John S. Campbell

Interior point tracking in shape evolving unstructured finite element meshes

An algorithm is presented for the tracking of interior points in a shape evolving unstructured FE mesh. Evolution of the boundary shape may be associated with a governing equation, as in moving boundary problems, or may be prescribed, as in structural shape optimisation. In the latter SSO case the point tracking algorithm may be used in conjunction with a FD approximation to determine geometric sensitivities: in this case the boundary deformation is a small perturbation. For meshes undergoing gross deformations of the boundary an incremental method is used. Reversibility tests are undertaken to assess the robustness and accuracy of the algorithm and examples are given to illustrate the general utility of the method.

A Hybrid Boundary-element/finite-elementMethod For The Computation Of Design SensitivitiesIn 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 pointtracking method, which is particularly applicable to unstructured meshes, is developed and used, in conjunction with FT) 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.