An Extended Approach to Error Control in Experimental and Numerical Data Smoothing and Evaluation Using the Meshless FDM
Keywords:
experimental data smoothing and evaluation, error control, meshless FDMAbstract
This work addresses the development of an approach to approximation, smoothing and error estimation of physical/numerical data. It includes: development of postprocessing techniques for approximation of data in discrete form, development of an iterative approach to additional enhancement of data at new (required in computer procedures) locations, validation of an a posteriori technique to trace loss of accuracy in original data, and application of above mentioned procedure in wheel stress recovery calculations (approximation of the physical and numerical - FEM data). Theoretical considerations and numerical analysis are based on the Adaptive Finite element Analysis (AFEM) and the Meshless Finite Difference approximation (MFDM).
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Belytschko T., Krongaus Y., Organ D., Flemming M., Krysl P., “Meshless Methods: An
Overwiew and Recent Development”, Comp. Meth. in Appl. Mech and Engng, 139, 3-44,
Bugeda G., Onate E, “New Adaptive Techniques for Structural Problems”, Numerical
Methods in Engng’92, Ch.Chirsh et al. (Editors), Elsevier Science Publishers B.V., 1992.
Czarnek R., Experimental Determination of Release Fields in Cut Railroad Car Wheels,
DOT/FRA/ORD-96/DOT-VNTSC-FRA-96, Final Report, Cambridge, USA, October,
Demkowicz L., Oden J.T., Rachowicz W., Westerman T.A, “Toward a Universal h-p
Adaptive Finite Element Strategy. Part2: A Posteriori Error Estimation”, Computer
Methods in Applied Mechanics and Engineering, 77(1-2)113-180, 1989.
Karmowski W., Orkisz J., “Physicall Based Enhanced Analysis of Stresses Using
Experimental Data”, in: Quality and Maintenance for Modern Railway Operation, editor
J.J.Kalker et al., pp. 287-296, Delft, 24-26 June, 1992.
Karmowski W., Orkisz J., “Physically Based Method of Enhanced of Experimental Data –
Concept, Formulation and Application to Identification of Residual Stresses”, Proc. of the
IUTAM Symposium on Inverse Problems in Engng Mechanics, May 11-15 Tokyo, Japan,
Springer-Verlag, 61-70, 1993.
Krok J., Orkisz J., “Application of the Generalized FDM to Calculation of Arbitrary
Loaded Axisymmetrical Massive Structures”, Proc of 28-th Conf. KILiW PAN and KN
PZITB, Krynica, Poland, 1982, 81-90 (in polish).
Krok J., New Approach of Error Control in Approximation and Smoothing of Physical
Data, Application to wheel Saw Cut Measurements Data, Report to the VNTSC,
Cambridge, USA, 1998.
Krok J., Orkisz J., “Application of the Generalized FD Approach to Stress Evaluation in the
FE Solution”, Int. Conf. on Comp. Mech., Tokyo 1986, XII, pp.31-36.
Krok J., Orkisz J., “A Unified Approach to the FE Generalized Variational FD Method in
Nonlinear Mechanics, Concept and Numerical Approach”, in: Discretization Method in
Structural Mechanics, IUTAM/IACM Symposium Vienna 1989, p. 353-362, Springer-
Verlag, 1990.
Krok J., Orkisz J., Skrzat A., “Reconstruction of Hoop Stresses in 3D Bodies of
Revolution Based on Simulated Saw Cut Data”, XIII Conf. on Comp. Meth. in Mechanics,
Poznań, Poland, 669-676, 1997.
Krok J., Orkisz J., “Unified Approach to the Adaptive FEM and Meshless FDM. Concept
and Tests”, 2nd European Conference on Computational Mechanics, June 26-29, Cracow,
Poland , 2001, p. 1-33.
Liszka T., Orkisz J., The finite difference method at arbitrary irregular grids and its
applications in applied mechanics, Computers and Structers, 11, 83-95, 1980
Liszka T., “An interpolation method for an irregular net of nodes”, International Journal
for Numerical Methods in Engineering, 20, 1599-1612, 1984.
Orkisz J., “The Finite Difference Method”, Part III, in: Numerical Methods in Mechanics,
in: Springer-Verlag, 1998.
Zhu J.Z., Hinton E., Zienkiewicz O.C., “Mesh Enrichment Against Mesh Regeneration
Using Quadrilateral Elements”, Comm. in Num. Meth. in Engng, Vol. 9, 547-554, 1993.
Zienkiewicz O.C., Zhu J.Z., “A Simple Error Estimator and Adaptive Procedure for
Practical Engineering Analysis”, Int. Journ. Num. Meth. Eng., 24, 337-357, 1987.
Zienkiewicz O.C., Zhu J.Z., “The Superconvergent Patch Recovery and A’Posteriori Error
Estimates”, Part 2: Error Estimates and Adaptivity, Int. J Num Meth Engng, Vol 33,
p. 1365-1382, 1992.
Zienkiewicz O.C., Taylor R.L., Finite Element Method, Butterworth, Oxford, 2000.
Gavette L., Cuesta J.L., Ruiz A., “A Procedure for Approximation of the Error in the EFG
Method”, Int. Journ. Num. Meth. Eng., Vol. 53, p. 677-690, 2002.
Skrzat A., Orkisz J., Krok J., “Residual Stress Reconstruction in Railroad Car Wheels
Based on Experimental Data Measured at Saw Cut Test”, 2nd European Conference on
Computational Mechanics, June 26-29, Cracow, Poland , 2001, p. 1-17.