An efficient numerical algorithm for cracks partly in frictionless contact

SIAM Journal on Applied Mathematics

Volumn 61, Issue 2, 2000, Pages 551-566

  Helsing, Johan ^a   Peters, Gunnar ^a  

^a ROYAL INSTITUTE OF TECHNOLOGY   (Sweden)

Author keywords

Contact; Contact zone; Cracks; Integral equations of Fredholm type; Linear elasticity; Numerical methods

Indexed keywords

ALGORITHMS; COMPUTER SIMULATION; CONVERGENCE OF NUMERICAL METHODS; ELASTICITY; INTEGRAL EQUATIONS; NONLINEAR EQUATIONS; NUMERICAL ANALYSIS; PERTURBATION TECHNIQUES;

FRICTIONLESS CONTACTS;

CRACKS;

EID: 0342501957     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/s0036139999356934     Document Type: Article

References (17)

1. R. CHAO AND N. LAWS, Closure of an arc crack in an isotropic homogeneous material due to uniaxial loading, Quart. J. Mech. Appl. Math., 45 (1992), pp. 629-640.
2. L. GREENGARD AND J. HELSING, On the numerical evaluation of elastostatic fields in locally isotropic two-dimensional composites, J. Mech. Phys. Solids, 46 (1998), pp. 1441-1462.
3. J. HELSING AND G. PETERS, Integral equation methods and numerical solutions of crack and inclusion problems in planar elastostatics, SIAM J. Appl. Math., 59 (1999), pp. 965-982.
4. N. J. HIGHAM, Accuracy and Stability of Numerical Algorithms, SIAM, Philadelphia, 1996.
5. D. HILDING, A. KLARBRING, AND J. PETERSSON, Optimization of structures in unilateral contact, Appl. Mech. Rev., 52 (1999), pp. 139-160.
6. H. HOCHSTADT, Integral Equations, John Wiley & Sons, New York, 1973.
7. W. KAHAN, Further remarks on reducing truncation errors, Comm. ACM, 8 (1965), p. 40.
8. N. KIKUCHI AND J. T. ODEN, Contact Problems in Elasticity: A Study of Variational Inequalities and Finite Element Methods, SIAM, Philadelphia, 1988.
9. L. M. MILNE-THOMPSON, Plane Elastic Systems, Springer, Berlin, 1968.
10. B. MUCKENHOUPT, Some weighted weak-type inequalities for the Hardy-Littlewood maximal function and the Hilbert transform, Indiana University Math. J., 26 (1977), pp. 801-816.
11. N. I. MUSKHELISHVILI, Some Basic Problems of the Mathematical Theory of Elasticity, P. Noordhoff Ltd., Groningen, The Netherlands, 1953.
12. F. PARÍS, J. C. CAÑO, AND J. VARNA, The fiber-matrix interface crack - a numerical analysis using boundary elements, Internat. J. Fracture, 82 (1996), pp. 11-29.
13. V. ROKHLIN, Rapid solution of integral equations of classical potential theory, J. Comput. Phys., 60 (1985), pp. 187-207.
14. Y. SAAD AND M. H. SCHULTZ, GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems, SIAM J. Sci. Stat. Comput., 7 (1986), pp. 856-869.
15. D. I. SHERMAN, On the problem of plane strain in non-homogeneous media, in Non-homogeneity in Elasticity and Plasticity, W. Olszak, ed., Pergamon Press, London, 1959, pp. 3-20.
16. P. S. THEOCARIS AND N. I. IOAKIMIDIS, The inclusion problem in plane elasticity, Quart. J. Mech. Appl. Math., 30 (1977), pp. 437-448.
17. B. TORSTENFELT, An Integrated Graphical System for Finite Element Analysis, User's Manual Version 2.0, Tech. Report LiTH-IKP-R-737, Linköping University, Linköping, Sweden, 1993.