Efficient formulation of a two-noded geometrically exact curved beam element
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21110%2F23%3A00360424" target="_blank" >RIV/68407700:21110/23:00360424 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1002/nme.7133" target="_blank" >https://doi.org/10.1002/nme.7133</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1002/nme.7133" target="_blank" >10.1002/nme.7133</a>
Alternative languages
Result language
angličtina
Original language name
Efficient formulation of a two-noded geometrically exact curved beam element
Original language description
The article extends the formulation of a 2D geometrically exact beam element proposed by Jirásek et al. (2021) to curved elastic beams. This formulation is based on equilibrium equations in their integrated form, combined with the kinematic relations and sectional equations that link the internal forces to sectional deformation variables. The resulting first-order differential equations are approximated by the finite difference scheme and the boundary value problem is converted to an initial value problem using the shooting method. The article develops the theoretical framework based on the Navier–Bernoulli hypothesis, with a possible extension to shear-flexible beams. Numerical procedures for the evaluation of equivalent nodal forces and of the element tangent stiffness are presented in detail. Unlike standard finite element formulations, the present approach can increase accuracy by refining the integration scheme on the element level while the number of global degrees of freedom is kept constant. The efficiency and accuracy of the developed scheme are documented by seven examples that cover circular and parabolic arches, a spiral-shaped beam, and a spring-like beam with a zig-zag centerline. The proposed formulation does not exhibit any locking. No excessive stiffness is observed for coarse computational grids and the distribution of internal forces is not polluted by any oscillations. It is also shown that a cross effect in the relations between internal forces and deformation variables arises, that is, the bending moment affects axial stretching and the normal force affects the curvature. This coupling is theoretically explained in the Appendix.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
20102 - Construction engineering, Municipal and structural engineering
Result continuities
Project
<a href="/en/project/GX19-26143X" target="_blank" >GX19-26143X: Non-periodic pattern-forming metamaterials: Modular design and fabrication</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
International Journal for Numerical Methods in Engineering
ISSN
0029-5981
e-ISSN
1097-0207
Volume of the periodical
124
Issue of the periodical within the volume
3
Country of publishing house
US - UNITED STATES
Number of pages
50
Pages from-to
570-619
UT code for WoS article
000865848200001
EID of the result in the Scopus database
2-s2.0-85139548797