Generalised Beam Theory (GBT) for stiffened sections

This paper presents an extension to the Generalised Beam Theory (GBT) approach to describe the response of prismatic thin-walled members stiffened by means of generic plate arrangements at different cross-sections along their length. The conventional deformation modes to be included in the GBT formulation are obtained as the dynamic modes of a planar frame, which represents the cross-section. Two numerical procedures are implemented to account for the presence of the stiffeners. One approach identifies different sets of deformation modes for the unstiffened and stiffened sections, which are then combined for the member analysis. The second procedure relies on the use of constraint equations at the stiffened locations to be included in the member analysis. For the cross-sectional analysis, a new mixed finite element is presented which incorporates the inextensibility condition usually adopted in the framework of the classical GBT, therefore simplifying the steps required for the evaluation of the conventional deformation modes. The proposed technique is applicable to open, closed and partially-closed stiffened sections. Two numerical examples are provided to highlight the ease of use of the method of analysis considering open and partially-closed sections, and their results are validated against those obtained with the commercial finite element software Abaqus.

[1]  J. M. Davies,et al.  First-order generalised beam theory , 1994 .

[2]  Dinar Camotim,et al.  Global buckling analysis of plane and space thin-walled frames in the context of GBT , 2008 .

[3]  Frederic Marimon,et al.  Calculation of pure distortional elastic buckling loads of members subjected to compression via the finite element method , 2009 .

[4]  R. Schardt.  Verallgemeinerte Technische Biegetheorie , 1989 .

[5]  Angelo Luongo,et al.  Mode localization by structural imperfections in one-dimensional continuous systems , 1992 .

[6]  Mahen Mahendran,et al.  Elastic buckling analysis of ideal thin-walled structures under combined loading using a finite strip method , 1986 .

[7]  Mark A. Bradford,et al.  A simple method for the inclusion of external and internal supports in the spline finite strip method (SFSM) of buckling analysis , 2008 .

[8]  Jeppe Jönsson,et al.  Distortional eigenmodes and homogeneous solutions for semi-discretized thin-walled beams , 2011 .

[9]  V. Vlasov.  Thin-walled elastic beams , 1961 .

[10]  K. Bathe.  Finite Element Procedures , 1995 .

[11]  Dinar Camotim,et al.  GBT formulation to analyse the buckling behaviour of thin-walled members with arbitrarily ‘branched’ open cross-sections , 2006 .

[12]  R. Cook,et al.  Concepts and Applications of Finite Element Analysis , 1974 .

[13]  Jeppe Jönsson,et al.  Distortional solutions for loaded semi-discretized thin-walled beams , 2012 .

[14]  Teoman T Peköz,et al.  The finite element method for thin-walled members—basic principles , 2003 .

[15]  M. Pignataro,et al.  Multiple interaction and localization phenomena in the postbuckling of compressed thin-walled members , 1988 .

[16]  Gianluca Ranzi,et al.  An analytical approach for the cross-sectional analysis of generalised beam theory , 2014 .

[17]  Nuno Silvestre,et al.  Generalised beam theory to analyse the buckling behaviour of circular cylindrical shells and tubes , 2007 .

[18]  Dinar Camotim,et al.  A new approach to the calculation of cross-section deformation modes in the framework of generalized beam theory , 2010 .

[19]  Ben Young.  Bifurcation analysis of thin-walled plain channel compression members , 2004 .

[20]  Giuseppe Piccardo,et al.  A direct approach for the evaluation of the conventional modes within the GBT formulation , 2014 .

[21]  Dinar Camotim,et al.  GBT buckling analysis of thin-walled steel frames: A state-of-the-art report , 2010 .

[22]  Angelo Luongo.  On the amplitude modulation and localization phenomena in interactive buckling problems , 1991 .

[23]  Ben Young,et al.  Cold-formed steel lipped channel columns at elevated temperatures , 2006 .

[24]  Benjamin W. Schafer,et al.  A full modal decomposition of thin-walled, single-branched open cross-section members via the constrained finite strip method , 2008 .

[25]  R. Schardt.  Generalized beam theory—an adequate method for coupled stability problems , 1994 .

[26]  Gianluca Ranzi,et al.  A new approach for thin-walled member analysis in the framework of GBT , 2011 .

[27]  Dinar Camotim,et al.  Local and global vibration of thin-walled members subjected to compression and non-uniform bending , 2008 .

[28]  Dinar Camotim,et al.  GENERALIZED BEAM THEORY REVISITED: FROM THE KINEMATICAL ASSUMPTIONS TO THE DEFORMATION MODE DETERMINATION , 2011 .

[29]  Kim J.R. Rasmussen,et al.  Geometric nonlinear isoparametric spline finite strip analysis of perforated thin-walled structures , 2009 .

[30]  Giuseppe Piccardo,et al.  A complete dynamic approach to the Generalized Beam Theory cross-section analysis including extension and shear modes , 2014 .

[31]  Gregory J. Hancock,et al.  Buckling of thin flat-walled structures by a spline finite strip method , 1986 .

[32]  Dinar Camotim,et al.  Second-order generalised beam theory for arbitrary orthotropic materials , 2002 .

[33]  Wei-Xin Ren,et al.  Finite-Element Simulation and Design of Cold-Formed Steel Channels Subjected to Web Crippling , 2006 .

[34]  Benjamin W. Schafer,et al.  Buckling mode decomposition of single-branched open cross-section members via finite strip method: Application and examples , 2006 .

[35]  Angelo Luongo,et al.  Mode Localization in Dynamics and Buckling of Linear Imperfect Continuous Structures , 2001 .

[36]  Mihai Nedelcu.  GBT-based buckling mode decomposition from finite element analysis of thin-walled members , 2012 .