Vol. 12, No. 1, 2019

Download this article
Download this article For screen
For printing
Recent Issues

Volume 12, 1 issue

Volume 11, 8 issues

Volume 10, 8 issues

Volume 9, 8 issues

Volume 8, 8 issues

Volume 7, 8 issues

Volume 6, 8 issues

Volume 5, 5 issues

Volume 4, 5 issues

Volume 3, 4 issues

Volume 2, 3 issues

Volume 1, 3 issues

The Journal
About the Journal
Subscriptions
Editorial Board
Editors’ Interests
Scientific Advantages
Submission Guidelines
Submission Form
Editorial Login
Contacts
Author Index
To Appear
 
ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
On a boundary value problem for conically deformed thin elastic sheets

Heiner Olbermann

Vol. 12 (2019), No. 1, 245–258
Abstract

We consider a thin elastic sheet in the shape of a disk that is clamped at its boundary such that the displacement and the deformation gradient coincide with a conical deformation with no stretching there. These are the boundary conditions of a so-called “d-cone”. We define the free elastic energy as a variation of the von Kármán energy, which penalizes bending energy in Lp with p (2, 8 3) (instead of, as usual, p = 2). We prove ansatz-free upper and lower bounds for the elastic energy that scale like hp(p1), where h is the thickness of the sheet.

Keywords
thin elastic sheets, d-cone
Mathematical Subject Classification 2010
Primary: 49Q10, 74K20
Milestones
Received: 4 January 2018
Revised: 5 March 2018
Accepted: 10 April 2018
Published: 2 August 2018
Authors
Heiner Olbermann
Universität Leipzig
Leipzig
Germany