PreprintCC BY 4.0arXiv
On the feasible set of a membrane shell under confinement. Smooth inactive admissible displacements are dense
Abstract
We establish a density property for the obstacle problem of a linearly elastic elliptic membrane shell required to remain confined in a prescribed half-space. For a bounded Lipschitz reference domain, and under the sole assumption that the reference configuration lies at a strictly positive distance from the confining plane, we prove that smooth admissible displacements for which the confinement constraint is inactive (satisfied with a strictly positive margin) are dense in the set of all admissible displacements. This removes the additional condition on the unit normal to the mid-surface required in previous work, and the approximation scheme is elementary and adaptable to other unilateral obstacle problems.
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BibTeX
@misc{piersanti2026feasible,
title = {{On the feasible set of a membrane shell under confinement. Smooth inactive admissible displacements are dense}},
author = {Paolo Piersanti},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.09570},
eprint = {2609.09570},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.09570},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On the feasible set of a membrane shell under confinement. Smooth inactive admissible displacements are dense
AU - Paolo Piersanti
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2609.09570
UR - https://arxiv.org/abs/2609.09570
AB - We establish a density property for the obstacle problem of a linearly elastic elliptic membrane shell required to remain confined in a prescribed half-space. For a bounded Lipschitz reference domain, and under the sole assumption that the reference configuration lies at a strictly positive distance from the confining plane, we prove that smooth admissible displacements for which the confinement constraint is inactive (satisfied with a strictly positive margin) are dense in the set of all admissible displacements. This removes the additional condition on the unit normal to the mid-surface required in previous work, and the approximation scheme is elementary and adaptable to other unilateral obstacle problems.
ER -