Design Theory and Similarity Mechanics

Graph-based design languages map terms (i.e. the "vocabulary") and assembly knowledge (i.e. the "rules") into recombineable language building blocks and operations. In the information representation of a design language, the nodes of a graph serve as abstract placeholders (i.e. as models) for real objects or processes. Thus a graph representation ("design graph") is machine-processed in place of the product design. This machine processing expands and modifies the graph dynamically at runtime by so-called "model-to-model transformations" (M2M). The abstract product representation allows a simple modularization and scalability and allows the consistent integration of different disciplinary domain models (see figure below). The coupling of the framework to domain-specific software systems is essential in order to integrate the existing knowledge and subprocesses. The couplings are implemented as interfaces that generate domain-specific models in the target format (DSL) from the abstract graph representation ("model-to-text transformations" (M2T)). There are already interfaces for geometry (CAD), multi-body systems (MBS), finite elements (FEM), flow analysis (CFD), etc. (see figure below).

Using Buckingham's Pi theorem it is possible to transform a physical relationship of n dimensioned variables into a dimensionless description with only m = n - g dimensionless variables. Where g stands for the number of basic variables used. This knowledge can also be transferred to drafts - which can also be described by dimensioned variables - and reinterpreted as evaluation.

Every minimal description in the sense of the Pi theorem is an evaluation.

In addition to a multitude of boundary conditions, a product has a significant influence on the associated (digital) factory. The information already provided by a product created with graph-based design languages can be further processed automatically and used to generate suitable production sites. The aim is to be able to automatically design an optimal factory (in terms of costs, energy, time, etc.). This concerns the resources used as well as the manufacturing processes. In addition, the "Pi Group" is also concerned with the question of the optimal factory layout.

An essential step in the design of complex products is cabling and piping. The "Pi-Group" researches algorithms for automated cable and pipe routing, as well as the physical simulation of cables and pipes for installation simulations and other applications.