Stress and strain field near tip of mode III growing crack in materials with creep behavior

Using a proposed constitutive relation for materials with creep behavior, the stress and strain distribution near the tip of a Mode III growing crack is examined. Asymptotic equations of the crack tip field are derived and solved numerically. The stresses remain finite at the crack tip. Obtained qualitatively is the crack tip velocity and the local autonomy of the near tip field solution is discussed.     

Numerical Investigation of a Bluff-Body Stabilised Nonpremixed Flame with Differential Reynolds-Stress Models

A numerical investigation of a bluff-body stabilised nonpremixedflame, and the corresponding nonreacting flow, has been performed withdifferential Reynolds-stress models (DRSMs). The equilibrium chemistry model is employed and an assumed-shape beta function PDFapproach is used to represent the interaction between turbulence andchemistry. The Reynolds flux of the mixture fraction is obtained from atransport equation, hence a full second moment closure is used. Toclarify the applicability of the existing DRSMs in this complex flame,several models, including LRR-IP model, JM model, SSG model as well as amodified LRR-IP model, have been applied and evaluated. The existingmodels, with default values of the coefficients, cannot provide overallsatisfactory predictions for this challenging test case. The standardLRR-IP model over predicts the centreline velocity decay rate, andtherefore does not perform satisfactory. The modified LRR-IP model, withmodel constant C _∈1 = 1.6 instead of the standard value1.44 (here named BM-M1), gives better results for the mean velocity.However in the nonreacting case this does not lead to improvement inpredicting rms fluctuating velocities especially downstream of therecirculation zone. Motivated by the need to improve the prediction, anew modification of the LRR-IP model is proposed (BM-M2), with modelconstant C ₂ = 0.7in the pressure strain correlation rather thanthe standard value 0.6. With the new modified model, a verysignificant improvement of the prediction of flow field is obtained inthe nonreacting case, whereas in the reacting case the prediction ofthe flow field is of the same overall quality as with BM-M1. This showsthat some DRSMs have different behaviour in the nonreacting case andthe reacting case. In the reacting case also the mean and variance ofmixture fraction are considered and it is found that the best resultsare obtained with the BM-M1 model, with SSG as second best. Combiningthe results for flow field and mixture fraction field it is concludedthat the BM-M1 model is recommended for further studies of thisbluff-body stabilised flame. Grid independence of the result isdemonstrated.     

Large strain field near a notch-tip under tension

This paper considers the plane strain notch-tip filed in a rubber-like material under tension. Based on a new constitutive relation, the asymptotic equations of the near tip field are derived and solved. It is shown that the notch tip field is composed of two narrowing sectors and an expanding sector. The dominant stress and strain near the notch tip are found to be in a state of uniaxial tension.     

The effective properties of composites with fiber-end cracks

The paper describes use of self-consistent finite element method (SCFEM) for predicting effective properties of fiber composite with partially debonded interface. The effective longitudinal Young's modulus and shear modulus for unidirectional fiber reinforced composites with fiber-end cracks are calculated. Numerical results show that the effective properties are considerably influenced by the fiber-end cracks. The effects of microstructural parameters, such as fiber volume fraction, modulus ratio of the constituents and fiber aspect, on the effective properties of the composites were discussed. The project supported by the National Natural Science Foundation of China     

边界元法边界层处理的一种新方法—拟多连域法

提出了处理边界元法边界层问题的新方法。这种方法在求得边界未知量后，在距边界较远的域中构造一工作边界，将实际边界与工作边界看作一多连域问题求得工作边界的未知量。再将工作边界与边界层边界视为一多连域问题求解，可得到满足精度要求的边界附近点的位移与应力。这种方法理论简洁、计算方便、有效、精度高，对于需求边界上多点的未知量问题很具优越性     

Density of first Poincaré returns,periodic orbits,and Kolmogorov–Sinai entropy

It is known that unstable periodic orbits of a given map give information about the natural measure of a chaotic attractor. In this work we show how these orbits can be used to calculate the density function of the first Poincaré returns. The close relation between periodic orbits and the Poincaré returns allows for estimates of relevant quantities in dynamical systems, as the Kolmogorov–Sinai entropy, in terms of this density function. Since return times can be trivially observed and measured, our approach to calculate this entropy is highly oriented to the treatment of experimental systems. We also develop a method for the numerical computation of unstable periodic orbits.     

Transient analysis of an M/G/1 retrial queue subject to disasters and server failures

An M/G/1 retrial queueing system with disasters and unreliable server is investigated in this paper. Primary customers arrive in the system according to a Poisson process, and they receive service immediately if the server is available upon their arrivals. Otherwise, they will enter a retrial orbit and try their luck after a random time interval. We assume the catastrophes occur following a Poisson stream, and if a catastrophe occurs, all customers in the system are deleted immediately and it also causes the server’s breakdown. Besides, the server has an exponential lifetime in addition to the catastrophe process. Whenever the server breaks down, it is sent for repair immediately. It is assumed that the service time and two kinds of repair time of the server are all arbitrarily distributed. By applying the supplementary variables method, we obtain the Laplace transforms of the transient solutions and also the steady-state solutions for both queueing measures and reliability quantities of interest. Finally, numerical inversion of Laplace transforms is carried out for the blocking probability of the system, and the effects of several system parameters on the blocking probability are illustrated by numerical inversion results.     

A characteristic quantity of P-matrices

In this note, we develop some new properties of a fundamental quantity associated with a P-matrix introduced by Mathias and Pang [1]. Also, based on extensions of such a quantity, we obtain global error bounds for the vertical and horizontal linear complementarity problems.     

A bound for Wilson's general theorem

Given any set K of positive integers and positive integer λ, let c(K,λ) denote the smallest integer such that v∈B(K,λ) for every integer v≥c(K,λ) that satisfies the congruences λv(v-1)≡0 (mod β(K) and λ(v-1)≡0 (mod α(K)). Let K0 be an equivalent set of K, k and k* be the smallest and the largest integers in K0. We prove that c(K,λ)≤exp exp{Q0}Qo=max{2(2p(ko)2-k2kk)p(ko)4,(Kk242y-k-2)(y2)}, whereand y=k*+k(k-1)+1.