Otimização sequencial aproximada de estruturas de material com gradação funcional

Abstract

Functionally Graded Materials (FGMs) are a class of composite materials that, due to the capability of gradually controlling the volume fraction of each material in the structure, have been receiving more and more attention in the last few years by the literature. FGMs applications can be found in a variety of areas, such as medicine and aerospace industry. Thus, the optimization of functionally graded structures is an area of great interest, especially to the design of engineering structures, where several constraints are typically considered to ensure stability and safety. However, there are few analytical formulations to estimate the structural response of these structures, leading to the usage of numerical methods. On the other hand, this may result in a high computational cost. In addition to that, in structural optimization, heuristic methods are usually used, in spite of its need of a high number of evaluations of the objective function and constraints. Thus, processes can become very time-consuming. With that in mind, this work proposes the use of Surrogate Models, specifically the Radial Basis Functions (RBFs), as a way to provide an approximate surface based on an easy and fast analysis. RBFs are built based on sampling points previously evaluated by the High Fidelity Model (HFM). With these data, this surrogate model uses a linear combination of radially symmetric kernel functions, whose centers are usually located in the sampling points. Then, the surrogate model can be used to predict the surface response. In this work, the basis functions are interpolated using the Gaussian function. In addition to that, static surrogate models are usually not good enough to provide a good prediction in regions close to the function’s optimum. Thus, the Sequential Approximate Optimization will be used to continuously improve on the current surrogate model to ensure the effectiveness of the proposed approach. Finally, different methods for defining new points for the sample will be tested, as well as different methods for defining the width parameter for the Gaussian function. The results show excellent results, and the proposed approach is capable of showing great effectiveness while maintaining a sharp decrease in the time spent and on the number of high fidelity evaluations needed.