Boundary Integral Formulation of Mass Matrices for Dynamic Analysis

Nardini, Dario; Brebbia, Carlos Alberto

doi:10.1007/978-3-642-82398-5_7

Cited by 27 publications

(13 citation statements)

References 6 publications

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“…It coincides with the origin of the co-ordinate systemx;ŷ;ẑ. The dimensionless radial co-ordinate is measured from the scaling centre along the position vector r =xi +ŷj +ẑk (7) is constant (equal to 1) on the boundary. For bounded (Figures 1 and 3) and unbounded ( Figure 4) media, 06 61 and 16 6∞, respectively, apply.…”

Section: Scaled Boundary Transformation Of Geometrymentioning

confidence: 99%

“…is written as Note that in the scaled boundary ÿnite element method the mass matrix follows from the lowfrequency behaviour of the equation without any additional assumptions. In the boundary element method a mass matrix can be constructed which, however, involves selecting an approximation for the function within the bounded medium [7]. In addition, the mass matrix will not be symmetric.…”

Section: Steady Statementioning

confidence: 99%

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The scaled boundary finite element method—alias consistent infinitesimal finite element cell method—for diffusion

Song¹,

Wolf²

1999

Int. J. Numer. Meth. Engng.

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SUMMARYThe scaled boundary ÿnite element method, alias the consistent inÿnitesimal ÿnite element cell method, is developed starting from the di usion equation. Only the boundary of the medium is discretized with surface ÿnite elements yielding a reduction of the spatial dimension by one. No fundamental solution is necessary, and thus no singular integrals need to be evaluated. Essential and natural boundary conditions on surfaces and conditions on interfaces between di erent materials are enforced exactly without any discretization. The solution of the function in the radial direction is analytical. This method is thus exact in the radial direction and converges to the exact solution in the ÿnite element sense in the circumferential directions. The semianalytical solution inside the domain leads to an e cient procedure to calculate singularities accurately without discretization in the vicinity of the singular point. For a bounded medium symmetric steady-state sti ness and mass matrices with respect to the degrees of freedom on the boundary result without any additional assumption.

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Section: Scaled Boundary Transformation Of Geometrymentioning

confidence: 99%

Section: Steady Statementioning

confidence: 99%

The scaled boundary finite element method—alias consistent infinitesimal finite element cell method—for diffusion

Song¹,

Wolf²

1999

Int. J. Numer. Meth. Engng.

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“…The last one uses the fundamental solutions of elastostatics and steady-state heat conduction, and it results in domain integrals in addition to the boundary integrals. The dual reciprocity BEM has been presented to eliminate the domain integrals by Kögl and Gaul [21,22], in which the dual reciprocity method (DRM) proposed by Nardini and Brebbia [23,24] is recognized as an efficient method to treat the domain integrals. However, the application of DRM to deal with domain integrals in the boundary-domain integral equations of the linear thermoelasticity requires particular solutions, whose construction is restricted to the approximation functions chosen.…”

Section: Introductionmentioning

confidence: 99%

Radial integration BEM for dynamic coupled thermoelastic analysis under thermal shock loading

Gao

Zheng

Yang

et al. 2015

Computers & Structures

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“…For inhomogeneous problems, the domain integration is inevitable. Dual reciprocity method (DRM) which was proposed to transform the domain integration to the boundary was first proposed by Nardini and Brebbia [17] and Wrobel and Brebbia [19], and some further researches of DRM were done by Agnantiaris et al [1,2]. Furthermore, in order to overcome the drawbacks of DRM, the analog equation method (AEM) [7,8] and the meshless analog equation method (MAEM) [9] are proposed, which can deal all problems and in which cases DRM can not handle.…”

Section: Introductionmentioning

confidence: 99%

A dual reciprocity hybrid radial boundary node method based on radial point interpolation method

Yan¹,

Feng²,

Zhou³

2010

Comput Mech

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A novel truly meshless method called dual reciprocity hybrid radial boundary node method (DHRBNM) is developed in present, which combines dual reciprocity method (DRM), hybrid boundary node method (HBNM) and radial point interpolation method (RPIM). Compared to the dual reciprocity hybrid boundary node method (DHBNM), RPIM is exploited to replace the moving least square in DHRBNM, unlike HBNM, the shape function obtained by present method has the delta function property, so the boundary conditions can be applied directly and easily, and computational expense is greatly reduced. In order to get the interpolation property of different basis function in DRM, different approximate functions are applied in DRM for comparison, and the accuracy and efficiency of them are discussed. Besides, RPIM is also exploited in DRM, which can greatly improve the accuracy of present method. Moreover, the accuracy of DRM is greatly influenced by the nodes number and their location, hence, some examples are investigated to show that the internal node number is equal to boundary node number and they are arranged parallel to the high gradient direction of the problem are the best choice. Finally, DHBNM is applied for comparison and some selected numerical examples are given to illustrate that the present method is efficient and less computational expense than that of DHBNM.

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Boundary Integral Formulation of Mass Matrices for Dynamic Analysis

Cited by 27 publications

References 6 publications

The scaled boundary finite element method—alias consistent infinitesimal finite element cell method—for diffusion

The scaled boundary finite element method—alias consistent infinitesimal finite element cell method—for diffusion

Radial integration BEM for dynamic coupled thermoelastic analysis under thermal shock loading

A dual reciprocity hybrid radial boundary node method based on radial point interpolation method

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