Efficient finite element formulation for geometrically exact beams

Olivier A. Bauchau*, Shilei Han

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

This paper proposes a new approach to the modeling of geometrically exact beams based on motion interpolation schemes. Motion interpolation schemes yield simple expressions for the sectional strains and linearized strain-motion relationships at the mesh nodes. The classical formulation of the finite element method starts from the weak form of the continuous governing equations obtained from a variational principle. Approximations, typically of a polynomial nature, are introduced to express the continuous displacement field in term of its nodal values. Introducing these approximations into the weak form of the governing equations then yields nonlinear discrete that can be solved with the help of a linearization process. In the proposed approach, the order of the first two steps of the procedure is reversed: approximations are introduced in the variational principle directly and the discrete equations of the problem then follow. This paper has shown that for geometrically exact beams, the discrete equations obtained from the two procedure differ significantly: far simpler discrete equations are obtained from the proposed approach.

Original languageEnglish
Title of host publication15th International Conference on Multibody Systems, Nonlinear Dynamics, and Control
PublisherAmerican Society of Mechanical Engineers (ASME)
ISBN (Electronic)9780791859261
DOIs
Publication statusPublished - 2019
Externally publishedYes
EventASME 2019 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC-CIE 2019 - Anaheim, United States
Duration: 18 Aug 201921 Aug 2019

Publication series

NameProceedings of the ASME Design Engineering Technical Conference
Volume6

Conference

ConferenceASME 2019 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC-CIE 2019
Country/TerritoryUnited States
CityAnaheim
Period18/08/1921/08/19

Fingerprint

Dive into the research topics of 'Efficient finite element formulation for geometrically exact beams'. Together they form a unique fingerprint.

Cite this