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

Acta Mechanica Sinica 2018年第4期34卷 728-743页

作者： Seyed Farhad Hosseini Ali Hashemian Behnam Moetakef-Imani Saied Hadidimoud Sun-Air Research Institute Ferdowsi University of Mashhad Department of Mechanical Engineering Hakim Sabzevari University Department of Mechanical Engineering Ferdowsi University of Mashhad Centre for Manufacturing and Materials Engineering Coventry University

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.

关键词： curved beams Nonlinear Timoshenko beam theory Large deformation Isogeometric analysis NURBS curves

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