PSI - Issue 72

Victor Rizov / Procedia Structural Integrity 72 (2025) 120–127

127

Fig. 4. Influence of h/b ratio on the maximum SERR (curve 1 – for the frame supported by three links, curve 2 - for the frame supported by two links and a pinned support, curve 3 - for the frame supported by two links and a fixed support).

For all the supporting conditions considered here, as the a/l ratio grows, so does the maximum SERR (Fig. 3). The curves in Fig. 3 again show that the maximum SERR reduces when the supporting conditions change from these in Fig. 1a, via these in Fig. 1b to that in Fig. 1c. The combined influences of the h/b ratio and the type of supporting conditions on the maximum SERR in the frames are explored too. The findings are illustrated through the curves reported in Fig. 4. As the h/b ratio grows, the maximum SERR reduces for all the types of supporting conditions under consideration (Fig. 4). 4. Conclusions A theoretical exploration of the influence of the supporting conditions of a single bay functionally graded frame on the longitudinal fracture is performed. The frame explored is under action of a periodic dynamic loading. The maximum and minimum SERR are derived. The combined effect of the supporting conditions and the frame geometry on the SERR is shown. It is seen that the SERR under periodic dynamic loading is highly sensitive to the frame supporting conditions which are used in the current exploration. It is determined that the SERR is highest in a frame supported by three links. The SERR reduces when the frame is supported by two links and a pinned support. Further reduction of the SERR is found in the frame supported by two links and a fixed support. These findings indicate that the SERR and the longitudinal fracture induced by periodic dynamic loadings can be regulated in a significant extend by the supporting conditions. References Alkunte, S., Rajeshirke, M., Fidan, I., et al. , 2023. Performance evaluation of fatigue behavior in extrusion-based functionally graded materials. Int. J. Adv. Manuf. Technol. 128, 863 – 875 Dowling, N., 2007. Mechanical Behavior of Materials. Pearson Hutchinson, J.W., Suo, Z., 1991. Mixed mode cracking in layered materials. Advances in Applied Mechanics 29, 63-191. Mahamood, R.M., Akinlabi, E.T., 2017. Functionally Graded Materials. Springer Malenov, R., 1993. Strength of materials. UPH Mladenov, K., Klecherov, J., Lilkova-Markova, S., Rizov, V. 2012. Strength of materials. ABC Tehnika Reichardt, A., Shapiro, A.A. , Otis, R., Dillon, R.P. , Borgonia, J.P., Mc-Enemey, B.W., 2020. Advances in additive manufacturing of metalbased functionally graded materials. International Materials Reviews 66, 1-29 Rizov, V. I., 2017. Non-linear analysis of delamination fracture in functionally graded beams. Coupled Systems Mechanics 6, 97-111 Rizov, V. I., 2017. An analytical solution to the strain energy release rate of a crack in functionally graded beams. European journal of mechanics A/solids 65, 301-312 Sanjeeviprakash, K., Kannan, A. R., Shanmugam, N. S., 2023. Additive manufacturing of metal-based functionally graded materials: overview, recent advancements and challenges. J Braz. Soc. Mech. Sci. Eng . 45, 241 Teacher, M., Velu, R., 2024. Additive Manufacturing of Functionally Graded Materials: A Comprehensive Review. Int. J. Precis. Eng. Manuf. 25, 165 – 197