Integrating the finite element method and genetic algorithms to solve structural damage detection and design optimisation problems

This thesis documents fundamental new research in to a specific application of structural box-section beams, for which weight reduction is highly desirable. It is proposed and demonstrated that the weight of these beams can be significantly reduced by using advanced, laminated fibre-reinforced composites in place of steel. Of the many issues raised during this investigation two, of particular importance, are considered in detail; (a) the detection and quantification of damage in composite structures and (b) the optimisation of laminate design to maximise the performance of loaded composite structuress ubject to given constraints. It is demonstrated that both these issues can be formulated and solved as optimisation problems using the finite element method, in which an appropriate objective function is minimised (or maximised). In case (a) the difference in static response obtained from a loaded structure containing damage and an equivalent mathematical model of the structure is minimised by iteratively updating the model. This reveals the damage within the model and subsequently allows the residual properties of the damaged structure to be quantified. Within the scope of this work is the ability to resolve damage, that consists of either penny-shaped sub-surface flaws or tearing damage of box-section beams from surface experimental data. In case (b) an objective function is formulated in terms of a given structural response, or combination of responses that is optimised in order to return an optimal structure, rather than just a satisfactory structure. For the solution of these optimisation problems a novel software tool, based on the integration of genetic algorithms and a commercially available finite element (FE) package, has been developed. A particular advantage of the described method is its applicability to a wide range of engineering problems. The tool is described and its effectiveness demonstrated with reference to two inverse damage detection and quantification problems and one laminate design optimisation problem. The tool allows the full suite of functions within the FE software to be used to solve non-convex optimisation problems, formulated in terms of both discrete and continuous variables, without explicitly stating the form of the stiffness matrix. Furthermore, a priori knowledge about the problem may be readily incorporated in to the method.