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Debabrata Biswas - One of the best experts on this subject based on the ideXlab platform.
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shielding effects in random large area Field emitters the Field enhancement factor distribution and current calculation
Physics of Plasmas, 2018Co-Authors: Rashbihari Rudra, Debabrata BiswasAbstract:A finite-size uniform random distribution of vertically aligned Field emitters on a planar surface is studied under the assumption that the Asymptotic Field is uniform and parallel to the emitter axis. A formula for Field enhancement factor is first derived for a 2-emitter system and this is then generalized for N-emitters placed arbitrarily (line, array, or random). It is found that geometric effects dominate the shielding of Field lines. The distribution of Field enhancement factor for a uniform random distribution of emitter locations is found to be closely approximated by an extreme value (Gumbel-minimum) distribution when the mean separation is greater than the emitter height but is better approximated by a Gaussian for mean separations close to the emitter height. It is shown that these distributions can be used to accurately predict the current emitted from a large area Field emitter.A finite-size uniform random distribution of vertically aligned Field emitters on a planar surface is studied under the assumption that the Asymptotic Field is uniform and parallel to the emitter axis. A formula for Field enhancement factor is first derived for a 2-emitter system and this is then generalized for N-emitters placed arbitrarily (line, array, or random). It is found that geometric effects dominate the shielding of Field lines. The distribution of Field enhancement factor for a uniform random distribution of emitter locations is found to be closely approximated by an extreme value (Gumbel-minimum) distribution when the mean separation is greater than the emitter height but is better approximated by a Gaussian for mean separations close to the emitter height. It is shown that these distributions can be used to accurately predict the current emitted from a large area Field emitter.
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shielding effects in random large area Field emitters the Field enhancement factor distribution and current calculation
Physics of Plasmas, 2018Co-Authors: Debabrata Biswas, Rashbihari RudraAbstract:A finite-size uniform random distribution of vertically aligned Field emitters on a planar surface is studied under the assumption that the Asymptotic Field is uniform and parallel to the emitter axis. A formula for Field enhancement factor is first derived for a 2-emitter system and this is then generalized for N-emitters placed arbitrarily (line, array, or random). It is found that geometric effects dominate the shielding of Field lines. The distribution of Field enhancement factor for a uniform random distribution of emitter locations is found to be closely approximated by an extreme value (Gumbel-minimum) distribution when the mean separation is greater than the emitter height but is better approximated by a Gaussian for mean separations close to the emitter height. It is shown that these distributions can be used to accurately predict the current emitted from a large area Field emitter.
Fei Yan - One of the best experts on this subject based on the ideXlab platform.
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continuous discontinuous hybrid boundary node method for frictional contact problems
Engineering Analysis With Boundary Elements, 2018Co-Authors: Bing-di Zhong, Fei YanAbstract:Abstract This paper presents a continuous–discontinuous hybrid boundary node method for frictional contact problems. In this method, the outer and internal boundaries are divided into several individual segments, for a continuous segment on outer boundary, the radial point interpolation method (RPIM) is employed for shape function construction, for discontinuous segments, the enriched discontinuous basis functions combined with RPIM are developed, in order to reflect the local Field property of displacement and stress around crack tip, different basis functions for displacement and traction are developed for shape function construction on discontinuous segments individually. And the near tip Asymptotic Field functions and Heaviside function are employed for simulating the high gradient of stress Field and discontinuous displacement Field on contact surfaces. Besides a frictional contact theory and complementation detail for the present method is proposed, and some additional equations are developed for frictional contact iteration. Based on above technique and theory, a continuous–discontinuous hybrid boundary node method is proposed for frictional contact problems. Some numerical examples are shown that the present method is effective and can be widely used for some frictional contact engineering.
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a continuous discontinuous hybrid boundary node method for solving stress intensity factor
Engineering Analysis With Boundary Elements, 2017Co-Authors: Fei Yan, Xia-ting FengAbstract:Abstract A novel boundary type meshless method called continuous–discontinuous hybrid boundary node method is proposed in this paper, in which the enriched discontinuous shape function is developed to solve linear elastic crack problems. Firstly, the whole boundary is divided into several individual segments, and variables on each one of those segments are interpolated, respectively. For continuous segments, radial point interpolation method is employed. In regard to discontinuous segments, the enriched discontinuous basis functions combining with radial point interpolation method are developed for simulating the discontinuity of displacement and stress Field on surfaces of crack, and the near tip Asymptotic Field functions are employed for simulating the high gradient of stress Field around crack tip, so that high accuracy and discontinuity property of a crack can be easily described. Stress intensity factors are calculated directly using displacement extrapolation by displacement Field near crack tip. Some numerical examples are shown that the present method is effective and can be widely applied in some practical engineering.
Q. Z. Xiao - One of the best experts on this subject based on the ideXlab platform.
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incremental secant modulus iteration scheme and stress recovery for simulating cracking process in quasi brittle materials using xfem
International Journal for Numerical Methods in Engineering, 2007Co-Authors: Q. Z. Xiao, Bhushan Lal KarihalooAbstract:In this paper, an incremental-secant modulus iteration scheme using the extended/generalized finite element method (XFEM) is proposed for the simulation of cracking process in quasi-brittle materials described by cohesive crack models whose softening law is composed of linear segments. The leading term of the displacement Asymptotic Field at the tip of a cohesive crack (which ensures a displacement discontinuity normal to the cohesive crack face) is used as the enrichment function in the XFEM. The opening component of the same Field is also used as the initial guess opening profile of a newly extended cohesive segment in the simulation of cohesive crack propagation. A statically admissible stress recovery (SAR) technique is extended to cohesive cracks with special treatment of non-homogeneous boundary tractions. The application of locally normalized co-ordinates to eliminate possible ill-conditioning of SAR, and the influence of different weight functions on SAR are also studied. Several mode I cracking problems in quasi-brittle materials with linear and bilinear softening laws are analysed to demonstrate the usefulness of the proposed scheme, as well as the characteristics of global responses and local Fields obtained numerically by the XFEM.
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improving the accuracy of xfem crack tip Fields using higher order quadrature and statically admissible stress recovery
International Journal for Numerical Methods in Engineering, 2006Co-Authors: Q. Z. Xiao, B.l. KarihalooAbstract:This study is concerned with improving the accuracy of crack tip Fields obtained using the extended/generalized finite element method (XFEM). First, the numerical integration of the element stiffness matrices, which guarantees convergence (with quadrature) of not only the regular nodal displacements but also additional degrees of freedom corresponding to the enrichment functions, is studied. As the accuracy of the stresses obtained by direct differentiation of the converged (with quadrature) regular nodal displacements and of the coefficients corresponding to enrichment functions is still not satisfactory, a statically admissible stress recovery (SAR) scheme is introduced. SAR uses basis functions, which meet the equilibrium equations within the domain and the local traction conditions on the boundary, and moving least squares (MLS) to fit the stresses at sampling points (e.g. quadrature points) obtained by the XFEM. Important parameters controlling the accuracy of crack tip Fields using the XFEM and SAR, namely the order of quadrature, the number of retained terms in the crack tip Asymptotic Field, the number of enriched layers and use of arbitrary branch functions, a proper choice of the sampling points in the enriched element and the size of the domain of influence (DOI) of MLS, are investigated. Copyright © 2005 John Wiley & Sons, Ltd.
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xfem for direct evaluation of mixed mode sifs in homogeneous and bi materials
International Journal for Numerical Methods in Engineering, 2004Co-Authors: X Y Liu, Q. Z. Xiao, Bhushan Lal KarihalooAbstract:The extended finite element method (XFEM) is improved to directly evaluate mixed mode stress intensity factors (SIFs) without extra post-processing, for homogeneous materials as well as for bimaterials. This is achieved by enriching the finite element (FE) approximation of the nodes surrounding the crack tip with not only the first term but also the higher order terms of the crack tip Asymptotic Field using a partition of unity method (PUM). The crack faces behind the tip(s) are modelled independently of the mesh by displacement jump functions. The additional coefficients corresponding to the enrichments at the nodes of the elements surrounding the crack tip are forced to be equal by a penalty function method, thus ensuring that the displacement approximations reduce to the actual Asymptotic Fields adjacent to the crack tip. The numerical results so obtained are in excellent agreement with analytical and numerical results available in the literature. Copyright © 2004 John Wiley & Sons, Ltd.
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Direct determination of SIF and higher order terms of mixed mode cracks by a hybrid crack element
International Journal of Fracture, 2004Co-Authors: Q. Z. Xiao, B.l. KarihalooAbstract:Recently, the authors (Karihaloo and Xiao, 2001a-c) extended the hybrid crack element (HCE) originally introduced by Tong et al. (1973) for evaluating the stress intensity factor (SIF) to calculate directly not only the SIF but also the coefficients of the higher order terms of the crack tip Asymptotic Field. Extensive studies have proved the versatility and accuracy of the element for pure mode I problems. This study is to show the versatility of the element for mode II and mixed mode cracks. Accuracy of the SIF and coefficients of higher order terms is validated by comparing with the available results in the literature, or results obtained by the boundary collocation method, which is powerful for relatively simple geometries and loading conditions.
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coefficients of the crack tip Asymptotic Field for wedge splitting specimens
Engineering Fracture Mechanics, 2003Co-Authors: Bhushan Lal Karihaloo, H M Abdalla, Q. Z. XiaoAbstract:The stress intensity factor (SIF) and the coefficients of higher order terms of the crack tip Asymptotic Field of typical wedge splitting specimens with two different loading arrangements are directly computed using a hybrid crack element. Accurate analytical expressions for the first five terms are obtained by fitting the computed data. Numerical results show that the coefficients of terms higher than three are negligibly small, this may explain that the wedge splitting specimen is more stable than other geometries. The first five terms are not sensitive to support conditions. However, for short cracks coefficients of terms, except the SIF, are quite sensitive to the loading arrangement even when the loads are statically equivalent.
Rashbihari Rudra - One of the best experts on this subject based on the ideXlab platform.
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shielding effects in random large area Field emitters the Field enhancement factor distribution and current calculation
Physics of Plasmas, 2018Co-Authors: Rashbihari Rudra, Debabrata BiswasAbstract:A finite-size uniform random distribution of vertically aligned Field emitters on a planar surface is studied under the assumption that the Asymptotic Field is uniform and parallel to the emitter axis. A formula for Field enhancement factor is first derived for a 2-emitter system and this is then generalized for N-emitters placed arbitrarily (line, array, or random). It is found that geometric effects dominate the shielding of Field lines. The distribution of Field enhancement factor for a uniform random distribution of emitter locations is found to be closely approximated by an extreme value (Gumbel-minimum) distribution when the mean separation is greater than the emitter height but is better approximated by a Gaussian for mean separations close to the emitter height. It is shown that these distributions can be used to accurately predict the current emitted from a large area Field emitter.A finite-size uniform random distribution of vertically aligned Field emitters on a planar surface is studied under the assumption that the Asymptotic Field is uniform and parallel to the emitter axis. A formula for Field enhancement factor is first derived for a 2-emitter system and this is then generalized for N-emitters placed arbitrarily (line, array, or random). It is found that geometric effects dominate the shielding of Field lines. The distribution of Field enhancement factor for a uniform random distribution of emitter locations is found to be closely approximated by an extreme value (Gumbel-minimum) distribution when the mean separation is greater than the emitter height but is better approximated by a Gaussian for mean separations close to the emitter height. It is shown that these distributions can be used to accurately predict the current emitted from a large area Field emitter.
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shielding effects in random large area Field emitters the Field enhancement factor distribution and current calculation
Physics of Plasmas, 2018Co-Authors: Debabrata Biswas, Rashbihari RudraAbstract:A finite-size uniform random distribution of vertically aligned Field emitters on a planar surface is studied under the assumption that the Asymptotic Field is uniform and parallel to the emitter axis. A formula for Field enhancement factor is first derived for a 2-emitter system and this is then generalized for N-emitters placed arbitrarily (line, array, or random). It is found that geometric effects dominate the shielding of Field lines. The distribution of Field enhancement factor for a uniform random distribution of emitter locations is found to be closely approximated by an extreme value (Gumbel-minimum) distribution when the mean separation is greater than the emitter height but is better approximated by a Gaussian for mean separations close to the emitter height. It is shown that these distributions can be used to accurately predict the current emitted from a large area Field emitter.
Bhushan Lal Karihaloo - One of the best experts on this subject based on the ideXlab platform.
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incremental secant modulus iteration scheme and stress recovery for simulating cracking process in quasi brittle materials using xfem
International Journal for Numerical Methods in Engineering, 2007Co-Authors: Q. Z. Xiao, Bhushan Lal KarihalooAbstract:In this paper, an incremental-secant modulus iteration scheme using the extended/generalized finite element method (XFEM) is proposed for the simulation of cracking process in quasi-brittle materials described by cohesive crack models whose softening law is composed of linear segments. The leading term of the displacement Asymptotic Field at the tip of a cohesive crack (which ensures a displacement discontinuity normal to the cohesive crack face) is used as the enrichment function in the XFEM. The opening component of the same Field is also used as the initial guess opening profile of a newly extended cohesive segment in the simulation of cohesive crack propagation. A statically admissible stress recovery (SAR) technique is extended to cohesive cracks with special treatment of non-homogeneous boundary tractions. The application of locally normalized co-ordinates to eliminate possible ill-conditioning of SAR, and the influence of different weight functions on SAR are also studied. Several mode I cracking problems in quasi-brittle materials with linear and bilinear softening laws are analysed to demonstrate the usefulness of the proposed scheme, as well as the characteristics of global responses and local Fields obtained numerically by the XFEM.
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xfem for direct evaluation of mixed mode sifs in homogeneous and bi materials
International Journal for Numerical Methods in Engineering, 2004Co-Authors: X Y Liu, Q. Z. Xiao, Bhushan Lal KarihalooAbstract:The extended finite element method (XFEM) is improved to directly evaluate mixed mode stress intensity factors (SIFs) without extra post-processing, for homogeneous materials as well as for bimaterials. This is achieved by enriching the finite element (FE) approximation of the nodes surrounding the crack tip with not only the first term but also the higher order terms of the crack tip Asymptotic Field using a partition of unity method (PUM). The crack faces behind the tip(s) are modelled independently of the mesh by displacement jump functions. The additional coefficients corresponding to the enrichments at the nodes of the elements surrounding the crack tip are forced to be equal by a penalty function method, thus ensuring that the displacement approximations reduce to the actual Asymptotic Fields adjacent to the crack tip. The numerical results so obtained are in excellent agreement with analytical and numerical results available in the literature. Copyright © 2004 John Wiley & Sons, Ltd.
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coefficients of the crack tip Asymptotic Field for wedge splitting specimens
Engineering Fracture Mechanics, 2003Co-Authors: Bhushan Lal Karihaloo, H M Abdalla, Q. Z. XiaoAbstract:The stress intensity factor (SIF) and the coefficients of higher order terms of the crack tip Asymptotic Field of typical wedge splitting specimens with two different loading arrangements are directly computed using a hybrid crack element. Accurate analytical expressions for the first five terms are obtained by fitting the computed data. Numerical results show that the coefficients of terms higher than three are negligibly small, this may explain that the wedge splitting specimen is more stable than other geometries. The first five terms are not sensitive to support conditions. However, for short cracks coefficients of terms, except the SIF, are quite sensitive to the loading arrangement even when the loads are statically equivalent.
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direct evaluation of accurate coefficients of the linear elastic crack tip Asymptotic Field
Fatigue & Fracture of Engineering Materials & Structures, 2003Co-Authors: Q. Z. Xiao, Bhushan Lal KarihalooAbstract:An improvement to the extended finite element method (XFEM) and generalised finite element method (GFEM) is introduced. It enriches the finite element approximation of the crack tip node as well as its surrounding nodes with not only the first term but also the higher order terms of the linear elastic crack tip Asymptotic Field using a partition of unity method (PUM). Numerical results show that together with a reduced quadrature rule to the enriched elements, this approach predicts accurate stress intensity factors (SIFs) directly (i.e. without extra post-processing) after constraining the enriched nodes properly. However, it does not predict accurately the coefficients of the higher order terms. For that a hybrid crack element (HCE) is introduced which is powerful and convenient not only for directly determining the SIF but also the coefficients of higher order terms in the plane linear elastic crack tip Asymptotic Field. Finally, the general expressions for the coefficients of the second to fifth terms of the linear elastic crack tip Asymptotic Field of three-point bend single edge notched beams (TPBs) with span to depth ratios widely used in testing are extended to very deep cracks with the use of the HCE.
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approximate green s functions for singular and higher order terms of an edge crack in a finite plate
Engineering Fracture Mechanics, 2002Co-Authors: Q. Z. Xiao, Bhushan Lal KarihalooAbstract:An edge crack in a finite plate (FSECP) subjected to wedge forces is solved by the superposition of the analytical solution of a semi-infinite crack, and the numerical solution of a FSECP with free crack faces, which is solved by the Williams expansion. The unknown coefficients in the expansion are determined by a continuous least squares method after comparing it with the direct boundary collocation and the point or discrete least squares methods. The results are then used to validate the stress intensity factor (SIF) formula provided by Tada et al. that interpolates the numerical results of Kaya and Erdogan, and an approximate crack face opening displacement formula obtained in this paper by Castigliano's theorem and the SIF formula of Tada et al. These approximate formulae are accurate except for point forces very close to the outer edge, and can be used as Green's functions in the crack-closure based crack growth analysis, as well as in interpreting the size effect of quasi-brittle materials. Green's functions for coefficients relevant to the second to the fifth terms in the crack tip Asymptotic Field are also provided. Finally, a FSECP with a uniform pressure over a part of the crack faces is solved to illustrate the application of the obtained Green's functions and to further assess their accuracy by comparing with a finite element analysis.
