Shear-flexible geometrically exact beam element based on finite differences

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985556%3A_____%2F25%3A00647372" target="_blank" >RIV/67985556:_____/25:00647372 - isvavai.cz</a>

Alternative codes found

RIV/68407700:21110/25:00380585

Result on the web

<a href="https://www.sciencedirect.com/science/article/pii/S0045782524009253?via%3Dihub" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0045782524009253?via%3Dihub</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.cma.2024.117671" target="_blank" >10.1016/j.cma.2024.117671</a>

Result language

angličtina

Original language name

Shear-flexible geometrically exact beam element based on finite differences

Original language description

The proposed two-dimensional geometrically exact beam element extends our previous work by including the effects of shear distortion, and also of distributed forces and moments acting along the beam. The general flexibility-based formulation exploits the kinematic equations combined with the inverted sectional equations and the integrated form of equilibrium equations. The resulting set of three first-order differential equations is discretized by finite differences and the boundary value problem is converted into an initial value problem using the shooting method. Due to the special structure of the governing equations, the scheme remains explicit even though the first derivatives are approximated by central differences, leading to high accuracy. The main advantage of the adopted approach is that the error can be efficiently reduced by refining the computational grid used for finite differences at the element level while keeping the number of global degrees of freedom low. The efficiency is also increased by dealing directly with the global centerline coordinates and sectional inclination with respect to global axes as the primary unknowns at the element level, thereby avoiding transformations between local and global coordinates. Two formulations of the sectional equations, namely the widely used Reissner model and a less common version referred to as the Ziegler model, are presented and compared. In particular, stability of an axially loaded beam/column is investigated and the connections to the Haringx and Engesser stability theories are discussed. Both approaches are tested in a series of numerical examples, which illustrate (i) high accuracy with quadratic convergence when the spatial discretization is refined, (ii) easy modeling of variable stiffness along the element (such as rigid joint offsets), (iii) efficient and accurate characterization of the buckling and post-buckling behavior.

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

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OECD FORD branch

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Project

Result was created during the realization of more than one project. More information in the Projects tab.

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2025

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Computer Methods in Applied Mechanics and Engineering

ISSN

0045-7825

e-ISSN

1879-2138

Volume of the periodical

436

Issue of the periodical within the volume

1

Country of publishing house

NL - THE KINGDOM OF THE NETHERLANDS

Number of pages

50

Pages from-to

117671

UT code for WoS article

001690440300001

EID of the result in the Scopus database

2-s2.0-85214560203