An asymptotic numerical method for inverse elastic shape design
- 27 July 2014
- journal article
- research article
- Published by Association for Computing Machinery (ACM) in ACM Transactions on Graphics
- Vol. 33 (4), 1-11
- https://doi.org/10.1145/2601097.2601189
Abstract
Inverse shape design for elastic objects greatly eases the design efforts by letting users focus on desired target shapes without thinking about elastic deformations. Solving this problem using classic iterative methods (e.g., Newton-Raphson methods), however, often suffers from slow convergence toward a desired solution. In this paper, we propose an asymptotic numerical method that exploits the underlying mathematical structure of specific nonlinear material models, and thus runs orders of magnitude faster than traditional Newton-type methods. We apply this method to compute rest shapes for elastic fabrication, where the rest shape of an elastic object is computed such that after physical fabrication the real object deforms into a desired shape. We illustrate the performance and robustness of our method through a series of elastic fabrication experiments.Keywords
Funding Information
- Lenovo's Program for Young Scientists
- Columbia Junior Faculty Startup Fund
- National Program for Special Support of Eminent Professionals of China
- Intel Corporation
- National Natural Science Foundation of China (61272305, 61303136, 61322204)
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