Integrated modeling, finite-element analysis, and engineering design for thin-shell structures using subdivision

Many engineering design applications require geometric modeling and mechani cal simulation of thin flexible structures, such as those found in the auto motive and aerospace industries. Traditionally, geometric modeling, mechani cal simulation, and engineering design are treated as separate modules requ iring different methods and representations. Due to the incompatibility of the involved representations the transition from geometric modeling to mech anical simulation, as well as in the opposite direction, requires substanti al effort. However, for engineering design purposes efficient transition be tween geometric modeling and mechanical simulation is essential. We propose the use of subdivision surfaces as a common foundation for modeling, simul ation, and design in a unified framework. Subdivision surfaces provide a fl exible and efficient toot 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 fi nite-element treatment of the so-called thin-shell equations, which describ e the mechanical behavior of the modeled structures. The resulting solvers are highly scalable, providing an efficient computational foundation for de sign exploration and optimization. We demonstrate our claims with several d esign examples, showing the versatility and high accuracy of the proposed m ethod. (C) 2001 Elsevier Science Ltd. All rights reserved.