Generalised Beam Theory Formulation to Analyse the Post-Buckling Behaviour of FRP Composite Thin-Walled Members

2009 ◽  
Author(s):  
N.F. Silva ◽  
N. Silvestre ◽  
D. Camotim
Keyword(s):  
Beam Theory ◽  
Frp Composite ◽  
Theory Formulation ◽  
Post Buckling ◽  
Thin Walled ◽  
Generalised Beam Theory

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 .

scholarly journals Geometrically and Physically Non-Linear GBT-Based Analysis of Thin-Walled Steel Members

2020 ◽  
Author(s):  
Abambres M ◽  
Camotim D ◽  
Silvestre N
Keyword(s):  
Beam Theory ◽  
Arbitrary Cross Section ◽  
Deformation Pattern ◽  
Equilibrium Equations ◽  
Steel Members ◽  
Non Linear ◽  
Geometrical Imperfections ◽  
Post Buckling ◽  
Thin Walled ◽  
Generalised Beam Theory

<p>This paper presents and illustrates the application of an elastic-plastic Generalised Beam Theory (GBT) formulation, based on J<sub>2</sub>-flow plasticity theory, that makes it possible to perform physically and geometrically non-linear (post-buckling) analyses of prismatic thin-walled members (i) with arbitrary cross-section shapes, (ii) exhibiting any type of deformation pattern (global, local, distortional, warping, shear), (iii) made from non-linear materials with isotropic strain-hardening and (iv) containing initial imperfections, namely residual stresses and/or geometric imperfections, having generic distributions. After providing a brief overview of the main GBT assumptions, kinematical relations and equilibrium equations, the development of a novel non-linear beam finite element (FE) is addressed in some detail. Moreover, its application is illustrated through the presentation and discussion of numerical results concerning the post-buckling behaviour of a fixed-ended I-section steel column exhibiting local initial geometrical imperfections, namely (i) non-linear equilibrium paths, (ii) displacement profiles, (iii) stress diagrams/distributions and (iv) deformed configurations. For validation purposes, the GBT results are also compared with values yielded by Abaqus rigorous shell FE analyses.</p>

scholarly journals Geometrically and Physically Non-Linear GBT-Based Analysis of Thin-Walled Steel Members

2019 ◽  
Author(s):  
Miguel Abambres ◽  
Dinar Camotim ◽  
Nuno Silvestre
Keyword(s):  
Beam Theory ◽  
Arbitrary Cross Section ◽  
Deformation Pattern ◽  
Equilibrium Equations ◽  
Steel Members ◽  
Non Linear ◽  
Geometrical Imperfections ◽  
Post Buckling ◽  
Thin Walled ◽  
Generalised Beam Theory

This paper presents and illustrates the application of an elastic-plastic Generalised Beam Theory (GBT) formulation, based on J2-flow plasticity theory, that makes it possible to perform physically and geometrically non-linear (post-buckling) analyses of prismatic thin-walled members (i) with arbitrary cross-section shapes, (ii) exhibiting any type of deformation pattern (global, local, distortional, warping, shear), (iii) made from non-linear materials with isotropic strain-hardening and (iv) containing initial imperfections, namely residual stresses and/or geometric imperfections, having generic distributions. After providing a brief overview of the main GBT assumptions, kinematical relations and equilibrium equations, the development of a novel non-linear beam finite element (FE) is addressed in some detail. Moreover, its application is illustrated through the presentation and discussion of numerical results concerning the post-buckling behaviour of a fixed-ended I-section steel column exhibiting local initial geometrical imperfections, namely (i) non-linear equilibrium paths, (ii) displacement profiles, (iii) stress diagrams/distributions and (iv) deformed configurations. For validation purposes, the GBT results are also compared with values yielded by ABAQUS rigorous shell FE analyses.

Post-buckling analysis of thin-walled steel frames using generalised beam theory (GBT)

2013 ◽  
Vol 62 ◽  
pp. 229-242 ◽  
Author(s):  
Cilmar Basaglia ◽  
Dinar Camotim ◽  
Nuno Silvestre
Keyword(s):  
Steel Frames ◽  
Beam Theory ◽  
Buckling Analysis ◽  
Post Buckling ◽  
Thin Walled ◽  
Generalised Beam Theory

scholarly journals Geometrically and Materially Non-Linear GBT Analysis of Tubular Thin-Walled Metal Members

2019 ◽  
Author(s):  
Miguel Abambres ◽  
Dinar Camotim ◽  
Nuno Silvestre
Keyword(s):  
Beam Theory ◽  
Finite Element Analyses ◽  
Collapse Mechanisms ◽  
Non Linear ◽  
Post Buckling ◽  
Linear Material ◽  
Thin Walled ◽  
Shell Finite Element ◽  
Deformation Modes ◽  
Generalised Beam Theory

After providing a brief overview of a recently developed and validated elastoplastic post-buckling Generalised Beam Theory (GBT) formulation, the paper presents and discusses illustrative numerical results concerning three tubular members exhibiting bi-linear and non-linear material behaviours. The GBT results consist of equilibrium paths, modal participation diagrams, stress contours, displacement profiles and collapse mechanisms, most of which are compared with values obtained from Abaqus shell finite element analyses. The GBT modal nature makes it possible to (i) acquire in-depth knowledge about the member behavioural mechanics at any given equilibrium state (elastic or elastic-plastic), as well as (ii) evidence the GBT computational efficiency (d.o.f. reduction of over 75%), partly due to the exclusion from the analyses of all deformation modes playing no role in a given member response.

scholarly journals Geometrically and Physically Non-Linear GBT-Based Analysis of Thin-Walled Steel Members

2020 ◽  
Author(s):  
Abambres M ◽  
Camotim D ◽  
Silvestre N
Keyword(s):  
Beam Theory ◽  
Arbitrary Cross Section ◽  
Deformation Pattern ◽  
Equilibrium Equations ◽  
Steel Members ◽  
Non Linear ◽  
Geometrical Imperfections ◽  
Post Buckling ◽  
Thin Walled ◽  
Generalised Beam Theory

<p>This paper presents and illustrates the application of an elastic-plastic Generalised Beam Theory (GBT) formulation, based on J<sub>2</sub>-flow plasticity theory, that makes it possible to perform physically and geometrically non-linear (post-buckling) analyses of prismatic thin-walled members (i) with arbitrary cross-section shapes, (ii) exhibiting any type of deformation pattern (global, local, distortional, warping, shear), (iii) made from non-linear materials with isotropic strain-hardening and (iv) containing initial imperfections, namely residual stresses and/or geometric imperfections, having generic distributions. After providing a brief overview of the main GBT assumptions, kinematical relations and equilibrium equations, the development of a novel non-linear beam finite element (FE) is addressed in some detail. Moreover, its application is illustrated through the presentation and discussion of numerical results concerning the post-buckling behaviour of a fixed-ended I-section steel column exhibiting local initial geometrical imperfections, namely (i) non-linear equilibrium paths, (ii) displacement profiles, (iii) stress diagrams/distributions and (iv) deformed configurations. For validation purposes, the GBT results are also compared with values yielded by Abaqus rigorous shell FE analyses.</p>

Generalised Beam Theory (GBT) for Shear Deformable Stiffened Sections

2014 ◽  
Vol 553 ◽  
pp. 600-605
Author(s):  
Gerard Taig ◽  
Gianluca Ranzi
Keyword(s):  
Cross Sections ◽  
Beam Theory ◽  
Element Model ◽  
Elastic Behaviour ◽  
Structural Behaviour ◽  
Thin Walled ◽  
Shell Finite Element ◽  
Linear Elastic Behaviour ◽  
Generalised Beam Theory ◽  
Shear Deformable

A Generalised Beam Theory (GBT) formulation is presented to analyse the structural behaviour of shear deformable thin-walled members with partially stiffened cross-sections located at arbitrary locations along their length. The deformation modes used in the formulation are taken as the dynamic eigenmodes of a planar frame representing the unstiffened cross-section. Constraint equations are derived and implemented in the GBT member analysis to model the influence of rigid stiffeners on the member response. The accuracy of the approach is validated against a shell finite element model developed in Abaqus. A numerical example describing the linear elastic behaviour of partially stiffened thin-walled member is provided to outline the usability and flexibility of the proposed method.

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