A Review of Boundary Element Quadratic Formulations in Elastoplastic Stress Analysis Problems

Gün, Halit; Becker, A.A.

doi:10.4203/ccp.55.2.2

Cited by 3 publications

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“…The second part of the first example consists of a square plate subjected to uniform tension in the x-direction [24]. The geometry and boundary conditions are presented in Fig.…”

Section: Uniaxial Tensile Stressmentioning

confidence: 99%

Parametric integral equation system (PIES) for 2D elastoplastic analysis

Bołtuć

2016

Engineering Analysis with Boundary Elements

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“…The second part of the first example consists of a square plate subjected to uniform tension in the x-direction [24]. The geometry and boundary conditions are presented in Fig.…”

Section: Uniaxial Tensile Stressmentioning

confidence: 99%

Parametric integral equation system (PIES) for 2D elastoplastic analysis

Bołtuć

2016

Engineering Analysis with Boundary Elements

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“…Example This example consists of a square plate subjected to uniform tension in the x‐direction . The geometry and boundary conditions are presented in Figure .…”

Section: Examplesmentioning

confidence: 99%

“…As mentioned earlier, points ı are not responsible for shape in 2D; therefore, their precise definition is not required. By moving control points of a rectangular bicubic surface (35), we can create different shapes. An example of such modeling is shown in Figure 6(a,b).…”

Section: Efficiency Of Bicubic Surfaces In Modeling Plastic Regionsmentioning

confidence: 99%

Modification of the boundary integral equation for the Navier–Lamé equations in 2D elastoplastic problems and its numerical solving

Zieniuk

Bołtuć

2017

Numerical Meth Engineering

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Summary The paper presents the generalization of the modification of classical boundary integral equation and obtaining parametric integral equation system for 2D elastoplastic problems. The modification was made to obtain such equations for which numerical solving does not require application of finite or boundary elements. This was achieved through the use of curves and surfaces for modeling introduced at the stage of analytical modification of the classic boundary integral equation. For approximation of plastic strains the Lagrange polynomials with various number and arrangement of interpolation nodes were used. Reliability of the modification was verified on examples with analytical solutions. Copyright © 2016 John Wiley & Sons, Ltd.

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“…A robust incremental iterative procedure and the details of the evaluation of the plastic strain rates and the initial plastic stress rates for both approaches are presented by Gun [29].…”

Section: ::\mentioning

confidence: 99%

“…Full details of the evaluation of stress and strain rates at boundary and interior nodes are presented by Gun [29] It is well known that the solution of partial differential equations (e.g [30]) can be obtained using a complementary function (CF) and a particular integral (P L) Therefore, the displacement in the governing differential equations can be defined as a combination of a complementary function and a particular integral, as follows:…”

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confidence: 99%

Boundary Emenet Formulation in Elastoplastic Stress Anaysis

Gün

Becker

1998

MCA

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This paper presents a review of different elasto-plastic Boundary Element (BE) formulations \\ith particular emphasis on two main approaches; the initial strain displaccmcnt-gradient approach with its modeling of the partial or full interior domain, and the particular integral approach which can be applied exclusively to the surface avoiding any modeling interior. The initial strain formulation is implemcntcd in a computer program using two-dimensional isoparametric quatratic elements to discretise either the complete intcrior domain or only the part associated with the plastic region. The BE solutions are shown to bc in good agreement with analytical and Finite Elcment (FE) solutions.The Boundary Element (BE) method is well established as an accurate numerical tool particularly well suited for linear elastic problems. Its extension to non-linear analysis such as elasto-plasticity, however, is not widespread and in many formulation the interior of the solution domain has to be discretized, thus losing the main BE advantage of surfaceonly modeling.An outline of different elasto-plastic BE formulation is presented in this paper with particular emphasis on two main approaches; (i) the initial strain displacement-gradient approach in which interior discretization is required either for whole domain or only in the region of expected plastic behaviour, and (ii) the particular integral approach in which interior modeling is not required and can be applied exclusively to the surface The analytical and numerical implementation of both approaches are presented. Details of a quadratic BE formulation for the displacement-gradient approach are presented for two-dimensional elasto-plastic problems in which three-node isoparametric quadratic elements are used to model boundary and eight-node isoparametric quadrilateral quadratic elements are used to model the interior domain. The values of stress and strain rates at interior nodes are calculated via the numerical differentiation of the displacement rates in an element-wise manner; an approach similar to that used in FE formulation. Details of the numerical implementation algorithm which uses load incrementation and an iterative procedure are presented To asses the accuracy of the BE formulation, the initial strain displacement-gradient BE formulation is implemented in a computer program and applied to some practical problems. The problems include a square subjected to uniform tension, and a thick cylinder under internal pressure. The BE solutions are compared with the corresponding FE solutions and exact or experimental solutions.The first elasto-plastic BE formulation presented by Swedlow and Cruse [1] was based on a direct analytical formulation.Riccardella [2] presented the initial strain formulation based

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A Review of Boundary Element Quadratic Formulations in Elastoplastic Stress Analysis Problems

Cited by 3 publications

References 0 publications

Parametric integral equation system (PIES) for 2D elastoplastic analysis

Parametric integral equation system (PIES) for 2D elastoplastic analysis

Modification of the boundary integral equation for the Navier–Lamé equations in 2D elastoplastic problems and its numerical solving

Boundary Emenet Formulation in Elastoplastic Stress Anaysis

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