<div class="csl-bib-body">
<div class="csl-entry">Mang, H. (2017). Evolution and verification of a kinematic hypothesis for splitting of the strain energy. <i>Computer Methods in Applied Mechanics and Engineering</i>, <i>324</i>, 74–109. https://doi.org/10.1016/j.cma.2017.05.028</div>
</div>
Splitting of the strain energy into its “non-membrane” and membrane percentage provides insight into the load-carrying mechanism of structures, subjected to proportional loading. It may be useful, for example, for sensitivity analysis of the initial postbuckling behavior of beams, arches, plates, and shells, and assemblies of such structures. The task of this work is to determine this percentage without computing insignificant numbers such as the values of the strain energy and its membrane part. It is hypothesized that this percentage is proportional to the acceleration of a fictitious particle, moving along a curve on the unit sphere. The curve is described by the vertex of the normalized “fundamental eigenvector” of the so-called “consistently linearized eigenvalue problem”. The proportionality factor is obtained from the initial condition for the “non-membrane” percentage of the strain energy, hypothesized as twice the initial velocity of the particle. The lower bound of this factor signals the constancy of this percentage with increasing load, whereas the upper bound indicates a monotonic increase or decrease up to its ab initio predictable value at a stability limit or to an unphysical asymptotic limiting value. The proof of the universal validity of the two hypotheses begins with their verification for the special cases of a membrane stress state and pure bending. The assertion that this is a sufficient condition for the universal validity of these hypotheses is subsequently verified for an example with a monotonically increasing “non-membrane” percentage of the strain energy. It is finally confirmed by an indirect proof of their validity for a non-monotonic course of this percentage. A by-product of this work are conditions for extreme values of the stiffness of structures, subjected to proportional loading.
en
dc.description.sponsorship
Austrian Science Fund (FWF)
-
dc.language
English
-
dc.language.iso
en
-
dc.publisher
Elsevier B.V
-
dc.relation.ispartof
Computer Methods in Applied Mechanics and Engineering
-
dc.rights.uri
http://creativecommons.org/licenses/by-nc-nd/4.0/
-
dc.subject
“Non-membrane” percentage of the strain energy
en
dc.subject
Membrane complement of this percentage
en
dc.subject
Initial value of this percentage
en
dc.subject
Acceleration vector
en
dc.subject
Consistently linearized eigenproblem
en
dc.subject
Extreme values of the structural stiffness
en
dc.title
Evolution and verification of a kinematic hypothesis for splitting of the strain energy
en
dc.type
Article
en
dc.type
Artikel
de
dc.rights.license
Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
en
dc.rights.license
Creative Commons Namensnennung - Nicht kommerziell - Keine Bearbeitungen 4.0 International
de
dc.description.startpage
74
-
dc.description.endpage
109
-
dc.relation.grantno
P24526-N26
-
dc.rights.holder
The Author(s) 2017
-
dc.type.category
Original Research Article
-
tuw.container.volume
324
-
tuw.journal.peerreviewed
true
-
tuw.peerreviewed
true
-
tuw.version
vor
-
dcterms.isPartOf.title
Computer Methods in Applied Mechanics and Engineering
-
tuw.publication.orgunit
E202 - Institut für Mechanik der Werkstoffe und Strukturen
-
tuw.publisher.doi
10.1016/j.cma.2017.05.028
-
dc.identifier.eissn
1879-2138
-
dc.identifier.libraryid
AC15534596
-
dc.identifier.urn
urn:nbn:at:at-ubtuw:3-7980
-
dc.rights.identifier
CC BY-NC-ND 4.0
en
dc.rights.identifier
CC BY-NC-ND 4.0
de
wb.sci
true
-
item.languageiso639-1
en
-
item.mimetype
application/pdf
-
item.openairecristype
http://purl.org/coar/resource_type/c_2df8fbb1
-
item.fulltext
with Fulltext
-
item.openairetype
research article
-
item.grantfulltext
open
-
item.openaccessfulltext
Open Access
-
item.cerifentitytype
Publications
-
crisitem.author.dept
E202 - Institut für Mechanik der Werkstoffe und Strukturen