Corner singularities of Kirchhoff plates and the boundary element method

Computer Methods in Applied Mechanics and Engineering

Volumn 173, Issue 3-4, 1999, Pages 273-285

  Maucher, Roland ^a   Hartmann, Friedel ^a  

^a UNIVERSITY OF KASSEL   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY ELEMENT METHOD; FUNCTIONS; INTEGRAL EQUATIONS; ITERATIVE METHODS; STRESS INTENSITY FACTORS; STRUCTURAL ANALYSIS;

KIRCHHOFF PLATES;

PLATES (STRUCTURAL COMPONENTS);

EID: 0032678708     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0045-7825(98)00287-4     Document Type: Article

References (16)

1. [1] H. Blum, Der Einfluss von Eckensingularitäten bei der numerischen Behandlung der Biharmonischen Gleichung, Vol. 140 of Bonner mathematische Schriften. Universität Bonn, 1982.
2. [2] H. Blum, Numerical treatment of corner and crack singularities, in: E. Stein and W.L. Wendland, Eds., Finite Element and boundary Element Techniques from Mathematical and Engineering Point of View (Springer, 1988) 171-212.
3. [3] H. Blum and M. Dobrowolski, On finite element methods for elliptic equations on domains with corners, Computing 28 (1982) 53-63.
4. [4] H. Blum and R. Rannacher, On the boundary value problem of the biharmonic operator on domains with angular corners, Math. Methods Appl. Sci. 2 (1980) 556-581.
5. [5] G.J. Fix, S. Gulati and G.I. Wakoff, On the use of singular functions with finite element approximations, J. Comput. Phys. 13 (1973) 209-228.
6. [6] F. Hartmann, Introduction to boundary Elements (Springer, 1989).
7. [7] A. Kufner and A.M. Sändig, Some Applications of weighted Sobolev Spaces, Vol. 100 of Teubner-Texte zur Mathematik (Teubner Verlag, 1987).
8. [8] V.G. Maz'ja and B.A. Plamenevskii, Coefficients in the asymptotics of solutions of elliptic boundary-value problems in a cone, J. Sov. Math. 9 (1978) 750-764.
9. [9] Yu.A. Melnikov, Green's Functions in Applied Mechanics, Vol. 27 of Topics in Engineering (Computational Mechanics Publications, 1995).
10. [10] H. Melzer and R. Rannacher, Spannungskonzentrationen in Eckpunkten der Kirchoffschen Platte, Der Bauingeniuer 55 (1980) 181-184.
11. [11] M. Renardy and R.C. Rogers, An Introduction to Partial Differential Equations, Vol. 13 of Texts in Applied Mathematics (Springer, 1993).
12. [12] J.B. Seif, On the Green's function for the biharmonic equation in an infinite wedge, Trans. Am. Math. Soc. 182 (1973) 241-260.
13. [13] M. Stern, A general boundary integral formulation for the numerical treatment of plate bending problems, Int. J. Solid Struct. 15 (1979) 769-782.
14. [14] M.L. Williams, Surface singularities resulting from various boundary conditions in angular plates under bending, in: Proc. First US National Congress on Applied Mechanics (1951) 325-329.
15. [15] J. Wloka, Partielle Differentialgleichungen (Teubner Verlag, 1982).
16. [16] L.S. Xanthis, M. Bernal and C. Atkinson, The treatment of singularities in the calculation of stress intensity factors using the boundary integral equation methods, Comput. Methods Appl. Mech. Engrg. 26 (1981) 285-304.