A high-precision curvature constrained Bernoulli–Euler planar beam element for geometrically nonlinear analysis

Zhang, Peng; Ma, Junjun; Duan, Menglan; Yuan, Ye; Wang, Jinjia

doi:10.1016/j.amc.2021.125986

Cited by 10 publications

(7 citation statements)

References 52 publications

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“…Recent studies have examined the performance of the developed elements under large rotations by solving this problem using meshes ranging from three up to a hundred of elements. 18,19 The exact solution to this problem is a circular arc with radius R = EI∕M. To deform the rod into a full closed circle, an end moment M = 2𝜋EI∕L needs to be applied.…”

Section: Pure Bending Of a Cantilever Beammentioning

confidence: 99%

“…The first test, serving as a benchmark, deals with a cantilever of length L and bending stiffness

E I

loaded by a concentrated end moment M on its right end. Recent studies have examined the performance of the developed elements under large rotations by solving this problem using meshes ranging from three up to a hundred of elements 18,19 . The exact solution to this problem is a circular arc with radius

R = E I / M

.…”

Section: Numerical Examplesmentioning

confidence: 99%

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Efficient finite difference formulation of a geometrically nonlinear beam element

Jirásek

Ribolla

Horák

2021

Numerical Meth Engineering

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The article is focused on a two-dimensional geometrically nonlinear formulation of a Bernoulli beam element that can accommodate arbitrarily large rotations of cross sections. The formulation is based on the integrated form of equilibrium equations, which are combined with the kinematic equations and generalized material equations, leading to a set of three first-order differential equations. These equations are then discretized by finite differences and the boundary value problem is converted into an initial value problem using a technique inspired by the shooting method. Accuracy of the numerical approximation is conveniently increased by refining the integration scheme on the element level while the number of global degrees of freedom is kept constant, which leads to high computational efficiency. The element has been implemented into an open-source finite element code. Numerical examples show a favorable comparison with standard beam elements formulated in the finite-strain framework and with analytical solutions.

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Section: Pure Bending Of a Cantilever Beammentioning

confidence: 99%

“…The first test, serving as a benchmark, deals with a cantilever of length L and bending stiffness

E I

R = E I / M

.…”

Section: Numerical Examplesmentioning

confidence: 99%

Efficient finite difference formulation of a geometrically nonlinear beam element

Jirásek

Ribolla

Horák

2021

Numerical Meth Engineering

View full text Add to dashboard Cite

show abstract

“…Then, the application range of their methods is limited. In addition, these elements [19][20][21][22][23][24][25] were all developed in an inertia coordinate system. The shape functions of these elements are used to ensure the continuity of the global displacement field and cannot take the constitutive relationship of the materials into account.…”

Section: Introductionmentioning

confidence: 99%

“…An element-independent framework is established by using the same shape functions to derive the nonlinear equations of motion of the element based on Hamilton's principle. In contrast with the curved beam elements [19][20][21][22][23][24][25][26][27][28] developed in the inertia coordinate system, the shape functions of the presented element are used to describe the local displacement field. Then, many standard elements, [5][6][7][8] developed based on exact solutions in a curvilinear coordinate system, can be embedded into the framework.…”

Section: Introductionmentioning

confidence: 99%

“…Doğruoğlu and Kömürcü 23 presented two mixed finite element formulations for the geometrically nonlinear analysis of planar curved beams. Zhang et al 24 developed a high‐precision curvature constrained beam element based on the gradient deficient beam elements of the ANCF. In recent years, Choi et al 25 developed a novel finite element formulation based on isogeometric analysis (IGA) 26 and GET to bridge the gap between computer‐aided design and finite element analysis.…”

Section: Introductionmentioning

confidence: 99%

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A two‐dimensional corotational curved beam element for dynamic analysis of curved viscoelastic beams with large deformations and rotations

Deng

Niu

Xue

et al. 2022

Numerical Meth Engineering

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This paper presents a two‐dimensional corotational curved beam element for the dynamic analysis of curved viscoelastic beams with large deformations and rotations. In contrast with traditional straight beam elements, the novelty of the presented formulation lies in introducing a curved reference configuration, which follows the rotation and translation of a corotational frame, to measure the pure elastic deformation of the beam and describe the spatial position of an arbitrary material point. A curvilinear coordinate system is fixed on this reference configuration to measure the local deformation of the element. Based on Hamilton's principle, the global elastic force vector, the global internal damping force vector, the global inertia force vector, and the global external damping force vector are derived using the same shape functions to ensure the consistency and independence of the element. An accurate two‐node curved element and the Kelvin–Voigt model are introduced to consider the axial deformation, bending deformation, shear deformation, rotary inertia, and viscoelasticity of the beam. Three examples are given to verify the validity, computational accuracy, and computational efficiency of the presented formulation. Moreover, the effects of the internal damping and external damping on the dynamic response of a rotating curved beam are investigated.

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Efficiency improvement on the ANCF cable element by using the dot product form of curvature

Zhang

Duan

Gao

et al. 2022

Applied Mathematical Modelling

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A high-precision curvature constrained Bernoulli–Euler planar beam element for geometrically nonlinear analysis

Cited by 10 publications

References 52 publications

Efficient finite difference formulation of a geometrically nonlinear beam element

Efficient finite difference formulation of a geometrically nonlinear beam element

A two‐dimensional corotational curved beam element for dynamic analysis of curved viscoelastic beams with large deformations and rotations

Efficiency improvement on the ANCF cable element by using the dot product form of curvature

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