Transactions of the Korean Society of Mechanical Engineers A (대한기계학회논문집A)

The Korean Society of Mechanical Engineers (대한기계학회)
권호 표지
DOI QR코드

DOI QR Code

Elastic Analysis of a Half-Plane Containing Multiple Inclusions Using Volume Integral Equation Method

체적 적분방정식법을 이용한, 다수의 함유체를 포함한 반무한 고체에서의 탄성해석

  • 이정기 (홍익대학교 기계정보공학과) ;
  • 구덕영 (홍익대학교 대학원 기계정보공학과)
  • Published : 2008.02.05
Download PDF
⟨ Previous Next ⟩

Abstract

A volume integral equation method (VIEM) is used to calculate the plane elastostatic field in an isotropic elastic half-plane containing multiple isotropic or anisotropic inclusions subject to remote loading. A detailed analysis of stress field at the interface between the matrix and the central inclusion in the first column of square packing is carried out for different values of the distance between the center of the central inclusion in the first column of square packing of inclusions and the traction-free surface boundary in an isotropic elastic half-plane containing multiple isotropic or anisotropic inclusions. The method is shown to be very accurate and effective for investigating the local stresses in an isotropic elastic half-plane containing multiple isotropic or anisotropic inclusions.

Keywords

References

  1. Richardson, M. K., 1969, 'Interference Stress in a Half Plane Containing an Elastic Disk of Same Material,' Transactions of ASME, Journal of Applied Mechanics, Vol. 36, pp. 128~130 https://doi.org/10.1115/1.3564571
  2. Melan, E., 1932, 'Der Spannungszustand der Durch Eine Einzelkraft im Innern beanspruchten Halbscheibe,' Zeitschrift fur Angewandte Mathematik und Mechanik, Vol. 12, pp. 343~346 https://doi.org/10.1002/zamm.19320120603
  3. Saleme, E. M., 1958, 'Stress Distribution Around a Circular Inclusion in a Semiinfinite Elastic Plate,' Transactions of ASME, Journal of Applied Mechanics, Vol. 25, pp. 129~135
  4. Shioya, S., 1967, 'On a Semi-Infinite Thin Plate with Circular Inclusion Under Uniform Tension,' Bulletin of the JSME-Japan Society of Mechanical Engineers, Vol. 10, pp. 1~9 https://doi.org/10.1299/jsme1958.10.1
  5. Lee, M., Jasiuk, I., and Tsuchida, E., 1992, 'The Sliding Circular Inclusion in an Elastic Half-Plane,' Transactions of the ASME, Journal of Applied Mechanics, Vol. 59, pp. 57~64 https://doi.org/10.1115/1.2899508
  6. Al-Ostaz, A., Jasiuk, I., and Lee, M., 1998, 'Circular inclusion in half-plane: effect of boundary conditions,' Journal of Engineering Mechanics, Vol. 124, pp. 293~300 https://doi.org/10.1061/(ASCE)0733-9399(1998)124:3(293)
  7. Dong, C. Y., Lo, S. H., and Cheung, Y. K., 2004, 'Numerical Solution for Elastic Half-Plane Inclusion Problems by Different Integral Equation Approaches,' Engineering Analysis with Boundary Elements, Vol. 28, pp. 123~130 https://doi.org/10.1016/j.enganabound.2003.06.002
  8. Legros, B., Mogilevskaya, S. G., and Crouch, S. L., 2004, 'A Boundary Integral Method for Multiple Circular Inclusions in an Elastic Half-Plane,' Engineering Analysis with Boundary Elements, Vol. 28, pp. 1083~1098 https://doi.org/10.1016/j.enganabound.2004.02.010
  9. Kushch, V. I., Shmegera, S. V., and Buryachenko, V. A., 2006, 'Elastic Equilibrium of a Half Plane Containing a Finite Array of Elliptic Inclusions,' International Journal of Solids And Structures, Vol. 43, pp. 3459~3483 https://doi.org/10.1016/j.ijsolstr.2005.05.016
  10. Banerjee, P. K., 1993, The Boundary Element Methods in Engineering, McGraw-Hill, England
  11. Hwu, C. and Yen, W. J., 1993 (Sep.), 'On the Anisotropic Elastic Inclusions in Plane Elastostatics,' Transactions of ASME, Journal of Applied Mechanics, Vol. 60, pp. 626~632 https://doi.org/10.1115/1.2900850
  12. Yang, H. C. and Chou, Y. T., 1976 (Sep.), 'Generalized Plane Problems of Elastic Inclusions in Anisotropic Solids1,' Transactions of the ASME, Journal of Applied Mechanics, Vol. 43, pp. 424~430 https://doi.org/10.1115/1.3423884
  13. Lee, J. K., Choi, S. J., and Mal, A., 2001, 'Stress Analysis of an Unbounded Elastic Solid with Orthotropic Inclusions and Voids Using a New Integral Equation Technique,' International Journal of Solids And Structures, Vol. 38 (16), pp. 2789~2802 https://doi.org/10.1016/S0020-7683(00)00182-7
  14. Lee, J. K., Han, H. D. and Mal, A., 2006, 'Effects of Anisotropic Fiber Packing on Stresses in Composites,' Computer Methods in Applied Mechanics and Engineering, Vol. 195, No. 33~36, pp. 4544~4556 https://doi.org/10.1016/j.cma.2005.10.012
  15. Lee, J. K. and Mal, A. K., 1997 (Mar.), 'A Volume Integral Equation Technique for Multiple Inclusion and Crack Interaction Problems,' Transactions of the ASME, Journal of Applied Mechanics, Vol. 64, pp. 23~31 https://doi.org/10.1115/1.2787282
  16. Mal, A. K. and Knopoff, L., 1967, 'Elastic Wave Velocities in Two Component Systems,' Journal of the Institute of Mathematics and its Applications, Vol. 3, pp. 376~387 https://doi.org/10.1093/imamat/3.4.376
  17. Lee, J. K. and Mal, A. K., 1995, 'A Volume Integral Equation Technique for Multiple Scattering Problems in Elastodynamics,' Applied Mathematics and Computation, Vol. 67, pp. 135~159 https://doi.org/10.1016/0096-3003(94)00057-B
  18. Lee, K. J. and Mal, A. K., 1990, 'A Boundary Element Method for Plane Anisotropic Elastic Media,' Transactions of the ASME, Journal of Applied Mechanics, Vol. 57, pp. 600~606 https://doi.org/10.1115/1.2897065
  19. Telles, J. C. F. and Brebbia, C. A., 1981, 'Boundary Element Solution for Half-Plane Problems,' International Journal of Solids And Structures, Vol. 17, pp. 1149~1158 https://doi.org/10.1016/0020-7683(81)90094-9
  20. Cerrolaza, M. and Alarcon, E., 1989, 'A Bi-Cubic Transformation for the Numerical Evaluation of the Cauchy Principal Value Integrals in Boundary Methods,' International Journal for Numerical Methods in Engineering, Vol. 28, pp. 987~999 https://doi.org/10.1002/nme.1620280502
  21. Li, H. B. and Han, G. M., 1985, 'A New Method for Evaluating Singular Integrals in Stress Analysis of Solids by the Direct Boundary Element Method,' International Journal for Numerical Methods in Engineering, Vol. 21, pp. 2071~2098 https://doi.org/10.1002/nme.1620211109
  22. Lu, S. and Ye, T. Q., 1991, 'Direct Evaluation of Singular Integrals in Elastoplastic Analysis by the Boundary Element Method,' International Journal for Numerical Methods in Engineering, Vol. 32, pp. 295~311 https://doi.org/10.1002/nme.1620320205
  23. Buryachenko, V. A. and Bechel, V. T, 2000, 'A Series Solution of the Volume Integral Equation for Multiple-Inclusion Interaction Problems,' Composites Science and Technology, Vol. 60, No. 12~13, pp. 2465~2469 https://doi.org/10.1016/S0266-3538(00)00041-5
  24. PATRAN User's Manual, 1998, Version 7.0, MSC/PATRAN
  25. Lee, J. K. and Mal, A., 1998, 'Characterization of Matrix Damage in Metal Matrix Composites Under Transverse Loads,' Computational Mechanics, Vol. 21, pp. 339~346 https://doi.org/10.1007/s004660050310
  26. Davi, G. and Milazzo, A., 1996, 'Stress Fields in Composite Cross-Ply Laminates,' Eleventh International Conference on Boundary Element Technology, BETECH 96, Ertekin, R. C., Brebbia, C. A., Tanaka, M. and Shaw, R., Eds., Computational Mechanics Publications, pp. 175~184