A bilateral relationship between stable profiles of pinned–pinned bistable shallow arches

A bilateral relationship between stable profiles of pinned–pinned bistable shallow arches Arch-profiles in the two force-free stable equilibrium states of shallow bistable arches are related to each other. We derive a two-way, i.e., bilateral, relationship between stress-free initial profile and stressed toggled profile so that pinned–pinned bistable arches of arbitrary profiles can be efficiently analyzed and designed. The derivation relies on representing the initial and toggled profiles with two sets of mode weights corresponding to the buckling mode shapes of a pinned–pinned column. Furthermore, we prove that the fundamental mode weights should be non-zero for an arch to be bistable. The following corollaries arise from the aforementioned relation: (1) symmetry in initial and toggled profiles remains unchanged; (2) all the mode weights other than the fundamental mode weight have the same sign in both stable states; (3) magnitudes of corrugations in stable force-free arch-profiles are approximately equal. Derivations and proofs of the principal relationship and its corollaries as well as examples of analysis and design of bistable arches of arbitrary arch-profiles are presented in the paper. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png International Journal of Solids and Structures Elsevier

A bilateral relationship between stable profiles of pinned–pinned bistable shallow arches

Loading next page...
 
/lp/elsevier/a-bilateral-relationship-between-stable-profiles-of-pinned-pinned-Fbhe34SzTU
Publisher
Elsevier
Copyright
Copyright © 2018 Elsevier Ltd
ISSN
0020-7683
eISSN
1879-2146
D.O.I.
10.1016/j.ijsolstr.2018.03.006
Publisher site
See Article on Publisher Site

Abstract

Arch-profiles in the two force-free stable equilibrium states of shallow bistable arches are related to each other. We derive a two-way, i.e., bilateral, relationship between stress-free initial profile and stressed toggled profile so that pinned–pinned bistable arches of arbitrary profiles can be efficiently analyzed and designed. The derivation relies on representing the initial and toggled profiles with two sets of mode weights corresponding to the buckling mode shapes of a pinned–pinned column. Furthermore, we prove that the fundamental mode weights should be non-zero for an arch to be bistable. The following corollaries arise from the aforementioned relation: (1) symmetry in initial and toggled profiles remains unchanged; (2) all the mode weights other than the fundamental mode weight have the same sign in both stable states; (3) magnitudes of corrugations in stable force-free arch-profiles are approximately equal. Derivations and proofs of the principal relationship and its corollaries as well as examples of analysis and design of bistable arches of arbitrary arch-profiles are presented in the paper.

Journal

International Journal of Solids and StructuresElsevier

Published: Jun 15, 2018

References

You’re reading a free preview. Subscribe to read the entire article.


DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Search

Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly

Organize

Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.

Access

Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

DeepDyve

Freelancer

DeepDyve

Pro

Price

FREE

$49/month
$360/year

Save searches from
Google Scholar,
PubMed

Create lists to
organize your research

Export lists, citations

Read DeepDyve articles

Abstract access only

Unlimited access to over
18 million full-text articles

Print

20 pages / month

PDF Discount

20% off