PreprintCC BY 4.0HAL
Energy scaling for von Kármán elastic plates with positional constraints
Abstract
The von Kármán energy functional
on the bending stiffness h of the plate, its vertical displacement v and the horizontal one w, is non-convex. We make use of a relatively recent convex integration result from Lewicka and Pakzad and geometrical approximations (similar to the ones using origami maps) to find an upper bound for the scaling of the elastic energy as h → 0. Through the interplay of the stretching and bending components of the energy we can attain a scaling of order h 5 3
for the upper-bound of a positional constraint problem. Furthermore, in doing so we will provide some new C 0 approximation results for vK short maps through piecewise affine vK solutions.
Related
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BibTeX
@misc{vizzari2026energy,
title = {{Energy scaling for von Kármán elastic plates with positional constraints}},
author = {Giacomo Vizzari},
howpublished = {HAL},
year = {2026},
month = oct,
url = {https://hal.science/hal-05841276v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Energy scaling for von Kármán elastic plates with positional constraints
AU - Giacomo Vizzari
PY - 2026
DA - 2026/10/28
PB - HAL
UR - https://hal.science/hal-05841276v1
AB - The von Kármán energy functional on the bending stiffness h of the plate, its vertical displacement v and the horizontal one w, is non-convex. We make use of a relatively recent convex integration result from Lewicka and Pakzad and geometrical approximations (similar to the ones using origami maps) to find an upper bound for the scaling of the elastic energy as h → 0. Through the interplay of the stretching and bending components of the energy we can attain a scaling of order h 5 3 for the upper-bound of a positional constraint problem. Furthermore, in doing so we will provide some new C 0 approximation results for vK short maps through piecewise affine vK solutions.
ER -