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. Indeed, one approach could be to begin with the optimal shape for the non cracked geometry. This initial near optimum shape could 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 rectangular 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 the optimal shape for the uncracked geometry was not the same as the optimal solution for the cracked problem. It was also found that for the optimal case, the stress intensity factors for same length cracks emanating at any arbitrary point around the hole were approximately constant along most of its circumference. This behaviour is intuitively expected for an optimised geometry where it all locations around the hole should be equally critical. The analysis also reveals that, as the geometry of the cut out or hole changes, the location of the crack that causes the maximum stress intensity factor can also change. This makes it necessary to consider flaws at a range of locations around the hole.