A quadratic formulation for two-dimensional elastoplastic analysis using the boundary integral equation method

Lee, K H; Fenner, R. T.

doi:10.1243/03093247v213159

Cited by 16 publications

(7 citation statements)

References 25 publications

(7 reference statements)

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“…Here only the basic formulation is outlined in its discretised form using quadratic elements in the initial strain formulation [3,4] where P a is the node at which the integral equation is written, P dðb;cÞ denotes the cth node of the bth boundary element, and P gðe;f Þ denotes the f th node of the eth interior element. s b and s e are the bth boundary and eth interior elements respectively.…”

Section: Two Dimensional Elastoplastic Analysis With Biementioning

confidence: 99%

“…s b and s e are the bth boundary and eth interior elements respectively. The discretised integral equation (1), if applied to every boundary node in both the cartesian coordinate directions can be written in matrix form For the initial strain formulation defined in (2) the plastic strain rates are obtained from the following flow rules (see also [3][4][5]…”

Section: Two Dimensional Elastoplastic Analysis With Biementioning

confidence: 99%

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Elastoplastic analysis with adaptive boundary element method

Astrinidis

Fenner

Tsamasphyros³

2004

Computational Mechanics

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The purpose of this paper is to examine the capabilities provided by an iterative -adaptive mesh redesign method developed for the Boundary Integral Equation (BIE) method for elastoplastic analysis.In previous papers [1, 2] the fundamentals of the method where presented in elasticity and elastoplasticity. It was shown there that the adaptive procedure converges fast and is specially developed to reveal the ability of the BIE to provide high accuracy with very economic deployment of quadratic boundary and interior elements. In this paper the results of method applied on particular problems in elastoplasticity are compared against well known experimental solutions. The ability of the adaptive scheme to converge fast is demonstrated, but more important finding is the fact that the progressive refinement of the discretisation gives more insight into the physical problem.

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Section: Two Dimensional Elastoplastic Analysis With Biementioning

confidence: 99%

Section: Two Dimensional Elastoplastic Analysis With Biementioning

confidence: 99%

Elastoplastic analysis with adaptive boundary element method

Astrinidis

Fenner

Tsamasphyros³

2004

Computational Mechanics

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“…The particular solution for stress can be obtained by differentiating the displacement functions to obtain the strain functions and then substituting in equation (13). The particular solution for the traction rate is obtained from the stress functions as follows:…”

Section: ::\mentioning

confidence: 99%

“…The elasto-plastic BE formulation was discussed in detail by Lee [11] who presented an accelerated convergence procedure using an initial strain approach and quadratic elements. Some authors, such as Tan and Lee [12] and Lee and Fenner [13], used this approach to analyse practical problems such as fracture problems…”

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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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“…More often than not the algorithms are 'explicit' methods as described in detail by Telles [13] and Banerjee [14]. These solution algorithms can be roughly divided into two groups, i.e., the initial strain approach [2,3,7,8,[15][16][17] and the initial stress approach [9,10,[18][19][20][21][22][23].…”

Section: Introductionmentioning

confidence: 99%