## 1 Introduction
They demonstrated that the obtained values from the ANN converged with a considerable margin of error compared to the analytical solution. [PERSON] [7] carried out studies involving linear and nonlinear theories to examine the deformations and stresses of functionally graded plates. [PERSON] and [PERSON] [8] studied the deformations of an FGM plate pinned from both ends in a mechanical and thermal environment by comparing different deformation theories. [PERSON] et al. [9] analyzed the behavior of a simply supported functionally graded plate using a third-order shear deformation theory. [PERSON] et al. [10] presented the sinusoidal shear deformation theory for vibration analysis of a functionally graded element. [PERSON] et al. [11] conducted a series of analyses of FG plates with an effective \({}^{\circ}\)C iso-parametric Lagrangian finite element with multiple degrees of freedom for each node, using higher-order deformation theory. [PERSON] [12] investigated the static bending and free vibration behaviors of Timoshenko and Euler-Bernoulli FGM beams using shear deformation and Timoshenko beam theories. [PERSON] and [PERSON] [13] studied the free vibration model of axially graded non-uniform beam cross-sections with the help of Fredholm integral equations. [PERSON] and [PERSON] [14] analyzed the free vibration behavior of a simply-supported FGM beam for different deformation theories using a Navier-type solution method. [PERSON] et al. [15] studied the free vibration behavior of temperature-dependent FGM beams. [PERSON] [16] presented elasticity solutions to the bending of Euler-Bernoulli FGM beams. [PERSON] and [PERSON] [17] studied an analytical solution that analyzes the behavior of beams subjected to mechanical loading with the Airy stress function. [PERSON] et al. [18] studied the behavior of functionally graded solar panels under stress using a second-order shear deformation theory. Bending and buckling behaviors of bi-directional Euler-Bernoulli and Timoshenko beams using the strain gradient elasticity and nonlocal elasticity methods were presented in studies [19; 20; 21]. Although the analytical solutions of functionally graded composites converge very precisely, the mechanical calculations of such advanced composite structures impose a significant computational load. However, in cases where thermal change and other dynamic effects occur together, the solution to the problem becomes more difficult. ANN methods provide us with a significant guide at this point. The ANN model converges to an outcome with a tolerance of \(10^{-4}\) within a second. This computational efficiency outperforms analytical solutions in terms of time, and with a low tolerance. There are very few studies in the literature that analyze free vibration, post-buckling behavior, etc. Other effects of advanced composite structures are under different mechanical and environmental conditions. In such situations, validating the research becomes grueling. When artificial intelligence is well-trained, it can be a crucial source for us to check the accuracy of the analysis, and also allows the development of advanced methods by other researchers. In addition, the ANN method offers us many advantages such as optimization of composite structures and estimating appropriate dimensions and material parameters for minimum deformation of the structure in the problem. The present study offers a new perspective and approach to the traditional methods used in solving such problems in the literature. In view of the current research, recent breakthroughs made in computer engineering and their applied science studies with other disciplines have shown that the machine learning approach is shaping our future daily in terms of material optimization and advanced structural analysis. From this point on, it is noticeable that there is a deficiency in the literature on machine learning-based studies such as ANN approaches.