探究基于数学思想的数学教学

不同中小学学校之间,学生的数学成绩存在明显差异。通过访察,部分学校的学生数学成绩普遍优异,但花的时间少;而有的学校的学生在数学上花费时间多,但成绩却不理想。那究竟是什么导致了这种差距呢?本文通过一个具体实例阐述了基于数学思想的数学教学对于学生轻松学好数学的作用。

Mechanical Behavior of Soybean Protein Fibers

In order to understand the relationship between the mechanical property and the effect of bleaching and dyeing to the soybean protein fibers(SPF),four mechanical models are chosen.The tensile and relaxation property of the soybean protein fibers are analyzed.The tensile and relaxation curves are fitted with the suitable model.It shows that the relaxation property of SPF is in accordance with the standard linear solid model.Estimates of the Hookean spring modulus at 8% and at 10% are different,so some structural modifications could be produced by the strain.Bleached fibers show a higher level of relaxation than raw fibers and dyed fibers.Bleaching has a remarkable influence on decreasing tenacity at break for each test modality.Knotted and looped modalities decrease fiber tenacity remarkably in all three samples.

Influence of water content and shear rate on the mechanical behavior of soil-rock mixtures

Soil-rock mixtures(S-RMs) are widely distributed in the nature. The mesoscopic deformation and failure mechanisms as well as the macro-mechanical behaviors of the S-RMs depend largely upon the rate of deformation, water content and particle sizes. In this research, a series of large-scale direct shear tests with different water contents and different grain-size distributions were conducted to study the influence of the aforementioned factors on the mechanical properties of the S-RMs. Due to the effect of the rock blocks' breakage in the S-RMs, the relationship between the shear strength and the vertical stress of S-RM follows a power law instead of a linear one. It is found that there exists a threshold value for the vertical stress during the shearing process,below which the soil strength is mainly determined by the inter-locking of particles and the re-arrangement of meso-structure,and otherwise large-sized rock blocks are gradually broken into smaller fragments, resulting in a decrease in the soil strength.The shear rate can also significantly influence the degree of particle breakage and the meso-structural rearrangement of the SRMs, namely, under low shear rate, the particles of the samples are fully broken resulting in enhanced macro-strength. As a result, the lower the shear rate, the higher the macroscopic strength. So under unsaturated conditions, the water content will affect the strength of the S-RMs by reducing the strength of rock blocks. As the water content increases, the soil strength decreases gradually, and assumes a moderate value when the water content reaches 8%. At the same water content, the soil strength increases with the sizes of large rock blocks. For the occlusion, breakage and structure re-arrangement of the oversized rock blocks inside S-RM, which have a huge influence on the mechanical characteristics of the samples.

Experimental research on the mechanism of non-monotonic characteristic between curing temperature and mechanical behaviors of Kevlar/epoxy composite

An experimental procedure is conducted to investigate the mechanism of the non-monotonic characteristic between curing temperature and mechanical behaviors of the Kevlar/epoxy composite in macro and micro levels. Different specimens are fabricated at four different curing temperatures and tested with ±45° off-axis tensile loading on a universal test machine coupled with digital image correlation(DIC). Moreover, the environmental scanning electron microscope(SEM) was used to obtain the micrographs and reveal their mechanism. The tested results show that the tensile mechanical behaviors are sensitive to the curing temperature and the relationship is non-monotonic. Also, as the temperature increases, the thicknesses of the specimens are significantly enlarged. By analyzing the SEM micrographs of the matrix grooves in the damage zone and DIC strain contours, it is concluded that the non-monotonic relationship is dominated by the properties of the Kevlar/epoxy interfaces and deformation of the distorted fibers.

Influence of Intertube Additional Atoms on Sliding Behaviors of Double-Walled Carbon Nanotube

The effects of intertube additional atoms on （DWCNTs） are investigated using molecular dynamics （MD） the sliding behaviors of double-walled carbon nanotubes simulation method. The interaction between carbon atoms is modeled using the second-generation reactive empirical bond-order potential coupled with the Lennard-Jones potential. The simulations indicate that intertube additional atoms of DWCNT can significantly enhance the load transfer between neighboring tubes of DWCNT. The improvement in load transfer is guaranteed by the addition of intertube atoms which are covalently bonded to the inner and outer tubes of DWCNT. The results also show that the sliding behaviors of DWCNT are strongly dependent of additional atom numbers. The results presented here demonstrate that the superior mechanical properties of DWCNT can be realized by controlling intertube coupling. The general conclusions derived from this work may be of importance in devising high-performance CNT composites.