The existing investigations on piezoelectric materials containing an elliptic hole mainly focus on remote uniform tensile loads. In order to have a better understanding of the fracture behavior of piezoelectric materi...The existing investigations on piezoelectric materials containing an elliptic hole mainly focus on remote uniform tensile loads. In order to have a better understanding of the fracture behavior of piezoelectric materials under different loading conditions, theoretical and numerical solutions are presented for an elliptic hole in transversely isotropic piezoelectric materials subjected to uniform internal shearing forces based on the complex potential approach. By solving ten variable linear equations, the analytical solutions inside and outside the hole satisfying the permeable electric boundary conditions are obtained. Taking PZT-4 ceramic into consideration, numerical results of electro-elastic fields along the edge of the hole and axes, and the electric displacements in the hole are presented. Comparison with stresses in transverse isotropic elastic materials shows that the hoop stress at the ends of major axis in two kinds of material equals zero for the various ratios of major to minor axis lengths; If the ratio is greater than 1, the hoop stress in piezoelectric materials is smaller than that in elastic materials, and if the ratio is smaller than 1, the hoop stress in piezoelectric materials is greater than that in elastic materials; When it is a circle hole, the shearing stress in two materials along axes is the same. The distribution of electric displacement components shows that the vertical electric displacement in the hole and along axes in the material is always zero though under the permeable electric boundary condition; The horizontal and vertical electric displacement components along the edge of the hole are symmetrical and antisymmetrical about horizontal axis, respectively. The stress and electric displacement distribution tends to zero at distances far from the elliptical hole, which conforms to the conclusion usually made on the basis of Saint-Venant’s principle. Unlike the existing work, uniform shearing forces acting on the edge of the hole, and the distribution of electro-elastic fields inside and outside the elliptic hole are considered.展开更多
为探究适合膜下滴灌加工番茄的磁化水施肥制度,本研究以产量和水肥利用效率为目标,设置4个磁化水强度0 Gs(M0)、2000 Gs(M1)、3000 Gs(M2)、4000 Gs(M3)和3个施氮量水平200 kg N·hm^(-2)(N1)、250 kg N·hm^(-2)(N2)和300 kg N...为探究适合膜下滴灌加工番茄的磁化水施肥制度,本研究以产量和水肥利用效率为目标,设置4个磁化水强度0 Gs(M0)、2000 Gs(M1)、3000 Gs(M2)、4000 Gs(M3)和3个施氮量水平200 kg N·hm^(-2)(N1)、250 kg N·hm^(-2)(N2)和300 kg N·hm^(-2)(N3),采用裂区试验设计,进行田间试验。通过监测加工番茄生育期内的土壤含水率、株高、茎粗及地上部生物量,并结合最终产量指标,探究各磁氮组合对加工番茄水肥利用效率的影响。结果表明:磁化水滴灌显著提高了加工番茄的土壤含水率,增加了土壤储水量,磁氮耦合显著提升了20~40 cm土层土壤含水率。磁化水强度在2270~3678 Gs,施氮量220~230 kg·hm^(-2)时,可促进加工番茄生长,磁化强度大于4000 Gs且施氮量超过250 kg·hm^(-2)时,不能进一步提高加工番茄的生长。随磁化强度的增加,加工番茄产量及水肥利用效率呈先增后减的变化,施氮量的增加,会提高产量和水分利用效率,但会降低氮肥偏生产力。其中,M2N3处理的产量和水分利用效率最大,为169.67 t·hm^(-2)和35.61 kg·m^(-3),M2N1处理的氮肥偏生产力最大,为822.54 kg·kg^(-1)。运用回归分析并结合空间分析的方法,综合考虑得到产量、水分利用效率和氮肥偏生产力三者取得较大值时的磁氮区间为2270~3678 Gs和220~230 kg N·hm^(-2)。本研究可为新疆加工番茄科学应用磁化水和氮肥提供理论支撑,为优化磁氮组合配置以提升加工番茄产量提供科学指导。展开更多
基金supported by Hebei Provincial Natural Science Foundation of China (Grant No. A2011210033)Foundation of Hebei Provincial Education Department of China (Grant No. ZH2011116)Hebei Provincial Research Program for Higher Education and Teaching Reform of China (Grant No. 103024)
文摘The existing investigations on piezoelectric materials containing an elliptic hole mainly focus on remote uniform tensile loads. In order to have a better understanding of the fracture behavior of piezoelectric materials under different loading conditions, theoretical and numerical solutions are presented for an elliptic hole in transversely isotropic piezoelectric materials subjected to uniform internal shearing forces based on the complex potential approach. By solving ten variable linear equations, the analytical solutions inside and outside the hole satisfying the permeable electric boundary conditions are obtained. Taking PZT-4 ceramic into consideration, numerical results of electro-elastic fields along the edge of the hole and axes, and the electric displacements in the hole are presented. Comparison with stresses in transverse isotropic elastic materials shows that the hoop stress at the ends of major axis in two kinds of material equals zero for the various ratios of major to minor axis lengths; If the ratio is greater than 1, the hoop stress in piezoelectric materials is smaller than that in elastic materials, and if the ratio is smaller than 1, the hoop stress in piezoelectric materials is greater than that in elastic materials; When it is a circle hole, the shearing stress in two materials along axes is the same. The distribution of electric displacement components shows that the vertical electric displacement in the hole and along axes in the material is always zero though under the permeable electric boundary condition; The horizontal and vertical electric displacement components along the edge of the hole are symmetrical and antisymmetrical about horizontal axis, respectively. The stress and electric displacement distribution tends to zero at distances far from the elliptical hole, which conforms to the conclusion usually made on the basis of Saint-Venant’s principle. Unlike the existing work, uniform shearing forces acting on the edge of the hole, and the distribution of electro-elastic fields inside and outside the elliptic hole are considered.
