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Efficient boundary element analysis of sharp notched plates. (English) Zbl 0758.73061
The paper develops the boundary element singularity subtraction technique, to provide an efficient and accurate method of analysing the general mixed-mode deformation of two-dimensional linear elastic structures containing sharp notches. The elastic field around sharp notches is singular. Because of the convergence difficulties that arise in numerical modelling of elastostatic problems with singular fields, these singularities are subtracted out of the original elastic field, using the first term of the Williams series expansion. This regularization procedure introduces the stress intensity factors as additional unknowns in the problem; hence extra conditions are required to obtain a solution. The accuracy and efficiency of the method is demonstrated with some benchmark tests of mixed-mode problems. New results are presented for the mixed-mode analysis of a non-symmetrical configuration of a single edge notched plate.

MSC:
74S15 Boundary element methods applied to problems in solid mechanics
74K20 Plates
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[1] Brahtz, Trans. Am. Soc. Mech. Eng. 55 pp 31– (1933)
[2] Williams, J. Appl. Mech. ASME 19 pp 526– (1952)
[3] Irwin, J. Appl. Mech. ASME 24 pp 361– (1957)
[4] ’Method of collocation applied to edge notched finite strip subjected to uniaxial and pure bending’, Boeing Company, Report D2-23551, 1964.
[5] and , ’Stress intensity factors for single edge notch specimens in bending or combined and traction by boundary collocation of a stress function’, NASA TN D-2603, 1965.
[6] ’Elastic stress fields and stress intensity factor for finite bodies’, University of Colorado, Ph.D. Thesis, 1967.
[7] Gross, Int. J. Fract. Mech. 8 pp 267– (1972)
[8] Tong, Int. J. Solids Struct. 3 pp 865– (1967)
[9] Tong, Int. J. Solid Struct. 9 pp 313– (1973)
[10] Lin, Int. j. numer. methods eng. 15 pp 1343– (1980)
[11] ’Finite element approach with the aid of analytical solutions’, in Recent Advances in Matrix Methods of Structural Analysis and Design, University of Alabama Press, 1971.
[12] Morley, Phil. Trans. Royal Soc. Lond. A275 pp 463– (1973)
[13] , and , ’The finite element calculation of stress intensity factors using superposition’, Computational Fracture Mechanics, Eds. and , ASME Special Publication, 1975, pp 21-34.
[14] Sinclair, Int. j. numer. methods eng. 18 pp 1587– (1982)
[15] Henshell, Int. j. numer. methods eng. 9 pp 495– (1975)
[16] Barsoum, Int. j. numer. methods eng. 10 pp 25– (1976)
[17] Parks, Int. J. Fracture 10 pp 487– (1974)
[18] Hellen, Int. j. numer. methods eng. 9 pp 187– (1975)
[19] Rice, J. Appl. Mech. ASME 35 pp 379– (1968) · doi:10.1115/1.3601206
[20] and , ’On the accuracy of boundary and finite element techniques for crack problems in fracture mechanics’, in (ed.), Proc. Eleventh Int. Conf. on Boundary Element Methods, Cambridge, U.S.A. Computational Mechanics Publications, Southampton, U.K., 1989.
[21] Babuška, Int. j. numer. methods eng. 20 pp 1085– (1984)
[22] Babuška, Int. j. numer. methods eng. 20 pp 1111– (1984)
[23] and , ’Computation of the amplitude of stress singular terms for cracks and reentrant corners’, in (ed.), Fracture Mechanics: Nineteenth Symposium, ASTM STP 969, American Society for Testing and Materials, 1988, pp. 101-124. · doi:10.1520/STP33072S
[24] Aliabadi, J. Strain Anal. 22 pp 1– (1987)
[25] ’Treatment of singularities in the solution of Laplace’s equation by an integral equation method’, Report NAC 31, National Physical Laboratory, 1973.
[26] Xanthis, Comp. Methods Appl. Mech. Eng. 26 pp 285– (1981)
[27] and , ’Boundary element analysis of V-notched plates’, in (ed.), Proc. Fourth Int. Conf. on Boundary Element Technology, Windsor, Canada, Computational Mechanics Publications, Southampton, U.K., 1989.
[28] ’Elastic stress singularity analysis using the eigenfunction-expansion method’, Ph.D. Thesis, University of London, Imperial College, 1973.
[29] Sternberg, J. Appl. Mech. ASME 25 pp 575– (1958)
[30] Vasilopoulos, Numer. Mathematik 53 pp 51– (1988)
[31] Rösel, Int. J. Fracture 33 pp 61– (1987)
[32] and , Boundary Elements–An Introductory Course, Computational Mechanics Publications, Southampton, U.K., 1989.
[33] Rizzo, Quart. Appl. Math. 25 pp 83– (1967)
[34] ’Theoretica basis of boundary solutions for linear theory of structures’, in (ed.), New Developments in Boundary Element Method, Proc. Second Int. Seminar on Recent Advances in Boundary Element Methods, University of Southampton, U.K., 1980.
[35] ’An enhanced boundary element method for determining fracture parameters’, Proc. 4th Int. Conf. on Numerical Methods in Fracture Mechanics, San Antonio, Texas, Pineridge Press, Swansea, U.K., 1987.
[36] ’Quadrature formulae for finite-part integrals’, Report WISK178, National Research Institute for Mathematical Sciences, Pretoria, 1975. · Zbl 0327.65027
[37] Telles, Int. j. numer. methods eng. 24 pp 959– (1987)
[38] Cerroloza, Int. j. numer. methods eng. 28 pp 987– (1989)
[39] , and , Numerical Recipies–The Art of Scientific Computing, Cambridge University Press, 1986.
[40] Delves, Math. Comp. 21 pp 543– (1967)
[41] Lyness, SIAM J. Numer. Anal. 4 pp 202– (1967)
[42] Lyness, Math. Comp. 21 pp 561– (1967)
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