Development of a 3D Biological method for fatigue life based optimisation and its application to structural shape design

Abstract

Damage tolerance design philosophy assumes that numerous cracks can be present at various arbitrary locations in a structure, which makes fatigue life based shape optimisation very computationally intensive. As a result, there have been limited applications of fatigue life based optimisation. To address this, the paper presents a gradient-less 3D Biological algorithm that uses fatigue life as the design objective for shape optimisation of damage tolerant structures. This formulation is used for optimisation with numerous 3D cracks located along the structural boundary. Fatigue life based shape optimisation is demonstrated via the problem of optimal design of ‘a through-hole in a rectangular block made of linear elastic isotropic material under biaxial loading’. A range of different initial flaws were analysed to investigate the effects of crack parameters on optimal shapes. A semi-analytical method was employed for computation of the stress intensity factors (SIF). These were subsequently used for evaluating fatigue life by allowing the cracks to grow up to an acceptable final size. The optimum hole shapes were approximately elliptical with the aspect ratios being dependent on the initial and final crack sizes, and the local geometry. A significant enhancement in the fatigue life of a structural component is achieved. A fatigue life optimisation leads to the generation of a ‘near uniform’ fatigue critical surface. The effect of initial flaw aspect ratio on the optimal solutions was investigated, and it is found that the fatigue crack growth law governs the nature of variation of the optimal shapes. It is also shown that the fatigue life optimised shape can be quite different from the corresponding fracture strength or stress optimised solution. This emphasises the need to explicitly consider fatigue life as the design criteria for optimisation of damage tolerant structures.