Discontinuous crack-tip elements: Application to 3D boundary element method

Deng

Int. J. Comput. Methods

et al. 2015

A boundary condition (BC) related mixed element method is presented to address the corner problem in boundary element method (BEM) for 3D elastostatic problems. In this method, noncontinuous elements (NCEs) are only used at the displacement-prescribed corners/edges and continuous elements (CEs) in other places, which can decrease the degrees of freedom (DOFs) compared to the approach using NCEs at all corners/edges. Moreover, an automatic generation algorithm of BC related mixed linear triangular elements is implemented with the help of 3D modeling engine ACIS, and the boundary element analysis (BEA) is integrated into CAD systems. In order to solve large scale problems, the fast multipole BEM (FMBEM) with mixed elements is proposed and utilized in the BEA. The examples show that the node shift scheme adopting 1/4 is optimal and the BEM/FMBEM using mixed elements can produce more accurate results by only increasing a small number of DOFs.

Section: Examplementioning

confidence: 99%

Boundary Condition Related Mixed Boundary Element and its Application in FMBEM for 3D Elastostatic Problem

Deng

Int. J. Comput. Methods

et al. 2015

Mathematical Problems in Engineering

“…Many special crack front elements have been defined to capture the asymptotic behavior of a specific node in the FEM [1]. In the 3D BEM, however, the available crack front elements are only of quadrilateral type, such as 8-node crack front elements proposed by Mi and Aliabadi [5], 9-node crack front elements in the pioneering work of Li et al [6], and also crack front elements in the work of Pan and Yuan [7]. e crack front elements of the triangular type have not been found by authors [8,9].…”

Section: Introductionmentioning

confidence: 99%

A Generation of Special Triangular Boundary Element Shape Functions for 3D Crack Problems

Xie

Zhou

2020

This paper focuses on tackling the two drawbacks of the dual boundary element method (DBEM) when solving crack problems with a discontinuous triangular element: low accuracy of the calculation of integrals with singularity and crack front element must be utilized to model the square-root property of displacement. In order to calculate the integrals with higher order singularity, the triangular elements are segmented into several subregions which consist of subtriangles and subpolygons. The singular integrals in those subtriangles are handled by the singularity subtraction technique in the integration space and can be regularized and accurately calculated. For the nearly singular integrals in those subpolygons, the element subdivision technique is employed to improve the calculation accuracy. In addition, considering the location of the crack front in the element, special crack front elements are constructed based on a 6-node discontinuous triangular element, in which the displacement extrapolation method is introduced to obtain the stress intensity factors (SIFs) without consideration of orthogonalization of the crack front mesh. Several numerical results are investigated to fully verify the validation of the presented approach.

Computers, Materials &Amp; Continua

“…For the crack surfaces, the relative crack opening displacement (RCOD) [Ammons and Vable (1996); Chang and Mear (1996)] or the tangential derivative of the RCOD [Xie, Zhang, Huang et al (2013)] can be chosen as unknowns therefore the traction boundary integral equation only needs to be considered on either side of crack surfaces. Recently, Mi et al [Mi and Aliabadi (1994)] proposed a promising single-domain method named direct traction boundary integral method for three-dimensional crack problems. In this study, a direct traction boundary integral method for two-dimensional crack problems is presented as a complementary formulation.…”

Section: Introductionmentioning

confidence: 99%

A Straightforward Direct Traction Boundary Integral Method for Two-Dimensional Crack Problems Simulation of Linear Elastic Materials

Zhang¹,

Yang²,

Wu³

et al. 2019

This paper presents a direct traction boundary integral equation method (DTBIEM) for two-dimensional crack problems of materials. The traction boundary integral equation was collocated on both the external boundary and either side of the crack surfaces. The displacements and tractions were used as unknowns on the external boundary, while the relative crack opening displacement (RCOD) was chosen as unknowns on either side of crack surfaces to keep the single-domain merit. Only one side of the crack surfaces was concerned and needed to be discretized, thus the proposed method resulted in a smaller system of algebraic equations compared with the dual boundary element method (DBEM). A new set of crack-tip shape functions was constructed to represent the strain field singularity exactly, and the SIFs were evaluated by the extrapolation of the RCOD. Numerical examples for both straight and curved cracks are given to validate the accuracy and efficiency of the presented method.