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Okabe, Masayuki; Kikuchi, Noboru

Semi-radial singularity mapping theory for line singularities in fracture mechanics. (English) Zbl 0489.73087

Comput. Methods Appl. Mech. Eng. 36, 257-276 (1983).
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MSC:

74S05 Finite element methods applied to problems in solid mechanics
74R05 Brittle damage
41A05 Interpolation in approximation theory

Keywords:

semi-radial singularity mapping; line singularities; stress; strain; brick-type semi-radial singularity mapping element; wedge-type one; element familization; polynomial interpolations; cube; simplex
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References:

[1] Argyris, J. H.; Buck, K. E.; Fried, I.; Mareczek, G.; Scharpf, D. W., Some new elements for matrix displacement methods, (Proc. 2nd Conf. Matrix Methods in Structural Mechanics (1968), Air Force Inst. Tech., Wright Patterson Air Force Base: Air Force Inst. Tech., Wright Patterson Air Force Base OH)
[2] Argyris, J. H.; Fried, I., The LUMINA element for the matrix displacement method, Aero, J., 72, 514-517 (1968)
[3] Taylor, R. L., On completeness of shape functions for finite element analysis, Internal. J. Numer. Meths. Engrg., 4, 17-22 (1970) · Zbl 0255.73095
[4] Zienkiewicz, O. C., The Finite Element Method (1977), McGraw-Hill: McGraw-Hill London · Zbl 0435.73072
[5] Ball, A. A., The interpolation function of a general Serendipity rectangular element, Internal. J. Numer. Meths. Engrg., 15, 773-778 (1980) · Zbl 0426.73070
[6] Okabe, M.; Yamada, Y.; Nishiguchi, I., Reconsideration of rectangular Lagrange families with hierarchyranking bases, Comput. Meths. Appl. Mech. Engrg., 23, 369-390 (1980) · Zbl 0442.73071
[7] Argyris, J. H., Triangular elements with linearly varying strain for the matrix displacement method, J. Roy. Aero. Soc., 69, 711-713 (1965)
[8] de Veubeke, B. F., Displacement and equilibrium models in the finite element method, (Zienkiewicz, O. C.; Holister, G. S., Stress Analysis (1965), Wiley: Wiley New York), Ch. 9. · Zbl 0327.73038
[9] Argyris, J. H.; Fried, I.; Scharpf, D. W., The TET20 and TEA8 elements for the matrix displacement method, Aero. J., 72, 618-625 (1968)
[10] Silvester, P., Higher order polynomial triangular finite elements for potential problems, Internat. J. Numer. Meths. Engrg., 7, 849-861 (1969) · Zbl 0185.42201
[11] Ciarlet, P. G.; Raviert, P. A., General Lagrange and Hermite interpolation in R\(^n\) with applications to finite element methods, Arch. Rational Mech. Anal., 46, 177-199 (1972) · Zbl 0243.41004
[12] Okabe, M.; Kikuchi, N., Some general Lagrange interpolations over simplex finite elements with reference to derivative singularities, Comput. Meths. Appl. Mech. Engrg., 28, 1-25 (1981) · Zbl 0466.73088
[13] Blackburn, W. S., Calculation of stress intensity factors, (Whiteman, J. R., The Mathematics of Finite Elements and Applications (1973), Academic Press: Academic Press London), 327-336 · Zbl 0278.73048
[14] Akin, J. E., The generation of elements with singularities, Internal. J. Numer. Meths. Engrg., 10, 1249-1259 (1976) · Zbl 0341.65078
[15] Tracey, D. M.; Cook, T. S., Analysis of power type singularities using finite elements, Internal. J. Numer. Meths. Engrg., 11, 1225-1233 (1977) · Zbl 0364.65090
[16] Stern, M., Families of consistent conforming elements with singular derivative fields, Internal. J. Numer. Meths. Engrg., 14, 409-421 (1979) · Zbl 0408.73071
[17] Henshell, P. D.; Shaw, K. G., Crack tip finite elements are unnecessary, Internat. J. Numer. Meths. Engrg., 9, 495-507 (1975) · Zbl 0306.73064
[18] Barsoum, R. S., On the use of isoparametric finite elements in linear fracture mechanics, Internat. J. Numer. Meths. Engrg., 10, 25-37 (1976) · Zbl 0321.73067
[19] Peano, A.; Pasini, A.; Riccioni, R.; Sardella, L., Adaptive approximations in finite element structural analysis, Computers and Structures, 10, 333-342 (1979) · Zbl 0394.73002
[20] Yamada, Y.; Ezawa, Y.; Nishiguchi, I.; Okabe, M., Reconsiderations on singularity or crack tip elements, Internal. J. Numer. Meths. Engrg., 14, 1525-1544 (1979) · Zbl 0411.73066
[21] Okabe, M., Fundamental theory of the semi-radial singularity mapping with applications to fracture mechanics, Comput. Meths. Appl. Mech. Engrg., 26, 53-73 (1981) · Zbl 0463.73091
[22] Yamamoto, Y.; Sumi, Y., Stress intensity factor for three-dimensional cracks, (Proc. 14th Internat. Congress Theor. Appl. Mech.. Proc. 14th Internat. Congress Theor. Appl. Mech., Delft (1976)) · Zbl 0374.73067
[23] Yagawa, G.; Nishioka, T., Three-dimensional finite element analysis for through-wall crack in thick plate, Internat. J. Numer. Meths. Engrg., 12, 1295-1310 (1978) · Zbl 0377.73082
[24] Akin, J. E., Elements for problems with line singularities, (Whiteman, J. R., The Mathematics of Finite Elements and Applications, Vol. III (1978), Academic Press: Academic Press London), 65-75 · Zbl 0443.73051
[25] Hughes, T. J.R.; Akin, J. E., Techniques for developing ‘special’ finite element shape functions with particular reference to singularities, Internat. J. Numer. Meths. Engrg., 15, 733-751 (1980) · Zbl 0428.73074
[26] Ingraffea, A. R.; Manu, C., Stress-intensity factor computation in three dimensions with quarter-point elements, Internat. J. Numer. Meths. Engrg., 15, 1427-1445 (1980) · Zbl 0438.73071
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