大几何参数的变厚度开顶扁薄壳的非线性屈曲问题的奇摄动解

该文利用修正多重尺度法研究了大几何参数的变厚度的具有刚性中心的开顶扁球壳，在均布载荷作用下的非线性稳定问题．求得了扁壳几何参数k值较大时，本问题的一致有效的渐进解，并进行了余项误差估计．     

多重尺度法应用于变厚度开顶扁球壳在复合载荷下的非线性稳定问题

利用改进多重尺度法研究了大几何参数的变厚度的具有刚性中心的开顶扁球壳,在复合载荷作用下的非线性稳定问题,求得了扁壳几何参数k值较大时,本问题的一致有效的渐近解,并进行了余项误差估计。     

扁球壳在均布压力与均匀温度场联合作用下的屈曲

根据扁壳几何非线性理论,推导了均布压力与均匀温度场联合作用下的扁球壳的位移型几何非线性控制方程.考虑夹紧边界条件,采用打靶法得到了扁球壳轴对称弯曲与屈曲的数值结果.讨论了壳体几何参数对平衡路径、临界荷载的影响.给出了壳体临界几何参数.当几何参数大于临界几何参数时,上、下临界荷载都随几何参数增加而增加.给定几何参数时,考察了不同均匀温度场对壳体上、下临界荷载、临界几何参数以及平衡构型的影响.均匀升温会使上临界荷载显著增加,会使下临界荷载略有减小.均匀变温会使临界几何参数改变.     

扁球壳在热-机械荷载作用下的稳定性分析

基于扁壳几何非线性理论,应用虚功原理和变分法推导了均匀变温场中圆底扁薄球壳在均布外侧压力作用下的位移型几何非线性控制方程.考虑周边不可移简支边界条件,运用打靶法计算获得了不同几何参数的扁球壳轴对称弯曲变形的数值结果.定义了壳体临界几何参数.考察了壳体几何参数对平衡路径和临界荷载的影响.当壳体几何参数大于壳体临界几何参数时,上临界荷载随几何参数的增加单调增加,下临界荷载在很小范围内随几何参数的增加而增加,之后随几何参数的增加而减小.给定几何参数时,考察了不同均匀温度变化对壳体临界几何参数、临界荷载和平衡构型的影响.均匀升温使上临界荷载显著增加,使下临界荷载和临界几何参数显著减小.     

线布载荷作用下碟形扁壳的非线性稳定*

本文对轴对称线布载荷作用下碟形扁壳的非线性稳定问题进行了分析,得到了各种常见边界条件下碟形扁壳特征关系的二次近似表达式.讨论了几何参数β,γ和k对非线性特性的影响.     

变厚度夹层截顶扁锥壳的非线性稳定性分析

对具有变厚度夹层截顶扁锥壳的非线性稳定问题进行了研究。利用变分原理导出表层为等厚度而夹心为变厚度的夹层截顶扁锥壳的非线性稳定问题的控制方程和边界条件,采用修正迭代法求得了具有双曲型变厚度夹层截顶扁锥壳的非线性稳定性问题的解析解,得到了内边缘与一刚性中心固结而外边缘为可移夹紧固支的变厚度夹层截顶扁锥壳临界屈曲载荷的解析表达式,讨论了几何参数和物理参数对壳体屈曲行为的影响。     

在边缘线布载荷作用下开顶扁球壳的非线性稳定问题的奇摄动解

本文利用奇异摄动方法计算了在内边缘线布载荷作用下无刚性中心的开顶扁球壳的非线性稳定问题,得到了几何参数k值较大时本问题的一致有效的渐近解.     

静载荷作用下正交各向异性旋转扁壳的非线性自由振动

本文用加权残值法和Lindstedt－Poincare摄动法研究了圆柱型正交各向异性扁薄球壳和锥壳在均布静载荷作用下的轴对称非线性自由振动问题，得到了其非线性固有频率和振幅间的特征关系，并讨论了静载荷及壳体的几何参数和材料参数对其振动特性的影响。     

双层网格圆底扁球壳的非线性稳定问题

从基于等效夹层壳思想的双层网格扁壳,非线性弯曲理论的变分方程出发,利用坐标变换方法和驻值余能原理,导出双层网格圆底扁球壳,在均布压力作用下的轴对称大挠度方程和边界条件．采用修正迭代法,求得了两类边界条件下双层网格圆底扁球壳的非线性载荷-位移关系式和临界屈曲载荷的解析表达式,并讨论了几何参数对临界屈曲载荷的影响．     

集中载荷作用下开顶扁球壳的非线性稳定问题的渐近解

本文利用奇异摄动法研究了具有刚性中心的边缘固定的开顶扁球壳在中心集中载荷作用下的非线性稳定问题,得到了几何参数κ值较大时的一致有效的渐近解.     

Regularization Using QR Factorization and the Estimation of the Optimal Parameter

In this paper we propose a direct regularization method using QR factorization for solving linear discrete ill-posed problems. The decomposition of the coefficient matrix requires less computational cost than the singular value decomposition which is usually used for Tikhonov regularization. This method requires a parameter which is similar to the regularization parameter of Tikhonov's method. In order to estimate the optimal parameter, we apply three well-known parameter choice methods for Tikhonov regularization.This revised version was published online in October 2005 with corrections to the Cover Date.     

On the problem concerning the points of semicontinuity of the stabilization index

We construct examples of families of linear homogeneous differential systems with coefficients continuously depending on a numerical parameter for which the absence of some form of semicontinuity of the stabilization index treated as a function of this parameter is typical.     

Identification problems for the damped Klein-Gordon equations

In this paper we study the identification problems for the damped Klein-Gordon equation (KG). In particular, when the diffusion parameter of KG is unknown, we prove the existence of the optimal parameter and deduce the necessary conditions on the optimal parameter by using the transposition method.     

On the nano-structural dependence of nonlocal dynamics and its relationship to the upper limit of nonlocal scale parameter

Nonlocal elasticity theory is one of the most popular theoretical approaches to investigate the intrinsic scale effect of nano-materials/structures. The coupling of an internal characteristic length and a material parameter can be regarded as a nonlocal scale parameter in nano-meters. The range of this non-dimensional scale parameter is from zero up to different values previously. There is no doubt that the zero nonlocal scale parameter corresponds to a situation without any nonlocal effect. However, the determination of a peak value for the scale parameter is still uncertain. In fact, we frequently ask a simple but unresolved question, i.e., how strong is the nonlocal scale effect? This question is equivalent to what the maximum value of the nonlocal scale parameter is, since it was introduced to characterize the scale effect theoretically. Until now, various maximum values have been selected without rigorous verifications. In this paper, the nano-structural dependence of nonlocal dynamical behavior is investigated to present the existence of an upper limit for the scale parameter. Through three typical examples, the size-dependent behavior of nonlocal dynamics for various nano-structures is analyzed. The upper limit of the scale parameter can be determined accordingly. It is shown that an interval for the scale parameter in the illustrative examples can be found on the basis of the nonlocal softening physical mechanism, in which the equivalent stiffness of nano-structures is weakened than that predicted by the classical continuum theory. The present study contributes to a fuzzy zone in nonlocal elasticity where people are puzzled over the question how to select the upper limit of the nonlocal scale parameter. It is not only beneficial to the refinement of the nonlocal theory of elasticity, and also useful for the exploration of similar theories in nano-mechanics.     

Stochastic orders of the Marshall-Olkin extended distribution

A general method of introducing a parameter, called tilt parameter, has been discussed by Marshall and Olkin (1997) to give more flexibility in modelling. In this paper, we take the tilt parameter of the Marshall-Olkin extended family as a random variable. The closure of this model under different stochastic orders viz. ageing intensity order, likelihood ratio order, shifted likelihood ratio orders and shifted hazard rate orders is discussed.     

Closing the gap in the purely elliptic generalized Davey–Stewartson system

In this note we improve the results presented previously on global existence and global nonexistence for the solutions of the purely elliptic generalized Davey–Stewartson system. These results left a gap in the parameter range where neither a global existence result nor a global nonexistence result could be established. Here we are able to show that when the coupling parameter is negative there is no gap. Moreover, in the case where the coupling parameter is positive we reduce the size of the gap.     

The selection of the optimal parameter in the modulus-based matrix splitting algorithm for linear complementarity problems

The modulus-based matrix splitting (MMS) algorithm is effective to solve linear complementarity problems (Bai in Numer Linear Algebra Appl 17: 917–933, 2010). This algorithm is parameter dependent, and previous studies mainly focus on giving the convergence interval of the iteration parameter. Yet the specific selection approach of the optimal parameter has not been systematically studied due to the nonlinearity of the algorithm. In this work, we first propose a novel and simple strategy for obtaining the optimal parameter of the MMS algorithm by merely solving two quadratic equations in each iteration. Further, we figure out the interval of optimal parameter which is iteration independent and give a practical choice of optimal parameter to avoid iteration-based computations. Compared with the experimental optimal parameter, the numerical results from three problems, including the Signorini problem of the Laplacian, show the feasibility, effectiveness and efficiency of the proposed strategy.

     

Apply a novel evolutionary algorithm to the solution of parameter selection problems

In this study, a modified line-up competition algorithm (LCA) is used to solve parameter selection problems. The so-called parameter selection problems contain parameter identification problems and optimal control problems. Once the later problems are transformed by control parametrization, the parameters embedded in both problems are selected by the proposed method under the framework of integration approach. Two parameter identification problems and one optimal control problem are given to demonstrate the use of LCA. The results show that in addition to being insensitive to the initial conditions, LCA is very efficient in solving highly nonlinear parameter selection problems.     

Application of M-PML absorbing boundary conditions to the numerical simulation of wave propagation in anisotropic media. Part II: Stability

This paper deals with detailed properties of M-PML (Multiaxial Perfectly Matched Layer) absorbing boundary conditions, which are used when the computational domain is limited. These conditions are stable for any type of anisotropy with the correct choice of a stabilization parameter. In the first part of this paper, [3], the authors show that the reflectivity is a linear function of the stabilization parameter. Based on this study, the problem of finding an optimal stabilization parameter that provides stability and minimal reflection is formulated. A necessary M-PML stability condition that allows limiting the lower values of the stabilization parameter is obtained. It is shown that this criterion is not sufficient.     

指数型一次Logistic迭代方程解的周期倍分岔现象

本文讨论了指数型一次Ｌｏｇｉｓｔｉｃ迭代方程解的周期倍分岔现象的存在性,给出了周期倍分合时的临界点参数应满足的方程,并证明了周期倍分岔的临界点参数序列的极限是存在的,进而证明了当参数越过这个极限时,指数型一次 Ｌｏｇｉｓｔｉｃ迭代方程存在混沌解．