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http://dx.doi.org/10.3795/KSME-A.2008.32.2.148

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

Lee, Jung-Ki (홍익대학교 기계정보공학과)
Ku, Duck-Young (홍익대학교 대학원 기계정보공학과)
Publication Information
Transactions of the Korean Society of Mechanical Engineers A / v.32, no.2, 2008 , pp. 148-161 More about this Journal
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
Volume Integral Equation Method; Half-Plane; Isotropic Inclusions; Anisotropic Inclusions; Multiple Inclusions; Green's Functions;
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1 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   DOI   ScienceOn
2 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   DOI   ScienceOn
3 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   DOI
4 Melan, E., 1932, 'Der Spannungszustand der Durch Eine Einzelkraft im Innern beanspruchten Halbscheibe,' Zeitschrift fur Angewandte Mathematik und Mechanik, Vol. 12, pp. 343~346   DOI
5 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
6 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   DOI
7 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   DOI
8 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   DOI   ScienceOn
9 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   DOI   ScienceOn
10 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
11 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   DOI   ScienceOn
12 Banerjee, P. K., 1993, The Boundary Element Methods in Engineering, McGraw-Hill, England
13 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   DOI   ScienceOn
14 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   DOI
15 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   DOI   ScienceOn
16 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   DOI   ScienceOn
17 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   DOI   ScienceOn
18 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   DOI   ScienceOn
19 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   DOI
20 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   DOI
21 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   DOI   ScienceOn
22 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   DOI   ScienceOn
23 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   DOI
24 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   DOI
25 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   DOI   ScienceOn
26 PATRAN User's Manual, 1998, Version 7.0, MSC/PATRAN