神秘的无穷大

本文详细论述了在无穷大里,部分可以等于总体,但是并不是所有的无穷大都相等。     

关于等价无穷小量

对等价无穷小量代换问题进行探讨.通过实例说明某文献中的一条定理存在不妥之处,并给出相应修正.结果可拓广等价无穷小量替换方法的使用范围.     

重要极限lim(x→0)(1+x)1/x=e的一个推广

我们把重要极限lim(x→0)(1+x)1/x=e推广为lim(x→0)(1+a(x))β(x)=elim(x)β(x)x→0,其中lim(x→0)a(x)=0,lim(x→0)β(x)=∞.从而可以简化这一类型的极限计算.     

洛必达法则在求极限中的方法

洛必达法则是微积分中重要的内容,是解决一类极限问题的重要方法.同时,熟练掌握求极限的方法对学好高等数学具有重要的意义.     

关于高等数学中极限求解的若干方法

极限理论,作为高等数学学习的基础和开端,分为数列极限和函数极限两种,是高等数学最基本、最重要的概念之一.对于极限的计算,应用非常广泛.极限的求法更是多种多样,本文也将介绍几种求极限的方法.     

T-S模糊控制系统的虚拟等价系统及稳定性判据

针对未知确定性被控对象和未知非线性时变对象,通过构造虚拟等价系统的方法研究T-S模糊控制系统的稳定性.采用虚拟等价系统的目的在于降低原问题的难度,改进现有稳定性判据的保守性.分析结果表明,T-S模糊控制系统的稳定性主要取决于局部模型的精度、模糊规则的正确性以及局部控制器的镇定性.     

数列上下极限的研究

上下极限概念是极限概念的延伸,它们在正项级数收敛性判别、求极限、证收敛等方面有着重要的作用.本文将给出有界数列与上下极限关系的一种新证法,并且更深层次的研究了上极限与数列极限收敛之间的关系.     

铝板成形极限的简化预测

本文基于一种集中失效模型，结合ＣＭＰＴ和Ｈｏｓｆｏｒｄ非二次各向异性屈服函数，假定材料服从各方向同性加工硬化，提出了一种形式上相对简单，便于工程应用的成形极限图的方法。对比该方法的理论预测和实验实测结果，表明本文采用的方法是有效的。     

函数、极限、连续的教与学

在高职的教学中,安排第一章的主要内容是函数、极限与连续的学习.一般老师认为高等数学中极限的学习是重要内容.函数的知识一带而过,有的让学生自己看书.笔者经过几年的教学发现,高职学生数学底子太差,很多高中的数学知识没有形成系统结构.再经过一暑假的大放松,所学数学知识几乎忘得差不多,有的也是模糊记忆.所以直接去讲极限的概念,学生会感觉十分的抽象,不好理解.以下是笔者总结在函数,极限、连续这一章的具体教学方法及学生如何学习的总结.     

轧制变形的极限模拟技术

本文对上限法的发展历史进行了简略的回顾,阐述了对轧制变形模拟的实际意义,列举了轧制变形的极限模拟技术的原理及上限模拟技术的发展动态,并提出了有关的一些看法。     

定积分极限问题中的三种典型方法及应用

讨论定积分极限问题中三种典型方法,即隔离法,拟合法,分段法的要点与综合应用技巧.并通过实例说明这三种方法在应用中的有机联系.     

Equivalent Stress Equation for Unsaturated Soils. I: Equivalent Stress

In 1959 Bishop stated his effective stress equation for unsaturated soils. However, the difficulties in estimating the value of its main parameter χ, made this equation useless and it was abandoned for some time. Only recently, it has been recognized that the use of Bishop’s stress equation can lead to simpler and more realistic constitutive models for unsaturated soils. However, up to now the most successful equations to quantify the value of parameter χ are empirical and not satisfactory for most soils. Based on the analysis of the equilibrium of the solid particles of a soil showing a bimodal structure and subject to certain suction, it was possible to establish an analytical expression for Bishop’s parameter χ. The resulting stress has been called equivalent stress (in contrast with effective stress) and can be used to predict the shear strength of unsaturated soils. The equivalent stress is written as a function of the net stress and suction and requires two parameters: the saturated fraction and the degree of saturation of the unsaturated fraction of the soil. This equivalent stress clarifies some features of the strength of unsaturated soils that up to now had no apparent explanation. However, the determination of its two parameters cannot be made from current experimental procedures. A method for the determination of these parameters and a comparison between experimental and theoretical results for the shear strength of unsaturated soils are presented in a companion paper.     

Slenderness Limit for Hybrid FRP-Concrete Columns

Due to confinement effects, concrete-filled fiber-reinforced polymer (FRP) tubes have an enhanced performance comparable to conventionally reinforced concrete members. However, the strength and ductility enhancements may result in slender sections, which may be susceptible to instability or geometric and loading imperfections. Because stiffness of FRP is less than that of steel, designers cannot directly use current specifications to size compression members. Uniaxial compression tests on a total of seven hybrid columns, with slenderness ratios up to 36, showed that strength is reduced by as much as 71% of the equivalent short column, and the axial and hoop strains are reduced by as much as 85 and 87%, respectively. These significant reductions result in underutilization of confinement in slender columns. An analytical tool with an incremental approach was developed and compared favorably with test results. A parametric study was carried out, which showed the modulus of elasticity of the tube to have a pronounced effect on the slenderness limit of the column. A new equation was proposed for the slenderness limit of hybrid columns based on a maximum of 5% strength reduction.     

小功率电动机接地装置安全电阻限值

介绍了小功率电动机接地装置安全电阻的限值问题,对人体的安全电压,电流及系统的接地电阻限值,接地电阻阻值的不同对人体所造成的危害进行了分析,得出电机内部接地电阻过大对人体具有较大的触电危害。     

Equivalent Viscous Damping for a Bilinear Hysteretic Oscillator

A bilinear hysteretic model is commonly used to study elastoplastic structures. In this paper, a damped, bilinear hysteretic oscillator is studied under harmonic loading. We show the existence of an equivalent viscous damping for small values of a loading parameter such that the associated linear structure and the hysteretic structure have the same frequency response curves. We use the Kryloff-Bogoliuboff method of averaging to find the equivalent viscous damping as a function of the steady state amplitude. We present a model of a bilinear elastic oscillator which captures the steady-state dynamics of the hysteretic oscillator for low values of the loading parameter. We also study the nature of the dependence of the equivalent viscous damping on the kinematic hardening parameter.     

Equivalent Continuum Model for Deployable Flat Lattice Structures

Deployable structures can be stored in a compact, folded configuration and are easily deployed into load‐bearing, open forms. Hence, they are suitable for applications where speed and ease of erection and reusability are desired. The structures investigated here are prefabricated space frames made of so called scissor‐like elements, sets of two straight bars connected to each other by a pivot. These structures are stress‐free and self‐standing in both their folded and deployed configurations, thus overcoming major disadvantages of previous designs. This study deals with deployable structures that are flat and subjected to normal loads in their deployed configuration. Although the behavior for that loading case is linear, the availability of an equivalent continuum model for stiffness prediction is desirable because it can significantly reduce the computational effort during preliminary design. The derivation of such a model is not straightforward because of the unorthodox geometry and the rotations allowed by the hinged and pivotal connections. This problem is addressed by first applying the direct stiffness method within a symbolic manipulation framework to transform the lattice structure to an equivalent single‐layer grid, and then using existing expressions to obtain the desired equivalent plate. The model exhibits good accuracy and convergence characteristics for uniform loads.