Download this article
Download this article For screen
For printing
Recent Issues
Volume 13, Issue 1
Volume 12, Issue 4
Volume 12, Issue 3
Volume 12, Issue 2
Volume 12, Issue 1
Volume 11, Issue 4
Volume 11, Issue 3
Volume 11, Issue 2
Volume 11, Issue 1
Volume 10, Issue 4
Volume 10, Issue 3
Volume 10, Issue 2
Volume 10, Issue 1
Volume 9, Issue 4
Volume 9, Issue 3
Volume 9, Issue 2
Volume 9, Issue 1
Volume 8, Issue 4
Volume 8, Issue 3
Volume 8, Issue 2
Volume 8, Issue 1
Volume 7, Issue 4
Volume 7, Issue 3
Volume 7, Issue 2
Volume 7, Issue 1
Volume 6, Issue 4
Volume 6, Issue 3
Volume 6, Issue 2
Volume 6, Issue 1
Volume 5, Issue 3-4
Volume 5, Issue 2
Volume 5, Issue 1
Volume 4, Issue 3-4
Volume 4, Issue 2
Volume 4, Issue 1
Volume 3, Issue 4
Volume 3, Issue 3
Volume 3, Issue 2
Volume 3, Issue 1
Volume 2, Issue 2
Volume 2, Issue 1
Volume 1, Issue 2
Volume 1, Issue 1
The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
 
Subscriptions
 
ISSN 2325-3444 (online)
ISSN 2326-7186 (print)
 
Author index
To appear
 
Other MSP journals
This article is available for purchase or by subscription. See below.
A three-dimensional Airy stress function

Salvatore Federico, Mawafag F. Alhasadi, Shoji Imatani and Marcelo Epstein
Vol. 11 (2023), No. 3, 429–449
DOI: 10.2140/memocs.2023.11.429
Abstract

The most general stress function in three dimensions is given by the symmetric Beltrami tensor, which consists of six scalar functions. In this brief communication, we explore the possibility of expressing a three-dimensional state of stress by means of a single scalar function, in the spirit of the Airy stress function in two dimensions. The price to pay for such a severe restriction is a loss of generality, in the sense that not every divergence-free stress field can be derived from the single stress function. Clearly, any such single scalar function gives rise to a particular case of the Beltrami tensor. One of these particular cases exhibits an interesting analogy with the tensor of inertia of a rigid body.

PDF Access Denied

We have not been able to recognize your IP address 18.97.14.88 as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription only.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recom­mendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Keywords
Airy stress function, Beltrami stress function, Maxwell stress function, Morera stress function, tensor of inertia, three-dimensional
Mathematical Subject Classification
Primary: 74B05, 74G05
Milestones
Received: 4 March 2023
Revised: 16 June 2023
Accepted: 21 July 2023
Published: 15 November 2023

Communicated by Francesco dell'Isola
Authors
Salvatore Federico
Deptment of Mechanical and Manufacturing Engineering
University of Calgary
Calgary, AB
Canada		 Department of Energy Conversion Science
Kyoto University
Sakyō-ku, Kyoto
Japan
Mawafag F. Alhasadi
Deptment of Mechanical and Manufacturing Engineering
University of Calgary
Calgary, AB
Canada
Shoji Imatani
Department of Energy Conversion Science
Kyoto University
Sakyō-ku, Kyoto
Japan
Marcelo Epstein
Deptment of Mechanical and Manufacturing Engineering
University of Calgary
Calgary, AB
Canada
© 2023 The Author(s), under exclusive license to MSP (Mathematical Sciences Publishers).