Abstract To describe the physical fields of the V-notch structure accurately, the structure is first divided into two parts, the notch tip sector containing singular stress field and the non-singular remained part. A twofold procedure is then carried out to obtain the stress intensity factors: (I) the asymptotic expansions are introduced to describe physical fields of the singular region and transform the elastic governing equation to the characteristic ordinary differential equations. The interpolating matrix method is then implemented to provide stress singular orders and related characteristic angular functions of this singular area. (II) The boundary integral equation for the left part is then discretized by the non-uniform rational B-splines (NURBS) elements and is solved under the isogeometric framework. The amplitudes of the asymptotic expansions in process (I) are calculated by coupling procedures (I) and (II) through utilizing the interfacial continuity conditions. The stress intensity factors are finally obtained and compared with the referenced results for both symmetric and inclined V-notch structures. Benefiting from the isogeometric analysis, satisfied results can be provided by discretizing the artificial arc boundary between the singular and non-singular parts with fewer NURBS elements. This method can also be integrated with the preprocessing of computer aided design (CAD) conveniently.

Abstract The traditional method of fundamental solutions (MFS) based on the “global” boundary discretization leads to dense and non-symmetric coefficient matrices that, although smaller in sizes, require huge computational cost to compute the system of equations using direct solvers. In this study, a localized version of the MFS (LMFS) is proposed for the large-scale modeling of two-dimensional (2D) elasticity problems. In the LMFS, the whole analyzed domain can be divided into small subdomains ...

Abstract We describe a local iterative corrector scheme that significantly improves the accuracy of the multiscale finite element method (MsFEM). Our technique is based on the definition of a local corrector problem for each multiscale basis function that is driven by the residual of the previous multiscale solution. Each corrector problem results in a local corrector solution that improves the accuracy of the corresponding multiscale basis function at element interfaces. We cast the strategy of...

Abstract In this paper, a new singular element is presented to evaluate stress intensity factors of V-shaped notches subjected to mixed-mode load. The proposed element takes into account special variation of displacements in the vicinity of the notch tip. The singularity at notch tip is variable unlike the crack problem where the displacements around the crack tip have variation of square root of r. In the proposed method, special basis functions considering the singularity order at notch tip ar...

Abstract An expanding element is obtained by adding virtual nodes along the perimeter of the traditional discontinuous element. There are two kinds of shape functions in the expanding element: (i) the raw shape function, i.e. shape function of the original discontinuous element, involving only inner nodes; (ii) the fine shape function, which involves all the nodes including inner nodes and the newly added virtual nodes. The polynomial order of fine shape functions of the expanding elements incre...

Abstract A double-layer interpolation method (DLIM) is proposed to improve the performance of the boundary element method (BEM). In the DLIM, the nodes of an element are sorted into two groups: (i) nodes inside the element, called source nodes, and (ii) nodes on the vertices and edges of the element, called virtual nodes. With only source nodes, the element becomes a conventional discontinuous element. Taking into account both source and virtual nodes, the element becomes a standard continuous e...

Abstract We present a novel numerical method to simulate crack growth in 3D, directly from the Computer-Aided Design (CAD) geometry of the component, without any mesh generation. The method is an isogeometric boundary element method (IGABEM) based on non-uniform rational B-splines (NURBS). NURBS basis functions are used for the domain and crack representation as well as to approximate the physical quantities involved in the simulations. A stable quadrature scheme for singular integration is prop...

#2Shenyu Ge(Hefei University of Technology)H-Index: 1

Last. Zhongrong Niu(Hefei University of Technology)H-Index: 11

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Abstract The accuracy of thermal stresses at internal points by the conventional boundary element method becomes deteriorate when the points are approaching to the boundary due to the inaccuracy of the calculation of nearly singular integrals by the Gaussian integration. Herein, a thermal stress natural boundary integral equation is proposed, in which the nearly hyper-strongly singular integral is reduced to a nearly strongly singular one and then dealt by the regularization method. Thus, it can...

#1S. L. Yao(Hefei University of Technology)H-Index: 1

#2C. Z. Cheng(Hefei University of Technology)H-Index: 1

Last. Naman Recho(Blaise Pascal University)H-Index: 14

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ABSTRACTThe stress field and heat flux singularities at the vertex of two-dimensional (2D) and three-dimensional (3D) V-notches are, respectively, investigated. By introducing typical terms in the series asymptotic expansions of displacement and temperature fields near the notch tip, the thermoelastic governing equations and radial boundary conditions of a V-notched structure are transformed into characteristic ordinary differential equations with respect to the singular order. These equations c...

#1M. P. Savruk(NASU: National Academy of Sciences of Ukraine)H-Index: 7

#1M. P. Savruk(NAS: National Academy of Sciences)H-Index: 8

Last. Andrzej Kazberuk(Bialystok University of Technology)H-Index: 2

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Abstract The problem of stress concentration in elastic orthotropic and quasi-orthotropic bodies weakened by sharp and rounded V-notches under symmetrical load (mode I) was considered. Particular attention was paid to the method of unified approach to problems of stress distribution around such concentrators, according to which the stress intensity factors for sharp notches are calculated on the bases of stress concentration factor at the vertex of corresponding V-notch rounded with small radius...

Last. Tinh Quoc Bui(TITech: Tokyo Institute of Technology)H-Index: 54

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Abstract The objective of this article is to simulate crack growth of complex Mindlin–Reissner plates by developing an adaptive multi-patch extended isogeometric analysis (XIGA). Nitsche’s method is used to treat continuity between multi-patches or the coupling of non-conforming meshes, exactly describing the geometry of complex plates. The computational meshes in XIGA are independent of the cracks by introducing some enrichment functions into the displacement approximation based on the partitio...

#1Yuxuan Zhang(Tianjin University of Science and Technology)

#2Xuecheng Ping(Tianjin University of Science and Technology)

Last. Mengcheng Chen(ECJTU: East China Jiaotong University)

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Defects in terms of three-dimensional voids are commonly encountered at bi-material interfaces. In the current study, the singular stress field near the circumferential corner line of a three-dimensional axisymmetric interfacial void is analyzed using our newly established singular interface edge elements. Under the premise that $\rho {\ll }R , the proposed singular element method does not depend on the size of the element; thereby, it is not necessary to use refined elements at the interface...

Last. Fei Qin(Beijing University of Technology)H-Index: 9

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Different from Neuber’s rule or Glinka’s energy method which are always adopted to characterize the notch tip field under elastoplastic condition, in this paper the strain energy rate density (SERD) rule is used for viscoplastic materials. In particular, based on the definition of generalized notch stress intensity factor (G-NSIF) for sharp V-notch in viscoplastic solids, the concept of SERD for sharp V-notch in viscoplastic solids is presented. Subsequently, by taking as a starting point the SE...

Last. Huanlin Zhou(Hefei University of Technology)H-Index: 15

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Abstract In the steady state heat conduction problem, the heat flux could be infinite at the re-entrant corner, at the point where the boundary condition is discontinuous, or at the place where the material properties are changing abruptly. The conventional numerical methods, such as the finite element method (FEM) and the boundary element method (BEM), have difficulties in analyzing the singular heat flux field. Herein, a new singular element employed in the boundary integral equation is develo...