# Trefftz functions for 3D stress concentration problems

• Zuzana Murcinkova Technical University Kosice
• Vladimir Kompis Academy of the Armed Forces of General Milan Rastislav Stefanik
• Mario Stiavnicky Academy of the Armed Forces of General Milan Rastislav Stefanik

### Abstract

The paper deals with solution of 3D problems with stress concentration using the Trefftz functions. The modelled stress concentrators are holes and cavities of spherical and ellipsoidal shapes. Moreover, the random spherical cavity microstructure is modelled. The Method of External Finite Element Approximation (MEFEA) is applied to simulate detailed stress state of mentioned stress concentrators. This boundary-type method was developed to build special approximation functions that are associated with surface which causes the stress concentration. The method does not need discretization by classical finite elements, however, instead of elements the domain is divided into Trefftz type subdomains. The displacement and force boundary conditions are met only approximately whereas the governing equations are fulfilled exactly in the volume for linear elasticity, making it possible to assess accuracy in terms of error in boundary conditions.

### References

[1] V.N. Apanovitch: The Method of External Finite Element Approximation. Minsk, 1.991.
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[3] B. Pluymers et al. Application of hybrid finite element - Trefftz approach for acoustic analysis. In: Numerical Methods in Continuum Mechanics, 4th Workshop on Trefftz Methods, University of Zilina, Zilina, 2005.
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[5] M. Zmindak, P. Novak. Meshless methods for analysis of composites reinforced by rigid inclusions. In: Proceedings: International Scientific Conference MITECH, CZU, Praha, 2008.
Published
Jul 20, 2022
How to Cite
MURCINKOVA, Zuzana; KOMPIS, Vladimir; STIAVNICKY, Mario. Trefftz functions for 3D stress concentration problems. Computer Assisted Methods in Engineering and Science, [S.l.], v. 15, n. 3-4, p. 305-318, july 2022. ISSN 2956-5839. Available at: <https://cames.ippt.pan.pl/index.php/cames/article/view/738>. Date accessed: 14 sep. 2024.
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