Velocity based elements for the quasi-static analysis of beams and frames

Kusuma Chandrashekhara, Sudhanva (author), Zupan, Dejan (author)

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.

• Language: English
• Keywords: beam elements, path following, arc-length method
• Work type: Proceedings
• Typology: 1.08 - Published Scientific Conference Contribution
• Organization: FGG - Faculty of Civil and Geodetic Engineering
• Publication status: Published
• Publication version: Version of Record
• Year: 2021
• Number of pages: Str. 23-30
• PID: 20.500.12556/RUL-132332
• UDC: 531:524.072(043)
• COBISS.SI-ID: 80897795
• Publication date in RUL: 21.10.2021

Record is a part of a monograph

• Title: Kuhljevi dnevi 2021 : zbornik del
• Editors: Janko Slavič, Martin Česnik
• Place of publishing: Ljubljana
• Publisher: Slovensko društvo za mehaniko
• Year: 2021
• ISBN: 978-961-93859-6-8
• COBISS.SI-ID: 74786051

Secondary language

• Language: Slovenian
• Title: Na hitrostih osnovana kvazistatična analiza nosilcev in okvirjev

Abstract

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

Projects

• Funder: EC - European Commission
• Project number: 860124
• Name: Joint Training on Numerical Modelling of Highly Flexible Structures for Industrial Applications
• Acronym: THREAD