Integration Constraints in Parametric Design of Physical Objects

Abstract

Design by constraint is a powerful approach to improve CAD systems and designer productivity. This paper addresses the topic of incorporating integration constraints concerning object mass and inertia in a CAD system. Two classes of generic objects are discussed that contain affine and conformal images of a given solid, usually derived from the initial design solution. Domain-derivatives are partial derivatives needed to solve the existence problem of an object instance satisfying all constraints and, eventually, to find an optimal design solution. In the paper, it is shown that these derivatives are closely linked to the topology of the solid. They are symbolically expressable as integrals over domains having a lower geometrical dimension than the original solid.