In this paper a unique design methodology known as 1stPRINCE (FIRST PRINciple Computational Evalualor) is developed to perform innovative design of mechanical structures from first principle knowledge. The method is based on the assumption that the creation of innovative designs of physical significance, concerning geometric and material properties, requires reasoning from first principles. The innovative designs discovered by 1stPRINCE differ from routine designs in that new primitives are created. Monotonicity analysis and computer algebra are utilized to direct design variables in a globally optimal direction relative to the goals specified. In contrast to strict constraint propagation approaches, formal qualitative optimization techniques efficiently search the solution space in an optimizing direction, eliminate infeasible and suboptimal designs, and reason with both equality and inequality constraints. Modification of the design configuration space and the creation of new primitives, in order to meet the constraints or improve the design, are achieved by manipulating mathematical quantities such as the integral. The result is a design system which requires a knowledge base only of fundamental equations of deformation with physical constraints on variables, constitutive relations, and fundamental engineering assumptions; no pre-compiled knowledge of mechanical behavior is needed. Application of this theory to the design of a beam under torsion leads to designs of a hollow tube and a composite rod exhibiting globally optimal behavior. Further, these optimally-behaved designs are described symbolically as a function of the material properties and system parameters. This method is implemented in a LISP environment as a module in a larger intelligent CAD system that integrates qualitative, functional and numerical computation for engineering applications.