A three-dimensional multilayered pipe beam element: Nonlinear analysis

Aguiar, L. L.; Almeida, Cristiane Maria Galdino de; Paulino, Gláucio H.

doi:10.1016/j.compstruc.2013.09.005

Cited by 8 publications

(2 citation statements)

References 22 publications

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“…Latin American Journal of Solids and Structures, 2019, 16(4), e185 7/22 where ( +∆ ) corresponds to the second Piola-Kirchoff stress tensor, ( +∆ ) the Green-Lagrange strain tensor, and ( +∆ ) the virtual work due to external loading, which could include body, surface, inertia and damping forces (Aguiar et al 2014).…”

Section: Updated Lagrangian Formulationmentioning

confidence: 99%

A Unified Approach to the Timoshenko Geometric Stiffness Matrix Considering Higher-Order Terms in the Strain Tensor

Rodrigues

Burgos

Martha

2019

Lat. Am. j. solids struct.

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Nonlinear analyses using an updated Lagrangian formulation considering the Euler-Bernoulli beam theory have been developed with consistency in the literature, with different geometric matrices depending on the nonlinear displacement parts considered in the strain tensor. When performing this type of analysis using the Timoshenko beam theory, in general, the stiffness and the geometric matrices present additional degrees of freedom. This work presents a unified approach for the development of a geometric matrix employing the Timoshenko beam theory and considering higher-order terms in the strain tensor. This matrix is obtained using shape functions calculated directly from the solution of the differential equation of the problem. The matrix is implemented in the Ftool software, and its results are compared against several matrices found in the literature, with or without higher-order terms in the strain tensor, as well as the Euler-Bernoulli or Timoshenko beam theories. Examples show that the use of the Timoshenko beam theory has a strong influence, especially when the structure has small slenderness (short members). For high axial load values, the consideration of higher-order terms in the strain tensor results in larger displacements as expected.

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Section: Updated Lagrangian Formulationmentioning

confidence: 99%

A Unified Approach to the Timoshenko Geometric Stiffness Matrix Considering Higher-Order Terms in the Strain Tensor

Rodrigues

Burgos

Martha

2019

Lat. Am. j. solids struct.

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“…[29][30][31] For a comprehensive survey of finite element beam theories and the presentation of up-to-date developments, the reader is addressed to the recent papers by Shabba et al 32 and by Aguiar et al 33 In general, all the published formulations are very complex, most address twodimensional problems and are basically limited to homogeneous materials. The main motivation behind the present study is finding a trade-off between accuracy and simplicity which is still lacking in the literature to deal with the specific bimaterial constructions under scrutiny.…”

Section: Introductionmentioning

confidence: 99%

Formulation of a three-dimensional shear-flexible bimaterial beam element with constant curvature

Dragoni

Bagaria

2014

Proceedings of the Institution of Mechanical Engineers, Part C:

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This paper presents the closed-form formulation for a three-dimensional curved beam element with round bimaterial section. The formulation includes the effects of shear forces on displacements and stresses and of the beam curvature on the distribution of bending and torsional stress over the cross section. The element is coherent with the well-known theory for straight beams, which is obtained exactly as the curvature radius becomes infinite. The numerical predictions for a test case compare favourably with published analytical and experimental results and with the outcome of a purposely developed, large-scale FE brick model

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A Lagrangian–Eulerian formulation for reeling analysis of history-dependent multilayered beams

Longva

Sævik

2015

Computers & Structures

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A three-dimensional multilayered pipe beam element: Nonlinear analysis

Cited by 8 publications

References 22 publications

A Unified Approach to the Timoshenko Geometric Stiffness Matrix Considering Higher-Order Terms in the Strain Tensor

A Unified Approach to the Timoshenko Geometric Stiffness Matrix Considering Higher-Order Terms in the Strain Tensor

Formulation of a three-dimensional shear-flexible bimaterial beam element with constant curvature

A Lagrangian–Eulerian formulation for reeling analysis of history-dependent multilayered beams

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