# Optimization of Metal-Ceramic Functionally Graded Plates Using the Simulated Annealing Algorithm
###### Abstract
[PERSON] [20] used PSO for the maximization of FGM sandwich beam bending stiffness. [PERSON] and [PERSON] [21] presented an optimization study of FGMs with the eigenfrequencies as constraints or objective function. [PERSON] et al. [22] used mathematical programming to solve the optimization problem. [PERSON] and [PERSON] [23] presented a shape optimization method to design FGM sandwich structures based in two sets of metal-ceramic materials. [PERSON] et al. [24] presented solutions for the optimization of FGM pressure vessels subjected to thermo-mechanical loading. [PERSON] et al. [25; 26] minimized the fundamental natural frequency of FGM beams using differential evolution optimization. [PERSON] and [PERSON] [27] presented a methodology to optimize the natural frequencies of axially functionally graded beams and arches. [PERSON] et al. [28] studied the minimization of stresses in multi-layer FGM cylinders subjected to pressure loading using the PSO. [PERSON] and [PERSON] [29] optimized FGM plates in a thermo-mechanical environment using the adaptive hybrid evolutionary firefly algorithm (AHEFA). [PERSON] et al. [30], optimized the layer thicknesses and the ceramic volume fraction in FGM sandwich plates in free vibration using AHEFA. [PERSON] et al. [31] compared the performance of a classical KKT optimization method with SA and PSO for the weight minimization of rotating disks. [PERSON] and [PERSON] [32] used a combination of a co-evolutionary particle swarm optimization (CPSO) approach coupled with a differential quadrature method to minimize the stresses and displacements in FGM rotating disks. [PERSON] et al. [33] used the feasible arc interior point gradient-based algorithm (FAIPA) for the optimization of general FGM plate-shell structures. Some other authorshave used multi-objective optimization approaches applied to the FGM design optimization, where essentially the same design variables and objective functions have been used: [PERSON] and [PERSON] [34], [PERSON] et al. [35], [PERSON] et al. [36], [PERSON] et al. [37, 38] and [PERSON] et al. [39], among others. The SA algorithm has been disregarded by most researchers in favor of the aforementioned optimization methods. Very recently, [PERSON] et al. [40] have presented an improved SA algorithm with better search capacities and tested it in several benchmarking functions, which could lead to future applications. In the present work, the basic SA algorithm is used and its performance in the context of design optimization of FGM plate structures is demonstrated. In addition, the ability of this algorithm to deal with continuous and discrete design variables is verified. As mentioned in previous works from the authors [37, 38], for the design optimization of FGM plate structures, the use of finite element models based on appropriated shear deformation theories is important, seeking a balance between accuracy and computational efficiency. A nine-nodes Lagrangian finite element plate model based on a higher order shear deformation theory, considering the transverse shear and transverse normal deformations and accounting for the temperature dependency of the material properties, has been used in the present work. The constrained optimization is performed for different objectives, namely the mass and cost minimization. Tsai-Hill failure criteria and other structural response constraints or design limitations are considered. The design variables are the index of the power-law distribution in the metal-ceramic graded material, the thickness of the graded material, and also the choice of metal and ceramic materials which can be combined from a discrete set of available materials.