Innovative design of mechanical structures from first principles

Design is a complex phenomenon which often requires solutions beyond the routine. Generation of innovative designs in the mechanical/structural domain requires deep level reasoning capabilities to determine how to modify an existing design. This dissertation proposes that computational methodologies can innovate optimally directed designs by reasoning from first principle knowledge. The dissertation introduces a non-routine design methodology called 1$\sp{\rm st}$PRINCE (FIRST PRINciple Computational Evaluator) based on the assumption that the creation of innovative designs of physical significance requires first principle knowledge to reason about geometric and material properties. The innovative designs discovered by 1$\sp{\rm st}$PRINCE differ from routine designs in that new prototypes are created. Monotonicity analysis and computer algebra algorithms drive design variables in an optimal direction relative to the goals specified. Manipulating mathematical quantities, in order to satisfy the constraints or improve the design, expands the design space and innovates new prototypes. The technique of Dimensional Variable Expansion is developed to perform the manipulation in structural domains. Inductive techniques observe trends in successive iterations to observe the optimally directed limit of the design modifications. The methodology emphasizes the importance of optimization among highly coupled constraints in real design problems. The dissertation develops a graph-theoretic representation to provide an environment which supports non-routine design of physical structures by considering geometric connectivity. The graph representation models regions as nodes while graph links demonstrate region connectivity. Design knowledge is organized in generic modules which are not region specific, but rather are general for a class of regions. This delineation enables computer implementation of the 1$\sp{\rm st}$PRINCE methodology. The resulting design method requires a knowledge base only of fundamental equations of deformation with physical constraints on variables, constitutive relations, and fundamental engineering assumptions; no precompiled knowledge of mechanical behavior is needed. Thus, although this discussion emphasizes the area of mechanical structures, the methodology is potentially domain-independent, requiring a problem formulation as an optimization problem whose variables can be manipulated to modify the relevant design space.