Three-dimensional structure optimal design for extending fatigue life by using biological algorithm D. Peng a, * , R. Jones a , S. Pitt b a Department of Mechanical Engineering, P.O. Box 38, Monash University, Victoria 3800, Australia b Air Vehicles Division, Defence Science and Technology Organisation, 506 Lorimer Street, Fishermans Bend, Victoria 3207, Australia Available online 30 October 2007 Abstract This paper presents some applications of a new structural shape optimization procedure for maximizing fatigue life or inspection intervals for damage tolerant structures. In this approach, a new and simple method, which we termed FAST (Failure Analysis of Structures), for estimating the stress intensity factor for cracks at a notch, as well as an extension of the biological algorithm was employed to study the problem of optimization with fatigue life as the design objective. Research by the authors has demonstrated that the optimum shape for minimizing stress is not necessarily the optimum shape for static strength or fatigue life of a damage tolerant structure. The examples are presented that highlight this dif- ference. The optimal shapes for stress are compared with optimized shapes found for static strength with different crack lengths. These are also compared with optimized shapes found for maximum fatigue life. The choice of initial crack size was found to have a significant effect on the optimal shapes for the structures presented. Ó 2007 Elsevier Ltd. All rights reserved. Keywords: Fatigue life; Shape optimization technique; Biological algorithm; Finite element analysis 1. Introduction Traditionally, the optimal shape of a structure was generally considered to be that which gave the lowest possible peak stress [1–10]. Presented in [11] is the performed shape optimization of an internal hole in a rotating disk with four symmetric cracks emanating from the hole. The boundary element analysis was used to model the cracked structure. The hole profile was shape optimized (using only three control points) to minimize the stress intensity factors. Optimized in [12] is a cracked pressure vessel of a turboshaft casing for plastic instability and critical stress intensity factor. In their simplified 3D finite element analysis models, they studied the effect of a growing crack and its effect on the opti- mal shape. However, this cannot be classified as a damage tolerance analysis as the crack location was fixed and cracking at other locations was not considered. The gradient-based nonlinear program- ming techniques [13] are used to solve 2D shape optimization problems of ‘cantilever beam with shear loads’ and ‘filp chip solder joints’. In their investigation, fatigue life of a single existing crack was chosen as objective function. In these approaches, crack locations are explicitly defined 0167-8442/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.tafmec.2007.10.005 * Corresponding author. E-mail address: Daren.Peng@eng.monash.edu.au (D. Peng). Available online at www.sciencedirect.com Theoretical and Applied Fracture Mechanics 49 (2008) 26–37 www.elsevier.com/locate/tafmec