Graph structures are fundamental in many aspects of design. This paper discusses a way to improve access to design spaces of graph structures, by converting graph structures into numerical values and vice versa. Mathematical properties of such conversions are described, and those that are desirable are identified. A candidate conversion algorithm, Indexed Stacked Blocks, is proposed. Its use and benefits are illustrated through an example graph-structure design problem. The example demonstrates that such conversions allow design spaces of graph structures to be visualized, sampled, and evaluated. In principle, they also allow other powerful numerical techniques to be applied to the design of graph-structure-based systems.

A product's architecture can affect many aspects of product and process quality, from technical performance to the design effort required, production costs and satisfaction of later lifecycle requirements. This paper explores how computational tools can augment creative methods in product architecture design. Based on an empirical study aiming to understand the context of product architecture design, a new computational method is proposed to support this activity. In the method, product architectures-networks of components linked by connections- can be synthesised using constraints on the structure of the network to define the set of 'realisable' architectures for a product. An example illustrates how the method might be used on a real design problem, including the construction of an appropriate set of network structure constraints and the identification of promising architectures from the synthesis results. Preliminary evaluation of the method's usability, assessed through a laboratory experiment, and its utility, assessed through application to a real historical design problem, supported by initial validation by an engineer from the case study company, suggests that the method has value for engineering design practice.

The choice of product architecture can affect many factors, from the technical performance of a product to the design effort required, production costs, and satisfaction of lifecycle requirements. This paper explores how computational tools can augment creative methods in product architecture design. It describes a method for synthesising product architectures in the form of networks of components. The set of architectures for a product is specified using constraints on the structure of the network. The method has been implemented as a software tool, and an example illustrates how this might be used in practice. Discussion of the example highlights some of the issues which arise through using the method, particularly those of constructing an appropriate set of constraints, and of identifying promising architectures from the large set of synthesis results. Further work will address these issues and evaluate the approach in practice, to compare the cost-benefit ratio with more conventional methods for architecture design (e.g. brainstorming).

To support the development and analysis of engineering designs at the embodiment stage, designers work iteratively with representations of those designs as they consider the function and form of their constituent parts. Detailed descriptions of "what a machine does" usually include flows of forces and active principles within the technical system, and their localization within parts and across the interfaces between them. This means that a representation should assist a designer in considering form and function at the same time and at different levels of abstraction. This paper describes a design modelling approach that enables designers to break down a system architecture into its subsystems and parts, while assigning functions and flows to parts and the interfaces between them. In turn, this may reveal further requirements to fulfil functions in order to complete the design. The approach is implemented in a software tool which provides a uniform, computable language allowing the user to describe functions and flows as they are iteratively discovered, created and embodied. A database of parts allows the user to search for existing design solutions. The approach is illustrated through an example: modelling the complex mechanisms within a humanoid robot.