An Explicit Stiffness Matrix for Parabolic Beam Element
Abstract This study is devoted to strain-based formulation for a curved beam. Arches with parabolic geometry, which have a variety of applications, belong to this structural type. Dependency of the curvature radius to the arch length creates some complexities in the solution process. To analyze thes...
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Marcílio Alves
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Series: | Latin American Journal of Solids and Structures |
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doaj-8a8e290397b14aafa7460de3444812312020-11-25T01:52:55ZengMarcílio AlvesLatin American Journal of Solids and Structures1679-78251391782180110.1590/1679-78252820S1679-78252016000901782An Explicit Stiffness Matrix for Parabolic Beam ElementMohammad Rezaiee-PajandNiloofar Rajabzadeh-SafaeiAbstract This study is devoted to strain-based formulation for a curved beam. Arches with parabolic geometry, which have a variety of applications, belong to this structural type. Dependency of the curvature radius to the arch length creates some complexities in the solution process. To analyze these complex structures, a two-node beam with six degrees of freedom is suggested by utilizing closed-form solution and the stiffness-based finite element method. Considering the effect of shear deformation, and incorporating equilibrium conditions into the finite element model, lead to the exact strains. Displacements and explicit stiffness matrix are found based on these exact strains. To validate the efficiency of the author's formulation, seven numerical tests are performed. The outcomes demonstrate that by employing only a single element, the locking-free answers can be found.http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1679-78252016000901782&lng=en&tlng=enFinite element methodparabolic beamexplicit stiffness matrixstrain-based formulationequilibrium conditions |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Mohammad Rezaiee-Pajand Niloofar Rajabzadeh-Safaei |
spellingShingle |
Mohammad Rezaiee-Pajand Niloofar Rajabzadeh-Safaei An Explicit Stiffness Matrix for Parabolic Beam Element Latin American Journal of Solids and Structures Finite element method parabolic beam explicit stiffness matrix strain-based formulation equilibrium conditions |
author_facet |
Mohammad Rezaiee-Pajand Niloofar Rajabzadeh-Safaei |
author_sort |
Mohammad Rezaiee-Pajand |
title |
An Explicit Stiffness Matrix for Parabolic Beam Element |
title_short |
An Explicit Stiffness Matrix for Parabolic Beam Element |
title_full |
An Explicit Stiffness Matrix for Parabolic Beam Element |
title_fullStr |
An Explicit Stiffness Matrix for Parabolic Beam Element |
title_full_unstemmed |
An Explicit Stiffness Matrix for Parabolic Beam Element |
title_sort |
explicit stiffness matrix for parabolic beam element |
publisher |
Marcílio Alves |
series |
Latin American Journal of Solids and Structures |
issn |
1679-7825 |
description |
Abstract This study is devoted to strain-based formulation for a curved beam. Arches with parabolic geometry, which have a variety of applications, belong to this structural type. Dependency of the curvature radius to the arch length creates some complexities in the solution process. To analyze these complex structures, a two-node beam with six degrees of freedom is suggested by utilizing closed-form solution and the stiffness-based finite element method. Considering the effect of shear deformation, and incorporating equilibrium conditions into the finite element model, lead to the exact strains. Displacements and explicit stiffness matrix are found based on these exact strains. To validate the efficiency of the author's formulation, seven numerical tests are performed. The outcomes demonstrate that by employing only a single element, the locking-free answers can be found. |
topic |
Finite element method parabolic beam explicit stiffness matrix strain-based formulation equilibrium conditions |
url |
http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1679-78252016000901782&lng=en&tlng=en |
work_keys_str_mv |
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