A methodology for structural optimisation with damage tolerance constraints

This paper presents recent developments in the optimal design of structural components with fracture constraints. To minimise the computational effort it is suggested that an initial "near optimum" shape be used. One approach could be to begin with the optimal shape for the non-cracked geometry. This initial near optimum shape would then be used in conjunction with the alternating finite element method, for multiple cracks, which builds on existing CAD based finite element models and the resultant formulation then linked to available optimisation codes. This approach is illustrated by considering the problem of an optimum cut-out geometry for a square plate subjected to a 4:1 and a 2:1 biaxial stress field. When considering the problem of shape optimisation with static fracture constraints it was found that an initial "near optimal" shape, based on the optimal shape for the uncracked geometry, was in fact an excellent approximation to the optimal solution for the cracked problem. It was also found that, in each case, for a given crack length the stress intensity factors, for cracks emanating at any arbitrary point around the hole, were essentially constant along most of the circumference. This behaviour is intuitively expected for an optimised geometry, where it would be hoped that all locations around the hole would be equally critical. A similar behaviour was found when considering shape optimisation with durability, i.e. crack growth, constraints. In this case it was hypothesised that the optimum shape would be such that all locations around the cut-out would be equally fatigue critical. However, in this case it is believed that the final optimal shape will depend on: the initial flaw size, the critical crack length, the load spectrum and the overall geometry of the structure. The analysis also reveals that, as the geometry of the cut-out or hole changes, the location of the crack which determines the minimum fatigue life can also change. This makes it necessary to consider flaws at a range of locations around the hole. (C) 2000 Published by Elsevier Science Ltd. All rights reserved.