Uncertainty Quantification for Topology Optimisation of Aerospace Structures

Abstract

The design and optimisation of aerospace structures is non-trivial. There are several reasons for this including, but not limited to, (1) complex problem instances (multiple objectives, constraints, loads, and boundary conditions), (2) the use of high fidelity meshes which impose significant computational burden, and (3) dealing with uncertainties in the engineering modelling. The last few decades have seen a considerable increase in research output dedicated to solving these problems, and yet the majority of papers neglect the effect of uncertainties and assume deterministic conditions. This is particularly the case for topology optimisation - a promising method for aerospace design that has seen relatively little practical application to date. This thesis will address notable gaps in the topology optimisation under uncertainty literature. Firstly, an observation underpinning the field of uncertainty quantification (UQ) is the lack of experimental studies and dealing with non-parametric variability (e.g. model unknowns, experimental and human errors etc.). Random Matrix Theory (RMT) is a method explored heavily in this thesis for the purpose of numerical and experimental UQ of aerospace structures for both parametric and non-parametric uncertainties. Next, a novel algorithm is developed using RMT to increase the efficiency of Reliability-Based topology optimisation, a formulation which has historically been limited by computational runtime. This thesis also provides contributions to Robust Topology optimisation (RTO) by integrating uncertain boundary conditions and providing experimental validation of the results. The final chapter of this thesis addresses uncertainties in multi-objective topology optimisation (MOTO), and also considers treating a single objective RTO problem as a MOTO to provide a more consistent distribution of solutions.