PSI - Issue 73

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Petr Frantík et al. / Procedia Structural Integrity 73 (2025) 14–18 Author name / Structural Integrity Procedia 00 (2025) 000 – 000

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Fig. 4. Comparison of numerical results and derived relationships Figure 4 shows the key results: all three FEM models yielded similar normal force values as predicted by the generalized relationship (14) with variable exponent p . In particular, the one-dimensional beam model corresponds to p = 0, the two-dimensional shell model to p = 2 (more precisely, for numerical results 1.996), and the three dimensional brick model to p = 4 (dtto 3.991). 4. Conclusions This paper presents derivations of analytical relationships for approximating the axial force resulting from a given displacement of a prismatic bar made of a homogeneous, isotropic linear material, considering two geometrically nonlinear effects: large elongations and cross-sectional changes due to transverse contraction. The derived expressions were validated against numerical results from the Dlubal RFEM application. It was found that the generalized formula accurately approximates the FEM results, with the exponent increasing with the dimensionality of the model. Acknowledgements The support of FEM Consulting, s.r.o. is gratefully acknowledged. I would like to thank Assoc. Prof. Ing. Ivan Němec, CSc., for his enduring interest in mechanical problems . References

Hencky, H., 1928. “ Über die Form des Elastizitätsgesetzes bei ideal elastischen Stoffen ”, Zeitschrift für technische Physik, 9, pp. 215 – 220. ‘ Poisson’s ratio’, 20 25. Wikipedia. Available at: https://en.wikipedia.org/wiki/ Poisson%27s_ratio (Accessed: 5 May 20 25).

Dlubal software, 2021. RFEM 6 [computer software] , Dlubal software GmbH. www.dlubal.com. FEM Consulting software, 1991 . NE-XX solver [computer software] , FEM Consulting, s.r.o. www.fem.cz.