Abstract:SUMMARYA new method for improving the approximations of stress intensity factors computed from pathindependent integrals is developed. The method uses Richardson's extrapolation. Numerical results are given to show the eciency and the stability of the present method. # 1998 John Wiley & Sons, Ltd.KEY WORDS stress intensity factors (SIF); ®nite element method (FEM); reciprocal work contour integral (RWCI); path-independent integrals (PII); displacement correlation technique (DCT); quarter-point displacement tec… Show more
SUMMARYThe results produced by Richardson extrapolation, though, in general, very accurate, are inexact. Numerical evaluation of this inexactness and implementation of the evaluation in practice are the objectives of this paper. First, considering linear changes of errors in the convergence plots, asymptotic upper bounds are proposed for the errors. Then, the achievement is extended to the results produced by Richardson extrapolation, and finally, an error-controlling procedure is proposed and successfully implemented in approximate computations originated in science and engineering.
SUMMARYThe results produced by Richardson extrapolation, though, in general, very accurate, are inexact. Numerical evaluation of this inexactness and implementation of the evaluation in practice are the objectives of this paper. First, considering linear changes of errors in the convergence plots, asymptotic upper bounds are proposed for the errors. Then, the achievement is extended to the results produced by Richardson extrapolation, and finally, an error-controlling procedure is proposed and successfully implemented in approximate computations originated in science and engineering.
SUMMARYIn this paper, we consider a general integral expression for mode I stress intensity factor along the fronts of convex planar cracks. For this integral approximation, we develop a simple numerical quadrature formula on every convex set which allows a precise estimation of the error. This permits the use of extrapolation techniques for the accurate computation of the integral.
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