结构的失效可能度及模糊概率计算方法

依据模糊可能性理论,系统地建立含模糊变量时结构的可靠性计算模型。旨在解决模糊结构、模糊-随机结构和模糊状态假设下结构的可靠性计算问题。所建模型可给出模糊结构失效的可能度和模糊-随机结构失效概率的可能性分布。研究表明:对同时含模糊变量和随机变量的混合可靠性计算问题,把失效概率(或可靠度)作为模糊变量,能更客观地反映系统的安全状况。算例分析说明了文中方法的合理性和有效性。     

寻找具有三个任意函数的变系数KdV-MKdV方程的类孤波解的新方法

给出了求具有三个任意函数的变系数非线性演化方程的类孤波解的截断展开方法.这种方法的关键是首先把形式解设为几个待定函数的截断展开形式,从而可将变系数非线性演化方程转化为一组待定函数的代数方程,然后进一步给出容易积分的待定函数的常微分方程组,从而构造出相应的类孤波解.     

Soliton Solutions and Interaction Between a Line Soliton and a y-Periodic Soliton in Generalized （2W1）-Dimensional Nizhnik-Novikov-Veselov Equation

Using the variable separation approach, many types of exact solutions of the generalized (2 1)-dimensional Nizhnik-Novikov-Veselov equation are derived. One of the exact solutions of this model is analyzed to study the interaction between a line soliton and a y-periodic soliton.     

Solving mKdV-sinh-Gordon equation by a modified variable separated ordinary differential equation method

By introducing a more general auxiliary ordinary differential equation (ODE), a modified variable separated ODE method is developed for solving the mKdV--sinh-Gordon equation. As a result, many explicit and exact solutions including some new formal solutions are successfully picked up for the mKdV--sinh-Gordon equation by this approach.     

柱塞泵油膜压力分析的高效有限单元法

The paper concerns numerical analysis of pressure distribution of an oil film on the valve plate in the variable height gap of an axial piston pump. The analysis employs the finite element method. For determination of oil pressure variations in the gap, the Reynolds equation, commonly applied in the theory of lubrication, is applied. The equation is solved numerically with the use of self-developed program based on the finite element method. In order to obtain high accuracy of the results, an adaptive mesh refinement based on residual estimations of solution errors is applied. The calculation results are represented as dependent on the geometric and working parameters of the pump.     

改进的有自由面非稳定渗流分析复合单元渗透矩阵调整法

应用连续的罚函数,提出了一种改进的自由面边界条件渗流分析复合单元渗透矩阵调整法,优化了此类算法的稳定性,提高了收敛速度和精度,并将此改进算法编制成相应的有限元分析程序,应用于上海地铁4号线董家渡隧道修复基坑降水工程的优化设计,解决了基坑降水过程中复杂三维渗流场的高效精细模拟问题,同时预测了基坑中心水位降至地面以下40 m,位于承压含水层顶面以下,基坑内外自由面落差很大时基坑周边渗流场以及地面沉降的分布特征.     

Variable bandwidth and one-step local M-estimator

A robust version of local linear regression smoothers augmented with variable bandwidth is studied. The proposed method inherits the advantages of local polynomial regression and overcomes the shortcoming of lack of robustness of least-squares techniques. The use of variable bandwidth enhances the flexibility of the resulting local M-estimators and makes them possible to cope well with spatially inhomogeneous curves, heteroscedastic errors and nonuniform design densities. Under appropriate regularity conditions, it is shown that the proposed estimators exist and are asymptotically normal. Based on the robust estimation equation, one-step local M-estimators are introduced to reduce computational burden. It is demonstrated that the one-step local M-estimators share the same asymptotic distributions as the fully iterative M-estimators, as long as the initial estimators are good enough. In other words, the one-step local M-estimators reduce significantly the computation cost of the fully iterative M-estimators without deteriorating their performance. This fact is also illustrated via simulations.     

一类非线性变系数差分方程正解的振动性

研究了一类具有时滞的非线笥变系数差分方程Ｘｎ＋１＝Ｘｎｅｘｐ（ｒｎ１－ｘｎ－ｋ／１－ｃｘｎ－ｋ解的振动性,获得了其正解关于正平衡点ｘ＝１振动的好的充分条件。     

Topological Invariants and Solutions with a High Complexity for Scalar Semilinear PDE

In this paper topological invariants of dynamics of scalar parabolic equations are defined. Conservation of these invariants causes persistence of complex spatially chaotic patterns in the dynamics. It implies, in particular, the existence of extremely many stable essentially different spatially complex solutions of scalar semilinear parabolic, elliptic and hyperbolic equations in the situation when coefficients of equations depend on the spatial variable strongly enough and the domain is large or unbounded, the number of different solutions exponentially depends on the volume of domain. Another implication of the conserved quantities is persistence of complexity of solutions in the dynamics.     

可伸长变截面杆的弹性过屈曲模型及其数值解

在Ｋｉｒｃｈｈｏｆｆ基本假设下,基于轴线可伸长弹性杆的几何非线性理论,建立了一端简支另一端固定夹紧变截面直什的过屈曲控制方程,并应用打靶法直接数值求解相应的强非线性过值问题,获得了数值意义上的精确解。