Elastoplastic analysis with adaptive boundary element method

Astrinidis, E.; Fenner, R. T.; Tsamasphyros, G.

doi:10.1007/s00466-003-0519-2

Cited by 4 publications

(4 citation statements)

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“…This example was solved for a load 2 / 0 = 0.91. The distribution of the tension stress y along the x-axis is shown in Figure 4, together with the adaptive BEM solution by Astrinidis et al [27], the particular integral BEM solution by Henry and Banerjee [28] and the experimental results [29]. Excellent agreement is obtained among the three BEM solutions.…”

Section: Iterative Processmentioning

confidence: 60%

Fast multipole boundary element analysis of two‐dimensional elastoplastic problems

Wang¹,

Yao²

2006

Commun. Numer. Meth. Engng.

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SUMMARYThis paper presents a fast multipole boundary element method (BEM) for the analysis of two-dimensional elastoplastic problems. An incremental iterative technique based on the initial strain approach is employed to solve the nonlinear equations, and the fast multipole method (FMM) is introduced to achieve higher runtime and memory storage efficiency. Both of the boundary integrals and domain integrals are calculated by recursive operations on a quad-tree structure without explicitly forming the coefficient matrix. Combining multipole expansions with local expansions, computational complexity and memory requirement of the matrix-vector multiplication are both reduced to O(N ), where N is the number of degrees of freedom (DOFs). The accuracy and efficiency of the proposed scheme are demonstrated by several numerical examples.

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Section: Iterative Processmentioning

confidence: 60%

Fast multipole boundary element analysis of two‐dimensional elastoplastic problems

Wang¹,

Yao²

2006

Commun. Numer. Meth. Engng.

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“…So the simple method to eliminate nearly singular integrals is adaptive integration technique based on element sub-division. So far, adaptive tactics have been widely used in tackling nearly singular integrals arising in many boundary element analyses of engineering problems, such as potential problems [34,35], contact problems [36], plate bending [37], thermoelastic problems [38], elastoplastic problems [39,40], etc. E. Kita and N. Kamiya [41] gave a comprehensive review on adaptive mesh refinement schemes for the BEM.…”

Section: Adaptive Integration Methods Based On Sub-division Technique mentioning

confidence: 99%

Adaptive Integration Method Based on Sub-Division Technique for Nearly Singular Integrals in Near-Field Acoustics Boundary Element Analysis

Chen

2014

Journal of Low Frequency Noise, Vibration and Active Control

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The aim of this paper is to present an efficient adaptive integration technique to perform near-field acoustics boundary element analysis, in which nearly singular integrals will be encountered as the source point in integral equation close to the boundary of acoustic domain. At this time the integrand varies sharply, so the conventional Gaussian quadrature becomes inefficient or even inaccurate. In this paper, an adaptive integration technique is proposed, which determines the required Gauss orders and the number of sub-elements according to the specified integration accuracy and the relative position from the source point in integral equation to the element under integration. By introducing the Jacobian of the sub-element, nearly singular integrals can be calculated numerically without the nodal values of sub-elements. Two numerical examples are presented to demonstrate the efficiency and accuracy of the proposed approach.

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“…More recently, this variable transformation method is extended to three-dimensional boundary element method [15]. Apart from the above methods, adaptive tactics have been widely used in tackling nearly singular integrals arising in many boundary element analyses of engineering problems, such as potential problem [16,17], contact problems [18], plate bending [19], thermoelastic problems [20], elasto-plastic problems [21,22], etc. Kita and Kamiya [23] gave a comprehensive review on adaptive mesh refinement schemes for boundary element methods.…”

Section: Introductionmentioning

confidence: 99%

Adaptive integration technique for nearly singular integrals in near-field acoustics boundary element analysis

Qu¹,

Chen²,

Bai³

et al. 2013

Boundary Elements and Other Mesh Reduction Methods XXXVI

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The aim of this paper is to present an efficient adaptive integration technique to perform near-field acoustics boundary element analysis, in which nearly singular integrals will be encountered as the source point in integral equations is close to the boundary of the acoustic domain. At this time the integrand varies sharply, so the conventional Gaussian quadrature becomes inefficient or even inaccurate. In this paper, an adaptive integration technique is proposed, which determines required Gauss orders and the number of sub-elements according to the specified integration accuracy and the relative position from the source point in integral equations to the element under integration. Two numerical examples have been presented to demonstrate the efficiency and accuracy of the proposed approach.

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Elastoplastic analysis with adaptive boundary element method

Cited by 4 publications

References 0 publications

Fast multipole boundary element analysis of two‐dimensional elastoplastic problems

Fast multipole boundary element analysis of two‐dimensional elastoplastic problems

Adaptive Integration Method Based on Sub-Division Technique for Nearly Singular Integrals in Near-Field Acoustics Boundary Element Analysis

Adaptive integration technique for nearly singular integrals in near-field acoustics boundary element analysis

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