A technique for optimally designing engineering structures with manufacturing tolerances accounted for

Abstract

Accurate optimal design solutions for most engineering structures present considerable difficulties due to the complexity and multi-modality of the functional design space. The situation is made even more complex when potential manufacturing tolerances must be accounted for in the optimizing process. The present study provides an in-depth analysis of the problem, and then a technique for determining the optimal design of engineering structures, with manufacturing tolerances in the design variables accounted for, is proposed and demonstrated. The examples used to demonstrate the technique involve the design optimization of simple fibre-reinforced laminated composite structures. The technique is simple, easy to implement and, at the same time, very efficient. It is assumed that the probability of any tolerance value occurring within the tolerance band, compared with any other, is equal, and thus it is a worst-case scenario approach. In addition, the technique is non-probabilistic. A genetic algorithm with fitness sharing, including a micro-genetic algorithm, has been found to be very suitable to use, and implemented in the technique. The numerical examples presented in the article deal with buckling load design optimization of an laminated angle ply plate, and evaluation of the maximum burst pressure in a thick laminated anisotropic pressure vessel. Both examples clearly demonstrate the impact of manufacturing tolerances on the overall performance of a structure and emphasize the importance of accounting for such tolerances in the design optimization phase. This is particularly true of the pressure vessel. The results show that when the example tolerances are accounted for, the maximum design pressure is reduced by 60.2% (in the case of a single layer vessel), and when five layers are specified, if the nominal fibre orientations are implemented and the example tolerances are incurred during fabrication, the actual design pressure could be 64% less than predicted.