Characteristics of the design surface of damage tolerance parameters and their relation to shape optimisation

Abstract

In parametric design studies, where stability is not a concern, the strength of a structure is often considered as the primary design criterion, and consequently the optimal (best) structural design is often chosen as the one that minimises the maximum stress generated. However, for structures, whereby failure is governed by fracture or fatigue, residual strength and fatigue life, as distinct from stress, need to be considered as the explicit design objectives.In this study, the design spaces for residual strength and fatigue life for different structural configurations are evaluated to demonstrate the utilities of design space exploration for damage tolerance design optimisation. This was illustrated using the problem of the optimum design of a cutout shape with boundary cracks under biaxial load. The maximum stress intensity factor and the minimum fatigue life associated with the cracks were evaluated for each cutout geometry.The design surfaces for residual strength and fatigue life establish that a design based on damage tolerance parameters poses a well-behaved optimisation problem with a well-defined minimum/maximum region. The design space was found to be flat for both residual strength and fatigue life, enabling the specification of design tolerances. The optimum values of the stress intensity factor and the fatigue life obtained from the design space agreed well with those determined using various optimisation methods. It is shown that a design space exploration can provide a systematic way to reduce the weight of a structure by adopting a ‘feasible non-optimal’ solution that meets the design criteria, rather than aiming for the ‘optimal’ (best) solution.