Browse > Article
http://dx.doi.org/10.12989/sem.2011.38.5.619

Solution of periodic notch problems in an infinite plate using BIE in conjunction with remainder estimation technique  

Chen, Y.Z. (Division of Engineering Mechanics, Jiangsu University)
Publication Information
Structural Engineering and Mechanics / v.38, no.5, 2011 , pp. 619-631 More about this Journal
Abstract
This paper provides a complex variable BIE for solving the periodic notch problems in plane plasticity. There is no limitation for the configuration of notches. For the periodic notch problem, the remainder estimation technique is suggested. In the technique, the influences on the central notch from many neighboring notches are evaluated exactly. The influences on the central notch from many remote notches are approximated by one term with a multiplying factor. This technique provides an effective way to solve the problems of periodic structures. Several numerical examples are presented, and most of them have not been reported previously.
Keywords
complex variable BIE; periodic notch problem; remainder estimation technique; stress concentration;
Citations & Related Records

Times Cited By Web Of Science : 2  (Related Records In Web of Science)
Times Cited By SCOPUS : 2
연도 인용수 순위
  • Reference
1 Brebbia, C.A., Telles, J.C.F. and Wrobel, L.C. (1984), Boundary Element Techniques - Theory and Applications in Engineering, Springer, Heidelberg.
2 Chen, J.T. and Hong, H.K. (1999), "Review of dual boundary element methods with emphasis on hypersingular integrals and divergent series", ASME Appl. Mech. Rev., 52, 17-33.   DOI   ScienceOn
3 Chen, J.T. and Chen, Y.W. (2004), "Dual boundary element analysis using complex variables for potential problems with or without a degenerate boundary", Eng. Anal. Boun. Elem., 24, 671-684.
4 Chen, J.T., Shen, W.C. and Wu, A.C. (2006), "Null-field integral equations for stress field around circular holes under antiplane shear", Eng. Anal. Boun. Elem., 30, 205-217.   DOI   ScienceOn
5 Chen, J.T. and Wu, A.C. (2007), "Null-field integral equation approach for the multi-inclusion problem under antiplane shears", ASME J. Appl. Mech., 74, 469-487.   DOI   ScienceOn
6 Chen, J.T., Lee, Y.T. and Chou, K.S. (2010), "Revisit of two classical elasticity problems by using the null-field integral equations", J. Mech., 26, 393-401.   DOI
7 Chen, Y.Z. (1985), "A special boundary element formulation for multiple circular hole problems in an infinite plate", Comput. Meth. Appl. Mech. Eng., 50, 263-273.   DOI   ScienceOn
8 Chen, Y.Z. and Lin, X.Y. (2007), "Solution of periodic group circular hole problems by using the series expansion variational method", Int. J. Numer. Meth. Eng., 69, 1405-1422.   DOI   ScienceOn
9 Chen, Y.Z., Wang, Z.X. and Li, F.L. (2008), "Periodic group edge crack problem of half-plane in antiplane elasticity", Commun. Numer. Meth. Eng., 24, 833-840.
10 Chen Y.Z., Wang, Z.X. and Lin, X.Y. (2009), "A new kernel in BIE and the exterior boundary value problem in plane elasticity", Acta Mech., 206, 207-224.   DOI
11 Chen, Y.Z., Lin, X.Y. and Wang, Z.X. (2010), "Formulation of indirect BIEs in plane elasticity using single or double layer potentials and complex variable", Eng. Anal. Boun. Elem., 34, 337-351.   DOI   ScienceOn
12 Cheng, A.H.D. and Cheng, D.S. (2005), "Heritage and early history of the boundary element method", Eng. Anal. Boun. Elem., 29, 286-302.
13 Cruse, T.A. (1969), "Numerical solutions in three-dimensional elastostatics", Inter. J. Solids Struct., 5, 1259-1274.   DOI   ScienceOn
14 Hong, H.K. and Chen, J.T. (1988), "Derivations of integral equations of elasticity", J. Eng. Mech. 114, 1028-1044.   DOI
15 Horii, H. and Nemat-Nassar, S. (1985), "Elastic fields of interacting inhomogeneities", Int. J. Solids Struct., 21, 731-745.   DOI   ScienceOn
16 Hromadka, T.V. (1987), The Complex Variable Boundary Element Method in Engineering Analysis, Springer, New York.
17 Isida, M. and Igawa, H. (1991), "Analysis of a zig-zag array of circular holes in an infinite solid under uniaxial tension", Int. J. Solids Struct., 27, 849-864.   DOI   ScienceOn
18 Jaswon, M.A. and Symm, G.T. (1967), Integral Equation Methods in Potential Theory and Elastostatics, Academic Press, London.
19 Linkov, A.M. (2002), Boundary Integral Equations in Elasticity, Kluwer, Dordrecht.
20 Muskhelishvili, N.I. (1953), Some Basic Problems of the Mathematical Theory of Elasticity, Noordhoff, The Netherlands.
21 Rizzo, F.J. (1967), "An integral equation approach to boundary value problems in classical elastostatics", Quart. J. Appl. Math., 25, 83-95.   DOI
22 Ting, K., Chen, K.T. and Yang, W.S. (1999), "Stress analysis of the multiple circular holes with the rhombic array using alternating method", Inter. J. Pres. Ves. Pip., 76, 503-514.   DOI   ScienceOn
23 Tsukrov, I. and Kachanov, M. (1997), "Stress concentrations and microfracturing patterns in a brittle-elastic solid with interacting pores of diverse shapes", Int. J. Solids Struct., 34, 2887-2904.   DOI   ScienceOn
24 Wang, J.L., Crouch, S.L. and Mogilevskaya, S.G. (2003), "A complex boundary integral for multiple circular holes in an infinite plane", Eng. Anal. Boun. Elem., 27, 789-802.   DOI   ScienceOn