Through-thickness shape optimisation of typical double lap-joints including effects of differential thermal contraction during curing

Repairs and reinforcements using bonded patches have been shown over a long period of time and in many applications to be effective and durable. However, cracking can occur in the adhesive near stress concentrations when the repairs are applied in certain severe service loading environments. Sensitivity-based numerical optimisation coupled with finite element analysis has previously been employed to provide free-form through-thickness shapes for the patch and the adhesive layer. These shapes reduce adhesive stress concentrations by evenly distributing the load transfer along the bond-line. In the present paper, automated and iterative finite-element-based shape optimisation methods were used to determine optimal shapes which account for the effects of the different thermal expansion coefficients of boron/epoxy patches and the aluminium alloy parent structure. The adhesive stress was considered to have a static component due to thermal effects and a cyclic component due to service loading. The benefits of optimising for minimal cyclic component were compared with the benefits of optimising for minimal combined component. The paper investigates how best to configure the optimisation problem in view of this mixture of cyclic and static loading.