Computer-Aided Design (2000).
Many engineering design applications require geometric modeling and mechanical simulation of
thin flexible structures, such as those found in the automotive and aerospace industries. Traditionally,
geometric modeling, mechanical simulation, and engineering design are treated as separate modules re-quiring
different methods and representations. Due to the incompatibility of the involved representations
the transition from geometric modeling to mechanical simulation, as well as in the opposite direction,
requires substantial effort. However, for engineering design purposes efficient transition between geo-metric
modeling and mechanical simulation is essential. We propose the use of subdivision surfaces as a
common foundation for modeling, simulation, and design in a unified framework. Subdivision surfaces
provide a flexible and efficient tool for arbitrary topology free-form surface modeling, avoiding many of
the problems inherent in traditional spline patch based approaches. The underlying basis functions are
also ideally suited for a finite element treatment of the so-called thin shell equations, which describe the
mechanical behavior of the modeled structures. The resulting solvers are highly scalable, providing an
efficient computational foundation for design exploration and optimization. We demonstrate our claims
with several design examples, showing the versatility and high accuracy of the proposed method.