Optimal routing of pipes in a virtual environment using nonlinear programming

Abstract

Nowadays the routing of pipes inside or outside of structural components is usually done with CAD tools like CATIA. Up to now it is the task of design-engineers to manually find a connection between two points in ℝ3 which on one hand respects all design directives and on the other hand minimises the weight of the pipe. As in general the number of feasible routings is very high, if not infinite, it is almost impossible to find an optimal solution without a powerful algorithm and an immense amount of development time. This paper presents a mathematical framework which allows the designer to automatically generate the optimal routing. To do so, the aforementioned problem is treated as an optimisation problem. With the mass of the pipe as the cost function to be minimised and the design directives handled as equality and inequality constraints, this leads to a nonlinear problem (NLP) which is solved by WORHP – a large-scale sparse NLP solver. A series of practically relevant scenarios like routings close to structural components, routings with standard bending angles as well as network routings for metallic and non-metallic pipes are investigated. First tests with real assemblies reveal that a significant reduction of the total mass is achieved by optimising the existing routing.