Alternative complementary shear and transversal elongation modes in Generalized Beam Theory (GBT) for thin‐walled circular cross‐sections

2021 ◽  
Author(s):  
Marcelo José Bianco ◽  
Abinet Habtemariam ◽  
Carsten Könke ◽  
Fabiola Tartaglione ◽  
Volkmar Zabel
Keyword(s):  
Cross Sections ◽  
Beam Theory ◽  
Thin Walled ◽  
Generalized Beam Theory

scholarly journals Generalized Beam Theory for Thin-Walled Beams with Curvilinear Open Cross-Sections

2020 ◽  
Vol 10 (21) ◽  
pp. 7802
Author(s):  
Jarosław Latalski ◽  
Daniele Zulli
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Beam Theory ◽  
Middle Surface ◽  
Fem Model ◽  
Out Of Plane ◽  
Thin Walled ◽  
Generalized Beam Theory ◽  
Load Conditions

The use of the Generalized Beam Theory (GBT) is extended to thin-walled beams with curvilinear cross-sections. After defining the kinematic features of the walls, where their curvature is consistently accounted for, the displacement of the points is assumed as linear combination of unknown amplitudes and pre-established trial functions. The latter, and specifically their in-plane components, are chosen as dynamic modes of a curved beam in the shape of the member cross-section. Moreover, the out-of-plane components come from the imposition of the Vlasov internal constraint of shear indeformable middle surface. For a case study of semi-annular cross-section, i.e., constant curvature, the modes are analytically evaluated and the procedure is implemented for two different load conditions. Outcomes are compared to those of a FEM model.

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.

An extended first-order generalized beam theory for perforated thin-walled members

2021 ◽  
Vol 161 ◽  
pp. 107492
Author(s):  
Liping Duan ◽  
Jincheng Zhao
Keyword(s):  
Beam Theory ◽  
First Order ◽  
Thin Walled ◽  
Generalized Beam Theory

Generalized beam theory-based advanced beam finite elements for linear buckling analyses of perforated thin-walled members

2022 ◽  
Vol 259 ◽  
pp. 106683
Author(s):  
Liping Duan ◽  
Jincheng Zhao ◽  
Jiexin Zou
Keyword(s):  
Finite Elements ◽  
Beam Theory ◽  
Linear Buckling ◽  
Thin Walled ◽  
Generalized Beam Theory
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