International Journal of Computational Engineering ScienceVol. 03, No. 03, pp. 305-338 (2002) No AccessTHREE-DIMENSIONAL POSTBUCKLING ANALYSIS OF CURVED BEAMSP. FRANK PAI and SEUNG-YOON LEEP. FRANK PAIDepartment of Mechanical and Aerospace Engineering, University of Missouri-Columbia, Columbia, MO 65211, USA Search for more papers by this author and SEUNG-YOON LEEDepartment of Mechanical and Aerospace Engineering, University of Missouri-Columbia, Columbia, MO 65211, USA Search for more papers by this author https://doi.org/10.1142/S1465876302000666Cited by:4 Previous AboutSectionsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack CitationsRecommend to Library ShareShare onFacebookTwitterLinked InRedditEmail AbstractPresented here is a method of solving highly flexible curved beams undergoing huge static or quasi-static deformations. A geometrically exact beam theory based on the use of Jaumann stresses and strains and exact coordinate transformations is presented in terms of 17 first-order ordinary differential equations, and a multiple shooting method is used to solve the corresponding nonlinear two-point boundary value problems. The geometrically exact beam theory accounts for large rotations, large displacements, initial curvatures, extensionality, and transverse shear strains. Four examples are used to demonstrate this method, including a rotating clamped-free beam under the influence of gravity and centrifugal forces, an L-frame subjected to an in-plane tip load, a circular arch subjected to a concentrated load, and a clamped-hinged helical spring subjected to an axial displacement. Results show that the combination of the multiple shooting method and the geometrically exact beam theory works very well. Moreover, the obtained numerically exact solutions can be used to verify the accuracy of nonlinear finite element codes for nonlinear analysis of complex structures.Keywords:Geometrically Exact Beam TheoryNumerically Exact Solutions FiguresReferencesRelatedDetailsCited By 4Three-dimensional equilibria of nonlinear pre-curved beams using an intrinsic formulation and shootingKyle N. Karlson and Michael J. Leamy1 Oct 2013 | International Journal of Solids and Structures, Vol. 50, No. 22-23Simple Mechanical Model of Curved Beams by a 3D ApproachStefano Lenci and Francesco Clementi1 Jul 2009 | Journal of Engineering Mechanics, Vol. 135, No. 7Total-Lagrangian Formulation and Finite-Element Analysis of Highly Flexible Plates and ShellsP. Frank Pai21 September 2005 | Mathematics and Mechanics of Solids, Vol. 12, No. 2Modeling, Analysis and Testing of some Deployable/Inflatable StructuresPerngjin Pai and Leyland Young26 June 2012 Recommended Vol. 03, No. 03 Metrics History KeywordsGeometrically Exact Beam TheoryNumerically Exact SolutionsPDF download