Design and optimisation of composite structures

Numerical analysis and design of structures is a field with ever growing potential. Advancements in technology and hardware enable designers to rely on numerical methods for the design of complex structures. Aeronautics and aerospace are examples of areas in which these complex structures exist. These complex structures are often made of composite materials, which aside from the numerous advantages are very complex in nature; thus, they require advanced methods and models for their design and mechanical analysis, especially when considering the failure of the material.
Optimisation is a design tool that enables the engineer to achieve a better design configuration of the structure through the aid of numerical methods. Topology optimisation is one method with the remit of optimising the mass distribution of a structure to satisfy some requirements and to provide better properties. Evolving or moving boundaries are an intrinsic part of topology optimisation. Traditionally, the efforts to model evolving boundaries rely on implicit schemes, which provide the means to efficiently model the evolution of a boundary but lack the ability to transmit information at the boundary. Explicit alternatives are often computationally expensive and inherently complex to implement. In this PhD, one objective is to investigate a solution to this dichotomy: a novel finite element method (FEM) based formulation, using the floating node method (FNM), capable of explicitly representing moving boundaries in a domain. Such methodology has the potential to bridge the gap between analysis and design by providing an accurate translation between the numerical domain and the design domain.
The simultaneous analysis of different time and length scales is designated multiscale analysis. Multiscale analysis of composite materials is paramount when one aims to investigate the failure mechanisms of composite materials. These mechanisms are varied and happen at very different time and length scales. Being able to capture all these scales within one numerical analysis leads to being able to capture the complex material behaviour in real structures. This project has the aim of investigating new multiscale techniques, using the floating node method, that enable the accurate and detailed analysis of the failure of real-world composite structures.
In summary, the overall aim of this PhD is to develop numerical methods that have the potential of being a step-change in the analysis and design of composite structures. The more detailed objectives include the development of methods that bridge the design and analysis domains through optimisation methods; the development of new methods capable of handling physical phenomena at different time and length scales simultaneously (multiscale); and the development of methods that join optimisation and multiscale analysis to tackle large-scale, non-linear failure of composite structures.