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
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 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
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
为探究配筋率和复合层厚度对ECC-NC(Engineered Cementitious Composites to Normal Concrete)复合梁抗弯性能的影响,设计了5根ECC-NC复合梁,通过四点弯曲试验,开展了ECC-NC复合梁抗弯性能研究,分析了复合梁破坏模式和裂缝发展规律,探...为探究配筋率和复合层厚度对ECC-NC(Engineered Cementitious Composites to Normal Concrete)复合梁抗弯性能的影响,设计了5根ECC-NC复合梁,通过四点弯曲试验,开展了ECC-NC复合梁抗弯性能研究,分析了复合梁破坏模式和裂缝发展规律,探讨了配筋率和复合层厚度对结构承载能力、韧性及延性的影响。研究结果表明:与普通混凝土梁相比,ECC-NC复合梁破坏模式不同,能有效发挥ECC材料特性,具有较好的抗弯性能;相同配筋率下,受拉区ECC层厚度增加,ECC-NC复合梁的抗弯承载力增强有限,弯剪区裂缝数量增多,延性增强,刚度退化缓慢,最佳复合层厚度为0.3h~0.5h;ECC层具有替代部分纵筋作用,受压与受拉区同时设置ECC层能极大地提高抗弯承载能力、延性及结构韧性;基于响应面法,配筋率对ECC-NC抗弯性能影响最大,最大配筋率与复合层厚度有关,0~0.5h呈负相关,0.5h~h间呈正相关,受压区设置ECC可提高界限配筋率,高配筋率有利于提高抗弯刚度,减缓裂缝扩展;弯曲荷载下,截面符合平截面假定,变形协调;基于条带法,建立了ECC-NC复合梁抗弯承载能力计算方法,与试验结果及已有文献数据校核,平均误差在6%以内,吻合度较高,可为工程应用提供理论支撑。ECC替代普通混凝土,不仅提高了结构抗弯承载力,还延缓了裂缝扩展,改善了复合梁带裂缝工作性能和抗裂性能,且抗弯性能较为优越。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.
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.
文摘为探究配筋率和复合层厚度对ECC-NC(Engineered Cementitious Composites to Normal Concrete)复合梁抗弯性能的影响,设计了5根ECC-NC复合梁,通过四点弯曲试验,开展了ECC-NC复合梁抗弯性能研究,分析了复合梁破坏模式和裂缝发展规律,探讨了配筋率和复合层厚度对结构承载能力、韧性及延性的影响。研究结果表明:与普通混凝土梁相比,ECC-NC复合梁破坏模式不同,能有效发挥ECC材料特性,具有较好的抗弯性能;相同配筋率下,受拉区ECC层厚度增加,ECC-NC复合梁的抗弯承载力增强有限,弯剪区裂缝数量增多,延性增强,刚度退化缓慢,最佳复合层厚度为0.3h~0.5h;ECC层具有替代部分纵筋作用,受压与受拉区同时设置ECC层能极大地提高抗弯承载能力、延性及结构韧性;基于响应面法,配筋率对ECC-NC抗弯性能影响最大,最大配筋率与复合层厚度有关,0~0.5h呈负相关,0.5h~h间呈正相关,受压区设置ECC可提高界限配筋率,高配筋率有利于提高抗弯刚度,减缓裂缝扩展;弯曲荷载下,截面符合平截面假定,变形协调;基于条带法,建立了ECC-NC复合梁抗弯承载能力计算方法,与试验结果及已有文献数据校核,平均误差在6%以内,吻合度较高,可为工程应用提供理论支撑。ECC替代普通混凝土,不仅提高了结构抗弯承载力,还延缓了裂缝扩展,改善了复合梁带裂缝工作性能和抗裂性能,且抗弯性能较为优越。
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.
