| The complexity of mechanical design is reflected in the coupling of the constraint relationship between requirements and design parameters for designs which can be parameterized. To deal with these interactions we can reformulate the constraints that model a design configuration. This is accomplished by a transformation to alternative design parameters, such as a critical ratio, a nondimensional parameter, or a simple difference; e.g. the ratio of surface area to volume for heat transfer loss, the Reynold's number in fluid mechanics, or the velocity difference across a fluid coupling. We have developed a method where the alternative parameters are chosen for physical significance and for the ability to create a more direct correspondence to functional behavior as determined by measures of serial and block decomposability of the constraints. Rules have been developed for the creation of physically significant new parameters from the algebraic combination of the original parameters. The rules are constructed according to engineering physical principles that rely on knowledge about what a parameter physically represents rather than other qualities like dimensions. The measure of serial decomposability reflects the number of constraints for which there is at least one new variable and block decomposability reflects the number of independent blocks of constraints that form smaller independent subproblems.; The successful reformulations can be used to expedite quantitative procedures and qualitative reasoning such as the computation of numerical solutions, and the determination of the active constraints of an optimization. As alternative views of the design configuration, the reformulations may promote design synthesis and other cognitive benefits to design.; A computer based system, called EUDOXUS, has been developed to identify important design relationships. The system operates on a set of design constraints to produce sets of transformed constraints in terms of alternative design parameters. The method and its implementation have demonstrated successful results for many highly nonlinear and highly coupled parameterized designs from many mechanical engineering domains. The new parameters maintain physical meaning and the serial and block decomposability measures reflect general properties desirable to achieve many design benefits. |
