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A TOPOLOGICAL FORMALISM FOR QUANTITATIVE ANALYSIS OF DESIGN SPACES

Published online by Cambridge University Press:  27 July 2021

Joshua Ortiz ,
Joshua Summers ,
James Coykendall ,
Travis Roberts  and
Rahul Rai
Joshua Ortiz
Affiliation:
Clemson University
Joshua Summers*
Affiliation:
The University of Texas at Dallas
James Coykendall
Affiliation:
Clemson University
Travis Roberts
Affiliation:
Clemson University
Rahul Rai
Affiliation:
Clemson University
*
Summers, Joshua, Clemson University, Mechanical Engineering, United States of America, joshua.summers@utdallas.edu

Abstract

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The objective of this paper is to present a mathematically grounded description of the two topological spaces for the design problem and the design solution. These spaces are derived in a generalized form such that they can be applied by researchers studying engineering design and developing new methods or engineers seeking to understand the influence that changes in the problem space have on the solution space. In addition to the formal definitions of the spaces, including assumptions and limitations, three types of supported reasoning are presented to demonstrate the potential uses. These include similarity analysis to compare spaces, an approach to sensitivity analysis of the solution space to changes in the problem space, and finally a distance measure to determine how far a current proposal is to the feasible solution space. This paper is presented to establish a common vocabulary for researchers when discussing, studying, and supporting the dyadic nature of engineering design (problem-solution co-evolution).

Keywords

Design theoryRequirementsEmbodiment design
Type
Article
Information
Proceedings of the Design Society , Volume 1: ICED21 , August 2021 , pp. 293 - 302
Creative Commons
Creative Common License - CCCreative Common License - BYCreative Common License - NCCreative Common License - ND
This is an Open Access article, distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives licence (http://creativecommons.org/licenses/by-nc-nd/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is unaltered and is properly cited. The written permission of Cambridge University Press must be obtained for commercial re-use or in order to create a derivative work.
Copyright
The Author(s), 2021. Published by Cambridge University Press

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