Velocity based elements for the quasi-static analysis of beams and frames
Kusuma Chandrashekhara, Sudhanva (Author), Zupan, Dejan (Author)

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In the present work, we propose the extension of the equilibrium equation based on the velocity based formulation with the introduction of an arc-length constraint. With the configuration variables defined in terms of time dependent quantities, the arc-length parameter in the original arc-length constraint equation can be replaced by increment of time step. Additionally, the constraint equation based on arc-length control is employed in its originally defined differential form. This eases the extension of the system of equations and the procedure can be applied in conjunction with the Newton-Raphson method. The proposed method also provides a flexibility to implement the stepsize control and in the present approach, we employ the local error control to determine the new step-size. The proposed method serves as a starting point in the post-critical analysis of the structures and aims at demonstrating the nonlinear responses in post-buckling regimes.

Keywords:beam elements, path following, arc-length method
Work type:Proceedings (z)
Tipology:1.08 - Published Scientific Conference Contribution
Organization:FGG - Faculty of Civil and Geodetic Engineering
Number of pages:Str. 23-30
COBISS.SI-ID:80897795 This link opens in a new window
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Record is a part of a monograph

Title:Kuhljevi dnevi 2021
Subtitle:zbornik del
Publisher:Slovensko društvo za mehaniko
COBISS.SI-ID:74786051 This link opens in a new window
Place of publishing:Ljubljana
Editors:Janko Slavič, Martin Česnik

Document is financed by a project

Funder:EC - European Commission
Project no.:860124
Name:Joint Training on Numerical Modelling of Highly Flexible Structures for Industrial Applications

Secondary language

Title:Na hitrostih osnovana kvazistatična analiza nosilcev in okvirjev
Predstavljamo razširitev sistema enačb na hitrostih in kotnih hitrostih osnovane numerične formulacije prostorskih nosilcev z vezno enačbo sledenja obtežno deformacijski krivulji. Tako lahko parameter poti iz statične analize nadomestimo s časovnim korakom, ki v diskretiziranih enačbah dinamike nosilcev že nastopa. Poleg tega lahko vezno enačbo obtežno deformacijske poti implementiramo v osnovni, šibki obliki. Tak pristop olajša razširitev sistema enačb in olajša izvedbo Newton-Raphsonove sheme. Predlagana metoda omogoča tudi kontrolo časovnega koraka z oceno lokalne napake rešitev. Tako dopolnjena formulacija je odlično orodje za analizo postkritičnega obnašanja konstrukcij.

Keywords:linijski elementi, obtežno-deformacijska pot, ločna dolžina

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