“端点效应”在一类不等式恒成立问题中的应用与思考

在研究一道不等式恒成立问题的解法时发现,可以由“端点效应”得到符合题意的必要条件,给解决这类问题提供思路与方向,然后结合实例介绍“端点效应”方法在解决这类问题中的应用与思考.     

Experimental and FEM study of windshield subjected to high speed bird impact

Both experimental and finite element model (FEM) results are presented for the dynamic strength behavior of windshield subjected to bird impact. The experimental data taken from a series of high speed photographs are compared with the numerical results predicted by using FEM in which the windshield was modeled entirely with solid elements and the bird body was approximately simulated by an elastic-plastic material with failure element behavior. Effective plastic strain and element pressure were adopted as the failure criteria and once the pressure or the effective plastic strain of an element reached the critical value, the element would lose the tensile resistance capability completely. The deflection and stress distribution in the windshield were obtained. It is shown that the result from the finite element analysis agrees with those from the full-scale bird impact test. The project supported by the National Natural Science Foundation of China (10272011)     

预应力钢梁体外索的张力增量分析

将预应力钢梁看作梁与索的组合结构,充分考虑了二者之间的相互作用．利用变分原理推导出在外荷载作用下,体外索张力增量的计算公式,并通过预应力钢梁模型试验对计算结果进行了验证．     

Nonlinear traveling waves in a compressible Mooney-Rivlin rod I. Long finite-amplitude waves

In literature, nonlinear traveling waves in elastic circular rods have only been studied based on single partial differential equation (pde) models, and here we consider such a problem by using a more accurate coupled-pde model. We derive the Hamiltonian from the model equations for the long finite-amplitude wave approximation, analyze how the number of singular points of the system changes with the parameters, and study the features of these singular points qualitatively. Various physically acceptable nonlinear traveling waves are also discussed, and corresponding examples are given. In particular, we find that certain waves, which cannot be counted by the single-equation model, can arise. The project supported by the Research Grants Council of the HKSAR, China (City U 1107/99P) and the National Natural Science Foundation of China (10372054 and 10171061)     

恒应变率下航空有机玻璃耗能模量温度谱的实验研究

通过动态实验和准静态实验测得了恒应变率下3~#航空有机玻璃(PMMA)在一定温度范围内的割线模量与温度的关系。通过付氏变换,转换成耗能模量与温度的关系,再与内耗变频温度谱进行了直接的比较,得到了两种实验条件下的实际对应关系,为非线性粘弹性高聚物的力学松弛谱中应变率敏感峰和耗能模量峰之间的关联提供了实验论证。文章还提出了温度负敏感性现象。     

对一道模块考试题的探究

在2014年4月28日下午举行的黄冈市2014年春季高二年级模块修习考试中,由于试题新颖别致,难度适中,学生普遍感到如沐春风,特别是第15题,充分体现"小、巧、活"的特征,学生做完后更是回味无穷,本文拟深入探究这道试题,寻找一般规律,以期收到抛砖引玉的效果.     

由两道高考数学真题解析引发的启示与思考

高考是无形的指挥棒,牵动着千千万万个家长、教师、学生的心,高考试题的示范性与导向性影响着高中数学课程教学的发展方向和深度控制,处于一线的高三数学教师与学生一直加强对高考数学真题的分析与思考,笔者在探析各地高考数学试题的过程中,偶然发现两道试题中部分问题的构思、情境创设、具体解析十分相似,由此也引发了不少启发与思考,现呈现给大家共享,旨在抛砖引玉,希望能够引起同仁们的进一步关注与思考,不当之处敬请批评指正.     

基本不等式几何探究及应用

一、教材探究(人教A版必修5第111页探究题)在图1中,AB是圆的直径,点C是AB上一点,AC=a,BC=b,过点C作垂直于AB的弦DE,连接AD、BD,你能利用这个图形得出不等式(a+b)/2≥ab(1/2)的几何解释吗?几何解释:如图1,易知△ABD为直角三角形,因为     

浅谈柯西不等式及其应用

柯西不等式是高中不等式内容的一个重要知识点,是高中不等式内容的升华,其具有非常鲜明的结构特点,形式优美,通过柯西不等式的学习,可以提升学生的探究与创新能力,激发学生的数学学习兴趣,提高学生的数学整体素质.柯西不等式在不等式的证明、最值的求解、参数范围的求解等方面有重要的运用.柯西不等式:若ai、bi∈R+(i=1、2…、n),则: