Optimal shape design with fatigue life as design constraint using a 3D biological method

The damage tolerance design philosophy assumes that cracks are present at all potentially critical locations in a structure. However, the numerical simulation of cracks using FEM requires a fine mesh to model the singularity at crack tip. This makes fracture calculations relatively computationally intensive. As a result, there have been limited applications of durability based optimisation to realistic structures. To overcome this, the paper presents a 3D biological algorithm for the shape optimisation of structures with fatigue life as the design objective. This formulation was used for optimisation of damage tolerant structures with numerous 3D flaws located along the structural surface. A semi-analytical method was employed for computing the stress intensity factors. This method uses the uncracked stress field, and thus does not require explicit modelling of cracks. The stress distribution in the uncracked structure was obtained using the finite element program NE-NASTRAN, and the fatigue life associated with the cracks around the surface being optimised was evaluated using a modified version of the NASA crack growth program FASTRAN. In this work the fatigue life based optimisation is illustrated via the problem of optimal design of 'a through hole in a rectangular block under biaxial loading'. It was found that the optimum hole shapes were approximately elliptical with the aspect ratios being dependent on crack size, structural geometry and boundary conditions. It has been shown that the fatigue life optimised shapes can be different from the corresponding stress optimised solution. This emphasises the need to explicitly consider fatigue life as the design objective. In all cases a significant improvement in the fatigue life was achieved with the generation of a 'near uniform' fracture critical surface. The design space near the 'optimal' region was found to be relatively flat. This is beneficial as a significant structural performance enhancement can be achieved without precise identification of the local/global optimum solution.