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A new implementation of the element free Galerkin method. (English) Zbl 0847.73064
A new implementation of the element free Galerkin method is developed based on a modified variational principle in which the Lagrange multipliers are replaced at the outset by their physical meaning so that the discrete equations are banded. In addition, weighted orthogonal basis functions are constructed so the need for solving equations at each quadrature point is eliminated. Numerical examples show that the present implementation effectively computes stress concentrations and stress intensity factors at cracks with very irregular arrangements of nodes.

74S05 Finite element methods applied to problems in solid mechanics
74G70 Stress concentrations, singularities in solid mechanics
74H35 Singularities, blow-up, stress concentrations for dynamical problems in solid mechanics
74R99 Fracture and damage
Full Text: DOI
[1] Nayroles, B.; Touzot, G.; Villon, P., Generalizing the finite element method: diffuse approximation and diffuse elements, Comput. mech., 10, 307-318, (1992) · Zbl 0764.65068
[2] T. Belytschko, Y.Y. Lu and L. Gu, Element free Galerkin methods, Internat. J. Numer. Methods and Engrg., in press.
[3] Lancaster, P.; Salkauskas, K., Surfaces generated by moving least squares methods, Math. comp., 37, 141-158, (1981) · Zbl 0469.41005
[4] Shepard, D., A two-dimensional interpolation function for irregularly spaced points, (), 517-524
[5] Washizu, K., Variational methods in elasticity and plasticity, (1975), Pergamon New York · Zbl 0164.26001
[6] Zienkiewicz, O.C.; Morgan, K., Finite elements and approximation, (1983), Wiley New York · Zbl 0582.65068
[7] Timoshenko, S.P.; Goodier, J.N., Theory of elasticity, (1970), McGraw-Hill New York · Zbl 0266.73008
[8] Belytschko, T.; Bachrach, W.E., Efficient implementation of quadrilaterals with high coarse-mesh accuracy, Comput. methods appl. mech. engrg., 54, 279-301, (1986) · Zbl 0579.73075
[9] Li, F.Z.; Shih, C.F.; Needleman, A., A comparison of methods for calculating energy release rates, Engrg. fract. mech., 21, 405-421, (1985)
[10] Moran, B.; Shih, C.F., Crack tip and associated domain integrals from momentum and energy balance, Engrg. fract. mech., 27, 615-642, (1987)
[11] Moran, B.; Shih, C.F., A general treatment of crack tip contour integrals, Int. J. fracture, 35, 295-310, (1987)
[12] Tada, H.; Paris, P.C.; Irwin, G.R., ()
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