无约束全局优化的一个可调参数的填充函数

A filled function with adjustable parameters is suggested in this paper for finding a global minimum point of a general class of nonlinear programming problems with a bounded and closed domain. This function has two adjustable parameters. We will discuss the properties of the proposed filled function. Conditions on this function and on the values of parameters are given so that the constructed function has the desired properties of traditional filled function.     

梯形重力坝的应力函数解及其有限元验证

弹性力学教材中通过取三次多项式应力函数给出三角形横截面的重力坝应力场,但工程中重力坝的横截面几乎均为梯形,其坝顶并非三角形尖顶。将应力函数的半逆解法与锲形体的应力函数相结合,寻找出适用于梯形重力坝的应力函数,根据梯形重力坝力的边界条件,并利用圣维南原理,给出了梯形重力坝的应力场解析式。用有限元计算给出了梯形重力坝应力场的数值仿真结果。应力场解析式与有限元仿真结果非常吻合,说明了梯形重力坝应力场解析式的正确性。梯形重力坝应力场解析式对水利工程中重力坝的结构强度及设计具有重要的理论指导意义和应用价值。

     

Differential FBG sensor for temperature-compensated high-pressure (or displacement) measurement

A differential fiber Bragg grating (FBG) sensor with a free active element bulk-modulus for high-pressure (or displacement) measurement is presented. Based on the differential measurement method and an isosceles triangle cantilever structure, problems of cross-sensitivity and chirped signal in FBG sensor are improved both theoretically and experimentally. Preliminary experiments indicate that temperature-compensated measurement results agree well with the theoretical analysis. Displacement measurement sensitivity is 1.75 pm/μm, and the estimated pressure measurement resolution can reach 0.27 MPa in case the wavelength shift measurement resolution is 0.01 nm.     

关于Euler-Maclaurin公式的一个注记

利用梯形公式的余项,将被积函数的二阶导数做幂级数展开,证明了余项是关于求积区间长度的奇数次幂级数.推导出了复合梯形公式的一类渐近展开式,从另一方面印证了Euler-Maclaurin公式.     

模糊多属性群决策一致性分析研究

群决策过程中各成员可能以不同的方式给出决策信息,讨论了四种不同决策信息的统一方法,设置了模糊环境下进行一致性判断的准则,介绍了梯形模糊数在群决策过程中的运算方法,举例说明了这种方法的应用步骤.     

梯形模糊数的有序表示及中心平均排序方法

模糊数的排序在决策分析和优化问题中占有十分重要的地位,而一般模糊数均可近似分解为若干分片小梯形的叠加形式,故梯形模糊数的排序问题至关重要!本文首先引入等距分片方法对梯形模糊数实施纵向分割,进而获得梯形模糊数的有序表示。其次,依中心平均加权准则改进梯形模糊数的横向和纵向中心坐标公式,并提出新的指标排序准则。最后,通过实例分析考证了新的排序方法的有效性。     

Hill‐climbing to Pasch valleys

Exhaustive enumeration of Steiner Triple Systems is not feasible, due to the combinatorial explosion of instances. The next‐best hope is to quickly find a sample that is representative of isomorphism classes. Stinson's Hill‐Climbing algorithm [ 20 ] is widely used to produce random Steiner Triple Systems, and certainly finds a sample of systems quickly, but the sample is not uniformly distributed with respect to the isomorphism classes of STS with ν ≤ 19, and, in particular, we find that isomorphism classes with a large number of Pasch configurations are under‐represented. No analysis of the non‐uniformity of the distribution with respect to isomorphism classes or the intractability of obtaining a representative sample for ν > 19 is known. We also exhibit a modification to hill‐climbing that makes the sample if finds closer to the uniform distribution over isomorphism classes in return for a modest increase in running time. © 2007 Wiley Periodicals, Inc. J Combin Designs 15: 405–419, 2007     

The best quadrature formula based on Hermite information for the class KW~2[a,b]

The best quadrature formula has been found in the following sense:for afunction whose norm of the second derivative is bounded by a given constant and thebest quadrature formula for the approximate evaluation of integration of that function canminimize the worst possible error if the values of the function and its derivative at certainnodes are known.The best interpolation formula used to get the quadrature formula aboveis also found.Moreover,we compare the best quadrature formula with the open compoundcorrected trapezoidal formula by theoretical analysis and stochastic experiments.     

梯形箱梁剪力滞后效应的精细化分析

引入剪滞翘曲应力自平衡条件的影响,考虑了剪切变形和剪滞效应等因素,设置了三个不同的剪滞纵向位移差函数以准确反映梯形箱梁不同宽度翼板的剪滞变化幅度,提出了一种能对工程中常用箱梁静力学特性分析的精确解法。本文以能量变分原理为基础建立了薄壁箱梁的弹性控制微分方程和自然边界条件,获得了相应广义位移的闭合解。算例中,分析了不同荷载形式、跨宽比和悬臂板长度等因素对箱梁静力学特性的影响,结果显示出引入剪滞翘曲应力自平衡条件的必要性。     

Energy theorems for solving equations of deflections

In this paper the unit-dummy-load method is generalized on the basis of Castigliano’s Theorem. On these grounds the general eguations of deflection surfaces of the structures, such as a kind of beams,plates and shells, are directly derived by the force method.We derived the eguations of the deflection surfaces of the rectangular thin plates and thick plates considering the effect of transverse shearing deformations with the inhomogeneous displacement boundary conditions. At the same time we give the equations of deflection axes of the corresponding straight beams.The applications of the reciprocal theorem are also generalized.Three simple calculated examples are given.