Non-Linear Generalised Beam Theory Formulation for Open-Section Thin-Walled Members with Arbitrary Support Conditions

2009 ◽  
Author(s):  
C. Basaglia ◽  
D. Camotim ◽  
N. Silvestre
Keyword(s):  
Beam Theory ◽  
Open Section ◽  
Theory Formulation ◽  
Non Linear ◽  
Thin Walled ◽  
Support Conditions ◽  
Generalised Beam Theory

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.

Non-linear GBT formulation for open-section thin-walled members with arbitrary support conditions

2011 ◽  
Vol 89 (21-22) ◽  
pp. 1906-1919 ◽  
Author(s):  
C. Basaglia ◽  
D. Camotim ◽  
N. Silvestre
Keyword(s):  
Open Section ◽  
Non Linear ◽  
Thin Walled ◽  
Support Conditions

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>

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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