Introduction to the Finite-Element Method

Desai, C. S.; Abel, John F.; Marcal, Pedro V.

doi:10.1115/1.3422995

Cited by 96 publications

(56 citation statements)

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“…The first step is to use the traditional finite-element formulation to derive the stiffness matrix of the polymer element. This formulation can be found in any basic finite-element text, such as those by Akin [58], Desai & Abel [59] and Zienkiewicz et al [60].…”

Section: (I) Representative Volume Element Generationmentioning

confidence: 99%

“…However, the iterative approach provides only final solution values; therefore, it has limited applicability for some applications. The general concepts of both approaches are described in detail by Desai & Abel [59]. To decide which approach to use for the elastic analysis and which to use for the thermal analysis, an understanding of the mechanisms of nonlinearity in both CNTs and epoxies is needed.…”

Section: (B) Nonlinear Modelmentioning

confidence: 99%

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Estimation of the physical properties of nanocomposites by finite-element discretization and Monte Carlo simulation

Spanos

Elsbernd

Ward

et al. 2013

Phil. Trans. R. Soc. A.

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This paper reviews and enhances numerical models for determining thermal, elastic and electrical properties of carbon nanotube-reinforced polymer composites. For the determination of the effective stress–strain curve and thermal conductivity of the composite material, finite-element analysis (FEA), in conjunction with the embedded fibre method (EFM), is used. Variable nanotube geometry, alignment and waviness are taken into account. First, a random morphology of a user-defined volume fraction of nanotubes is generated, and their properties are incorporated into the polymer matrix using the EFM. Next, incremental and iterative FEA approaches are used for the determination of the nonlinear properties of the nanocomposite. For the determination of the electrical properties, a spanning network identification algorithm is used. First, a realistic nanotube morphology is generated from input parameters defined by the user. The spanning network algorithm then determines the connectivity between nanotubes in a representative volume element. Then, interconnected nanotube networks are converted to equivalent resistor circuits. Finally, Kirchhoff's current law is used in conjunction with FEA to solve for the voltages and currents in the system and thus calculate the effective electrical conductivity of the nanocomposite. The model accounts for electrical transport mechanisms such as electron hopping and simultaneously calculates percolation probability, identifies the backbone and determines the effective conductivity. Monte Carlo analysis of 500 random microstructures is performed to capture the stochastic nature of the fibre generation and to derive statistically reliable results. The models are validated by comparison with various experimental datasets reported in the recent literature.

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Section: (I) Representative Volume Element Generationmentioning

confidence: 99%

Section: (B) Nonlinear Modelmentioning

confidence: 99%

Estimation of the physical properties of nanocomposites by finite-element discretization and Monte Carlo simulation

Spanos

Elsbernd

Ward

et al. 2013

Phil. Trans. R. Soc. A.

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“…The FEM is used to obtain solutions to the differential equations that describe, or approximately describe a wide variety of physical (and non-physical) problems [38,39]. The BEM is basically derived through the discretisation of an integral equation that is mathematically equivalent to the original partial differential equation [40].…”

Section: Numerical Modelsmentioning

confidence: 99%

Sound radiation from perforated plates

Putra

Thompson

2010

Journal of Sound and Vibration

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FACULTY OF ENGINEERING, SCIENCE AND MATHEMATICS INSTITUTE OF SOUND AND VIBRATION RESEARCH Doctor of Philosophy SOUND RADIATION FROM PERFORATED PLATES by Azma PutraPerforated plates are quite often used as a means of engineering noise control to reduce the sound radiated by structures. However, there appears to be a lack of representative models to determine the sound radiation from a perforated plate. The aim of this thesis is to develop such a model that can be used to give quantitative guidance corresponding to the design and effectiveness of this noise control measure.Following an assessment of various models for the radiation efficiency of an unbaffled plate, Laulagnet's model is implemented. Results are calculated and compared with those for baffled plates. From this, simple empirical formulae are developed and give a very good agreement with the analytical result. Laulagnet's model is then modified to include the effect of perforation in terms of a continuously distributed surface impedance to represent the holes. This produces a model for the sound radiation from a perforated unbaffled plate. It is found that the radiation efficiency reduces as the perforation ratio increases or as the hole size reduces. An approximate formula for the effect of perforation is proposed which shows a good agreement with the analytical calculation up to half the critical frequency. This could be used for an engineering application to predict the noise reduction due to perforation.The calculation for guided-guided boundary conditions shows that the radiation efficiency of an unbaffled plate is not sensitive to the edge conditions. It is also shown that perforation changes the plate bending stiffness and mass and hence increases the plate vibration.The situation is also considered in which a perforated unbaffled plate is located close to a reflecting rigid surface. This is established by modifying the Green's function in the perforated unbaffled model to include an imaginary source to represent the reflected sound. The result shows that the presence of the rigid surface reduces the radiation efficiency at low frequencies.The limitation of the assumption of a continuous acoustic impedance is investigated using a model of discrete sources. The perforated plate is discretised into elementary sources representing the plate and also the holes. It is found that the uniform surface impedance is only valid if the hole distance is less than an acoustic wavelength for a vibrating rectangular piston and less than half an acoustic wavelength for a rectangular plate in bending vibration. Otherwise, the array of holes is no longer effective to reduce the sound radiation.Experimental validation is conducted using a reciprocity technique. A good agreement is achieved between the measured results and the theoretical calculation for both the unbaffled perforated plate and the perforated plate near a rigid surface.

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“…time series data of the objects shape under in#uence of external forces, this leads to inverse, mostly ill-posed non-linear problems, which are still a "eld of mathematical research [13]. The design of "nite element models is usually very time consuming, since an appropriate structure has to be de"ned [10]. The existing neural network based models on the other hand, need training data for learning, which is usually not available and has to be created, e.g.…”

Section: Modelling Deformable Virtual Objectsmentioning

confidence: 99%

Using recurrent neuro-fuzzy techniques for the identification and simulation of dynamic systems

Nürnberger

Radetzky²,

Kruse

2001

Neurocomputing

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The identi"cation and simulation of dynamic systems is still a challenging problem. In this article some basic aspects of neuro-fuzzy techniques for the identi"cation and simulation of time-dependent physical systems are presented. In particular, a neuro-fuzzy model that can be used for the identi"cation and the (real-time) simulation of viscoelastic models, is described. The presented model is motivated by a cooperative neuro-fuzzy approach based on a vectorized recurrent neural network architecture. The physical motivation of this model is illustrated and speci"c propagation procedures and a learning algorithm are presented. Moreover, the usability in practice is demonstrated by an application of the model in the area of surgical simulation.

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Introduction to the Finite-Element Method

Cited by 96 publications

References 0 publications

Estimation of the physical properties of nanocomposites by finite-element discretization and Monte Carlo simulation

Estimation of the physical properties of nanocomposites by finite-element discretization and Monte Carlo simulation

Sound radiation from perforated plates

Using recurrent neuro-fuzzy techniques for the identification and simulation of dynamic systems

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