Post-Buckling Analysis of Thin-Walled Channel Columns in the Framework of the Generalized Beam Theory

2009 ◽  
Author(s):  
P. Simão ◽  
L. Simões da Silva
Keyword(s):  
Beam Theory ◽  
Buckling Analysis ◽  
Post Buckling ◽  
Walled Channel ◽  
Thin Walled ◽  
Generalized Beam Theory

Distortional Buckling of Cold-Formed Thin-Walled Channel Beams in Combined Compression and Minor Axis Bending

2010 ◽  
Vol 163-167 ◽  
pp. 507-510 ◽  
Author(s):  
Hong Guang Luo ◽  
Yao Jie Guo ◽  
Yun Xu
Keyword(s):  
Excellent Agreement ◽  
Critical Stress ◽  
Beam Theory ◽  
Minor Axis ◽  
Elastic Analysis ◽  
Distortional Buckling ◽  
Walled Channel ◽  
Thin Walled ◽  
Research And Design ◽  
Generalized Beam Theory

On the basis of the Generalized Beam Theory (GBT), this paper presents an elastic analysis of the distortional critical stress of cold-formed thin-walled lipped channels in combined compression and minor axis bending. The results obtained using the exact analysis presented herein have shown excellent agreement with previous available results. And the accuracy, validity and effectiveness of the presented solution were demonstrated. The calculating process was displayed by an example which can give reference to the research and design. This paper will contribute to the understanding of distortional mechanics in thin-walled members.

scholarly journals Ritz solution for buckling analysis of thin-walled composite channel beams based on a classical beam theory

2019 ◽  
Vol 13 (3) ◽  
pp. 34-44
Author(s):  
Nguyen Ngoc Duong ◽  
Nguyen Trung Kien ◽  
Nguyen Thien Nhan
Keyword(s):  
Ritz Method ◽  
Beam Theory ◽  
Buckling Analysis ◽  
Governing Equations ◽  
Buckling Loads ◽  
Composite Channel ◽  
Fiber Angle ◽  
Walled Channel ◽  
Thin Walled ◽  
Classical Beam Theory

Buckling analysis of thin-walled composite channel beams is presented in this paper. The displacement field is based on classical beam theory. Both plane stress and plane strain state are used to achieve constitutive equations. The governing equations are derived from Lagrange’s equations. Ritz method is applied to obtain the critical buckling loads of thin-walled beams. Numerical results are compared to those in available literature and investigate the effects of fiber angle, length-to-height’s ratio, boundary condition on the critical buckling loads of thin-walled channel beams. Keywords: Ritz method; thin-walled composite beams; buckling.

Post-buckling inelastic analysis of thin-walled metal members using the Generalised Beam Theory

2019 ◽  
Author(s):  
Miguel Abambres ◽  
Dinar Camotim ◽  
Miguel Abambres
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Beam Theory ◽  
Flow Theory ◽  
Promising Alternative ◽  
Inelastic Analysis ◽  
Post Buckling ◽  
Thin Walled ◽  
Shell Finite Element ◽  
Generalised Beam Theory

A 2nd order inelastic Generalised Beam Theory (GBT) formulation based on the J2 flow theory is proposed, being a promising alternative to the shell finite element method. Its application is illustrated for an I-section beam and a lipped-C column. GBT results were validated against ABAQUS, namely concerning equilibrium paths, deformed configurations, and displacement profiles. It was concluded that the GBT modal nature allows (i) precise results with only 22% of the number of dof required in ABAQUS, as well as (ii) the understanding (by means of modal participation diagrams) of the behavioral mechanics in any elastoplastic stage of member deformation .

First and Second Order Elastoplastic Analyses of Thin-Walled Metal Members using Generalized Beam Theory

2018 ◽  
Author(s):  
Miguel Abambres
Keyword(s):  
Finite Element ◽  
Stainless Steel ◽  
Cross Section ◽  
Beam Theory ◽  
Second Order ◽  
Flow Rule ◽  
Non Linear ◽  
Thin Walled ◽  
Shell Finite Element ◽  
Generalized Beam Theory

Original Generalized Beam Theory (GBT) formulations for elastoplastic first and second order (postbuckling) analyses of thin-walled members are proposed, based on the J2 theory with associated flow rule, and valid for (i) arbitrary residual stress and geometric imperfection distributions, (ii) non-linear isotropic materials (e.g., carbon/stainless steel), and (iii) arbitrary deformation patterns (e.g., global, local, distortional, shear). The cross-section analysis is based on the formulation by Silva (2013), but adopts five types of nodal degrees of freedom (d.o.f.) – one of them (warping rotation) is an innovation of present work and allows the use of cubic polynomials (instead of linear functions) to approximate the warping profiles in each sub-plate. The formulations are validated by presenting various illustrative examples involving beams and columns characterized by several cross-section types (open, closed, (un) branched), materials (bi-linear or non-linear – e.g., stainless steel) and boundary conditions. The GBT results (equilibrium paths, stress/displacement distributions and collapse mechanisms) are validated by comparison with those obtained from shell finite element analyses. It is observed that the results are globally very similar with only 9% and 21% (1st and 2nd order) of the d.o.f. numbers required by the shell finite element models. Moreover, the GBT unique modal nature is highlighted by means of modal participation diagrams and amplitude functions, as well as analyses based on different deformation mode sets, providing an in-depth insight on the member behavioural mechanics in both elastic and inelastic regimes.

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