Amended influence matrix method for removal of rigid motion in the interior BVP for plane elasticity

doi:10.1007/s10483-017-2244-6

Abstract

Abstract:

A conventional complex variable boundary integral equation (CVBIE) in plane elasticity is provided. After using the Somigliana identity between a particular fundamental stress field and a physical stress field, an additional integral equality is obtained. By adding both sides of this integral equality to both sides of the conventional CVBIE, the amended boundary integral equation (BIE) is obtained. The method based on the discretization of the amended BIE is called the amended influence matrix method. With this method, for the Neumann boundary value problem (BVP) of an interior region, a unique solution for the displacement can be obtained. Several numerical examples are provided to prove the efficiency of the suggested method.

Key words: complementary boundary problem, penalty method, Bernstein estimate, regularity, Neumann boundary value problem(BVP), complex variable boundary integral equation(CVBIE), amended influence matrix method, removal of rigid body motion

2010 MSC Number:

30E25
80M15

Yizhou CHEN. Amended influence matrix method for removal of rigid motion in the interior BVP for plane elasticity. Applied Mathematics and Mechanics (English Edition), 2017, 38(10): 1471-1480.

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References

[1] Blazquez, A., Matic, V., Paris, F., and Canas, J. On the removal of rigid motions in the solution of elastostatic problems by direct BEM. International Journal for Numerical Methods in Engineering, 39(23), 4021-4038(1996)
[2] Lutz, E., Ye, W. J., and Mukherjee, S. Elimination of rigid body modes from discretized boundary integral equations. International Journal of Solids and Structures, 35(33), 4427-4436(1998)
[3] Vodicka, R. and Mantic, V. On invertibility of elastic single-layer potential operator. Journal of Elasticity, 74(2), 147-173(2004)
[4] Vodicka, R., Mantic, V., and Paris, F. On the removal of the non-uniqueness in the solution of elastostatic problems by symmetric Galerkin BEM. International Journal for Numerical Methods in Engineering, 66(12), 1884-1912(2006)
[5] Chen. J. T., Huang, W. S., Lee, J. W., and Tu, Y. C. A self-regularized approach for deriving the free-free flexibility and stiffness matrices. Computers and Structures, 145, 12-22(2014)
[6] Chen, J. T., Yang, J. L., Lee, Y. T., and Chang, Y. L. Formulation of the MFS for the twodimensional Laplace equation with an added constant and constraint. Engineering Analysis with Boundary Elements, 46, 96-107(2014)
[7] Vodicka, R. and Petrik, M. Degenerate scales for boundary value problems in anisotropic elasticity. International Journal of Solids and Structures, 52(1), 209-219(2015)
[8] Chen, Y. Z. Numerical solution of elastic inclusion problem using complex variable boundary integral equation. Acta Mechanica, 223(4), 705-720(2012)
[9] Chen, Y. Z. and Wang, Z. X. Properties of integral operators and solutions for complex variable boundary integral equation in plane elasticity for multiply connected regions. Engineering Analysis with Boundary Elements, 52, 44-55(2015)
[10] Chen, J. T., Huang, W. S., Lee, Y. T., Kuo, S. R., and Kao, S. K. Revisit of degenerate scales in the BIEM/BEM for 2D elasticity problems. Mechanics of Advanced Materials and Structures, 24, 1-15(2017)
[11] Chen, J. T., Lee, Y. T., Chang, Y. L., and Jian, J. A self-regularized approach for rank-deficiency systems in the BEM of 2D Laplace problems. Inverse Problems in Science and Engineering, 25, 89-113(2017)
[12] Brebbia, C. A., Telles, J. C. F., and Wrobel, L. C. Boundary Element Techniques:Theory and Applications in Engineering, Springer, Heidelberg (1984)
[13] Cheng, A. H. D. and Cheng, D. S. Heritage and early history of the boundary element method. Engineering Analysis with Boundary Elements, 29(3), 286-302(2005)