3D Analytical Solutions of Stress Fields at Griffith Crack Tips in Functionally Graded Plates

SUN Yeli; SHEN Lulu; YANG Bo

doi:10.21656/1000-0887.410143

Volume 42 Issue 1

Jan. 2021

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SUN Yeli, SHEN Lulu, YANG Bo. 3D Analytical Solutions of Stress Fields at Griffith Crack Tips in Functionally Graded Plates[J]. Applied Mathematics and Mechanics, 2021, 42(1): 36-48. doi: 10.21656/1000-0887.410143

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3D Analytical Solutions of Stress Fields at Griffith Crack Tips in Functionally Graded Plates

doi: 10.21656/1000-0887.410143

Department of Civil Engineering, School of Civil Engineering and Architecture,Zhejiang SciTech University, Hangzhou 310018, P.R.China

Funds: The National Natural Science Foundation of China（11872336）

Received Date: 2020-05-19
Rev Recd Date: 2020-06-05
Publish Date: 2021-01-01

Abstract

Abstract

Based on the generalized England-Spencer plate theory, the 3D stress field at the Griffith crack tip in a transversely isotropic functionally graded plate was investigated. With the material parameters assumed to vary continuously and arbitrarily along the thickness direction, by means of the complex function theory and the conformal mapping technology, the analytical results of the 3D stress field at the Griffith crack tip under loading at infinity and uniform internal pressure were obtained respectively. With the material reduced to an isotropic homogeneous material, the validity of the solution was verified through comparison with the classical 2D solution. Numerical examples were given to demonstrate the effects of material gradient factors and load conditions on the stress field.
- functionally graded material,
- Griffith crack,
- conformal mapping,
- stress field,
- 3D analytical solution

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References(17)

References

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