A Comparative Study of Gradient Descent Method and a Novel Non-Gradient Method for Structural Shape Optimization

Abstract

Motivated by the works on non-gradient techniques in the domain of shape optimization of the structure, the present work intends to suggest a novel non-gradient procedure for shape optimization of structures and compare it to an existing gradient-based method. The presented technique optimizes the shape of structural parts using a fuzzy controlled integrated zero-order methodology incorporating the notion of design elements and automated mesh construction with mesh refinement at each iteration. The movement of nodes and convergence monitoring is taken care of using the triangular fuzzy membership function. The changes in shape occur according to the selected target maximum shear stress (σt) with a view of reaching as near to the target as possible at all the points. The present methodology is packaged in a piece of software termed GSO (Gradientless shape optimization) coded in FORTRAN language. To explain the efficacy of the current approach, a few basic structural shapes have been optimized under various constraints, and the results of the same are compared to those obtained using Optistruct (a part of software suite HyperWorks from Altair engineering), which works on gradient descent method. The proposed approach works well and produces more industry fabricable results than what is produced by the gradient descent method in Optistruct.

Keywords

• shape optimization
• fuzzy set
• fuzzy membership function
• finite element
• non-gradient
• design element
• optistruct