|
|||||
 |
|
|
|
|
|
|
On jets, almost
symmetric tensors, and traction hyper-stresses
Reuven Segev and Jędrzej Śniatycki
Vol. 6 (2018), No. 2, 101–124
|
Abstract |
|
This paper considers the formulation of higher-order continuum mechanics on differentiable manifolds devoid of any metric or parallelism structure. For generalized velocities modeled as sections of some vector bundle, a variational -th order hyper-stress is an object that acts on jets of generalized velocities to produce power densities. The traction hyper-stress is introduced as an object that induces hyper-traction fields on the boundaries of subbodies. Additional aspects of multilinear algebra relevant to the analysis of these objects are reviewed. |
Keywords
high-order continuum mechanics, differential geometry,
vector bundle, hyper-stress, traction, multilinear algebra
|
Mathematical Subject Classification 2010
Primary: 74A10
Secondary: 53Z05
|
Milestones
Received: 28 October 2017
Revised: 8 February 2018
Accepted: 21 March 2018
Published: 29 May 2018
Communicated by Francesco dell'Isola
|
Authors |
| Reuven Segev | |
| Department of Mechanical
Engineering Ben-Gurion University of the Negev Beer-Sheva Israel |
|
| Jędrzej Śniatycki | |
| Department of Mathematics and
Statistics University of Victoria Victoria, BC Canada |
Department of Mathematics and
Statistics University of Calgary Calgary, AL Canada |
