# Optimization of Metal-Ceramic Functionally Graded Plates Using the Simulated Annealing Algorithm
###### Abstract  
This work involves the design optimization of metal-ceramic through the thickness of functionally graded material (FGM) plates subjected to thermomechanical loadings. Constrained optimization was performed for minimum mass and minimum material cost of the FGM plates. The design process of FGM plate structures requires a good choice of metal and ceramic materials and the adequate definition of the components volume fractions through the thickness direction in order to accomplish a certain structural behavior, while optimizing the material costs and/or the plate mass. Here, the optimization problems are solved with the simulated annealing (SA) algorithm, not requiring the calculation of the derivatives of the objective or constraint functions. Constrained single objective optimization cases are studied, and validated with alternative solutions, considering the \(p\)-index and the FGM plate thickness as design variables. New optimization cases, involving additionally the metal and ceramic materials as design variables, are presented both  
According to those review papers [1; 2; 3; 4] among the research publications, involving FGM structures, there is a lack of research in the area of the design optimization. Very recently, [PERSON] et al. [5] published a review on the optimization of FGM structures. This review addressed several types of structure constituted from FGM, and noted that the most common optimization design variable in the reviewed researches is the material distribution pattern. Stress distribution, critical buckling load, fundamental frequency and the weight of FGM structures were the most popular objectives, which the researchers have improved through optimization studies. In addition, it was noted that the methodologies based on genetic algorithms (GA) and particle swarm optimization (PSO) are, so far, the most frequently used algorithms. This review also suggested some additional topics for future research in the area, pointing out that there are few optimization studies involving manufacturing aspects or noting that the cost of the design is an important issue and there are few studies using this objective function. Regarding the structural optimization involving FGM plates and shell structures, in a closer relation with the present work, the following publications can be mentioned. [PERSON] and [PERSON] [6] have used artificial neural networks (ANN) in the optimization of material composition of heat-resisting FGMs. [PERSON] and [PERSON] [7] presented a numerical technique for the sensitivity analysis of the coupled thermomechanical problem of FGM parts by using sequential linear programming (SLP). [PERSON] and [PERSON] [8] optimized the volume fraction distribution of FGMs using a multi-objective genetic algorithm. [PERSON] and [PERSON] [9] performed a two-dimensional optimization of material distribution in FGMs using GA. [PERSON] and [PERSON] [10] performed the optimization of the volume fraction and the topology of FGM structures. [PERSON] and [PERSON] [11] presented the minimization of the interlaminar stresses at the interface with the core in sandwich FGM plates. [PERSON] and [PERSON] [12; 13; 14] optimized the stresses and the thermo-mechanical buckling behavior of FGMs by using the quasi-Newton method and the finite difference method as optimizer. [PERSON] et al. [15] used the imperialist competitive algorithm (ICA) for the optimization of critical buckling load on FGM plates and performed comparisons with the GA. [PERSON] et al. [16] showed that the PSO method outperforms the classical mathematical programming methods in FGM problems. [PERSON] et al. [17] proposed a reliability-based design optimization (RBDO) to deal with uncertainty in the manufacturing process of FGMs. [PERSON] et al. [18], used topology optimization and homogenization to design FGM piezocomposites for energy-harvesting applications. [PERSON] and [PERSON] [19] used GA and PSO in optimization problems and analyzed the accuracy and convergence of those algorithms.