Adaptive finite element refinement

Zienkiewicz, O.C.; Taylor, Robert L.; Zhu, J.Z.

doi:10.1016/b978-075066431-8.50182-x

Cited by 413 publications

(639 citation statements)

References 24 publications

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“…As discussed in O'Sullivan and Bray [24] and Otsubo et al [25], the particles in a DEM simulation are analogous to the nodes in a finite element model, while the contacts are roughly equivalent to the elements. This conceptual model of a granular material is used in implicit discrete element method formulations such as the particulate form of discontinuous deformation analysis (DDA) as outlined in [26][27][28]. For the 3-D analyses considered here, each particle has 3 translational degrees of freedom and 3 rotational degrees of freedom and so the diagonal mass matrix (M) includes the mass (m) and rotational inertia values for each particle.…”

Section: Eigenmode Anaysismentioning

confidence: 99%

“…The global stiffness matrix (K) can be created using the stiffness matrix assembly techniques described in [28] once the local contact stiffness matrix describing pairwise interaction of two particles is obtained. Here the local contact stiffness matrix was created using the data available in the DEM model once the inter-particle friction was set at μ wave .…”

Section: Eigenmode Anaysismentioning

confidence: 99%

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Influence of packing density and stress on the dynamic response of granular materials

et al. 2017

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Laboratory geophysics tests including bender elements and acoustic emission measure the speed of propagation of stress or sound waves in granular materials to derive elastic stiffness parameters. This contribution builds on earlier studies to assess whether the received signal characteristics can provide additional information about either the material's behaviour or the nature of the material itself. Specifically it considers the maximum frequency that the material can transmit; it also assesses whether there is a simple link between the spectrum of the received signal and the natural frequencies of the sample. Discrete element method (DEM) simulations of planar compression wave propagation were performed to generate the data for the study. Restricting consideration to uniform (monodisperse) spheres, the material fabric was varied by considering face-centred cubic lattice packings as well as random configurations with different packing densities. Supplemental analyses, in addition to the DEM simulations, were used to develop a more comprehensive understanding of the system dynamics. The assembly stiffness and mass matrices were extracted from the DEM model and these data were used in an eigenmode analysis that provided significant insight into the observed overall dynamic response. The close agreement of the wave velocities estimated using eigenmode analysis with the DEM results confirms that DEM wave propagation simulations can reliably be used to extract material stiffness data. The data show that increasing either stress or density allows higher frequencies to propagate through the media, but the low-pass wavelength is a function of packing density rather than stress level. Prior research which had hypothesised that there is a simple link between the spectrum of the received signal and the natural sample frequencies was not substantiated.

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Section: Eigenmode Anaysismentioning

confidence: 99%

Section: Eigenmode Anaysismentioning

confidence: 99%

Influence of packing density and stress on the dynamic response of granular materials

et al. 2017

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“…More details about how to compute the displacement gradient at the integration point of an element can be found in every FE textbook, cf. Zienkiewicz and Taylor [55], for instance.…”

Section: Computation Of the Plastic Flow Direction From The Displacemmentioning

confidence: 99%

Identification of plastic constitutive parameters at large deformations from three dimensional displacement fields

Rossi

Pierron

2011

Comput Mech

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The aim of this paper is to provide a general procedure to extract the constitutive parameters of a plasticity model starting from displacement measurements and using the Virtual Fields Method. This is a classical inverse problem which has been already investigated in the literature, however several new features are developed here. First of all the procedure applies to a general three-dimensional displacement field which leads to large plastic deformations, no assumptions are made such as plane stress or plane strain although only pressure-independent plasticity is considered. Moreover the equilibrium equation is written in terms of the deviatoric stress tensor that can be directly computed from the strain field without iterations. Thanks to this, the identification routine is much faster compared to other inverse methods such as finite element updating. The proposed method can be a valid tool to study complex phenomena which involve severe plastic deformation and where the state of stress is completely triaxial, e.g. strain localization or necking occurrence. The procedure has been validated using a three dimensional displacement field obtained from a simulated experiment. The main potentialities as well as a first sensitivity study on the influence of measurement errors are illustrated.

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“…After finite element procedures (Zienkiewicz, Taylor, 2000), when using Galerkin method, Eq. (11) is given by:…”

Section: Mathematical Model Of Coupled Mechanical and Acoustic Fieldmentioning

confidence: 99%

Digital Synthesis of Sound Generated by Tibetan Bowls and Bells

Gołaś¹,

Filipek²

2016

Archives of Acoustics

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The aim of this paper is to present methods of digitally synthesising the sound generated by vibroacoustic systems with distributed parameters. A general algorithm was developed to synthesise the sounds of selected musical instruments with an axisymmetrical shape and impact excitation, i.e., Tibetan bowls and bells. A coupled mechanical-acoustic field described by partial differential equations was discretized by using the Finite Element Method (FEM) implemented in the ANSYS package. The presented synthesis method is original due to the fact that the determination of the system response in the time domain to the pulse (impact) excitation is based on the numerical calculation of the convolution of the forcing function and impulse response of the system. This was calculated as an inverse Fourier transform of the system's spectral transfer function. The synthesiser allows for obtaining a sound signal with the assumed, expected parameters by tuning the resonance frequencies which exist in the spectrum of the generated sound. This is accomplished, basing on the Design of Experiment (DOE) theory, by creating a meta-model which contains information on its response surfaces regarding the influence of the design parameters. The synthesis resulted in a sound pressure signal in selected points in space surrounding the instrument which is consistent with the signal generated by the actual instruments, and the results obtained can improve them.

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Adaptive finite element refinement

Cited by 413 publications

References 24 publications

Influence of packing density and stress on the dynamic response of granular materials

Influence of packing density and stress on the dynamic response of granular materials

Identification of plastic constitutive parameters at large deformations from three dimensional displacement fields

Digital Synthesis of Sound Generated by Tibetan Bowls and Bells

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