Complete tangent stiffness matrix considering higher-order terms in the strain tensor and large rotations for a Euler Bernoulli - Timoshenko space beam-column element

This paper presents a unified method developed by Rodrigues et al. [1] to obtain a complete tangent stiffness matrix for spatial geometric nonlinear analysis using minimal discretization. The formulation presents four distinct important aspects to a complete analysis: interpolation (shape) functions...

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Autores principales:	Marcos Antonio Campos Rodrigues, Rodrigo Bird Burgos, Luiz Fernando Martha
Formato:	article
Lenguaje:	EN
Publicado:	Elsevier 2021
Materias:	Tangent stiffness matrix Analytical interpolation functions Higher-order terms in strain tensor Large rotations Science Q
Acceso en línea:	https://doaj.org/article/a41703258531441cbff0476c0587724e
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spelling	oai:doaj.org-article:a41703258531441cbff0476c0587724e2021-12-04T04:34:24ZComplete tangent stiffness matrix considering higher-order terms in the strain tensor and large rotations for a Euler Bernoulli - Timoshenko space beam-column element2215-016110.1016/j.mex.2021.101591https://doaj.org/article/a41703258531441cbff0476c0587724e2021-01-01T00:00:00Zhttp://www.sciencedirect.com/science/article/pii/S2215016121003812https://doaj.org/toc/2215-0161This paper presents a unified method developed by Rodrigues et al. [1] to obtain a complete tangent stiffness matrix for spatial geometric nonlinear analysis using minimal discretization. The formulation presents four distinct important aspects to a complete analysis: interpolation (shape) functions, higher-order terms in the strain tensor and in the finite rotations, an updated Lagrangian kinematic description, and shear deformation effect (Timoshenko beam theory). Thus, the tangent stiffness matrix is calculated from the differential equation solution of deformed infinitesimal element equilibrium, considering the axial load and the shear deformation in this relation. This solution provides interpolation functions that are used in an updated Lagrangian formulation to construct the spatial tangent stiffness matrix considering higher-order terms in the strain tensor and in the finite rotations. The method provides an efficient formulation to perform geometric nonlinear analyses and predict the critical buckling load for spatial structures with moderate slenderness and with the interaction between axial and torsion effects, considering just one element in each member or a reduced discretization. • Complete expressions for a geometric nonlinear analyses considering one element per member • Spatial analyses considering higher-order terms in the strain tensor and large rotations • Shear deformation influence includedMarcos Antonio Campos RodriguesRodrigo Bird BurgosLuiz Fernando MarthaElsevierarticleTangent stiffness matrixAnalytical interpolation functionsHigher-order terms in strain tensorLarge rotationsScienceQENMethodsX, Vol 8, Iss , Pp 101591- (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Tangent stiffness matrix Analytical interpolation functions Higher-order terms in strain tensor Large rotations Science Q
spellingShingle	Tangent stiffness matrix Analytical interpolation functions Higher-order terms in strain tensor Large rotations Science Q Marcos Antonio Campos Rodrigues Rodrigo Bird Burgos Luiz Fernando Martha Complete tangent stiffness matrix considering higher-order terms in the strain tensor and large rotations for a Euler Bernoulli - Timoshenko space beam-column element
description	This paper presents a unified method developed by Rodrigues et al. [1] to obtain a complete tangent stiffness matrix for spatial geometric nonlinear analysis using minimal discretization. The formulation presents four distinct important aspects to a complete analysis: interpolation (shape) functions, higher-order terms in the strain tensor and in the finite rotations, an updated Lagrangian kinematic description, and shear deformation effect (Timoshenko beam theory). Thus, the tangent stiffness matrix is calculated from the differential equation solution of deformed infinitesimal element equilibrium, considering the axial load and the shear deformation in this relation. This solution provides interpolation functions that are used in an updated Lagrangian formulation to construct the spatial tangent stiffness matrix considering higher-order terms in the strain tensor and in the finite rotations. The method provides an efficient formulation to perform geometric nonlinear analyses and predict the critical buckling load for spatial structures with moderate slenderness and with the interaction between axial and torsion effects, considering just one element in each member or a reduced discretization. • Complete expressions for a geometric nonlinear analyses considering one element per member • Spatial analyses considering higher-order terms in the strain tensor and large rotations • Shear deformation influence included
format	article
author	Marcos Antonio Campos Rodrigues Rodrigo Bird Burgos Luiz Fernando Martha
author_facet	Marcos Antonio Campos Rodrigues Rodrigo Bird Burgos Luiz Fernando Martha
author_sort	Marcos Antonio Campos Rodrigues
title	Complete tangent stiffness matrix considering higher-order terms in the strain tensor and large rotations for a Euler Bernoulli - Timoshenko space beam-column element
title_short	Complete tangent stiffness matrix considering higher-order terms in the strain tensor and large rotations for a Euler Bernoulli - Timoshenko space beam-column element
title_full	Complete tangent stiffness matrix considering higher-order terms in the strain tensor and large rotations for a Euler Bernoulli - Timoshenko space beam-column element
title_fullStr	Complete tangent stiffness matrix considering higher-order terms in the strain tensor and large rotations for a Euler Bernoulli - Timoshenko space beam-column element
title_full_unstemmed	Complete tangent stiffness matrix considering higher-order terms in the strain tensor and large rotations for a Euler Bernoulli - Timoshenko space beam-column element
title_sort	complete tangent stiffness matrix considering higher-order terms in the strain tensor and large rotations for a euler bernoulli - timoshenko space beam-column element
publisher	Elsevier
publishDate	2021
url	https://doaj.org/article/a41703258531441cbff0476c0587724e
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Complete tangent stiffness matrix considering higher-order terms in the strain tensor and large rotations for a Euler Bernoulli - Timoshenko space beam-column element

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