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http://dx.doi.org/10.12989/acd.2021.6.2.077

Solution for null field CVBIE in plane elasticity using an accurate shape function  

Chen, Y.Z. (Division of Engineering Mechanics, Jiangsu University)
Publication Information
Advances in Computational Design / v.6, no.2, 2021 , pp. 77-98 More about this Journal
Abstract
This paper provides a numerical solution for null field complex variable boundary integral equation (CVBIE) in plane elasticity. All kernels in the null field CVBIE are regular function. An accurate shape function for the displacement and traction along the contour is suggested. With the usage of suggested shape function, a discretization for the boundary integral equation (BIE) is carried out. The Dirichlet and the Neumann boundary value problems (BVPs) for the interior region and the exterior region are studied. Two numerical examples are provided in the paper. It is shown that a higher accuracy has been achieved in the examples with the usage of the suggested shape function.
Keywords
null field formulation; complex variable boundary integral equation; interior BVP; exterior BVP; accurate shape function;
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Times Cited By KSCI : 3  (Citation Analysis)
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1 Liu, Y.J. and Rudolphi, T.J. (1999), "New identities for fundamental solutions and their applications to nosingular boundary element formulation", Comput. Mech., 24, 286-292.   DOI
2 Brebbia, C.A., Telles, J.C.F. and Wrobel, L.C. (1984), Boundary Element Techniques - Theory and Applications in Engineering, Springer, Heidelberg
3 Chen, J.T. and Lee, Y.T. (2009), "Torsional rigidity of a circular bar with multiple circular inclusions using the null-field integral approach", Comput. Mech., 44, 221-232. https://doi.org/10.1007/s00466-009-0365-8.   DOI
4 Chen, J.T. and Wu, A.C. (2007), "Null-field approach for the multi-inclusion problem under antiplane shears", J. Appl. Mech., 74, 469-487. https://doi.org/10.1115/1.2338056.   DOI
5 Chen, J.T., Kuo, S.R. and Lin, J.H. (2002), "Analytical study and numerical experiments for degenerate scale problems in the boundary element method for two-dimensional elasticity", Int. J. Numer. Meth. Eng., 54, 1669-1681. https://doi.org/10.1002/nme.476.   DOI
6 Chen, Y.Z. (2012a), "Boundary integral equation method for two dissimilar elastic inclusions in an infinite plate", Eng. Anal. Bound. Elem., 36(2), 137-146. https://doi.org/10.1016/j.enganabound.2011.07.006.   DOI
7 Chen, Y.Z. and Wang, Z.X. (2013), "Properties of integral operators in complex variable boundary integral equation in plane elasticity", Struct. Eng. Mech., 45(4), 495-519. http://dx.doi.org/10.12989/sem.2013.45.4.495.   DOI
8 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. Bound. Elem., 34, 337-351. https://doi.org/10.1016/j.enganabound.2009.10.009.   DOI
9 Cruse, T.A. (1969), "Numerical solutions in three-dimensional elastostatics", Int. J. Solids Struct., 5(12), 1259-1274. https://doi.org/10.1016/0020-7683(69)90071-7.   DOI
10 Hildebrand, F.B. (1974), Introduction to numerical analysis, McGraw-Hill, New York.
11 Jaswon, M.A. and Symm, G.T. (1977), Integral Equation Methods in Potential Theory and Elastostatics, Academic Press, London.
12 Rizzo, F.J. (1967), "An integral equation approach to boundary value problems in classical elastostatics", Quart. J. Appl. Math., 25, 83-95.   DOI
13 Zhang, X.S. and Zhang X.X. (2008), "Exact solution for the hypersingular boundary integral equation of two-dimensional elastostaticcs", Struct. Eng. Mech., 30(3), 279-296.   DOI
14 Chen, Y.Z. (2012b), "An iteration approach for multiple notch problem based on complex variable boundary integral equation", Struct. Eng. Mech., 41(5), 591-604. http://dx.doi.org/10.12989/sem.2012.41.5.591.   DOI
15 Cheng, A.H.D. and Cheng, D.S. (2005), "Heritage and early history of the boundary element method", Eng. Anal. Bound. Elem., 29(3), 286-302. https://doi.org/10.1016/j.enganabound.2004.12.001.   DOI
16 Hong, H.K. and Chen, J.T. (1988), "Derivations of integral equations of elasticity", J. Eng. Mech., 114(6), 1028-1044. https://doi.org/10.1061/(ASCE)0733-9399(1988)114:6(1028).   DOI
17 Liu, Y.J., Ye, W. and Deng, Y. (2013), "On the identities for electrostatic fundamental solution and nonuniqueness of the traction BIE solution for multiconnected domains", J. Appl. Mech., 80(5), 051012-1 to -9. https://doi.org/10.1115/1.4023640.   DOI
18 Vodicka, R. and Mantic, V. (2008), "On solvability of a boundary integral equation of the first kind for Dirichlet boundary value problems in plane elasticity", Comput. Mech., 41(6), 817-826. https://doi.org/10.1007/s00466-007-0202-x.   DOI
19 Muskhelishvili, N.I. (1953), Some Basic Problems of the Mathematical Theory of Elasticity, Noordhoff, The Netherlands.