Thermo-elastic Singularity Analysis on V-notches in Orthotropic Materials

Abstract

Abstract: Thermo-elastic singularities of V-notches in orthotropic materials are studied. By introducing series asymptotic expansions of physics fields near notch tip, stress and flux equilibrium equations are transformed into characteristic ordinary differential equations with respect to singularity orders. Singularity orders and corresponding characteristic angular functions can be derived synchronously as interpolating matrix method is introduced to solve characteristice quations. The method evaluates stress and flux singularity orders at the same time. Numerical results show that it has high accuracy and strong adaptability.

Key words: orthotropic, V-notch, thermo-elastic, singularity

CLC Number:

O343.6

YAO Shanlong, CHENG Changzheng, NIU Zhongrong. Thermo-elastic Singularity Analysis on V-notches in Orthotropic Materials[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2016, 33(4): 419-426.

References

[1] FU X R, LONG Y Q. Analysis of plane notch problems with analytical trial functions' method[J]. Engineering Mechanics, 2003, 20(4):33-38.
[2] XU J Q, MUTOH Y. Analytical solution for interface stresses due to concentrated surface force[J]. International Journal of Mechanical Sciences, 2003, 45:1877-1892.
[3] ZHANG M, YAO Z H, DU Q H. Boundary element analysis of stress intensity factors of bimaterial interface crack[J]. Chinese Journal of Applied Mechanics,1999, 16(4):21-26.
[4] ZHENG B L, DAI Y, JI X, et al. The stress singularity analysis of an antiplane problem near the interface end[J]. Chinese Journal of Applied Mechanics, 1999,4:21-26,164.
[5] GE R Y, NIU Z R, CHENG C Z, et al. Propagation analysis of two-dimensional linear elastic crack with boundary element method[J]. Chinese Journal of Computational Physics, 2015, 32(3):310-320.
[6] CHENG C Z, GE R Y, XUE W W, et al. Singularity at tip of a composite notch under anti-plane loading[J]. Chinese Journal of Computational Physics, 2013, 30(5):700-705.
[7] PRASAD N N V, ALIABADI M H, ROOKE D P. Effect of thermal singularities on stress intensity factors:edge crack in rectangular and circular plate[J]. Theoretical and Applied Fracture Mechanics, 1996, 24:203-215.
[8] CAICEDO J, PORTELA A. Cracked plate analysis with the dual boundary element method and Williams' eigenexpansion[J]. Engineering Analysis with Boundary Elements, 2015, 52:16-23.
[9] YOSIBASH Z, SZABO B A. Numerical analysis of singularities in two-dimensions Part 1:computation of eigenpairs[J]. International Journal for Numerical Methods in Engineering, 1995, 38:2055-2082.
[10] PING X C, XU X X, CHENG M C. Singular stress analysis of an irregular shaped inclusion under thermo-mechanical loads[J]. Chinese Journal of Computational Mechanics, 2014, 6:749-754.
[11] AYATOLLASHI M R, MIRSAYAR M M, DEHGHANY M. Experimental determination of stress field parameters in bi-material notches using photoelasticity[J]. Materials and Design, 2011, 32:4901-4908.
[12] NIU Z R, GE D L, CHENG C Z, et al. Evaluation of the stress singularities of plane V-notches in bonded dissimilar materials[J]. Applied Mathematical Modelling, 2009, 33, 1776-1792.
[13] CHENG C Z, HAN Z L, YAO S L, et al. Analysis of heat flux singularity at 2D notch tip by singularity analysis method combined with boundary element technique[J]. Engineering Analysis with Boundary Elements, 2014, 46:1-9.
[14] MANTIC V, PARIS F, CANAS J. Stress singularities in 2D orthotropic corners[J]. International Journal of Fracture, 1997, 83:67-90.