Hybrid boundary-element/finite-element method for the computation of design sensitivities in structural shape optimisation

This paper presents an accurate method of calculating design sensitivities of behaviour variables, such as displacements and stress, in FE structural shape optimisation problems. Its applicability to unstructured meshes is emphasised. The semi-analytical method is applied to the determination of the design sensitivities of behaviour variables in structural shape optimisation. It is shown how the computation of the geometric sensitivities (i.e. the sensitivity of internal points in the problem domain to boundary perturbations) is a primary task to carry out the sensitivity analysis. A BEM based point-tracking method, which is particularly applicable to unstructured meshes, is developed and used, in conjunction with FD approximation, to determine these geometric sensitivities. Three benchmark examples, with unstructured meshes, are used to show the application of the method and results from these show that the geometric sensitivity calculations are easily carried out using the BEM point tracking approach. Design sensitivities calculated compare favourably with analytical solutions.