关于剩余类环的扩展的研究

作者对非结合环给出扩展的概念,即给定2个非结合环A和B,对任一非结合环R,称R是A被B的扩展,当且仅当A是R的理想且R/A≌B.对非结合环的扩展,文中证明了一个类似于Schreier群扩张定理的结果.作为应用,对给定的自然数m≥2,n≥2,文章刻画了模n的剩余类环Z_n被模m的剩余类环Z_m扩展所得到的有限环R的构造,证明了R可以用满足一定条件的自然数对(u,r)来描述,同时写出了R的理想和单侧理想的具体形状.作者还进一步证明,R是结合的当且仅当R=Z_nZ_m,且当R=Z_nZ_m时,R的每个理想都是Z_n的一个理想与Z_m的一个理想的直和,即此时R的理想是相对平凡的.     

Synergy effects of multi-walled carbon nanotube and graphene nanoplate filled epoxy adhesive on the shear properties of unidirectional composite bonded joints

In this paper, multi-walled carbon nanotubes (MWCNTs) and graphene nanoplates (GNPs) were dispersed into epoxy adhesive by sonication method to investigate their synergy effects on the shear properties of unidirectional composite bonded single lap joints (SLJs). The effect of the viscosity of epoxy resin and hardener on the dispersion process was studied. Testing results showed that the incorporation of MWCNTs and GNPs significantly improved the shear strength and elongation of SLJs at failure. 0.75 wt% MWCNTs/GNPs hybrids reached the highest enhancement of shear strength and elongation by 36.6% and 33.2%, respectively. In addition, the thermal stability of epoxy adhesive was improved by nanofillers in some extent. Finally, the failure mode of SLJs and fracture surfaces of the bonding area as well as the damage mechanism of nanofillers were analyzed.     

Numerical investigation on the position of holes for reducing stress concentration in composite plates with bolted and riveted joints

This paper studies the effects of fiber orientaion and holes position on stress concentration and the determination of weakened areas in the composite of glass fiber reinforced epoxy resin around the hole for joints by using the finite element method. In this study, for the observation of areas affected by stress concentration Tsai-Wu failure criterion is used to determine the failed elements and ANSYS Software is implemented for modeling. In order to compare the effect of geometric parameters on stress concentration around the holes, two types of hole position arrangement along with fibers orientation have been studied. Results show that the stress concentration coefficient is lower in the second type of holes arrangement in comparison with the first type for the same component dimensions. Increasing the distance from hole center to upper or lower edge of the sample and also decreasing the distance between holes, would result in an increase in the stress concentration.     

Cohesive zone model for high-cycle fatigue of adhesively bonded joints under mode I loading

A cohesive zone model adequate for simulating the behaviour of adhesively bonded joints subjected to high-cycle fatigue and pure mode I loading is presented. The bilinear cohesive zone law with linear softening relationship was considered. The main advantage of the proposed formulation is the use of a unique damage parameter accounting for cumulative damage resulting from static and fatigue loading. The method was implemented in a user subroutine of the commercial finite element software Abaqus®. Two-dimensional numerical simulations of the double cantilever beam test using different representative combinations of the modified Paris law coefficients were performed. It was verified that the results of the model simulate with excellent agreement the several Paris laws used as input, thus demonstrating the good performance of the method as a predictive tool.     

Analysis of a three-dimensional dissimilar material joint with one real singularity using a conservative integral

In the present study, a conservative integral based on the Betti reciprocal principle is formulated to determine the intensity of singularity at a vertex of the interface in three-dimensional dissimilar material joints with one real singularity. Eigenanalysis formulated using a three-dimensional finite element method (FEM) is used to calculate the order of stress singularity, angular functions of displacements and stresses. Models with various element sizes and various integral areas are used to investigate the effect of the integration area on the accuracy of the results. The results are compared with those obtained from the boundary element method (BEM) using a curve-fitting technique to calculate the intensity of singularity. In addition, models of various lengths and various material combinations are used to investigate the stress singularity characteristics in three-dimensional dissimilar material joints. The results of the present study indicate that the conservative integral can be used to determine the intensity of singularity in three-dimensional bi-material joints. The accuracy of the results can be improved by mesh refinement. Finally, the relationships among the intensity of singularity, the order of stress singularity and the model geometry are discussed.     

The Behaviors of Expansion Functor on Monomial Ideals and Toric Rings

In this article, we study some algebraic and combinatorial behaviors of expansion functor. We show that on monomial ideals some properties like polymatroidalness, weakly polymatroidalness, and having linear quotients are preserved under taking the expansion functor.

The main part of the article is devoted to study of toric ideals associated to the expansion of subsets of monomials which are minimal with respect to divisibility. It is shown that, for a given discrete polymatroid P, if toric ideal of P is generated by double swaps, then toric ideal of any expansion of P has such a property. This result, in a special case, says that White's conjecture is preserved under taking the expansion functor. Finally, the construction of Gröbner bases and some homological properties of toric ideals associated to expansions of subsets of monomials is investigated.     

基于彩色图像分割技术的SMT焊点质量检测

图像分割的策略和方法是SMT焊点图像处理的一项关键技术,也一直是SMT焊点计算机质量检测的瓶颈;以SMT焊点的颜色和几何特征作为分析对象,在灰度图像分割所用二维阈值化的分割方法的基础上,提出一种从颜色直方图的量化级数和二维直方图概率密度不均匀化两个方面改进后的适用于HSV彩色空间图像分割技术,并将其应用于SMT焊点的质量检测;通过其得到SMT片式元器件焊点的图像,对其进行形态学处理后,利用Matlab软件将SMT焊点成功地从PCB板上分离出来,为三维重建提供良好的基础。     

一维光子晶体的反射率特性

基于平面波展开法,设计九层一维光子晶体结构,通过改变结构中介质层的厚度,运用MATLAB编程计算一维光子晶体反射率特性,厚度差值变小时,不存在反射波的区域将增加变大。研究结果为一维光子晶体器件的设计提供理论参考。     

光子晶体缺陷结构的特性

基于平面波展开法,设计了二维正方晶格和三角晶格光子晶体缺陷结构,数值模拟了TE模、TM模式的光子晶体禁带特性,计算了二维三角晶格光子晶体缺陷结构的模式分布。结果表明,光子晶体缺陷结构能够形成很好的禁带特性和模式结构,研究结论为光子晶体波导器件的开发提供参考。     

考虑塑性和刚度不匹配的焊接残余应力估算

现有残余应力计算方法未能考虑材料塑性变形和焊接接头刚度不匹配的影响,使得焊接残余应力计算结果和实际残余应力存在较大偏差.在2219-T87铝合金钨极氩弧焊焊接头残余应力测试基础上,提出一种基于非线性有限元和材料弹性模量分区的残余应力—释放应变曲线的残余应力计算方法,研究了材料塑性变形和接头刚度不匹配对焊接残余应力计算的影响.结果表明,焊接接头中非均质材料塑性不匹配可以引起对于残余应力计算的较大误差;材料塑性变形对残余应力的影响大于接头刚度不匹配对残余应力的影响.所提出方法修正了传统方法在焊接接头的残余应力计算中由于未考虑接头非均质材料塑性不匹配而引起的误差.