An application of the response surface method to structural optimization problems

Structural problems are commonly analyzed using implicit solvers, such as the finite element method (FEM), which often demand manual processes and are computationally intensive, especially for structural optimization problems that involve multiple FEM evaluations to identify the optimal design solutions. In addition, implementing optimization algorithms also demands significant expertise for accurate application. This study proposes a simple yet efficient procedure to address structural optimization problems by transforming the implicit analysis into explicit performance functions using the response surface method and simulating the space of input variables by random samples. The explicit performance functions enable quick evaluations for all generated samples of inputs, and a search routine is developed to identify optimal solutions efficiently. The proposed procedure is validated through three case studies, demonstrating its ability to achieve accurate solutions within minutes of analysis.