Weight Function Method Research Articles

北京农户叶类蔬菜营销渠道绩效评价

评价北京农户的叶类蔬菜渠道绩效时，首先建立相应评价指标体系；其次通过层次分析法建立多阶层次分析模型并计算影响绩效的各因素指标权重，同时基于三角白化权函数的灰色评估方法，评估渠道各层次指标，得到相应渠道绩效的等级和综合评价值。定量评价结论是：“农户 + 企业或合作社”模式的渠道绩效最高，其次是“农户 + 产地集贸市场”和“农户 + 产地收购商”。“农户 + 批发市场”模式的渠道绩效最低，不适于农户进行叶类蔬菜的销售。Marketing channel efficiency of leafy vegetables was evaluated in this study. The impact factors of leafy vegetable marketing channel efficiency were identified, and then its corresponding evaluation index system was constructed. An evaluation model for multi-hierarchy process based on AHP was established, and the index weights of various factors were calculated. Meanwhile, on the basis of grey evaluation method of triangular whitening weight function, the indexes of various hierarchies in different channels were evaluated and the level and comprehensive evaluation value of performance of marketing channels efficiency were got. The quantitative evaluation results showed that the mode of “Farmers + enterprise (cooperatives)” achieved the highest channel efficiency and the mode of “Farmers + Wholesale” achieved the lowest channel efficiency. The mode of “Farmers + Wholesale” is unsuitable for farmers selling leafy vegetables.

A more accurate half-discrete Hilbert-type inequality with a general non-homogeneous kernel and operator expressions

In this paper, by the use of the methods of weight functions and technique of real analysis, a more accurate half-discrete Hilbert-type inequality with a general non-homogeneous kernel and a best possible constant factor is given. The equivalent forms and some reverses are obtained. We also consider the operator expressions with the norm and some particular examples. Mathematics subject classification (2010): 26D15, 47A07.

Crack Growth Prediction under Variable Amplitude Loading Considering Elastic-Plastic Stress Field ahead of Crack Tip

Reliable prediction of fatigue life of the structural components under variable amplitude loading requires accurate computation of the residual stresses ahead of crack tip. In present study, a novel method of estimation of linear elastic stress field using concept of fictitious notch rounding is presented. The stress field is later used for evaluation of residual stress distribution. Corrective stress intensity factor is calculated from the residual stress field using modified weight function method. Corrective residual stress intensity factor is used to find the effective maximum stress intensity factor and effective stress intensity range. The values of root radius of aluminium alloys computed using proposed method is found to be closely matching with the values available in literature. Numerical investigation has been carried out to predict remaining life of plate panel with and without considering load interaction effects.

Nonuniform Ferro-elastic Domain Switching for the Interfacial Crack

Existing theoretical researches about interfacial crack of bimaterial piezoelectric composites are confined to linear piezoelectric constitutive relation, neglecting the nonlinear part driven by domain switching. This paper attempts to extend the research of mode III interfacial crack from linear piezoelectricity to nonlinear ferroelectricity. The analysis focuses on the variation of stress intensity factor caused by domain switching, with an arbitrary three-dimensional initial poling orientation. Due to the mismatch of material properties, an asymmetric nonuniform domain switching zone is achieved around the interfacial crack under the nonuniform domain switching criterion. By employing the weight function method, analytic forms of mono-domain and multi- domain toughening effects about stationary and quasi-static steady-state crack are obtained, respectively. The conclusions come to that domain switching of mode III quasi-static steady-state growing interfacial crack has a positive effect to toughen the material. The research can provide some guidance for material selection to maximize the effect of ferro-elastic switch toughening.

Analytical methods for determination of double-K fracture parameters of concrete

This paper presents a comparative study on the double-K fracture parameters of concrete obtained using four existing analytical methods such as Gauss-Chebyshev integral method, simplified Green's function method, weight function method and simplified equivalent cohesive force method. Two specimen geometries: three point bend test and compact tension specimen for sizes 100-500 mm at initial notch length to depth ratios 0.25 and 0.4 are used for the comparative study. The required input parameters for determining the double-K fracture parameters are derived from the developed fictitious crack model. It is found that the cohesive toughness and initial cracking toughness determined using weight function method and simplified equivalent cohesive force method agree well with those obtained using Gauss-Chebyshev integral method whereas these fracture parameters determined using simplified Green's function method deviates more than by 11% and 20% respectively as compared with those obtained using Gauss-Chebyshev integral method. It is also shown that all the fracture parameters related with double-K model are size dependent.

A multidimensional half-discrete Hilbert-type inequality and the Riemann zeta function

In this paper, by applying methods of weight functions and techniques of real analysis, a more accurate multidimensional half-discrete Hilbert’s inequality with the best possible constant factor related to the Riemann zeta function is proved. Equivalent forms and some reverses are also obtained. Additionally, we consider the operator expressions with the norms and finally present a corollary related to the non-homogeneous kernel.

Calculation of stress intensity factors for functionally graded materials by using the weight functions derived by the virtual crack extension technique

The weight function method provides a powerful approach for calculating the stress intensity factors for a homogeneous cracked body subjected to mechanical loadings. In this paper, the basic equations of weight function method for mode I and mixed mode crack problems in a two-dimensional functionally graded crack system are derived based on the Betti’s reciprocal theorem. The weight functions derived by the virtual crack extension technique are further used to calculate the stress intensity factors of functionally graded materials (FGMs). The practicability and accuracy of this proposed method has been confirmed by the comparison with theoretical or numerical solutions available in the literatures. On account that the repeated extractions of the distributions of normal stress and shear stress in the uncracked component along the prospective crack line under different loadings can be avoided using the method presented in this paper, this method can be potentially used for optimal design for FGMs under multiple-load cases.

Determination of Stress Intensity Factor for Cracked Brazilian Disc Using Weight Function

To reduce stress concentration near the loading point, Brazilian test, normally used for the indirect determination of tensile strength for rock or concrete quasi-brittle materials, is usually subjected to uniformly distributed pressure over finite width (or arc) of the Brazilian disc. As an extension, the same geometry, in which a central notch is introduced in the symmetrical plane of applied forces, can be used to determine fracture toughness of the materials. For this purpose, accurate expression for stress intensity factor (SIF) for central cracked Brazilian disc should be provided first. To this end, weight function method is used in this paper where weight function for central cracked disc is available in general SIF handbooks. Meanwhile, the exact stress solution in the intact Brazilian disc subjected to uniformly distributed pressure is derived by use of numerical method. In the end, some finite element analysis is carried out using the program package ABAQUS on the Brazilian disc, and the comparison results regarding the SIF between the weight function method and numerical method prove the validity of the proposed method.

Technical Basis for Application of Weight Function Method for Calculation of Stress Intensity Factor for Surface Flaws Proposed for ASME Section XI Appendix A

Analytical evaluation procedures for determining the acceptability of flaws detected during in-service inspection of nuclear power plant components are provided in Section XI of the ASME Boiler and Pressure Vessel Code. Linear elastic fracture mechanics based evaluation procedures in ASME Section XI require calculation of the stress intensity factor. A method for calculating the stress intensity factor is provided in Appendix A of ASME Section XI. This method consists of a two-step process. In the first step, the stress distribution, as calculated in the absence of the flaw, is obtained at the flaw location. For a surface flaw, the stress distribution at the flaw location is then fitted to a third-order polynomial equation. In the second step, the fitted polynomial representation of the stress distribution is used with standardized influence coefficients to calculate the stress intensity factor. An alternate method for calculation of the stress intensity factor for a surface flaw that makes explicit use of the universal weight function method and does not require a polynomial fit to the actual stress distribution is proposed in this paper for implementation into Appendix A of ASME Section XI. Universal weight function coefficients are determined from standardized influence coefficients through closed-form equations. Closed-form equations for calculation of the stress intensity factor are provided. The technical basis and verification for this alternate method for calculation of the stress intensity factor are described in this paper.

Application of the weight function method on a high incidence research aircraft model

AbstractThis paper assesses the application of a new method for system stability analysis, the weight functions method, to the longitudinal and lateral motions of a High Incidence Research Aircraft Model. The method consists of finding the number of weight functions that is equal to the number of differential equations required for system modelling. The aircraft’s stability is determined from the sign of the total weight function; which should be negative for a stable model. The Aero-Data Model In Research Environment (ADMIRE) simulation, developed by the Swedish Defence Research Agency, was used for the aerodynamic aircraft modelling, with the following configurations: Mach number = 0·25, altitude = 500m, angle-of-attack [–10 to 30]°, elevon deflection angle [–30 to 30]°, canard deflection [0° and 25°] and rudder deflection angles [–30° and 30°]. These flight configurations were selected because they are among the flight conditions for Cat. II Pilot Induced Oscillation (PIO) criteria validation, performed on the FOI aircraft model presented in the PIO Handbook by the Group for Aeronautical Research and Technology in Europe, Flight Mechanics/Action Group 12. This aircraft model has a known instability for longitudinal and lateral motions and so a control law was introduced to stabilise its flight.

Measurement of physical parameters with a weight function method and its application to the Higgs boson mass reconstruction

We propose a new method to measure various physical parameters, using characteristic weight functions. This method requires only lepton energy distribution and ideally it does not depend on the velocity of the parent particle. We demonstrate an application of this method by simulating a reconstruction of the Higgs boson mass in the H-> WW -> lnu lnu decay mode at the LHC. We show that systematic errors are suppressed compared to statistical errors. In the vector boson fusion channel, the statistical accuracy of the mass determination is estimated to be +12% and -14% at an integrated luminosity of 100fb^{-1}, assuming the Higgs boson mass to be 125GeV and root{s}=14TeV.

Residual Stresses and Stress Intensity Factor Calculations in T-Welded Joints

In welded joint, the residual stresses effect can be considered using the residual stress intensity factor (K res). In this study, K res is calculated using the analytic weight function method (WFM) and the polynomial distribution of residual stresses (σ res). The different residual stress distributions have been used analytically. It is to be emphasized that the current approach is little investigated. This is because the weight function has already been developed to calculate K for a crack that had already existed, and hence to calculate the stress distribution and stress intensity factor over the crack face. Therefore, the current approach calculates K res with σ res consideration for the crack which initiates and propagates until failure. The validity to use the proposed weight function has been shown. The results of K res have been compared with those obtained from FEM.

Analysis of crack opening stresses for center- and edge-crack tension specimens

Accurate determination of crack opening stress is of central importance to fatigue crack growth analysis and life prediction based on the crack-closure model. This paper studies the crack opening behavior for center- and edge-crack tension specimens. It is found that the crack opening stress is affected by the crack tip element. By taking the crack tip element into account, a modified crack opening stress equation is given for the center-crack tension specimen. Crack surface displacement equations for an edge crack in a semi-infinite plate under remote uniform tension and partially distributed pressure are derived by using the weight function method. Based on these displacements, a crack opening stress equation for an edge crack in a semi-infinite plate under uniform tension has been developed. The study shows that the crack opening stress is geometry-dependent, and the weight function method provides an effective and reliable tool to deal with such geometry dependence.

Determination of Residual Fracture Toughness of Post-Fire Concrete

Determination of double-K fracture parameter using both analytical and weight function method is carried out in present research. In calculating the cohesive fracture toughness, two situations are divided at critical load. Wedge-splitting tests with ten temperatures varying from 20oC to 600oC are implemented. The complete load-crack opening displacement curves are obtained from which the initial and critical fracture toughness could be calculated experimentally. The validation of double-K fracture model to the post-fire concrete specimens is proved. Meanwhile the weight function method agrees well with the analytical method.

Consideration of the residual stress distributions in fatigue crack growth calculations for assessing welded steel joints

ABSTRACTTo better understand the crack closure and propagation, an analytical model is established. The residual stress effect on fatigue crack growth equations has been considered using the residual stress intensity factor (SIF) (Kres). The joint geometries, residual stress distributions (σres) and residual stress ratio (Rres) were considered also. Kres are calculated using the analytical weight function (WF) method and different residual stress distributions. It is to be emphasized that the current approach is little investigated. This is because the WF has already been developed to calculate SIF for an existing crack. The current approach calculates Kres for the crack that initiates and propagates until failure. Different stress distributions have been used, and Rres is defined. The validity of using the WF has been shown. SIF due to applied load (Kapp) and applied stress ratio (Rapp) have been considered. Fatigue crack growth rate was investigated in accordance with the current approach. The results have been verified and benchmarked.

Fracture mechanics-based estimation of fatigue lives of welded joints

The effects of the lack of penetration flaw and misalignment on fatigue life of cruciform welded joints made of low-alloy steel were studied experimentally and theoretically. It was found that two locations of fatigue fracture were possible under cyclic tension loading, depending on the relative magnitude of the misalignment. In the absence of misalignment, all fatigue failures occurred as a result of fatigue growth of cracks emanating from the weld root. In the presence of misalignment, fatigue life depended on the fatigue growth of cracks growing from the weld toe. It has been shown that the entire fatigue life can be modeled as a fatigue growth of cracks starting either from the weld toe or the weld root. The initial crack size was selected as a small crack characteristic for a given material, i.e., being dependent only on the material. The weight function method was used to calculate the required stress intensity factors.

Stress Intensity Factors and Weight Function for Internal Surface Faults in Cylindrical Vessels

Failure of cylindrical vessels can be caused by stress singularity at pitting corrosion induced cracks. Literature suggests that most of research focuses on how to determine stress intensity factors for surface cracks with low aspect ratios, i.e.,a/c1.0. Situation may well arise where the aspect ratio of cracks is larger than one. This paper attempts to propose a weight function method to determine stress intensity factors for high aspect ratio semi-elliptical cracks in cylindrical vessels. The weight functions are derived based on three dimensional finite element analysis. The proposed weight function method is verified numerically. It is found that the higher the aspect ratio of cracks the larger the stress intensity factors, and that the aspect ratio of cracks may alter the failure mode of cylindrical vessels.

Weight functions for the determination of stress intensity factor and T‐stress for semi‐elliptical cracks in finite thickness plate

ABSTRACTThis paper presents the application of weight function method for the calculation of stress intensity factors (K) and T‐stress for surface semi‐elliptical crack in finite thickness plates subjected to arbitrary two‐dimensional stress fields. New general mathematical forms of point load weight functions for K and T have been formulated by taking advantage of the knowledge of a few specific weight functions for two‐dimensional planar cracks available in the literature and certain properties of weight function in general. The existence of the generalised forms of the weight functions simplifies the determination of specific weight functions for specific crack configurations. The determination of a specific weight function is reduced to the determination of the parameters of the generalised weight function expression. These unknown parameters can be determined from reference stress intensity factor and T‐stress solutions. This method is used to derive the weight functions for both K and T for semi‐elliptical surface cracks in finite thickness plates, covering a wide range of crack aspect ratio (a/c) and relative depth (a/t) at any point along the crack front. The derived weight functions are then validated against stress intensity factor and T‐stress solutions for several linear and nonlinear two‐dimensional stress distributions. These derived weight functions are particularly useful for the development of two‐parameter fracture and fatigue models for surface cracks subjected to fluctuating nonlinear stress fields, such as these resulting from surface treatment (shot peening), stress concentration or welding (residual stress).

Weight function method to determine stress intensity factor for semi-elliptical crack with high aspect ratio in cylindrical vessels

Failure of cylindrical vessels can be caused by stress singularity at pitting corrosion induced cracks. Literature suggests that most of research focuses on stress intensity factors for surface cracks with low aspect ratios, i.e., a/c⩽1.0. Situation may well arise where the aspect ratio of cracks is larger than one. This paper attempts to propose a weight function method to determine stress intensity factors for high aspect ratio semi-elliptical cracks in cylindrical vessels. The weight functions are derived based on three dimensional finite element analysis. The proposed weight function method is verified both numerically and analytically. It is found that the higher the aspect ratio of cracks the larger the stress intensity factors at the surface point, and that the aspect ratio of cracks tends to change the distribution of stress intensity factor along the cracks which can alter the failure mode of cylindrical vessels. The paper concludes that the proposed weight function method can serve as a useful tool for the accurate and efficient prediction of stress intensity factors for longitudinal surface cracks with various aspect ratios in cylindrical vessels subjected to arbitrary loads.

Determining residual double-K fracture toughness of post-fire concrete using analytical and weight function method

Determination of double-K fracture parameter using both analytical and weight function method is carried out in present research. In calculating the cohesive fracture toughness, two situations are divided at critical load. Wedge-splitting tests with ten temperatures varying from 20 to 600 °C are implemented. The complete load-crack opening displacement curves are obtained from which the initial and critical fracture toughness could be calculated experimentally. The validation of double-K fracture model to the post-fire concrete specimens is proved. Meanwhile the weight function method agrees well with the analytical method. Finally, an index to indicate the brittleness of concrete specimen through the ratio of initial fracture toughness and unstable fracture toughness is proposed.