The method of fundamental solutions for the Cauchy problem in two-dimensional linear elasticity

International Journal of Solids and Structures

Volumn 41, Issue 13, 2004, Pages 3425-3438

  Marin, Liviu ^a   Lesnic, Daniel ^a  

^a UNIVERSITY OF LEEDS   (United Kingdom)

Author keywords

Cauchy problem; Inverse problem; Linear elasticity; Meshless method; Method of fundamental solutions; Regularisation

Indexed keywords

BOUNDARY CONDITIONS; LINEAR EQUATIONS; NUMERICAL METHODS; PARAMETER ESTIMATION; SOLUTIONS; STRESS ANALYSIS;

ISOTROPIC LINEAR ELASTICITY; L-CURVE METHOD; LINEAR ALGEBRAIC EQUATIONS; LINEAR STRESS;

ELASTICITY;

ELASTICITY;

EID: 2342463081     PISSN: 00207683     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijsolstr.2004.02.009     Document Type: Article

References (35)

1. Balakrishnan K. Ramachandran P.A. A particular solution Trefftz method for non-linear Poisson problems in heat and mass transfer Journal of Computational Physics 150 1999 239-267
2. Balakrishnan K. Sureshkumar R. Ramachandran P.A. An operator splitting-radial basis function method for the solution of transient nonlinear Poisson problems Computers and Mathematics with Applications 43 2002 289-304
3. Berger J.A. Karageorghis A. The method of fundamental solutions for heat conduction in layered materials International Journal for Numerical Methods in Engineering 45 1999 1681-1694
4. Berger J.A. Karageorghis A. The method of fundamental solutions for layered elastic materials Engineering Analysis with Boundary Elements 25 2001 877-886
5. Fairweather G. Karageorghis A. The method of fundamental solutions for elliptic boundary value problems Advances in Computational Mathematics 9 1998 69-95
6. Golberg M.A. Chen C.S. Discrete Projection Methods for Integral Equations 1996 Computational Mechanics Publications Southampton
7. Golberg M.A. Chen C.S. The method of fundamental solutions for potential, Helmholtz and diffusion problems Golberg M.A. Boundary Integral Methods: Numerical and Mathematical Aspects 1999 105-176 WIT Press and Computational Mechanics Publications Boston
8. Hadamard J. Lectures on Cauchy Problem in Linear Partial Differential Equations 1923 Oxford University Press London
9. Hanke M. Limitations of the L-curve method in ill-posed problems BIT 36 1996 287-301
10. Hansen P.C. Rank-deficient and discrete ill-posed problems: Numerical aspects of linear inversion 1998 SIAM Philadelphia
11. Hansen P.C. The L-curve and its use in the numerical treatment of inverse problems Johnston P. Computational Inverse Problems in Electrocardiology 2001 119-142 WIT Press Southampton
12. Huang, C.H., Shih, W.Y., 1997. A boundary element based solution of an inverse elasticity problem by conjugate gradient and regularization method. In: Proceedings of the 7th International Offshore Polar Engineering Conference, Honolulu, USA, pp. 338-395
13. Karageorghis A. The method of fundamental solutions for the calculation of the eigenvalues of the Helmholtz equation Applied Mathematics Letters 14 2001 837-842
14. Karageorghis A. Fairweather G. The method of fundamental solutions for the numerical solution of the biharmonic equation Journal of Computational Physics 69 1987 434-459
15. Karageorghis A. Fairweather G. The method of fundamental solutions for axisymmetric elasticity problems Computational Mechanics 25 2000 524-532
16. Katsurada M. Okamoto H. The collocation points of the fundamental solution method for the potential problem Computers and Mathematics with Applications 31 1996 123-137
17. Knops R.J. Payne L.E. Uniqueness Theorems in Linear Elasticity 1986 Pergamon Press Oxford
18. Koya T. Yeih W.C. Mura T. An inverse problem in elasticity with partially overspecified boundary conditions. II. Numerical details ASME Journal of Applied Mechanics 60 1993 601-606
19. Kupradze V.D. Aleksidze M.A. The method of functional equations for the approximate solution of certain boundary value problems USSR Computational Mathematics and Mathematical Physics 4 1964 82-126
20. Landau L.D. Lifshits E.M. Theory of Elasticity 1986 Pergamon Press Oxford
21. Marin L. Elliott L. Ingham D.B. Lesnic D. Boundary element method for the Cauchy problem in linear elasticity Engineering Analysis with Boundary Elements 25 2001 783-793
22. Marin L. Elliott L. Ingham D.B. Lesnic D. An alternating boundary element algorithm for a singular Cauchy problem in linear elasticity Computational Mechanics 28 2002 479-488
23. Marin L. Háo D.N. Lesnic D. Conjugate gradient-boundary element method for the Cauchy problem in elasticity Quarterly Journal of Mechanics and Applied Mathematics 55 2002 227-247
24. Marin L. Lesnic D. Regularized boundary element solution for an inverse boundary value problem in linear elasticity Communications in Numerical Methods in Engineering 18 2002 817-825
25. Marin L. Lesnic D. Boundary element solution for the Cauchy problem in linear elasticity using singular value decomposition Computer Methods in Applied Mechanics and Engineering 191 2002 3257-3270
26. Mathon R. Johnston R.L. The approximate solution of elliptic boundary value problems by fundamental solutions SIAM Journal on Numerical Analysis 14 1977 638-650
27. Poullikkas A. Karageorghis A. Georgiou G. Methods of fundamental solutions for harmonic and biharmonic boundary value problems Computational Mechanics 21 1998 416-423
28. Poullikkas A. Karageorghis A. Georgiou G. The method of fundamental solutions for inhomogeneous elliptic problems Computational Mechanics 22 1998 100-107
29. Poullikkas A. Karageorghis A. Georgiou G. The numerical solution of three-dimensional Signorini problems with the method of fundamental solutions Engineering Analysis with Boundary Elements 25 2001 221-227
30. Poullikkas A. Karageorghis A. Georgiou G. The numerical solution for three-dimensional elastostatics problems Computers and Structures 80 2002 365-370
31. Ramachandran P.A. Method of fundamental solutions: Singular value decomposition analysis Communications in Numerical Methods in Engineering 18 2002 789-801
32. Tikhonov A.N. Arsenin V.Y. Methods for Solving Ill-posed Problems 1986 Nauka Moscow
33. Tikhonov A.N. Leonov A.S. Yagola A.G. Nonlinear Ill-posed Problems 1998 Chapman - Hall London
34. Vogel C.R. Non-convergence of the L-curve regularization parameter selection method Inverse Problems 12 1996 535-547
35. Yeih W.C. Koya T. Mura T. An inverse problem in elasticity with partially overspecified boundary conditions. I. Theoretical approach ASME Journal of Applied Mechanics 60 1993 595-600