Of the many valid configurations that a curved fold may assume, it is of particular interest to identify natural—or lowest energy—configurations that physical models will preferentially assume. We present normalized coordinate equations—equations that relate fold surface properties to their edge of regression—to simplify curved-fold relationships. An energy method based on these normalized coordinate equations is developed to identify natural configurations of general curved folds. While it has been noted that natural configurations have nearly planar creases for curved folds, we show that nonplanar behavior near the crease ends substantially reduces the energy of a fold.
Normalized Coordinate Equations and an Energy Method for Predicting Natural Curved-Fold Configurations
Contributed by the Applied Mechanics Division of ASME for publication in the Journal of Applied Mechanics. Manuscript received January 17, 2019; final manuscript received March 21, 2019; published online April 12, 2019. Assoc. Editor: Yihui Zhang.
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Badger, J. C., Nelson, T. G., Lang, R. J., Halverson, D. M., and Howell, L. L. (April 12, 2019). "Normalized Coordinate Equations and an Energy Method for Predicting Natural Curved-Fold Configurations." ASME. J. Appl. Mech. July 2019; 86(7): 071006. https://doi.org/10.1115/1.4043285
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