Dr. Hesham A. Hegazi

Shape Optimization of NURBS Modeled 3D Frames Using Hybrid

Genetic Algorithm

Abstract

The present paper introduces a new methodology for designing machine element shapes. The element is represented using non-uniform rational B-Spline (NURBS) in order to give it a form of shape flexibility. A special form of genetic algorithms known as real-coded genetic algorithms is used to conduct the search for the design objectives. Shape optimization of 3D C-frames are used as an application of the proposed methodology. The design parameters of these frames include the dimensions of their cross-sections, which should be chosen to withstand the applied loads and minimize the elements overall weight.

In a further development, the hybridization of different optimization methods has been used to find the optimum shape of the element. Real coded genetic algorithm is used as a random search method, while Nelder-Mead is used as a direct search method, where the result of the genetic algorithm search is used as the starting point of direct search. The results showed that the use of Nelder-Mead with Real coded Genetic Algorithms has been very significant in improving the optimum shape of a solid 3D C-frames subjected to a combined tension and bending stresses. The hybrid optimization method could be extended to more complex shape optimization problems. For the purpose of analysis, curved beam theory is applied on local cross- sections on the NURBS surface. A finite elements analysis was conducted on SDRC- IDEAS for verifying the results obtained using the curved beam theory.

Keywords: Shape Optimization, NURBS, CAD, Genetic Algorithms, C-Frames.