Quasi-static transient thermal stresses in a thick annular disc

The present paper deals with the determination of transient thermal stresses in a thick annular disc. A thick annular disc is considered having zero initial temperature and subjected to arbitrary heat flux on the upper and lower surfaces where as the fixed circular edges are at zero temperature. The governing heat conduction equation have been solved by using integral transform technique. The results are obtained in series form in terms of Bessel’s functions. The results for displacement and stresses have been computed numerically and are illustrated graphically.     

Fast solution of the elasticity problem for a planar crack of arbitrary shape in 3D-anisotropic medium

A planar crack of arbitrary shape in a 3D-anisotropic elastic medium subjected to an arbitrary external stress field is considered. An efficient numerical method of the solution of the problem is proposed. The problem is reduced to an integral equation for the crack opening vector on the crack surface. For discretization of this equation, Gaussian (radial) approximation functions centered at a system of nodes that covers the crack surface are used. For such functions, the elements of the matrix of the discretized problem are calculated in a quasi analytical form that involves standard non-singular integrals. If the node grid is regular, the matrix of the discretized system has Teoplitz’s structure, and the Fast Fourier Transform algorithm may be used for the calculation of matrix-vector products with such a matrix. It accelerate substantially the process of the iterative solution of the discretized system. Examples of the solutions for a circular crack in a transversally isotropic elastic medium are presented.     

向量值函数的Henstock-Stieltjes积分

本文引入闭区间上实值函数关于向量值函数的Henstock-Stieltjes积分,研究了Henstock- Stieltjes积分的性质,给出了Henstock-Stieltjes积分可积的充要条件,并得到了Henstock- Stieltjes积分的收敛定理,最后证明了向量值函数在闭区间上关于实值右连续函数是Pettis可积,那么必为Henstock-Stieltjes可积。     

Influence of laser parameters on the geometric characteristics of a beam transformed by an optical system

The influence of the parameters of a laser on the divergence and the light radii of a beam formed by a plane optical resonator and transformed by an optical system is considered. The studies are conducted for a broad range of Fresnel numbers characteristic of lasers. __________ Translated from Izmeritel’naya Tekhnika, No. 1, pp. 24–27, January, 2008.     

不连续位移超奇异积分方程法解三维多裂纹问题

本文采用Beti互等功定理,导出了三维不连续位移基本解的一般形式,然后以该基本解为核函数,建立了求解三维多裂纹问题的超奇异边界积分方程组,并采用三角形单元变换技术和有限部分积分的方法给出了超奇异积分的数值解法,引入非协调单元处理技术解决了法向不确定的角点问题。最后,由裂纹面间断位移可直接求得裂纹前沿任意点的应力强度因子。     

可对称化不定非线性问题的不精确Newton法

本文讨论了处理可对称化不定问题的不精确Newton方法,并针对问题的特殊结构提出了不精确Newton-PSMINRES算法。理论分析与数值试验表明,Newton-PSMINRES算法优于其它处理可对称化不定问题的不精确Newton-Krylov算法。     

Mass lumping strategies for X‐FEM explicit dynamics: Application to crack propagation

This paper deals with the numerical modelling of cracks in the dynamic case using the extended finite element method. More precisely, we are interested in explicit algorithms. We prove that by using a specific lumping technique, the critical time step is exactly the same as if no crack were present. This somewhat improves a previous result for which the critical time step was reduced by a factor of square root of 2 from the case with no crack. The new lumping technique is obtained by using a lumping strategy initially developed to handle elements containing voids. To be precise, the results obtained are valid only when the crack is modelled by the Heaviside enrichment. Note also that the resulting lumped matrix is block diagonal (blocks of size 2 × 2). For constant strain elements (linear simplex elements) the critical time step is not modified when the element is cut. Thanks to the lumped mass matrix, the critical time step never tends to zero. Moreover, the lumping techniques conserve kinetic energy for rigid motions. In addition, tensile stress waves do not propagate through the discontinuity. Hence, the lumping techniques create neither error on kinetic energy conservation for rigid motions nor wave propagation through the crack. Both these techniques will be used in a numerical experiment. Copyright © 2007 John Wiley & Sons, Ltd.     

Analyzing the effect of introducing a kurtosis parameter in Gaussian Bayesian networks

Gaussian Bayesian networks are graphical models that represent the dependence structure of a multivariate normal random variable with a directed acyclic graph (DAG). In Gaussian Bayesian networks the output is usually the conditional distribution of some unknown variables of interest given a set of evidential nodes whose values are known. The problem of uncertainty about the assumption of normality is very common in applications. Thus a sensitivity analysis of the non-normality effect in our conclusions could be necessary. The aspect of non-normality to be considered is the tail behavior. In this line, the multivariate exponential power distribution is a family depending on a kurtosis parameter that goes from a leptokurtic to a platykurtic distribution with the normal as a mesokurtic distribution. Therefore a more general model can be considered using the multivariate exponential power distribution to describe the joint distribution of a Bayesian network, with a kurtosis parameter reflecting deviations from the normal distribution. The sensitivity of the conclusions to this perturbation is analyzed using the Kullback-Leibler divergence measure that provides an interesting formula to evaluate the effect.     

Radiation of sound waves from a rigid stepped cylindrical waveguide

The radiation of plane harmonic sound waves from a rigid stepped cylindrical waveguide is treated by using the mode-matching method in conjunction with theWiener-Hopf technique. The solution is exact, but formal, since infinite series of unknowns and some branch-cut integrals with unknown integrands are involved. Approximation procedures based on rigorous asymptotics are used and the approximate solution to the Wiener-Hopf equations is derived in terms of infinite series of unknowns, which are determined from infinite systems of linear algebraic equations. Numerical solutions of these systems are obtained for various values of the parameters of the problem and their effects on the directivity of the stepped waveguide is presented.     

Central limit theorem for the estimator of the value of an optimal stopping problem

We consider an optimal stopping problem defined on a finite Markov chain whose transition probabilities are unknown. We prove a central limit theorem for the maximum likelihood estimator and the stretch estimator of the optimal value of the optimal stopping problem. Also, we propose a perturbation technique to weaken the hypotheses of the central limit theorem. The author was supported by a grant from the SpanishScretaría de Estado de Educación y Universidades in cooperation with the European Social Funds.     

下限问题中基于四边形单元平衡方程的边界积分法

相对于三角形单元的下限分析,基于四边形单元的下限分析具有更高的精度和求解效率。该文利用格林公式把平衡方程的弱形式化为边界积分,从而得到简洁的线性方程,取代了以往的数值积分方案,克服了高斯积分中坐标变换等复杂的求解过程。此外还对应力连续性方程进行了简化。该积分方案不仅大大简化了计算,而且更易于编程实现。算例表明该文方法具有较高的精度。     

Sequential Experiment Design for Contour Estimation From Complex Computer Codes

Computer simulation often is used to study complex physical and engineering processes. Although a computer simulator often can be viewed as an inexpensive way to gain insight into a system, it still can be computationally costly. Much of the recent work on the design and analysis of computer experiments has focused on scenarios where the goal is to fit a response surface or process optimization. In this article we develop a sequential methodology for estimating a contour from a complex computer code. The approach uses a stochastic process model as a surrogate for the computer simulator. The surrogate model and associated uncertainty are key components in a new criterion used to identify the computer trials aimed specifically at improving the contour estimate. The proposed approach is applied to exploration of a contour for a network queuing system. Issues related to practical implementation of the proposed approach also are addressed.     

A SINGULAR INTEGRAL EQUATION SOLUTION FOR THE LINEAR ELASTIC CRACK OPENING DISPLACEMENT OF AN ARBITRARILY SHAPED PLANE CRACK: PART II REGULAR INTEGRAL SOLUTIONS

Abstract— The boundary value problem for an arbitrarily shaped plane crack embedded in a 3D linear elastic solid can be reduced to a governing hyper-singular integral equation. A discretizing procedure based on a triangulation of the crack area has been offered in Part I of this work. The main goal of Part I is to introduce the analytical results for the 18 resulting finite-part integrals defined over a triangular mesh area. The finite-part integrals occur in those triangles where the source point coincides with one of the element nodes. Mostly the source point lies outside of the considered triangle. In these cases the occurring area integrals are regular.
The aim of Part II is, therefore, the derivation of the closed form expressions for the relevant 18 regular area integrals. The resulting relations are of algebraic form which can easily be coded in compact form. Their numerical proof by two different methods shows the highest accuracy and, therefore, the correctness of the final solutions. The relevant numerical results are offered in Appendix I.
With the formulae provided in Part I and Part II of the paper the determination of the coefficient matrix, necessary for the calculation of COD values from a linear equation system, is precise and needs only minimum computer time.