Surrogate Based Optimization of Functionally Graded Plates

Functionally Graded Materials (FGM) are composites, usually made of ceramic and metal, in which the volume fraction of their constituents varies smoothly along an interest direction. These materials were initially proposed as a solution for the development of thermal barriers, but are currently used in different applications. The variation in composition results in a gradual change in their properties, improving the performance of structures subjected to thermal and mechanical loads, but making structural analysis more complex. Plates, on the other hand, are three-dimensional flat structures in which the thickness is much smaller than their other two dimensions. For projects involving functionally graded plates, both the choice of their constituents and the definition of the distribution of volume fractions are necessary. Computational methods, which simulate the behavior of these structures, and optimization techniques, which explore the design space, are used to obtain a more efficient solution. However, the computational cost of structural analyses can be a limiting factor in the optimization process, since bioinspired algorithms require the analysis of a large number of trial solutions to find the optimal design. Thus, this work addresses the use of surrogate models capable of efficiently approximating the results of numerical simulations. These models are an alternative to reduce the computational cost of the design optimization of complex structures. Surrogates have been incorporated into an optimization methodology known as Sequential Approximate Optimization (SAO), where the approximate response surface is continuously updated and improved by the insertion of new points, enhancing the model approximation. The proposed methodology will be used in the design optimization functionally graded plates considering buckling and free vibration. The results will be evaluated in terms of accuracy and efficiency based on a set of benchmarks.