Postprocessing and reliability evaluation of the one-dimensional numerical simulation results in mechanical problems

  • Jan Wojtas Cracow University of Technology


This work addresses extended formulation of a new approach proposed to control numerical data error. It  includes developing postprocessing techniques for the approximation of data given in a discrete form and estimation (evaluation) of this data a posteriori error and the reliability index. Theoretical consideration and numerical analysis are based on the adaptive meshless finite difference (MFDM) approach.


meshless FDM, experimental data approximation and smoothing, a posteriori error estimation of experimental data, adaptive methods,


[1] W. Karmowski, J. Orkisz. A Physically Based Method of Enhancement of Experimental Data Concepts, Formulation and Application to Identification of Residual Stresses. In: M. Tanaka, H.D. Bui [Eds.], Inverse Problems in Engineering Mechanics. International Union of Theoretical and Applied Mechanics. Springer, Berlin, Heidelberg, 1993.
[2] J. Krok. An extended approach to error control in experimental and numerical data smoothing and evaluation using the meshless FDM. Revue Europ´eenne des ´ El´ements Finis, 7–8: 913–935, 2002.
[3] J. Krok, M. Stanuszek, J. Wojtas. A procedure for adaptive evaluation of numerical and experimental data. In: Proceedings of the 14th International Conference on Computational Methods and Experimental Measurements, 2009, Algarve, Portugal, WIT Transactions on Modelling and Simulation, 48: 25–36, 2009.
[4] J. Krok, J. Wojtas. An adaptive approach to experimental data collection based on a posteriori error estimation of data. In: Comp. Meth. in Mechanics – CMM-2007, June 2007, Spała–Łódz, Poland, pp. 1–13, 2007.
[5] J. Krok, J. Wojtas. Estimation of a posteriori errors and density of experimental and numerical data points. Technical Transactions, 104(1): 81–103, 2007.
[6] S.A. Łukasiewicz, M. Stanuszek, J.A. Czyz. Filtering of the experimental or FEM data in plane stress and strain fields. Experimental Mechanics, June 1993, pp. 139–147, 1993.
[7] S.A. Łukaszewicz, M. Stanuszek. Constrained, weighted, least square technique for correcting experimental data. In: 6th Int. Conf. on Comp. Methods and Experimental Measurements 93, Vol 2: Stress analysis, pp. 467–480, Elsevier Applied Science, London New York, 1993.
[8] J. Magiera. Non-statistical physically reasonable technique for a posteriori estimation of experimental data error. Computer Assisted Mechanics and Engineering Sciences, 13: 593–611, 2006.
Feb 17, 2019
How to Cite
WOJTAS, Jan. Postprocessing and reliability evaluation of the one-dimensional numerical simulation results in mechanical problems. Computer Assisted Methods in Engineering and Science, [S.l.], v. 25, n. 1, p. 59-68, feb. 2019. ISSN 2299-3649. Available at: <>. Date accessed: 26 jan. 2022. doi: