This paper aims to experimentally and numerically probe fatigue behaviours and lifetimes of 3D4D(three-dimensional four-directional)braided composite I-beam under four-point flexure spectrum loading.New fatigue damage...This paper aims to experimentally and numerically probe fatigue behaviours and lifetimes of 3D4D(three-dimensional four-directional)braided composite I-beam under four-point flexure spectrum loading.New fatigue damage models of fibre yarn,matrix and fibre–matrix interface are proposed,and fatigue failure criteria and PFDA(Progressive Fatigue Damage Algorithm)are thus presented for meso-scale fatigue damage modelling of 3D4D braided composite I-beam.To validate the aforementioned model and algorithm,fatigue tests are conducted on the 3D4D braided composite I-beam under four-point flexure spectrum loading,and fatigue failure mechanisms are analyzed and discussed.Novel global–local FE(Finite Element)model based on the PFDA is generated for modelling progressive fatigue failure process and predicting fatigue life of 3D4D braided composite I-beam under four-point flexure spectrum loading.Good agreement has been achieved between experimental results and predictions,demonstrating the effective usage of new model.It is shown that matrix cracking and interfacial debonding initially initiates on top surface of top flange of I-beam,and then gradually propagates from the side surface of top flange to the intermediate web along the braiding angle,and considerable fiber breakage finally causes final fatigue failure of I-beam.展开更多
This paper deals with the existence of multiple positive solutions for a class of nonlinear singular four-point boundary value problem with p-Laplacian：{（φ（u′））′＋a（t）f（u（t））=0, 0〈t〈1, αφ（u（...This paper deals with the existence of multiple positive solutions for a class of nonlinear singular four-point boundary value problem with p-Laplacian：{（φ（u′））′＋a（t）f（u（t））=0, 0〈t〈1, αφ（u（0））-βφ（u′（ξ））=0,γφ（u（1））＋δφ（u′（η））0,where φ（x） = ｜x｜^p-2x,p 〉 1, a（t） may be singular at t = 0 and/or t = 1. By applying Leggett-Williams fixed point theorem and Schauder fixed point theorem, the sufficient conditions for the existence of multiple （at least three） positive solutions to the above four-point boundary value problem are provided. An example to illustrate the importance of the results obtained is also given.展开更多
A class of higher-order four-point boundary value problems with a p-Laplacian operator is studied. By use of a fixed point theorem in cones, sufficient conditions for the existence of positive solutions for the bounda...A class of higher-order four-point boundary value problems with a p-Laplacian operator is studied. By use of a fixed point theorem in cones, sufficient conditions for the existence of positive solutions for the boundary value problems are obtained.展开更多
In this study,we explored the deformation mechanisms of Mg single crystals using a combination of scanning electron microscopy and electron backscattered diffraction in conjunction with a dedicated four-point bending ...In this study,we explored the deformation mechanisms of Mg single crystals using a combination of scanning electron microscopy and electron backscattered diffraction in conjunction with a dedicated four-point bending tester.We prepared two single-crystal samples,oriented along the<1120>and<1010>directions,to assess the mechanisms of deformation when the initial basal slip was suppressed.In the<1120>sample,the primary{1012}twin(T1)was confirmed along the<1120>direction of the sample on the compression side with an increase in bending stress.In the<1010>sample,T1 and the secondary twin(T2)were confirmed to be along the<1120>direction,with an orientation of±60°with respect to the bending stress direction,and their direction matched with(0001)in T1 and T2.This result implies that crystallographically,the basal slip occurs readily.In addition,the<1010>sample showed the double twin in T1 on the compression side and the tertiary twin along the<1010>direction on the tension side.These results demonstrated that the maximum bending stress and displacement changed significantly under the bend loading because the deformation mechanisms were different for these single crystals.Therefore,the correlation between bending behavior and twin orientation was determined,which would be helpful for optimizing the bending properties of Mg-based materials.展开更多
This paper deals with the existence of solutions to the p（t）-Laplacian equation with four-point boundary conditions. It is shown, by Leray-Schauder fixed point theorem and degree method, that under suitable conditio...This paper deals with the existence of solutions to the p（t）-Laplacian equation with four-point boundary conditions. It is shown, by Leray-Schauder fixed point theorem and degree method, that under suitable conditions, solutions of the problem exist. The interesting point is that p（t） is a general function.展开更多
The scalar one-loop four-point function with one massless vertex is evaluated analytically by employing the loop regularization method. According to the method, a characteristic scale μs is introduced to regularize t...The scalar one-loop four-point function with one massless vertex is evaluated analytically by employing the loop regularization method. According to the method, a characteristic scale μs is introduced to regularize the divergent integrals. The infrared divergent parts, which take the form of ln2(λ^(2)/μ_(s)^(2))and ln(λ^(2)/μ_(s)^(2))as μ_(s)→ 0 where λ is a constant and expressed in terms of masses and Mandelstam variables, and the infrared stable parts are well separated. The result is shown explicitly via 44 dilogarithms in the kinematic sector in which our evaluation is valid.展开更多
Clearance not only affects the startup torque,rotation precision and stiffness of bearing,but also affects the load distribution,load-carrying capacity and life of bearing.A computational model in which the clearance ...Clearance not only affects the startup torque,rotation precision and stiffness of bearing,but also affects the load distribution,load-carrying capacity and life of bearing.A computational model in which the clearance of bearing is first included is presented for determining the contact force distribution and static load-carrying capacity of a double row four-point contact ball bearing which is subjected to the combined radial,axial and overturning moment loadings.The relation between the negative axial clearance and the contact force distribution is analyzed.The static load-carrying capacity curves are established,and the effects of the changes in negative axial clearance,curvature radius coefficient of raceway groove and initial contact angle on the static load-carrying capacity are analyzed.The results show that,with the increase in the absolute value of negative clearance,the maximum contact load decreases first and then increases.The clearance values in the range of 0.2 mme0 mm have little effect on the static load-carrying capacity of bearing.With the increase in the curvature radius coefficient of raceway groove and the decrease in the initial contact angle,the static load capacity of bearing decreases.展开更多
This paper deals with a four-point boundary value problem [φ(u')]' = f(t, u, u'),a < t < b with u(a) - u(ao) = A, u(b) - u(bo) = B, where a < a0 <b0 < b.
采用三维编织技术和真空辅助树脂灌注成型工艺制备了碳/玻混杂三维五向编织复合材料工字梁,对不同混杂比例和不同混杂部位的复合材料工字梁进行四点弯曲测试,结合三维数字图像相关(3D Digital Image Correlation,3D-DIC)技术分析其应变...采用三维编织技术和真空辅助树脂灌注成型工艺制备了碳/玻混杂三维五向编织复合材料工字梁,对不同混杂比例和不同混杂部位的复合材料工字梁进行四点弯曲测试,结合三维数字图像相关(3D Digital Image Correlation,3D-DIC)技术分析其应变分布和损伤过程。结果表明:采用不同混杂比例时,1/3碳纤维轴纱和2/3碳纤维轴纱相比纯玻璃纤维试样的强度提升了4.5%和11.5%,随着碳纤维占比的增加,复合材料的强度逐渐提升,但提升幅度较小;而碳纤维分布位置不同时,工字梁弯曲失效形式也不同,纯玻璃纤维和碳纤维在下翼缘的2种试样属于下压头附近边缘断裂的失效形式,碳纤维在腹板、腹板和下翼缘的2种试样属于腹板前后错位倾斜的失效形式,碳纤维在上翼缘、上翼缘和下翼缘、上翼缘和腹板的3种试样都属于腹板中心纵向断裂的失效形式;结合位移-载荷曲线及失效形式分析可知,1/3碳纤维分布于上翼缘,2/3碳纤维分布于上翼缘和下翼缘时,工字梁强度及抵抗变形的能力更佳,碳纤维更适合混杂于上翼缘。展开更多
This paper is concerned with the existence of solutions for a second-order four-point boundary value problem at resonance.The main methods depend on the technique of the upper and lower solutions and the coincidence d...This paper is concerned with the existence of solutions for a second-order four-point boundary value problem at resonance.The main methods depend on the technique of the upper and lower solutions and the coincidence degree theory.展开更多
基金supported by the National Natural Science Foundation of China(No.12472340).
文摘This paper aims to experimentally and numerically probe fatigue behaviours and lifetimes of 3D4D(three-dimensional four-directional)braided composite I-beam under four-point flexure spectrum loading.New fatigue damage models of fibre yarn,matrix and fibre–matrix interface are proposed,and fatigue failure criteria and PFDA(Progressive Fatigue Damage Algorithm)are thus presented for meso-scale fatigue damage modelling of 3D4D braided composite I-beam.To validate the aforementioned model and algorithm,fatigue tests are conducted on the 3D4D braided composite I-beam under four-point flexure spectrum loading,and fatigue failure mechanisms are analyzed and discussed.Novel global–local FE(Finite Element)model based on the PFDA is generated for modelling progressive fatigue failure process and predicting fatigue life of 3D4D braided composite I-beam under four-point flexure spectrum loading.Good agreement has been achieved between experimental results and predictions,demonstrating the effective usage of new model.It is shown that matrix cracking and interfacial debonding initially initiates on top surface of top flange of I-beam,and then gradually propagates from the side surface of top flange to the intermediate web along the braiding angle,and considerable fiber breakage finally causes final fatigue failure of I-beam.
基金Tutorial Scientific Research Program Foundation of Education Department of Gansu Province(0710-04).
文摘This paper deals with the existence of multiple positive solutions for a class of nonlinear singular four-point boundary value problem with p-Laplacian：{（φ（u′））′＋a（t）f（u（t））=0, 0〈t〈1, αφ（u（0））-βφ（u′（ξ））=0,γφ（u（1））＋δφ（u′（η））0,where φ（x） = ｜x｜^p-2x,p 〉 1, a（t） may be singular at t = 0 and/or t = 1. By applying Leggett-Williams fixed point theorem and Schauder fixed point theorem, the sufficient conditions for the existence of multiple （at least three） positive solutions to the above four-point boundary value problem are provided. An example to illustrate the importance of the results obtained is also given.
基金Sponsored by the National Natural Science Foundation of China (10671012)Doctoral Program Foundation of Education Ministry of China(20050007011)
文摘A class of higher-order four-point boundary value problems with a p-Laplacian operator is studied. By use of a fixed point theorem in cones, sufficient conditions for the existence of positive solutions for the boundary value problems are obtained.
基金supported by The AMADA FOUNDATION[grant number AF-2022030-B3]JSPS KAKENHI[grant numbers JP16K05961 and JP19K04065]。
文摘In this study,we explored the deformation mechanisms of Mg single crystals using a combination of scanning electron microscopy and electron backscattered diffraction in conjunction with a dedicated four-point bending tester.We prepared two single-crystal samples,oriented along the<1120>and<1010>directions,to assess the mechanisms of deformation when the initial basal slip was suppressed.In the<1120>sample,the primary{1012}twin(T1)was confirmed along the<1120>direction of the sample on the compression side with an increase in bending stress.In the<1010>sample,T1 and the secondary twin(T2)were confirmed to be along the<1120>direction,with an orientation of±60°with respect to the bending stress direction,and their direction matched with(0001)in T1 and T2.This result implies that crystallographically,the basal slip occurs readily.In addition,the<1010>sample showed the double twin in T1 on the compression side and the tertiary twin along the<1010>direction on the tension side.These results demonstrated that the maximum bending stress and displacement changed significantly under the bend loading because the deformation mechanisms were different for these single crystals.Therefore,the correlation between bending behavior and twin orientation was determined,which would be helpful for optimizing the bending properties of Mg-based materials.
基金The NSF(11271154)of Chinathe Key Lab of Symbolic Computation and Knowledge Engineering of Ministry of Education+1 种基金the 985 program of Jilin Universitythe DR Fund(150152)of Henan University of Technology
文摘This paper deals with the existence of solutions to the p（t）-Laplacian equation with four-point boundary conditions. It is shown, by Leray-Schauder fixed point theorem and degree method, that under suitable conditions, solutions of the problem exist. The interesting point is that p（t） is a general function.
文摘The scalar one-loop four-point function with one massless vertex is evaluated analytically by employing the loop regularization method. According to the method, a characteristic scale μs is introduced to regularize the divergent integrals. The infrared divergent parts, which take the form of ln2(λ^(2)/μ_(s)^(2))and ln(λ^(2)/μ_(s)^(2))as μ_(s)→ 0 where λ is a constant and expressed in terms of masses and Mandelstam variables, and the infrared stable parts are well separated. The result is shown explicitly via 44 dilogarithms in the kinematic sector in which our evaluation is valid.
基金supported by NSFC(51105131)Excellent Youth Foundation of Henan Scientific Committee(124100510002)Creative Talent Foundation in University of Henan Province(2011HASTIT016)
文摘Clearance not only affects the startup torque,rotation precision and stiffness of bearing,but also affects the load distribution,load-carrying capacity and life of bearing.A computational model in which the clearance of bearing is first included is presented for determining the contact force distribution and static load-carrying capacity of a double row four-point contact ball bearing which is subjected to the combined radial,axial and overturning moment loadings.The relation between the negative axial clearance and the contact force distribution is analyzed.The static load-carrying capacity curves are established,and the effects of the changes in negative axial clearance,curvature radius coefficient of raceway groove and initial contact angle on the static load-carrying capacity are analyzed.The results show that,with the increase in the absolute value of negative clearance,the maximum contact load decreases first and then increases.The clearance values in the range of 0.2 mme0 mm have little effect on the static load-carrying capacity of bearing.With the increase in the curvature radius coefficient of raceway groove and the decrease in the initial contact angle,the static load capacity of bearing decreases.
文摘This paper deals with a four-point boundary value problem [φ(u')]' = f(t, u, u'),a < t < b with u(a) - u(ao) = A, u(b) - u(bo) = B, where a < a0 <b0 < b.
文摘采用三维编织技术和真空辅助树脂灌注成型工艺制备了碳/玻混杂三维五向编织复合材料工字梁,对不同混杂比例和不同混杂部位的复合材料工字梁进行四点弯曲测试,结合三维数字图像相关(3D Digital Image Correlation,3D-DIC)技术分析其应变分布和损伤过程。结果表明:采用不同混杂比例时,1/3碳纤维轴纱和2/3碳纤维轴纱相比纯玻璃纤维试样的强度提升了4.5%和11.5%,随着碳纤维占比的增加,复合材料的强度逐渐提升,但提升幅度较小;而碳纤维分布位置不同时,工字梁弯曲失效形式也不同,纯玻璃纤维和碳纤维在下翼缘的2种试样属于下压头附近边缘断裂的失效形式,碳纤维在腹板、腹板和下翼缘的2种试样属于腹板前后错位倾斜的失效形式,碳纤维在上翼缘、上翼缘和下翼缘、上翼缘和腹板的3种试样都属于腹板中心纵向断裂的失效形式;结合位移-载荷曲线及失效形式分析可知,1/3碳纤维分布于上翼缘,2/3碳纤维分布于上翼缘和下翼缘时,工字梁强度及抵抗变形的能力更佳,碳纤维更适合混杂于上翼缘。
文摘This paper is concerned with the existence of solutions for a second-order four-point boundary value problem at resonance.The main methods depend on the technique of the upper and lower solutions and the coincidence degree theory.
