An SQP algorithm for mathematical programs with nonlinear complementarity constraints

In this paper, we describe a successive approximation and smooth sequential quadratic programming （SQP） method for mathematical programs with nonlinear complementarity constraints （MPCC）. We introduce a class of smooth programs to approximate the MPCC. Using an 11 penalty function, the line search assures global convergence, while the superlinear convergence rate is shown under the strictly complementary and second-order sufficient conditions. Moreover, we prove that the current iterated point is an exact stationary point of the mathematical programs with equilibrium constraints （MPEC） when the algorithm terminates finitely.     

NEWTON METHOD FOR SOLVING A CLASS OF SMOOTH CONVEX PROGRAMMING

1ConvexProgrammingandExactPenaltyFunction Weconsiderthefollowingconvexprogramming:(P)minf(x)s.t.x∈S={x∈Rn:gi(x)≤0,i=1,…,m}.SupposethatSisacompactset.ThusthereexistsalargeboundedboxX,suchthatS={x∈Rn:gi(x)≤0,i=1,…,m}intX.Assumethatf(x),gi(x),i=1,…,m     

一种基于训练数据的迭代改进核函数

To improve performance of a support vector regression, a new method for a modified kernel function is proposed. In this method, information of all samples is included in the kernel function with conformal mapping. Thus the kernel function is data-dependent. With a random initial parameter, the kernel function is modified repeatedly until a satisfactory result is achieved. Compared with the conventional model, the improved approach does not need to select parameters of the kernel function. Sim- ulation is carried out for the one-dimension continuous function and a case of strong earthquakes. The results show that the improved approach has better learning ability and forecasting precision than the traditional model. With the increase of the iteration number, the figure of merit decreases and converges. The speed of convergence depends on the parameters used in the algorithm.     

Convergence of gradient method for Elman networks

The gradient method for training Elman networks with a finite training sample set is considered. Monotonicity of the error function in the iteration is shown. Weak and strong convergence results are proved, indicating that the gradient of the error function goes to zero and the weight sequence goes to a fixed point, respectively. A numerical example is given to support the theoretical findings.     

粉末冶金涡轮盘简单模拟件低周疲劳寿命研究

采用光滑圆棒试样和带孔平板试样,对不同温度下的镍基粉末高温合金(FGH95)的低周疲劳(LCF)寿命进行了试验研究和有限元分析。在详细分析试验和有限元计算结果的基础上,提出了复杂应力状态下的低周疲劳寿命模型。模型寿命表达为真实应力幅的函数,模型参数由不同应力水平加载作用下的光滑圆棒试样试验结果给定,进一步采用涡轮盘简单模拟件即带孔平板试样对比验证LCF寿命模型的有效性。有限元计算结果显示,理论预测寿命与试验结果能很好地吻合。     

弹性半平面中边界裂纹研究的新方法

讨论了载荷作用在裂纹面上的弹性半平面边界裂纹问题.研究以线弹性断裂力学为基础,采用复变函数方法以及Riemann-Hilbert(R-H)边值问题的一般理论,将问题分拆为含有限裂纹的全平面问题与无裂纹的半平面问题的叠加,计算得到裂纹尖端的应力强度因子.与文献结果比较,该方法具有精度高的优点.     

Modified integral-level set method for the constrained solving Global Optimization

The constrained global optimization problem being considered, a modified integral-level set method was illustrated based on Chew-Zheng‘s paper on Integral Global Optimizationand Wu‘s paper on Implementable Algorithm Convergence of Mottled Integral-Level SetMethod for Global Optimization Problem. It has two characters : 1 ) Each phase must constructa new function which has the same global optimal value as that of primitive objective function ;2) Comparing it with Zheng‘s method, solving level set procedure is avoided. Animplementable algorithm also is given and it is proved that this algorithm is convergent.     

Direct specturm analysis of the state space for random vibration of MDOF linear damped system

This paper proceeds from the general case of the unsymmetric linearized multi-degrees of freedom (MDOF) systems. By adopting the general complex modal theory of the state space, the response analysis for a system subjected to random excitation of the same source is carried out using as a kind of direct spectrum analysis method in frequency domain. With the input of power spectral density function given, the explicit expression of the power spectral density function matrix of the output response can be obtained. By taking Fourier inverse transform, the integrated expressions of the correlation function matrix and of the spectrum moment matrix are obtained. Comparing with the time domain method, this method enjoys the merit of visualization and avoids the procedure of transformation from the obtained response correlation function to be solved for the output spectrum utilizing Fourier transform. This paper has extended the application range of the traditional frequency domain analysis method. The mean square values and variety of statistical values can be obtained conveniently. This method and the time domain method are different in approach but equally satisfactory in their results. The project is supported by National Natural Science Foundation of China and National Education Commission Science Foundation of China     

New smooth gap function for box constrained variational inequalities

A new smooth gap function for the box constrained variational inequality problem(VIP) is proposed based on an integral global optimality condition.The smooth gap function is simple and has some good differentiable properties.The box constrained VIP can be reformulated as a differentiable optimization problem by the proposed smooth gap function.The conditions,under which any stationary point of the optimization problem is the solution to the box constrained VIP,are discussed.A simple frictional contact problem is analyzed to show the applications of the smooth gap function.Finally,the numerical experiments confirm the good theoretical properties of the method.     

WAY TO DETERMINE STIFFNESS FUNCTION OF STRUCTURE

For calculating the stiffness function of a structure, the differential equation of the vibration of the structure was divided into the differential equation on the original stiffness function that was known, and Fredholm integral equation of the first kind on the undetermined stiffness function that was unknown. And the stable solutions of the integral equation, when the smooth factor was equal to zero, was solved by the extrapolation with p smooth factors. So the stiffness function of the structure is obtained. Applied examples show that the method is feasible and effective.     

可压缩多介质流动的间断有限元方法

采用间断有限元方法、LS方法和通量装配技术相结合,建立了一种计算可压缩多介质流动的有效 方法。计算中以光滑Heavside函数构造流体比热比和重新初始化方程中的符号距离函数,并采用通量装配 技术抑制界面附近的非物理振荡。为解决可压缩多介质流动提供一种新的手段。     

A method for conformal mapping of a two-connected region onto an annulus

This paper presents a method for conformal of a two-connectedregion onto an annulus.The philosophy of the method is toconvert the problem into a Dirichlet problem and to prove thereal part of the analytic function transformation should be aharmonic function satisfying certain boundary conditions.Ac-cording to the theory of harmonic function we can determine theinner radius of the annulus from the condition that the harmonic function defined in two-connected region should be single-valued.It is then easy to see that the imaginary part can directly beobtained with the aid of Cauchy-Riemann conditions.The unknownconstants of integration only influence the argument of imagepoints and can easily be derived by using the one-to-one mappingof region onto an annulus.Without loss of generality,themethod can be used to conformally map other two-connected regionsonto an annulus if they can be subdivided into several rectang-ulars.The method has been programmed for a digital computer.It is demonstrated that the meth     

Prediction of Turbulent Separated Flow in a Turnaround Duct Using Wall Functions and Adaptivity

This paper presents an application of adaptive remeshing to the prediction of turbulent separated flows. The paper shows that the κ - ε model with wall functions can predict separated flows along smooth curved surfaces. Success is achieved if the wall functions exhibit values of y⁺ close to 30, and if meshes are fine enough to guarantee that wall function boundary conditions are grid converged. Adaptive remeshing proves to be a very cost effective tool in this context. The methodology is demonstrated on a problem possessing a closed form solution to establish the performance and reliability of the proposed approach. The method is then applied to prediction of turbulent flow in an annular, axisymmetric turnaround duct (TAD). Predictions from two computational models of the TAD are compared with experimental measurements. The importance of appropriate meshes to achieve grid independent solutions is demonstrated in both cases. Better agreement with measurements is obtained when partially developed profiles of u, κ, and ε are specified at the TAD inlet.     

一种SPH应力修正算法及自由表面流中的应用

提出了一种SPH应力修正算法,即模型中的拉应力和压应力分别采用不同的插值核函数和状态方程来处理,改善应力稳定性问题。介绍了一种改进的Quintic核函数,用于改善模型中压应力的稳定性。通过增加钟型核函数的光滑长度,改善模型中拉应力的稳定性。采用该应力修正算法模拟了无重力条件下方形液滴的震荡变形过程,对比分析了不同算法的模拟结果。此外,为进一步验证算法的适用性,模拟了溃坝算例。研究表明,改进的Quintic型核函数明显改善了粒子聚集现象,该SPH应力修正方法可以使液滴具有更均匀的粒子分布以及更光滑的自由表面,有效改善了SPH方法中的压应力不稳定作用以及自由表面流的模拟精度。     

基于流形覆盖思想的无网格方法的研究

本语言基于流形思想,利用有限覆盖,单位分解等概念,引入建立在覆盖上的覆盖函数和具有紧支撑特性的单位分解函数,建立场逼近的近似表达,由弱形式的Galerkin变分得到数值分析模型,结合边界条件用于边值问题的求解,由此建立了一类新的无网格数值方法,论文采用这种方法分析了平面弹性问题,分析了体积闭锁现象,h、p型收敛性等,提出了一种选择覆盖大小的方案,且对狭长城采用了椭圆覆盖形式,取得了比较好的效果。     

基于改进的双向渐进结构优化法的应力约束拓扑优化

工程结构设计时经常需要限制最大名义应力,以避免发生断裂或疲劳破坏,一个有效的策略是采用拓扑优化方法. 常规的双向渐进结构优化法(bi-evolutionary structural optimization, BESO)不能有效求解应力约束拓扑优化问题,为此本文提出一种改进的双向渐进结构优化方法,处理体积和应力约束下的最小柔顺性问题. 引入基于K-S函数的全局应力度量,以减小大量局部应力约束引起的计算代价. 采用拉格朗日乘子法将应力约束函数引入到目标函数,然后由二分法确定合适的拉格朗日乘子的值使得应力约束得到满足. 而且,详细推导了基于BESO方法的应力约束拓扑优化模型及其灵敏度列式,最后通过三个典型拓扑优化算例验证改进方法的有效性. 为展示考虑应力约束的优点,将应力约束设计与传统的基于刚度的设计进行了比较. 结果表明, 改进的BESO方法优化迭代过程稳健,获得了边界灰度单元很少的清晰的拓扑构型,并实现了有效降低应力集中效应的设计.      

New exact penalty function for solving constrained finite min-max problems

This paper introduces a new exact and smooth penalty function to tackleconstrained min-max problems.By using this new penalty function and adding justone extra variable,a constrained min-max problem is transformed into an unconstrainedoptimization one.It is proved that,under certain reasonable assumptions and when thepenalty parameter is sufficiently large,the minimizer of this unconstrained optimizationproblem is equivalent to the minimizer of the original constrained one.Numerical resultsdemonstrate that this penalty function method is an effective and promising approach forsolving constrained finite min-max problems.     

一种采用小波神经网络的GPS精密单点定位方法

针对GPS精密单点定位对高精度的需求,提出了一种采用小波神经网络的GPS精密单点定位解算方法。该方法利用小波变换和神经网络学习功能,无需准确系统先验信息,误差函数能够快速收敛,逼近真实误差模型,从而提高GPS精密单点定位精度。仿真结果表明,静态条件下与传统最小二乘法和卡尔曼滤波算法相比,该算法定位收敛时间缩短50%,定位精度分别提升90%和50%。动态情况下,较最小二乘法和卡尔曼滤波算法定位精度提高20%~80%。     

热传导问题的非协调数值流形方法

数值流形方法通过引入数学与物理双重网格,将插值域与积分域分别定义在两个不同的覆盖上,其优点是网格划分随意,不受复杂边界形状和材料界面的限制,是较之于有限元方法更一般化的数值模拟方法。在计算精度方面,数值流形方法远远高于有限元法。但它的精度还是不够理想。为此本文在单元总体位移场上附加非协调位移基本项,使单元位移函数趋于完全,构造了非协调流形单元来改善流形单元的计算精度和计算效率,并将其应用于热传导问题,推导了势问题的非协调数值流形方法。     

Elastic plates under bending solved by pseudocaustics

The method pf pseudocaustics was applied to the study of out-of-plane bending in elastic plates. It is shown that for bending problems where the loading mode is given, the method determines experimentally the complex potential function at selected points along the boundaries. A conformal mapping of the closed smooth curves of each boundary of the plate on to a unit circle allows the determination of the complex potential ϕ (ζ), expressed in the form of a Laurent series. This in turn yields the complete solution of the bent plate. In order to show the efficiency of the method it was applied to two typical examples of thin infinite plates in cylindrical bending, having either a circular central hole, or a square hole. The experimental results corroborate the theoretical results, thus proving that this combined theoretical and experimental method is suitable for solving elastic problems in applications with high accuracy, where other methods fail to yield satisfactory results.