Symmetric boundary element method versus finite element method

Panzeca, T.; Cucco, F.; Terravecchia, S.

doi:10.1016/s0045-7825(02)00239-6

Cited by 26 publications

(22 citation statements)

References 7 publications

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“…of the displacements and the tractions the domain integrals, caused by inelastic actions, are substituted by boundary ones 186 T. PANZECA, S. TERRAVECCHIA AND L. ZITO so that a subsequent integration, performed as a Galerkin weighting process, makes it possible to evaluate the load coefficients. These terms were obtained in closed form and implemented in the Karnak.sGbem calculus code [19] according to a strategy that works in the substructuring approach [20,21]. The strategy for evaluation in closed form was shown by Terravecchia [22].…”

Section: D Sbem Analysis With Domain Inelastic Actions 185mentioning

confidence: 99%

“…The latter are considered zone-wise constant in both examples. The use of the multi-domain approach, developed by some of the present authors [20,21] and implemented in the Karnak.sGbem calculus code [19], contemplates the case of inelastic actions transferred onto the boundary in order to overcome the related computation of the domain integrals. Among the main characteristics of the multi-domain strategy, the analysis performed through the displacement method via SBEM allows the coexistence of very small substructures and of substructures having big dimensions.…”

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Computational aspects in 2D SBEM analysis with domain inelastic actions

Panzeca

Terravecchia

Zito

2009

Numerical Meth Engineering

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The Symmetric Boundary Element Method, applied to structures subjected to temperature and inelastic actions, shows singular domain integrals.\ud In the present paper the strong singularity involved in the domain integrals of the stresses and tractions is removed and, by means of a limiting operation, this traction is evaluated on the boundary. First the weakly singular domain integral in the Somigliana Identity of the displacements is regularized and the singular integral is transformed into a boundary one using the Radial Integration Method; subsequently, using the differential operator applied to the displacement field, the Somigliana Identity of the tractions inside the body is obtained and through a limit operation its expression is evaluated on the boundary. The latter operation makes it possible to substitute the strongly singular domain integral in a strongly singular boundary one, defined as a Cauchy Principal Value, with which the related free term is associated. The expressions thus obtained for the displacements and the tractions, in which domain integrals are substituted by boundary integrals, were utilized in the Galerkin approach, for the evaluation in closed form of the load coefficients connected to domain inelastic actions.\ud This strategy makes it possible to evaluate the load coefficients avoiding considerable difficulties due to the geometry of the solid analyzed; the obtained coefficients were implemented in the Karnak.sGbem calculus code

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Section: D Sbem Analysis With Domain Inelastic Actions 185mentioning

confidence: 99%

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confidence: 99%

Computational aspects in 2D SBEM analysis with domain inelastic actions

Panzeca

Terravecchia

Zito

2009

Numerical Meth Engineering

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“…The symmetric formulation is motivated by the high efficiency achieved within classical elasticity by the method in [9] with regard to the techniques used to eliminate the singularities of the fundamental solutions, the evaluation of the coefficients of the solving system and the computational procedures characterized by great implementation simplicity. This has already led to the birth of the computer code Karnak sGbem [10] operating in the classical elasticity.…”

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Strain gradient elasticity within the symmetric BEM formulation

Terravecchia¹,

Panzeca²,

Polizzotto³

2014

Frattura Ed Integrità Strutturale

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ABSTRACT. The symmetric Galerkin Boundary Element Method is used to address a class of strain gradient elastic materials featured by a free energy function of the (classical) strain and of its (first) gradient. With respect to the classical elasticity, additional response variables intervene, such as the normal derivative of the displacements on the boundary, and the work-coniugate double tractions. The fundamental solutions -featuring a fourth order partial differential equations (PDEs) system -exhibit singularities which in 2D may be of the order 4 1/ r . New techniques are developed, which allow the elimination of most of the latter singularities. The present paper has to be intended as a research communication wherein some results, being elaborated within a more general paper [1], are reported.

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“…This strategy shows the advantage of providing the multiplier with very low CPU times, in comparison with the incremental elastoplastic analysis, presented here, in which however much other information regarding plastic collapse may be obtained.Even though the formulation via SGBEM, applied to plasticity problems, provides a high level of knowledge, computational difficulties have reduced the application of the method in practical engineering problems. Indeed, in literature there are very few applications, often utilizing simplified procedures to obtain the elastoplastic response.In the present paper, a multidomain SGBEM strategy, based on an initial strain approach for two-dimensional body analysis in the hypothesis of elastic-perfectly plastic behaviour, von Mises materials, associated flow and plane strain condition, is shown.Let us start from the discretization of the domain through a substructuring used following an SGBEM multidomain strategy [11,12] for both the substructures (called macro-elements), generally of large dimensions, having merely elastic behaviour and the substructures (called bem-elements or bem-e), generally having very small dimensions, used in the elastoplastic phenomenon. Then, let us utilize the displacement method, introduced by Panzeca et al [11], by imposing the regularity (or coupling) conditions at the interface boundaries among substructures, in which the unknowns are the interface nodal displacements.…”

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Incremental elastoplastic analysis for active macro‐zones

Zito

Cucco

Parlavecchio

et al. 2012

Numerical Meth Engineering

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SUMMARY In this paper a strategy to perform incremental elastoplastic analysis using the symmetric Galerkin boundary element method for multidomain type problems is shown. The discretization of the body is performed through substructures, distinguishing the bem‐elements characterizing the so‐called active macro‐zones, where the plastic consistency condition may be violated, and the macro‐elements having elastic behaviour only. Incremental analysis uses the well‐known concept of self‐equilibrium stress field here shown in a discrete form through the introduction of the influence matrix (self‐stress matrix). The nonlinear analysis does not use updating of the elastic response inside each plastic loop, but at the end of the load increment only. This is possible by using the self‐stress matrix, both, in the predictor phase, for computing the stress caused by the stored plastic strains, and, in the corrector phase, for solving a nonlinear global system, which provides the elastoplastic solution of the active macro‐zones. The use of active macro‐zones gives rise to a nonlocal and path‐independent approach, which is characterized by a notable reduction of the number of plastic iterations. The proposed strategy shows several computational advantages as shown by the results of some numerical tests, reported at the end of this paper. These tests were performed using the Karnak.sGbem code, in which the present procedure was introduced as an additional module.Copyright © 2012 John Wiley & Sons, Ltd.

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Symmetric boundary element method versus finite element method

Cited by 26 publications

References 7 publications

Computational aspects in 2D SBEM analysis with domain inelastic actions

Computational aspects in 2D SBEM analysis with domain inelastic actions

Strain gradient elasticity within the symmetric BEM formulation

Incremental elastoplastic analysis for active macro‐zones

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