## 6 Conclusions  
The obtained results presented in the already published articles have been the foundation for developing and introducing the new shape function. The results obtained put an emphasis on the significance and topicality of the research in the field of functionally graded materials. A comprehensive and detailed investigation and systematization of the literature according to the topic have been guided related to the type of problems that authors tried to solve during the analysis of the functionally graded materials. Special focus and attention has been paid to different shear deformation theories that authors have used during the research. The new introduced shape function has been compared to 13 other shape functions that were originally proposed by different authors for the purpose of analysing composite laminates. However, this article implemented the previously mentioned shape 13 shape functions as well as new proposed shape function in order to analyse FGM plates. By comparing obtained results related to the static and dynamic analysis of moderately thick and thick plates, it is possible to conclude that the newly presented shape function can be applied during the analysis of FGM plates. Generally, based on the above research as well as obtained results, the following conclusions could be emphasized:  
Figure 10: 3D diagrams of the non-dimensional natural frequencies \(\overline{\omega}\) of the plates placed on an elastic foundation for different ratios a/h, a/b, values \(\mathrm{k}_{0}\), \(\mathrm{k}_{1}\) and index p: (a) p = 5, m = 1, n = 1, \(\mathrm{k}_{0}\) = 100, \(\mathrm{k}_{1}\) = 100; (b) a/b = 1, m = 1, n = 1, \(\mathrm{k}_{0}\) = 100, \(\mathrm{k}_{1}\) = 100; (c) a/b = 1, a/h = 5, m = 1, n = 1.  
* Decreasing the volume fraction of ceramics and increasing the volume fraction of metal in the FGM (the value of p index increases) decreases the value of the critical buckling temperature for both linear and nonlinear cases of temperature distribution through plate thickness
* Comparative analysis of the results for the linear and nonlinear distribution of the temperature across the plate thickness, and for other fixed parameters of the plate, it can be concluded that higher critical buckling temperatures are obtained for nonlinear distribution
* The elastic foundation effect shows that critical buckling temperature rapid rise because of the change of Pasternak coefficient k\({}_{1}\), rather than when Winkler coefficient k\({}_{0}\) changes
* Based on the analysis of the impact of the Winkler-Pasternak elastic foundation model parameters, similar to the thermal analysis, it was pointed out that the Pasternak coefficient k\({}_{1}\) has a far greater influence on natural frequencies than the Winkler coefficient k\({}_{0}\)  
Conceptualization, G.B. and D.C.; methodology, A.R. and G.B.; validation, M.B., B.S. and D.D.; formal analysis, A.R., D.C. and N.M.; writing-original draft preparation, D.C. and A.R.; writing-review and editing, D.C. and A.R. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Research presented in this paper was supported by Ministry of Education, Science and Technological Development of Republic of Serbia, TR32036, TR33015 and multidisciplinary project III 44007.  
The authors declare no conflict of interest.