A free vibration analysis of three-dimensional sandwich beams using hierarchical one-dimensional finite elements

Hui, Yilong; Giunta, Gaetano; Belouettar, Salim; Huang, Qun; Hu, Heng; Carrera, Erasmo

doi:10.1016/j.compositesb.2016.10.065

Cited by 55 publications

(19 citation statements)

References 44 publications

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“…As the beam becomes less and less slender or flexible, its mechanics is increasingly threedimensional, and the classical models cannot yield accurate results [11]. Thus, over the years, much effort has been put to enhance and refine the classical beam theories [12], for example, refined beam theories [11,13], beam analysis via hierarchical finite element approach [14], or fiber beam elements [15]. The description methods of the beam theories mentioned above are suitable for structural vibration analysis and composite beam, and there is a more suitable description method for the large-motion, very flexible objects such as yarn, that is, absolute nodal coordinate formulation (ANCF) description.…”

Section: Introductionmentioning

confidence: 99%

Modeling and Simulation of a Moving Yarn Segment: Based on the Absolute Nodal Coordinate Formulation

Wang

et al. 2019

Mathematical Problems in Engineering

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A new finite element dynamic model of a moving yarn segment has been proposed in this paper based on the absolute nodal coordinate formulation (ANCF). Apart from taking into account the elastic properties of the yarn in three dimensions, the model also considers the viscosity in the longitudinal direction and takes into account the effect of gravity and air resistance. In this paper, the simulation described the movement of the yarn segment that is pulled by the fixer on the guideway. Then, a corresponding experiment was proposed to evaluate the theoretical model. The theoretical and experimental comparisons of the motion tracing exhibited good agreement, demonstrating that the new model could predict the actual moving trace of the yarn segment. Moreover, another simulation of the spatial motion of the yarn segment was presented, to elucidate the role of the model in predicting the movement of the yarn segment. After considering the parameters of the actual process and its constraints, the authors established that the proposed model could be used to predict the trajectory of a yarn segment in the actual production process, which is vital when fabricating textile products.

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Section: Introductionmentioning

confidence: 99%

Modeling and Simulation of a Moving Yarn Segment: Based on the Absolute Nodal Coordinate Formulation

Wang

et al. 2019

Mathematical Problems in Engineering

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“…As opposed to the FE approach, where mesh refinement is required for solutions at high frequencies and conversely smaller wavelengths, the HFE formulation keeps the mesh size fixed and increases the degree of the approximating functions used in the element formulation, which makes it very appealing to energy distribution or power flow calculations [30,31]. It has been used in many applications, including the vibration analysis of beams [32][33][34], shafts [35], plates and cylinders, including composite laminates or stiffened structures [28,29,[36][37][38]. Compared to the standard h-version FE, the HFE method produces smaller mass and stiffness matrices and tends to be computationally more efficient.…”

Section: Introductionmentioning

confidence: 99%

Structural vibration analysis with random fields using the hierarchical finite element method

Fabro

Ferguson

Mace

2019

J Braz. Soc. Mech. Sci. Eng.

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Element based techniques, like the Finite Element method, are the standard approach in industry for low frequency applications in structural dynamics. However, mesh requirements can significantly increase the computational cost for increasing frequencies. In addition, randomness in system properties starts to play a significant role and its inclusion in the model further increases the computational cost. In this paper, a hierarchical finite element formulation is presented which incorporates spatially random properties. Polynomial and trigonometric hierarchical functions are used in the element formulation. Material and geometrical spatially correlated randomness are represented by the Karhunen-Loève expansion, a series representation for random fields. It allows the element integration to be performed only once for each term of the series which has benefits for a sampling scheme and can be used for non-Gaussian distributions. Free vibration and forced response statistics are calculated using the proposed approach. Compared to the standard h-version, the hierarchical finite element approach produces smaller mass and stiffness matrices, without changing the number of nodes of the element, and tends to be computationally more efficient. These are key factors not only when considering solutions for higher frequencies but also in the calculation of response statistics using a sampling method such as Monte Carlo simulation.

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“…Accurate yet computational attractive modeling strategies are, therefore, required making composite structures modeling an actual research field. In this way, note the substantial works related to the so-called Carrera's Unified Formulation (CUF) applied to the beam structures [1][2][3]. It allows to implement easily hierarchical models from classical to higherorder beam theories.…”

Section: Introductionmentioning

confidence: 99%

Modeling of composite and sandwich beams with a generic cross-section using a variable separation method

Vidal¹,

Giunta²,

Gallimard³

et al. 2019

Composites Part B: Engineering

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In this work, the modeling of laminated composite and sandwich beams with a generic cross-section is performed through a variable separation approach. For this purpose, the displacement is approximated as a sum of separated functions of the cross-section coordinates y z , and the axial coordinate x. This choice yields to a non-linear problem that can be solved by an iterative process. This latter consists of solving a 2D and 1D Finite Element problem successively at each iteration. Numerical examples involving several representative sandwich and laminated beams are addressed to show the accuracy of the present method. It is shown that it can provide 3D results and capture local effects for various types of cross-section.

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A free vibration analysis of three-dimensional sandwich beams using hierarchical one-dimensional finite elements

Cited by 55 publications

References 44 publications

Modeling and Simulation of a Moving Yarn Segment: Based on the Absolute Nodal Coordinate Formulation

Modeling and Simulation of a Moving Yarn Segment: Based on the Absolute Nodal Coordinate Formulation

Structural vibration analysis with random fields using the hierarchical finite element method

Modeling of composite and sandwich beams with a generic cross-section using a variable separation method

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