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

Ishan Jha,Ashutosh Ranjan,Mrigank Jha,Krishna K Pathak

doi:10.33889/ijmems.2022.7.2.017

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.

Highlights

All the different ways of optimization have proved their utility in the real world, among which shape optimization techniques have been gaining popularity over time (Upadhyay et al, 2021) as it enhances the structure’s fundamental shape without adding additional cut-outs or holes while adhering to the parameters laid over it
Gradient-based methods has much more widely been accepted around the globe, and almost all the optimization software works on gradient-based method while cornering out the non-gradient methods and works done on it
Continuing and taking inspiration from previous works, the present study presents a novel integrated zero-order method using fuzzy membership functions

Summary

Introduction

In the era of wanting to have the best returns for the best possible cost minimization, it is very necessary even in the engineering field to have minimised cost of construction without compromising with the strength and serviceability of the structures. Initial works on non-gradient methods can be seen (Mattheck, 1989; Mattheck & Burkhardt, 1990; Baumgartner et al, 1992; Chen & Tsai, 1993) using ideas motivated from living things where they recommended material addition at the higher stressed area and material removal from lower stressed areas to achieve an optimal shape of the structure. Mortazavi (2020a, 2020b) proposed a metaheuristic technique based on fuzzy algorithms for parameter-free optimization of large scale structures These studies have proved the effectiveness of non-gradient methods in the field of shape optimization. The mobility of design nodes as well as the ultimate convergence are controlled using fuzzy set theory This proposed approach is based upon the notion of non-gradient shape optimization and packaged in a piece of software termed GSO (Gradientless shape optimization) coded in FORTRAN language. The proposed approach (GSO) seems to give a more industryfriendly and fabricable final optimized shape of structure compared to the Optistruct

Optimization Procedure

Fuzzy Membership Function

Convergence Criteria

Findings

Conclusion