The engineering design methodology of Pahl and Beitz is good in the detailed stages, but needs enhancement in the early stages of conceptualizing and embodiment-in-principle. The concept of ‘functions’ has been enhanced by Hubka and colleagues. A ‘functional basis’ (Hirtz et al) has improved the definitions of ‘flows’ and ‘functions’, their work does not go far enough to provide a basis for conceptualizing. ‘Affordances’ (Maier and Fadel) are covered by full use of systematic conceptualizing of design engineering solutions. The Pahl-Beitz model and method of ‘decomposition of functions’, ‘physics’, and components is contrasted with the Hubka models of a transformation system, TrfS, its constituents, structures, properties life cycle, etc., and their use as method for design engineering by searching for alternative embodiments at each of these levels of abstraction. These steps are illustrated in (to date) 21 case examples published between 1976 and 2012, several of them in the CEEA conferences and their predecessors.
A convex-nonconvex variational method for the additive decomposition of functions on surfaces
