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Isogeometric analysis of free-form Timoshenko curved beams including the nonlinear effects of large deformations

Isogeometric analysis of free-form Timoshenko curved beams including the nonlinear effects of... Abstract In the present paper, the isogeometric analysis (IGA) of free-form planar curved beams is formulated based on the nonlinear Timoshenko beam theory to investigate the large deformation of beams with variable curvature. Based on the isoparametric concept, the shape functions of the field variables (displacement and rotation) in a finite element analysis are considered to be the same as the non-uniform rational basis spline (NURBS) basis functions defining the geometry. The validity of the presented formulation is tested in five case studies covering a wide range of engineering curved structures including from straight and constant curvature to variable curvature beams. The nonlinear deformation results obtained by the presented method are compared to well-established benchmark examples and also compared to the results of linear and nonlinear finite element analyses. As the nonlinear load-deflection behavior of Timoshenko beams is the main topic of this article, the results strongly show the applicability of the IGA method to the large deformation analysis of free-form curved beams. Finally, it is interesting to notice that, until very recently, the large deformations analysis of free-form Timoshenko curved beams has not been considered in IGA by researchers. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png "Acta Mechanica Sinica" Springer Journals

Isogeometric analysis of free-form Timoshenko curved beams including the nonlinear effects of large deformations

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References (43)

Publisher
Springer Journals
Copyright
2018 The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences and Springer-Verlag GmbH Germany, part of Springer Nature
ISSN
0567-7718
eISSN
1614-3116
DOI
10.1007/s10409-018-0753-4
Publisher site
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Abstract

Abstract In the present paper, the isogeometric analysis (IGA) of free-form planar curved beams is formulated based on the nonlinear Timoshenko beam theory to investigate the large deformation of beams with variable curvature. Based on the isoparametric concept, the shape functions of the field variables (displacement and rotation) in a finite element analysis are considered to be the same as the non-uniform rational basis spline (NURBS) basis functions defining the geometry. The validity of the presented formulation is tested in five case studies covering a wide range of engineering curved structures including from straight and constant curvature to variable curvature beams. The nonlinear deformation results obtained by the presented method are compared to well-established benchmark examples and also compared to the results of linear and nonlinear finite element analyses. As the nonlinear load-deflection behavior of Timoshenko beams is the main topic of this article, the results strongly show the applicability of the IGA method to the large deformation analysis of free-form curved beams. Finally, it is interesting to notice that, until very recently, the large deformations analysis of free-form Timoshenko curved beams has not been considered in IGA by researchers.

Journal

"Acta Mechanica Sinica" – Springer Journals

Published: Aug 1, 2018

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