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

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

DOI QR Code

Development of an Elastic Analysis Technique Using the Mixed Volume and Boundary Integral Equation Method

혼합 체적-경계 적분방정식법을 이용한 탄성해석 방법 개발

  • Lee, Jeong-Gi (Dept. of Mechanical Information Engineering, Hongik University) ;
  • Heo, Gang-Il (Dept.of Mechanical Design Engineering, Graduate School of Hong-Ik University) ;
  • Jin, Won-Jae (Dept.of Mechanical Design Engineering, Graduate School of Hong-Ik University)
  • 이정기 (홍익대학교 기계정보공학과) ;
  • 허강일 (홍익대학교 대학원 기계설계학과) ;
  • 진원재 (홍익대학교 대학원 기계설계학과)
  • Published : 2002.04.01
Download PDF
⟨ Previous Next ⟩

Abstract

A Mixed Volume and Boundary Integral Equation Method is applied for the effective analysis of elastic wave scattering problems and plane elastostatic problems in unbounded solids containing general anisotropic inclusions and voids or isotropic inclusions. It should be noted that this newly developed numerical method does not require the Green's function for anisotropic inclusions to solve this class of problems since only Green's function for the unbounded isotropic matrix is involved in their formulation for the analysis. This new method can also be applied to general two-dimensional elastodynamic and elastostatic problems with arbitrary shapes and number of anisotropic inclusions and voids or isotropic inclusions. In the formulation of this method, the continuity condition at each interface is automatically satisfied, and in contrast to finite element methods, where the full domain needs to be discretized, this method requires discretization of the inclusions only. Finally, this method takes full advantage of the pre- and post-processing capabilities developed in FEM and BIEM. Through the analysis of plane elastostatic problems in unbounded isotropic matrix with orthotropic inclusions and voids or isotropic inclusions, and the analysis of plane wave scattering problems in unbounded isotropic matrix with isotropic inclusions and voids, it will be established that this new method is very accurate and effective for solving plane wave scattering problems and plane elastic problems in unbounded solids containing general anisotropic inclusions and voids/cracks or isotropic inclusions.

Keywords

References

  1. Banerjee, P. K., 1993, The Boundary Element Methods in Engineering, McGraw-Hill, England
  2. 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 (12-13), pp. 2465-2469 https://doi.org/10.1016/S0266-3538(00)00041-5
  3. 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
  4. 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
  5. 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
  6. 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
  7. 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
  8. 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
  9. Lee, K. J. and Mal, A. K., 1990, 'A Boundary Element Method for Plane Anisotropic Elastic Media,' Journal of Applied Mechanics, Vol. 57, pp. 600-606 https://doi.org/10.1115/1.2897065
  10. Mal, A. K. and Knopoff, L.. 1967, 'Elastic Wave Velocities in Two Component Systems,' J. Inst. Math. Applics., Vol. 3, pp. 376-387 https://doi.org/10.1093/imamat/3.4.376
  11. Yang, H. C. and Chou, Y. T., 1976 (Sep.), 'Generalized Plane Problems of Elastic Inclusions in Anisotropic Solids,' Transactions of the ASME, Journal of Applied Mechanics, Vol. 43, pp. 424-430 https://doi.org/10.1115/1.3423884
  12. 이정기, 최성준, 라원석, 1997,' 직교 이방성 함유체가 포함된 2차원 무한 고체의 탄성 해석에 관한 연구,' 대한기계학회 추계학술대회논문집 A, KSME 97F072, pp. 420-425