Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-10T17:15:58.776Z Has data issue: false hasContentIssue false
  • English
  • Français

Dynamic Stress Analysis Around a Circular Cavity in Two-Dimensional Inhomogeneous Medium with Density Variation

Published online by Cambridge University Press:  04 April 2016

B.-P. Hei ,
Z.-L. Yang ,
B.-T. Sun  and
D.-K. Liu
B.-P. Hei
Affiliation:
College of Aerospace and Civil Engineering Harbin Engineering University Harbin, China
Z.-L. Yang*
Affiliation:
College of Aerospace and Civil Engineering Harbin Engineering University Harbin, China
B.-T. Sun
Affiliation:
Institute of Engineering Mechanics China Earthquake Administration Harbin, China
D.-K. Liu
Affiliation:
College of Aerospace and Civil Engineering Harbin Engineering University Harbin, China
*
*Corresponding author (yangzailin00@163.com)
Get access

Abstract

Based on the complex function theory and the homogenization principle, an universal approach of solving the dynamic stress concentration around a circular cavity in two-dimensional (2D) inhomogeneous medium is developed. The Helmholtz equation with variable coefficient is converted to the standard Helmholtz equation by means of the general conformal transformation method (GCTM) analytically. As an example, the inhomogeneous medium with density varying as a function of two spatial coordinates and the constant elastic modulus is studied. The dynamic stress concentration factors (DSCF) are calculated numerically. It shows that medium inhomogeneous parameters and wave numbers have significant influence on the dynamic stress concentration by the circular cavity in two-dimensional inhomogeneous medium.

Keywords

Complex function theory2D inhomogeneous mediumVariable coefficient Helmholtz equationDynamic stress concentration
Type
Research Article
Information
Journal of Mechanics , Volume 32 , Issue 5 , October 2016 , pp. 519 - 526
Copyright
Copyright © The Society of Theoretical and Applied Mechanics 2016 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Pao, Y. H. and Mow, C. C., Diffraction of Elastic Waves and Dynamic Stress Concentrations, Crane and Russak, New York (1973).Google Scholar
2. Baron, M. L. and Matthews, A. T., “Diffraction of a Pressure Wave by a Cylindrical Cavity in an Elastic Medium,” ASME Journal of Applied Mechanics, 28, pp. 347–354 (1961).Google Scholar
3. Baron, M. L. and Matthews, A. T., “Diffraction of a Shear Wave by a Cylindrical Cavity in an Elastic Medium,” ASME Journal of Applied Mechanics, 29, pp. 205–207 (1962).Google Scholar
4. Mow, C. C. and Mente, L. J., “Dynamic Stresses and Displacements Around Cylindrical Discontinuities Due to Plane Harmonic Shear Waves,” ASME Journal of Applied Mechanics, 30, pp. 598–604 (1962).Google Scholar
5. Moodie, T. B. and Barclay, D. W., “Wave Propagation from a Cylindrical Cavity,” Acta Mechanica, 27, pp. 103–120 (1977).Google Scholar
6. Luco, J. E. and De Barros, F. C. P., “Dynamic Displacements and Stresses in the Vicinity of a Cylindrical Cavity Embedded in a Half-space,” Earthquake Engineering and Structural Dynamics, 23, pp. 321–340 (1994).Google Scholar
7. Coşkun, İ., Engin, H. and Özmutlu, A., “Dynamic Stress and Displacement in an Elastic Half-space with a Cylindrical Cavity,” Shock and Vibration, 18, pp. 827–838 (2011).Google Scholar
8. Liao, W. I. and Teng, T. J., “Dynamic Stress Concentration of a Cylindrical Cavity in Half-Plane Excited by Standing Goodier-Bishop Stress Wave,” Journal of Mechanics, 28, pp. 269–277 (2012).Google Scholar
9. Shi, W. P., Liu, D. K., Song, Y. T., Chu, J. L. and Hu, A. Q., “Scattering of Circular Cavity in Right-angle Planar Space to Steady SH-wave,” Applied Mathematics and Mechanics (English Edition), 27, pp. 1619–1626 (2006).Google Scholar
10. Liu, G., Ji, B. H., Chen, H. T. and Liu, D. K., “Antiplane Harmonic Elastodynamic Stress Analysis of an Infinite Wedge with a Circular Cavity,” ASME Journal of Applied Mechanics, 76, pp. 061008.1–061008.9 (2009).Google Scholar
11. Pao, Y. H., “Dynamical Stress Concentrations in an Elastic Plate,” ASME Journal of Applied Mechanics, 29, pp. 299–305 (1962).Google Scholar
12. Mccoy, J. J., “On Dynamic Stress Concentrations in Elastic Plates,” International Journal of Solids and Structures, 3, pp. 399–411 (1967).Google Scholar
13. Gao, S. W., Meng, Q. Y., Wang, B. L. and Ma, X. R., “BEM for Diffraction of Elastic Wave and Dynamic Stress Concentrations in Thin Plate with a Circular Hole,” Journal of Harbin Institute of Technology, 6, pp. 40–46 (1999).Google Scholar
14. Ewing, W. M., Jardetzky, W. S. and Press, F., Elastic Waves in Layered Media, McGraw-Hill Book Co., New York (1957).Google Scholar
15. Brekhovskikh, L. M., Waves in Layered Media, Academic Press, New York (1960).Google Scholar
16. Brekhovskikh, L. M. and Godin, O. A., Acoustics of Layered Meida 1. Plane and Quasi-Plane Waves, Spring-Verlag Berlin Heidelberg, New York (1998).Google Scholar
17. Zhang, H. L., Theoretical Acoustics (Revised Edition), Higher Education Press, Beijing (2012).Google Scholar
18. Butrak, I. O., Kil'nitskaya, T. I. and Mikhas'kiv, V. V., “The Scattering of a Harmonic Elastic Wave by a Volume Inclusion with a Thin Interlayer,” Journal of Applied Mathematics and Mechanics, 76, pp. 342–347 (2012).Google Scholar
19. Cieszko, M., Drelich, R. and Pakula, M., “Acoustic Wave Propagation in Equivalent Fluid Macroscopically Inhomogeneous Materials,” The Journal of the Acoustical Society of America, 132, pp. 2970–2977 (2012).Google Scholar
20. Yang, Q., Gao, C. F. and Chen, W., “Stress Analysis of a Functional Graded Material Plate with a Circular Hole,” Archive of Applied Mechanics, 80, pp. 895–907 (2010).Google Scholar
21. Zhang, X. Z., Kitipornchai, S., Liew, K. M., Lim, C. W. and Peng, L. X., “Thermal Stresses around a Circular Hole in a Functionally Graded Plate,” Journal of Thermal Stresses, 26, pp. 379–390 (2003).Google Scholar
22. Sburlati, R., “Stress Concentration Factor due to a Functionally Graded Ring around a Hole in an Isotropic Plate,” International Journal of Solids and Structures, 50, pp. 3649–3658 (2013).Google Scholar
23. Mohammadi, M., Dry den, J. R. and Jiang, L., “Stress Concentration around a Hole in a Radially Inhomogeneous Plate,” International Journal of Solids and Structures, 48, pp. 483–491 (2011).Google Scholar
24. Kubair, D. V. and Bhanu-Chandar, B., “Stress Concentration Factor due to a Circular Hole in Functionally Graded Panels under Uniaxial Tension,” International Journal of Mechanical Sciences, 50, pp. 732–742 (2008).Google Scholar
25. Afsar, A. M. and Go, J., “Finite Element Analysis of Thermoelastic Field in a Rotating FGM Circular Disk,” Applied Mathematical Modelling, 34, pp. 3309–3320 (2010).Google Scholar
26. Ashrafi, H., Asemi, K. and Shariyat, M., “A Three-dimensional Boundary Element Stress and Bending Analysis of Transversely/Longitudinally Graded Plates with Circular Cutouts under Biaxial Loading,” European Journal of Mechanics—A/Solids, 42, pp. 344–357 (2013).Google Scholar
27. Fang, X. Q., Hu, C. and Du, S. Y., “Strain Energy Density of a Circular Cavity Buried in Semi-infinite Functionally Graded Materials Subjected to Shear Waves,” Theoretical and Applied Fracture Mechanics, 46, pp. 166–174 (2006).Google Scholar
28. Martin, P. A., “Scattering by a Cavity in an Exponentially Graded Half-space,” Journal of Applied Mechanics, 76, pp. 31009-1–31009-4 (2009).Google Scholar
29. Martin, P. A., “Scattering by Eefects in an Exponentially Graded Layer and Misuse of the Method of Images,” International Journal of Solids and Structures, 48, pp. 2164–2166. (2011).Google Scholar
30. Yang, Q. and Gao, C. F., “Dynamic Stress Analysis of a Functionally Graded Material Plate with a Circular Hole,” Meccanica, 48, pp. 91–101 (2013).Google Scholar
31. Ramo, S., Whinnery, J. R. and Duzer, T. V., Field and Waves in Communication Electronics, Third Edition, Wiley, New York (2007).Google Scholar
32. Manolis, G. D. and Shaw, R. P., “Fundamental Solutions for Variable Density Two-dimensional Elastodynamic Problems,” Engineering Analysis with Boundary Elements, 24, pp. 739–750 (2000).Google Scholar