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[1] Florence, A.L. & Goodier, J.N., The linear thermoelastic problem of uniform heat flow disturbed by a penny-shaped insulated crack. International Journal of Engineering Science, 1, pp. 533–540, 1963. [Crossref]
[2] Rizzo, F.J. & Shippy, D.J., An advanced boundary integral equation method for three-dimensional thermoelasticity. International Journal for Numerical Methods in Engineering, 11, pp. 1753–1768, 1977. [Crossref]
[3] Dell’Erba, D.N. & Aliabadi, M.H., On the solution of three-dimensional thermoelastic mix- mode edge crack problems by the dual boundary element method. International Journal of Fracture, 66, pp. 269–285, 2000.
[4] Mukherjee, Y.X., Shah, K. & Mukherjee, S., Thermoelastic fracture mechanics with regularized hypersingular boundary integral equations. Engineering Analysis with Boundary elements, 23, pp. 89–96, 1999. [Crossref]
[5] Crouch, S.L., Solution of plane elasticity problems by the displacement discontinuity method. International Journal for Numerical Methods in Engineering, 10, pp. 301–343, 1976. [Crossref]
[6] Zhao, M.H., Shen, Y.P., Liu, Y.J. & Liu, G.N., The method of analysis of cracks in three-dimensional transversely isotropic media: boundary integral equation approach. Engineering Analysis with Boundary elements, 21, pp. 169–178, 1998. [Crossref]
[7] Zhao, M.H., Fan, C.Y., Liu, T. & Yang, F., Extended displacement discontinuity Green functions for three-dimensional transversely isotropic magneto-electro-elastic media and applications. Engineering Analysis with Boundary Elements, 31, pp. 547–558, 2007. [Crossref]
[8] Zhao, M.H., Dang, H.Y., Li, Y., Fan, C.Y. & Xu, G.T., Displacement and temperature discontinuity boundary integral equation and boundary element method for analysis of cracks in three-dimensional isotropic thermoelastic media. International Journal of Solids and Structure, 81, pp. 179–187, 2016. [Crossref]
[9] Fan, C.Y., Dang, H.Y. & Zhao, M.H., Nonlinear solution of the PS model for a semi-permeable crack in a 3D piezoelectric medium. Engineering Analysis with Boundary Elements, 46, pp. 23–29, 2014. [Crossref]
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Open Access
Research article

Temperature and Displacement Discontinuity Boundary Element Method for Analysis of Cracks in Three-Dimensional Isotropic Thermoelastic Media

m.h. zhao1,
h.y. dang2,
y. li2,
c.y. fan3,
g.t. xu3
1
School of Mechanical Engineering, Zhengzhou University, 450001 Zhengzhou, China School of Mechanics and Engineering Science, Zhengzhou University, 450001 Zhengzhou, China
2
School of Mechanics and Engineering Science, Zhengzhou University, 450001 Zhengzhou, China
3
School of Mechanical Engineering, Zhengzhou University, 450001 Zhengzhou, China
International Journal of Computational Methods and Experimental Measurements
|
Volume 5, Issue 3, 2017
|
Pages 241-249
Received: N/A,
Revised: N/A,
Accepted: N/A,
Available online: N/A
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Abstract:

For the analysis of cracks in three-dimensional isotropic thermoelastic media, a temperature and displacement discontinuity boundary element method is developed. The Green functions for unit-point temperature and displacement discontinuities are derived, and the temperature and displacement discontinuity boundary integral equations are obtained for an arbitrarily shaped planar crack. Our boundary element method is based on the Green functions for a triangular element. As an application, elliptical cracks are analyzed to validate the developed method. The influence of various thermal boundary conditions is studied.

Keywords: Boundary element method, Boundary integral equation method, Displacement and temperature discontinuity, Green function, Isotropic thermoelastic medium, Planar crack, Stress intensity factor, Thermal boundary condition, Triangular element

1. Introduction

2. Temperature and Displacement Discontinuity Boundary Integral Equation Method

3. Temperature and Displacement Discontinuity Boundary Element Method

4. Numerical Results and Discussion

5. Concluding Remarks

Data Availability

The data used to support the findings of this study are available from the corresponding author upon request.

Acknowledgments

This work was supported by the National Natural Science Foundation of China (Nos.11272290 and 11572289).

Conflicts of Interest

The authors declare that they have no conflicts of interest.

References
[1] Florence, A.L. & Goodier, J.N., The linear thermoelastic problem of uniform heat flow disturbed by a penny-shaped insulated crack. International Journal of Engineering Science, 1, pp. 533–540, 1963. [Crossref]
[2] Rizzo, F.J. & Shippy, D.J., An advanced boundary integral equation method for three-dimensional thermoelasticity. International Journal for Numerical Methods in Engineering, 11, pp. 1753–1768, 1977. [Crossref]
[3] Dell’Erba, D.N. & Aliabadi, M.H., On the solution of three-dimensional thermoelastic mix- mode edge crack problems by the dual boundary element method. International Journal of Fracture, 66, pp. 269–285, 2000.
[4] Mukherjee, Y.X., Shah, K. & Mukherjee, S., Thermoelastic fracture mechanics with regularized hypersingular boundary integral equations. Engineering Analysis with Boundary elements, 23, pp. 89–96, 1999. [Crossref]
[5] Crouch, S.L., Solution of plane elasticity problems by the displacement discontinuity method. International Journal for Numerical Methods in Engineering, 10, pp. 301–343, 1976. [Crossref]
[6] Zhao, M.H., Shen, Y.P., Liu, Y.J. & Liu, G.N., The method of analysis of cracks in three-dimensional transversely isotropic media: boundary integral equation approach. Engineering Analysis with Boundary elements, 21, pp. 169–178, 1998. [Crossref]
[7] Zhao, M.H., Fan, C.Y., Liu, T. & Yang, F., Extended displacement discontinuity Green functions for three-dimensional transversely isotropic magneto-electro-elastic media and applications. Engineering Analysis with Boundary Elements, 31, pp. 547–558, 2007. [Crossref]
[8] Zhao, M.H., Dang, H.Y., Li, Y., Fan, C.Y. & Xu, G.T., Displacement and temperature discontinuity boundary integral equation and boundary element method for analysis of cracks in three-dimensional isotropic thermoelastic media. International Journal of Solids and Structure, 81, pp. 179–187, 2016. [Crossref]
[9] Fan, C.Y., Dang, H.Y. & Zhao, M.H., Nonlinear solution of the PS model for a semi-permeable crack in a 3D piezoelectric medium. Engineering Analysis with Boundary Elements, 46, pp. 23–29, 2014. [Crossref]
Cite this:
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GB-T-7714-2015
Zhao, M., Dang, H., Li, Y., Fan, C., & Xu, G. (2017). Temperature and Displacement Discontinuity Boundary Element Method for Analysis of Cracks in Three-Dimensional Isotropic Thermoelastic Media. Int. J. Comput. Methods Exp. Meas., 5(3), 241-249. https://doi.org/10.2495/CMEM-V5-N3-241-249
M. Zhao, H. Dang, Y. Li, C. Fan, and G. Xu, "Temperature and Displacement Discontinuity Boundary Element Method for Analysis of Cracks in Three-Dimensional Isotropic Thermoelastic Media," Int. J. Comput. Methods Exp. Meas., vol. 5, no. 3, pp. 241-249, 2017. https://doi.org/10.2495/CMEM-V5-N3-241-249
@research-article{Zhao2017TemperatureAD,
title={Temperature and Displacement Discontinuity Boundary Element Method for Analysis of Cracks in Three-Dimensional Isotropic Thermoelastic Media},
author={M.H. Zhao and H.Y. Dang and Y. Li and C.Y. Fan and G.T. Xu},
journal={International Journal of Computational Methods and Experimental Measurements},
year={2017},
page={241-249},
doi={https://doi.org/10.2495/CMEM-V5-N3-241-249}
}
M.H. Zhao, et al. "Temperature and Displacement Discontinuity Boundary Element Method for Analysis of Cracks in Three-Dimensional Isotropic Thermoelastic Media." International Journal of Computational Methods and Experimental Measurements, v 5, pp 241-249. doi: https://doi.org/10.2495/CMEM-V5-N3-241-249
M.H. Zhao, H.Y. Dang, Y. Li, C.Y. Fan and G.T. Xu. "Temperature and Displacement Discontinuity Boundary Element Method for Analysis of Cracks in Three-Dimensional Isotropic Thermoelastic Media." International Journal of Computational Methods and Experimental Measurements, 5, (2017): 241-249. doi: https://doi.org/10.2495/CMEM-V5-N3-241-249
ZHAO MH， DANG HY， LI Y， et al. Temperature and Displacement Discontinuity Boundary Element Method for Analysis of Cracks in Three-Dimensional Isotropic Thermoelastic Media[J]. International Journal of Computational Methods and Experimental Measurements， 2017， 5(3)： 241-249. https://doi.org/10.2495/CMEM-V5-N3-241-249