Three-Node Euler-Bernoulli Beam Element Based on Positional FEM

Liu, Jian; Zhou, Shenjie; Dong, Meiling; Yan, Yinfei

doi:10.1016/j.proeng.2012.01.556

Cited by 7 publications

(5 citation statements)

References 2 publications

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“…Three-node beam element has a great advantage over two-node elements, which provides solving large displacement geometry in nonlinear static and dynamic analysis. 41 Although three-node elements increased computational efforts at element level, the computers' treatment polynomial function efficiency is very high, and thus overall, efforts of computation are not increased. Raft and internal domain of soil are modelled using 8 noded brick elements.…”

Section: Raft Piles and Soil: Fem Modelling And Formulationmentioning

confidence: 99%

“…Three noded embedded beam element is used for the finite element modelling of piles with each node having three translations and three rotational degrees of freedom. Three‐node beam element has a great advantage over two‐node elements, which provides solving large displacement geometry in nonlinear static and dynamic analysis 41 . Although three‐node elements increased computational efforts at element level, the computers’ treatment polynomial function efficiency is very high, and thus overall, efforts of computation are not increased.…”

Section: Raft Piles and Soil: Fem Modelling And Formulationmentioning

confidence: 99%

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A new nonlinear spring‐dashpot model of CPRF of NPP structure based on coupled BEM‐FEM approach

Firoj

Maheshwari

2022

Earthq Engng Struct Dyn

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In this paper, a BEM‐FEM coupled model of combined piled raft foundation (CPRF) is proposed for both the frequency domain and the time domain dynamic analyses of a NPP structure in the linear, equivalent linear and nonlinear soil domain. The piles are modeled using the finite element method as a beam element, while the raft and internal domain of soil are modeled using the eight nodded brick element. It is assumed that the piles are rigidly connected with the raft. The nonlinearity of soil is modeled using the hyperbolic stress–strain relation and Modified Drucker–Prager Model. The boundary of the layered soil domain is modeled using the boundary element method. For simplification, it is assumed that the raft and piles are rigidly connected with the soil that means there are no slip and separation conditions at the interface of pile‐soil and raft‐soil. In order to validate the proposed approach, numerical results, that is, impedances in the horizontal, vertical and rocking directions, are compared with the published literature. Further, dynamic analyses of a lumped structure founded on CPRF is carried out in the time domain and frequency domain using these impedances and results are compared with the FEM. It is found that the spring‐dashpot models give the reasonably good agreement with finite element method for linear, equivalent linear and nonlinear models for both frequency domain and time domain analyses. Moreover, practical application of proposed model is shown for a very large problem of raft‐pile‐soil‐structure interaction such as a NPP structure on the layered soil. It was found that the nonlinearity significantly increases the response of the NPP structure. The proposed model has many advantage over the finite element model, for example, first it is very simple and second it reduced the computation time significantly with the good accuracy.

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Section: Raft Piles and Soil: Fem Modelling And Formulationmentioning

confidence: 99%

Section: Raft Piles and Soil: Fem Modelling And Formulationmentioning

confidence: 99%

A new nonlinear spring‐dashpot model of CPRF of NPP structure based on coupled BEM‐FEM approach

Firoj

Maheshwari

2022

Earthq Engng Struct Dyn

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“…The positional formulation of the Finite Element Method used for this paper is based on the formulations found in Coda and Greco (2004) and Greco et al (2006). The method was selected due to its efficiency in the applications and developments shown in recent published work concerning nonlinear numerical analysis (Carrazedo and Coda, 2010;Jian et al, 2012;Ma et al, 2012). It is supported by physics principles based on energy equilibrium that are both consistent and easy to understand.…”

Section: Nonlinear Positional Formulation For Viscoelastic Space Trusmentioning

confidence: 99%

Modeling the creep behavior of GRFP truss structures with Positional Finite Element Method

Rabelo

Becho

Greco

et al. 2018

Lat. Am. j. solids struct.

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This paper presents the development of a formulation, based on Positional Finite Element Method, to describe the viscoelastic mechanical behavior of space trusses. The numerical method used was chosen due to its efficiency in the applications concerning nonlinear numerical analyses. The formulation describes the positional variation over time under constant stress state (creep). The objective is to provide a way to quantify the creep behavior for space truss structures and thus contribute to the encouragement of GFRP usage in such structural components. Time-dependent behavior of such materials is one the most important factors for their use in design of structures, demanding studies about the deformations expected within the operational life of the structural systems. To perform this study, the proposed methodology considers a standard solid rheological model to describe stress-strain time-dependent law. This model is implemented in the formulation for quantify the total strain energy. The effects of the model parameters in the mechanical response of the structure with accentuated geometric nonlinearity were presented. In this analysis, it was possible to identify the influence of the elastic and the viscous moduli on the creep response. Model calibration was performed using test data obtained from literature and a GFRP transmission line tower cross-arm was simulated to predict the evolution of displacements under real operational loads. From the results, it was possible to observe a fast evolution of displacements due to the creep effect in the first 7,500 h. This increase was close to 0.6% in relation to the displacement obtained in the elastic behavior. The presented methodology provided a simple and efficient way to quantify the creep phenomenon in viscoelastic GFRP composites truss structures, as can be seen in the developed analyses.

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“…If the stiffness values k * from the Bernoulli model are considered a good approximation then we can choose the solution which is the closest to k * in the sense of the distance D. In this case study, this closest set k I ∞ is the same as the result of the single iteration from k 0 = k * (see Figs. [13][14], but this coincidence is not necessary.…”

Section: Fitting To the Measured Frequencies Of A Spindlementioning

confidence: 99%

“…In the model, we use a new type of beam element, which contains 3 nodes with a single translational degree of freedom at each node. Beam elements with three nodes can be found in the literature (see [13,14]), but omitting the rotational degrees of freedom has advantages at the numerical fitting.…”

Section: Introductionmentioning

confidence: 99%

Experimental Fitting of Rotor Models by Using a Special Three-Node Beam Element

Antali

Takács²,

Stépàn

2017

Journal of Computational and Nonlinear Dynamics

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In this paper, a special type of beam element is developed with three nodes and with only translational degrees-of-freedom (DOFs) at each node. This element can be used effectively to build low degree-of-freedom models of rotors. The initial model from the Bernoulli theory is fitted to experimental results by nonlinear optimization. This way, we can avoid the complex modeling of contact problems between the parts of squirrel cage rotors. The procedure is demonstrated on the modeling of a machine tool spindle.

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Three-Node Euler-Bernoulli Beam Element Based on Positional FEM

Cited by 7 publications

References 2 publications

A new nonlinear spring‐dashpot model of CPRF of NPP structure based on coupled BEM‐FEM approach

A new nonlinear spring‐dashpot model of CPRF of NPP structure based on coupled BEM‐FEM approach

Modeling the creep behavior of GRFP truss structures with Positional Finite Element Method

Experimental Fitting of Rotor Models by Using a Special Three-Node Beam Element

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