May 22, 2018. Assoc. Editor: George S. Dulikravich.
J. Heat Transfer. Sep 2018, 140(9): 091301 (13 pages)
Published Online: May 22, 2018
Article history
Received:
October 24, 2017
Revised:
April 20, 2018
Citation
Hu, X. F., Yao, W. A., and Yang, S. T. (May 22, 2018). "A Symplectic Analytical Singular Element for Steady-State Thermal Conduction With Singularities in Anisotropic Material." ASME. J. Heat Transfer. September 2018; 140(9): 091301. https://doi.org/10.1115/1.4040085
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