Layout Optimization of Structures: Novel Methods and Applications

Computational optimization methods have become widely used in various fields of engineering in recent years. However, the field of structural design still largely relies on past experience and a limited number of well known structural forms for the majority of problems. This thesis aims to identify and address factors that limit the uptake of computational optimization methods for the design of structural frameworks in practice. Novel methods to address three major issues are presented here: the accurate modelling of self-weight of structural elements and auxiliary components, user-friendly methods for reducing the complexity of the resulting structures, and numerical methods that produce a more easily interpretable output. The contribution of the self-weight of a structure to the loads it must carry is often significant for structures of large dimensions. Here a novel formulation of the ground structure based layout optimization method is presented; this uses curved elements that must take the form of an equally stressed catenary. This is the minimum weight form for an axially loaded member that must also support its own weight, and allows accurate numerical results to be obtained for long span problems, eliminating the non-conservative errors that are caused by current methods. Using this formulation novel layouts are proposed, which can allow much longer spans to be obtained with the same amount of material. A further extension is also presented that allows modelling of lumped masses at points where they are of use. This allows generation of solutions incorporating counterweights, anchorages and abutments. A further issue that is addressed in this work is the complexity of the structures typically produced by numerical optimization methods. Two approaches to reducing complexity are considered, addressing physical and conceptual complexity respectively. Resolving the former involves using mixed integer programming to impose specific constraints designed to improve the buildablilty of the identified truss structures. Several different constraint types are compared, including limiting the number of joints and the angle between adjacent members. So-called `lazy constraints', generated at run-time, are used to efficiently allow consideration of these constraints at the large number of potential crossover joints. Simple example problems are used to allow more detailed analytical examination of the characteristics of structures subjected to these constraints. It is observed that the set of optimal structures may be discontinuous, and that symmetrical problems under these constraints may not have symmetrical optimal solutions. The second approach to reducing complexity is based on allowing better understanding of the identified form, by increasing the level of abstraction of the results. A method is proposed by which region based elements are incorporated into the ground structure method. This is found to be capable of producing numerical results that very closely approach the volumes of known theoretical solutions, whilst simultaneously allowing for easier interpretation and communication. This can then be used to suggest discretised layouts of the required degree of complexity. A number of case studies based on real-world projects are used alongside more academic numerical examples to demonstrate the applicability and relevance of the proposed methods