Over-deterministic method: The influence of rounding numbers on the accuracy of the values of Williams’ expansion terms

Vladimir Ruzicka; Lucie Malikova; Stanislav Seitl

doi:10.3221/IGF-ESIS.42.14

Over-deterministic method: The influence of rounding numbers on the accuracy of the values of Williams’ expansion terms

Authors

Vladimir Ruzicka Brno University of Technology, Faculty of Civil Engineering, Institute of Structural Mechanics, Veveří 331/95, 602 00 Brno, Czech Republic
Lucie Malikova Academy of Sciences of the Czech Republic, Institute of Physics of Materials, v. v. i., Žižkova 22, 616 62 Brno, Czech Republic http://orcid.org/0000-0001-5868-5717
Stanislav Seitl Academy of Sciences of the Czech Republic, Institute of Physics of Materials, v. v. i., Žižkova 22, 616 62 Brno, Czech Republic http://orcid.org/0000-0002-4953-4324

DOI:

https://doi.org/10.3221/IGF-ESIS.42.14

Keywords:

Over-deterministic method, Rounding numbers, Williams’ expansion, Fracture mechanics, Stress field

Abstract

A study on the accuracy of the values of Williams’ expansion terms influenced by rounding numbers is presented. The results are presented taking into account a three-point bend single edge notched beam. Crack tip stress tensor components are expressed using the linear elastic fracture mechanics (LEFM) theory in this work, more precisely via its multi-parameter formulation, i.e. by Williams’ power series (WPS). Determination of the coefficients of the terms of this series is performed using the least squaresbased regression technique known as the over-deterministic method (ODM), for which displacements data obtained numerically in software ANSYS are taken as inputs. The values of Williams’ expansion terms based on the displacement data obtained are calculated by using various levels of rounding numbers and the results are compared and discussed.

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Published

29-09-2017

Issue

Vol. 11 No. 42 (2017): October 2017

Section

Miscellanea

License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Copyright
Authors are allowed to retain both the copyright and the publishing rights of their articles without restrictions.

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How to Cite

Over-deterministic method: The influence of rounding numbers on the accuracy of the values of Williams’ expansion terms. (2017). Frattura Ed Integrità Strutturale, 11(42), Pages 128-135. https://doi.org/10.3221/IGF-ESIS.42.14