PSI - Issue 41

Efstathios E. Theotokoglou et al. / Procedia Structural Integrity 41 (2022) 361–371 Efstathios E.Theotokoglou/ Structural Integrity Procedia 00 (2022) 000–000

370 10

Table 2. maximum stresses. ceramic core p=0.5

p=1

p=5

p=10

4,109E+09 4,04E+09 6,65E+09 1,23E+09 1,21E+09 1,99E+09 8,91E+08 8,48E+08 1,02E+09

7,83E+09 2,35E+09 1,08E+09

σ xx σ yy σ xy

metal core

p=0.5

p=1

p=5

p=10

1,492E+10 1,225E+10 9,9E+09 4,476E+09 3,674E+09 2,97E+09 2,97E+09 2,41E+09 1,95E+09

9,637E+09 2,891E+09 1,91E+09

σ xx σ yy σ xy

8. Conclusions As it can be seen from our results, for the case with the ceramic core and FGM face sheets, as the volume fraction index increases, the normal stresses initially have a very small decrease and then they both increase and approximate the discontinuous case with ceramic core and metal face sheets. On the other hand for the case with the metal core and FGM face sheets, as the volume fraction index increases, the normal stresses both decrease and they approximate the discontinuous case with metal core and ceramic face sheets. For the shear stress it can be seen from Figure 9 and Table 2 that for the case with the ceramic core and FGM face sheets as the volume fraction index increases, the shear stress initially has a small decrease and then increase. For the case with the metal core and FGM face sheets as the volume fraction index increases, the shear stress decreases. Comparing the stress distributions for the two cases with homogeneous cores and FGM face sheets, it can be seen that for every stress the maximum stress (tensile and compressive) is smaller for the case corresponding to the ceramic core. Also it can be observed that in the case with the ceramic core and FGM face sheets as the volume fraction index increases, a stress concentration at the interface between the core and the face sheets is created. For the minimization of the stresses for the given boundary conditions we have to use the configuration with the ceramic core and the FGM face sheets. Also we can conclude that in the case with the ceramic core, the volume fraction index should be 1 or 0.5 in order to avoid stress concentration and have lower stresses, and thus the transition from the one phase of the material to the other must be as smooth as possible. Finally we can also observe that in cases with homogeneous core and FGM face sheets, the normal and shear stresses are continuous along the y axis in contrast to the cases with ceramic core and metal face sheets and with metal core and ceramic face sheets where the stresses are discontinuous. 9. References Asemi, K., Salehi, M. & Akhlaghi, M., 2014. Transient thermal stresses in functionally graded thick truncated cones by graded finite element method. International Journal of Pressure Vessels and Piping , 119, pp. 52-61. Avhad, P. V. & Sayyad, A. S., 2020. On the static deformation of FG sandwich beams curved in elevation using a new higher order beam theory. Sådhanå , 45, pp. 1-16. Belarbi, M.O., Houari, M. S., Hirane, H., Daikh, A. A., & Bordas, S. P, 2022. On the finite element analysis of functionally graded sandwich curved beams via a new refined higher order shear deformation theory. Composite Structures , 279, pp. 1-19. Burlayenko, V. N., Altenbach, H., Sadowski, T., Dimitrova, S. D., & Bhaskar, A, 2017. Modelling functionally graded materials in heat transfer and thermal stress analysis by means of graded finite elements. Applied Mathematical Modelling , 45 ,pp. 422–438. Çömez, İ., 2014. Elasticity solution for a functionally graded two-layer beam with simple supported edges. Turkish J Eng Env Sci , 38, pp. 373 381. Cook, R. D., Malkus, D. S., Plesha, M. E. & Witt, R. J., 2001. Concepts and Applications of Finite Element Analysis. fourth ed. s.l.:Wiley.