An optimization technique using the finite element method and orthogonal arrays

Abstract

The objective of this research was to develop an optimization technique that can be used interactively by design engineers to approach an optimal design with minimal computational effort. The technique can be applied to both continuous and discrete values of design variables. A large number of design variables can be also considered. In order to meet the objective, an optimization procedure was developed by coupling the finite element analysis (FEA) to the orthogonal array experimentation technique, because FEA is a common analysis tool for design engineers. From the results of the FEA and an orthogonal array, an average Jacobian matrix was constructed that showed the average overall sensitivity of the design variables. These sensitivities were then used to optimize the design parameters. The process could then be repeated at the discretion of the engineer until a satisfactory design is obtained. In general, the designer can predict and control the number of FEA calculations before an optimization process so that one can plan a budget and time for an optimal design. Some examples of structural optimization with truss and frame structures with continuous and discrete values of design variables were studied using the technique developed in this paper. Their optimal solutions were found with a small number of iterations.