A novel formulation of infinite elements for static analysis

Abdel-Fattah, Tarek T.; Hodhod, Hossam; Akl, Adel

doi:10.1016/s0045-7949(00)00029-8

Cited by 17 publications

(6 citation statements)

References 11 publications

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“…The results comparing the analytical solution as given in the work of T.T. Abdel-Fattah [21] are given in Fig. 4.…”

Section: Verification Of Static Infinite Elements -Plate With Circulamentioning

confidence: 99%

“…In the study, efficiency of the developed infinite element is also compared with the results of the numerical simulations conducted by the FE-code ABAQUS [21]. ABAQUS is a general-purpose analysis software that can solve a wide range of linear and nonlinear problems comprising the static and dynamic response of the components [22].…”

Section: Absorbing Infinite Elements In Abaqusmentioning

confidence: 99%

See 1 more Smart Citation

Development of infinite elements for simulation of unbounded media

Edip¹,

Sheshov²,

Bojadjieva³

et al. 2018

Građ materijali i konstrukcije

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“…The results comparing the analytical solution as given in the work of T.T. Abdel-Fattah [21] are given in Fig. 4.…”

Section: Verification Of Static Infinite Elements -Plate With Circulamentioning

confidence: 99%

Section: Absorbing Infinite Elements In Abaqusmentioning

confidence: 99%

Development of infinite elements for simulation of unbounded media

Edip¹,

Sheshov²,

Bojadjieva³

et al. 2018

Građ materijali i konstrukcije

View full text Add to dashboard Cite

“…5 (Marques & Owen 1984;Kumar 1985). Similarly, shape functions for particular decay functions, such as exponential or logarithmic decay, can also be derived (Abdel-Fattah et al 2000). A typical mapping of a 3-D infinite element in a general physical domain to an element in the natural domain is shown in Fig.…”

Section: Infinite Elementsmentioning

confidence: 99%

Spectral-infinite-element simulations of gravity anomalies

Gharti

Tromp

Zampini

2018

Geophysical Journal International

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Gravity anomalies induced by density heterogeneities are governed by Poisson's equation. Most existing methods for modelling such anomalies rely on its integral solution. In this approach, for each observation point, an integral over the entire density distribution needs to be carried out, and the computational cost is proportional to the number of observation points. Frequently, such methods are sensitive to high density contrasts due to inaccurate resolution of the volume integral. We introduce a new approach which directly solves a discretized form of the Poisson/Laplace equation. The main challenge in our approach involves the unbounded nature of the problem, because the potential exists in all of space. To circumvent this challenge, we combine a mapped infinite-element approach with a spectral-element method. Spectral elements represent the domain of interest, and a single layer of infinite elements captures outer space. To solve the weak form of the Poisson/Laplace equation, we use Gauss-Legendre-Lobatto (GLL) quadrature in spectral elements inside the domain of interest. Outside the domain, we use Gauss-Radau quadrature in the infinite direction, and GLL quadrature in the other directions. We illustrate the efficiency and accuracy of our method by comparing calculated gravity anomalies for various density heterogeneities with corresponding analytical solutions. Finally, we consider a complex 3-D model of an ore mine, which consists of both positive and negative density anomalies.

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“…Generally, in analyzing the dynamic behavior of three dimensional structures, particularly when considering the soil-structure interaction or structuresoil-water interaction, modeling of continuous soil environment is necessary in order to illustrate the real behavior [1,2]. Dynamic analysis of structures occurs in frequency domain or time domain.…”

Section: Introductionmentioning

confidence: 99%

Application of 2D-infinite beam elements in dynamic analysis of train-track interaction

Zakeri

Xia

2009

J Mech Sci Technol

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Railway structure is a structure with an infinite length for which its modeling is usually carried out by accepting some assumptions for boundary conditions. In practice, there are various methods of modeling by forming equations of motions and dynamic analysis. One of these methods is modeling the railway track by finite element method. Generally in such modeling, a limited length of a track is modeled and executed by implementing some boundary conditions. Assortment of boundary conditions has an effect on dynamic responses. To reduce such effects, usually the length of the track is chosen to such a measure to minimize the dynamic responses of the end points of the track elements to zero. Doing so would cause an increase in the length of the track and hence add to an equation's degrees of freedom, volume of output and prolongation of analysis time. For this reason, a combination of finite elements and infinite beam elements (two end elements) has been proposed for railway track modeling. Also, matrices of mass, damping and stiffness of one infinite element which has been laid on a visco-elastic bed, have been calculated by implementing selected shape functions. Therefore, by applying two infinite beam elements on either side of the model, a railway track is formed like a beam on an elastic bed which creates the possibility of eliminating the boundary condition effects.

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A novel formulation of infinite elements for static analysis

Cited by 17 publications

References 11 publications

Development of infinite elements for simulation of unbounded media

Development of infinite elements for simulation of unbounded media

Spectral-infinite-element simulations of gravity anomalies

Application of 2D-infinite beam elements in dynamic analysis of train-track interaction

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