Example-Based Subspace Stress Analysis for Interactive Shape Design

Xiang Chen, Changxi Zheng, Kun Zhou

Abstract: Stress analysis is a crucial tool for designing structurally sound shapes. However, the expensive computational cost has hampered its use in interactive shape editing tasks. We augment the existing example-based shape editing tools, and propose a fast subspace stress analysis method to enable stress-aware shape editing. In particular, we construct a reduced stress basis from a small set of shape exemplars and possible external forces. This stress basis is automatically adapted to the current user edited shape on the fly, and thereby offers reliable stress estimation. We then introduce a new finite element discretization scheme to use the reduced basis for fast stress analysis. Our method runs up to two orders of magnitude faster than the full-space finite element analysis, with average L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> estimation errors less than 2 percent and maximum L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> errors less than 6 percent. Furthermore, we build an interactive stress-aware shape editing tool to demonstrate its performance in practice.