Optimally-Directed Innovative Design

Abstract

Innovative designs, having some relation to previous design prototypes, are derived by manipulating the design space to generate new design features or prototypes. Our research effort [1,2] is aimed at developing a computer-based innovative design methodology known as 1^stPRINCE (FIRST PRINciple Computational Evaluator) which incorporates the qualitative, functional, and numerical levels of reasoning outlined by Agogino [3]. These methods utilize monotonicity analysis, which observes the sign of the algebraic first derivative of design variables, to make qualitative decisions that direct globally optimal behavior and detect flaws in the problem formalization. Mathematical functional information is used by computer algebra routines as deemed important from the monotonicity analysis. Monotonicity analysis and functional backsubstitution are implemented in the SYMON-SYMFUNE programs [4,5]. If constraints cannot be met or a designer wishes to investigate alternative designs, 1^stPRINCE goes one step further in modifying the design space by breaking integrals into smaller ranges to create novel design prototypes. Algebraic solutions to the design problem are reduced by computer algebra routines which can be solved numerically to obtain specific solutions and quantitative comparisons between solutions. 1^stPRINCE has been applied to a beam under torsion load and a beam under flexure load. In each case the system was told to minimize the weight of the beam subject to various physical constraints (maximum stress, deflection, weight, etc.) By starting with a solid round beam as the only structural prototype for the torsion load, 1^stPRINCE derives a hollow and composite rod. For the flexural beam, a series of stepped beams are created, approaching a tapered beam. Some designs proposed by 1^stPRINCE may be unusual, but all geometric modifications that lead to new design prototypes satisfy all assumed constraints and are optimally-directed within those constraints. Because 1^stPRINCE treats material properties as design variables, combinations of various materials lead to optimally-directed composite beam configurations.