Constitutive Modelling of Resins in the Stiffness Domain

An analytic method for inverting the constitutive compliance equations of viscoelasticity for resins is developed. These equations describe the HWKK/H rheological model, which makes it possible to simulate, with a good accuracy, short-, medium- and long-term viscoelastic processes in epoxy and polyester resins. These processes are of first-rank reversible isothermal type. The time histories of deviatoric stresses are simulated with three independent strain history functions of fractional and normal exponential types. The stiffness equations are described by two elastic and six viscoelastic constants having a clear physic meaning (three long-term relaxation coefficients and three relaxation times). The time histories of axiatoric stresses are simulated as perfectly elastic.The inversion method utilizes approximate constitutive stiffness equations of viscoelasticity for the HWKK/H model. The constitutive compliance equations for the model are a basis for determining the exact complex shear stiffness, whereas the approximate constitutive stiffness equations are used for determining the approximate complex shear stiffness. The viscoelastic constants in the stiffness domain are derived by equating the exact and approximate complex shear stiffnesses. The viscoelastic constants are obtained for Epidian 53 epoxy and Polimal 109 polyester resins. The accuracy of the approximate constitutive stiffness equations are assessed by comparing the approximate and exact complex shear stiffnesses. The constitutive stiffness equations for the HWKK/H model are presented in uncoupled (shear/bulk) and coupled forms. Formulae for converting the constants of shear viscoelasticity into the constants of coupled viscoelasticity are given as well.     

Stress analysis of orthotropic planes weakened by cracks

The stress fields in an orthotropic infinite plane containing Volterra type climb and glide edge dislocations are derived. The dislocation solutions are utilized to formulate integral equations for dislocation density functions on the surfaces of smooth cracks. The integral equations are of Cauchy singular type and are solved for several different cases of crack configurations and arrangements. The results are used to evaluate modes I and II stress intensity factors for multiple smooth cracks.     

Manufacturing flow line systems: a review of models and analytical results

The most important models and results of the manufacturing flow line literature are described. These include the major classes of models (asynchronous, synchronous, and continuous); the major features (blocking, processing times, failures and repairs); the major properties (conservation of flow, flow rate-idle time, reversibility, and others); and the relationships among different models. Exact and approximate methods for obtaining quantitative measures of performance are also reviewed. The exact methods are appropriate for small systems. The approximate methods, which are the only means available for large systems, are generally based on decomposition, and make use of the exact methods for small systems. Extensions are briefly discussed. Directions for future research are suggested.     

Fuzzy理论在工程环境灾害预测中的应用

针对矿山大型排土场所出现的滑坡等工程环境灾害的预测与防治问题,着重探讨排土场边坡失稳破坏预测问题.文中采用Fuzzy数学中的Fuzzy概率测度理论建立理论预测分析模型,并对大型排土场边坡失稳破坏的Fuzzy概率测度进行具体的预测分析,所获结果与已有的经典分析方法所获理论结果一致.针对矿山大型排土场所出现的滑坡等工程环境灾害防治问题,提出了具体的防治技术措施.     

双无限随机环境中的常返马氏链

对双无限随机环境中的马氏链,给出了常返的两种可能的定义,讨论了它们间的联系和基本性质,给出了状态或链为常返的判断准则.讨论了双无限随机环境中马氏链的不变测度的存在性,首次给出了双无限随机环境中马氏链的正常返及零常返的概念,并讨论了其相关性质.特别地,应用不变函数的性质,给出了状态具有正常返性或零常返性的判断准则.     

SOR-like Methods for Augmented Systems

Several SOR-like methods are proposed for solving augmented systems. These have many different applications in scientific computing, for example, constrained optimization and the finite element method for solving the Stokes equation. The convergence and the choice of optimal parameter for these algorithms are studied. The convergence and divergence regions for some algorithms are given, and the new algorithms are applied to solve the Stokes equations as well.     

Constitutive Modelling of Resins in the Compliance Domain

A rheological HWKK/H model for resins is developed taking into consideration the up-to-date analyses of experimental results. Constitutive compliance equations of linear are formulated for this model in the shear/bulk form, which describes, among other things, the first-rank reversible isothermal creep. The shear (distorsional) deformations are simulated with three independent stress history functions of fractional and normal exponential types. The volume deformations are simulated as perfectly elastic. The model is described by two elastic and six viscoelastic constants, namely three long-term creep coefficients and three retardation times.The constitutive compliance equations of viscoealsticity for resins are also formulated in the coupled form. Formulae for converting the constants of shear/bulk (uncoupled) viscoelasticity into the constants of coupled viscoelasticity are given too.An algorithm for identifying the material constants, based on the creep of uniaxially tensioned bar samples, is formulated in a way that gives unique results. The material constants are fiund for Epidian 53 epoxy and Polimal 109 polyester resins. The creep processes, simulated based on the experimental data, are presented graphically for both the resins examined.     

The Fixed Point Property for Posets of Small Width

The fixed point property for finite posets of width 3 and 4 is studied in terms of forbidden retracts. The ranked forbidden retracts for width 3 and 4 are determined explicitly. The ranked forbidden retracts for the width 3 case that are linearly indecomposable are examined to see which are minimal automorphic. Part of a problem of Niederle from 1989 is thus solved.     

Rank-Score Tests in Factorial Designs with Repeated Measures

Nonparametric factorial designs for multivariate observations are considered under the framework of general rank-score statistics. Unlike most of the literature, we do not assume the continuity of the underlying distribution functions. The models studied include general repeated measures designs, compound symmetry designs, and designs for longitudinal data. In particular, designs for ordered categorical data are included. The vectors of the multivariate observations may have different lengths. Moreover, our general framework includes missing values and singular covariance matrices which occur quite frequently in practical data analysis problems. The asymptotic properties of the proposed statistics are studied under general nonparametric hypotheses as well as under a sequence of nonparametric contiguous alternatives. L₂-consistent estimators for the unknown covariance matrices are given and two types of quadratic forms are considered for testing the nonparametric hypotheses. The results are applied to a two-way mixed model assuming compound symmetry and to a factorial design for longitudinal data. The main idea of the proofs is based on some moment inequalities for empirical distribution functions in mixed models. The details are provided in the Appendix.     

一族Bloch函数的单叶半径与覆盖半径

研究了Bloch函数族B中的一个子族Bg,给出了Bg中函数的单叶半径.作为应用建立了Bg中函数的覆盖定理,从而刻画了Bg中函数的有关性质.     

A Note on the Stability of the Integral-Differential Equation of the Hyperbolic Type in a Hilbert Space

In this paper, the initial-value problem for integral-differential equation of the hyperbolic type in a Hilbert space H is considered. The unique solvability of this problem is established. The stability estimates for the solution of this problem are obtained. The difference scheme approximately solving this problem is presented. The stability estimates for the solution of this difference scheme are obtained. In applications, the stability estimates for the solutions of the nonlocal boundary problem for one-dimensional integral-differential equation of the hyperbolic type with two dependent limits and of the local boundary problem for multidimensional integral-differential equation of the hyperbolic type with two dependent limits are obtained. The difference schemes for solving these two problems are presented. The stability estimates for the solutions of these difference schemes are obtained.     

The effect of the slip condition on flows of an Oldroyd 6-constant fluid

The steady flows of a non-Newtonian fluid are considered when the slippage between the plate and the fluid is valid. The constitutive equations of the fluid are modeled by those for an Oldroyd 6-constant fluid. They give rise to non-linear boundary value problems. The analytical solutions are obtained using powerful, easy-to-use analytic technique for non-linear problems, the homotopy analysis method. It is shown that solutions exist for all values of non-Newtonian parameters. The solutions valid for no-slip condition for all values of non-Newtonian parameters can be derived as the special cases of the present analysis. Finally, graphs are plotted and critical assessment is made for the cases of slip and no-slip conditions.     

Logical regularities in pattern recognition (Parametric Approach)

The search for logical regularities of classes in the recognition by precedents problems and the use of logical regularities for solving recognition and prediction problems are considered. Logical regularities of classes are defined as conjunctions of one-place predicates that determine the membership of a value of a feature in a certain interval of the real axis. The conjunctions are true on the subsets of reference objects of a certain class and are optimal. Various optimality criteria are considered and the problem of finding logical regularities is formulated as an integer programming problem. A qualitative analysis of these problems is performed. Models for evaluating estimates on the basis of systems of logical regularities are considered. Modifications of linear decision rules for finding estimates of how close the reference objects are to classes are proposed that are based on the search for the maximum gap. Approximations of logical regularities of classes by smooth functions is proposed. The concept of the dynamic logical regularity of classes is introduced, an algorithm for finding dynamic logical regularities is proposed, and a prediction method is developed.     

Sine-Gordon theory in a semi-strip

Initial-boundary value problems for sine-Gordon and complex sine-Gordon equations in a semi-strip are treated. The evolution of the Weyl function and a uniqueness result are obtained for the complex sine-Gordon equation. The evolution of the Weyl function as well as an existence result and a procedure to recover solution are given for the sine-Gordon equation. It is shown that for a wide class of examples the solutions of the sine-Gordon equation are unbounded in the quarter-plane.     

Calculating safety stocks for assembly systems with random component procurement lead times: A branch and bound algorithm

In this paper, a discrete single-level multi-component inventory control model for assembly systems with random component procurement lead times is considered. The economic order quantity (EOQ) policy is used for a type of finished product. The requirements of the components are constant and cyclic (periodic), and their values per period are deduced from the EOQ for the finished product. The paper focuses on the components safety stock calculation. The objective is to minimise the average holding cost of the components while keeping the desired service level for the finished product. For this, an upper bound, two lower bounds, two dominance properties and an efficient branch and bound algorithm are suggested. Several tests are executed and conclusions are drawn. The proposed model provides a substantial saving for assembly systems with a large number and unreliable delivery of components as in semi-conductor and automotive industries.     

开孔浅球壳的非线性动力响应及其动力稳定

本文建立了具轴对称变形、考虑横向剪切影响的浅球壳的非线性运动方程:对周边弹性支承开孔浅球壳的非线性静、动力响应及动力稳定问题进行了探讨.在解题方法上,对位移函数在空间上采用正交配点法离散.在时间上采用平均加速度法(Newmark-β法)离散.变求解一组非线性微分方程为求解一组线性代数方程.文中给出了不同情况下的若干数值结果,且与有关文献的结果作了比较.     

Moving Cracks in Composite Materials with Initial Stresses

The dynamic problems of fracture mechanics for composite materials with initial stresses are considered in the case of cracks moving at a constant rate along a straight line. In the continuum approximation, composite materials are modeled by orthotropic nonlinearly elastic bodies with an arbitrary form of the elastic potential. A three-dimensional linearized theory of elasticity is used. The complex potentials of plane and antiplane problems of the linearized theory are used for dynamic problems. Exact solutions for Modes I, II, and III in the case of moving cracks are obtained using the Keldysh-Sedov methods. Asymptotic formulas for stresses and displacements near the crack tip for Modes I, II, and III are presented. The basic mechanical effects are analyzed with respect to the problems considered.     

Cost-effective modeling strategies for the analysis of spliced steel connections

The paper presents several cost-effective modeling strategies that can be used by structural engineers in practice to determine the stresses in the spliced members. The computational efficiency and the modeling effort required for the several modeling options are also discussed. The deformation mechanisms and load transfer for several types of connections are illustrated. Optimization techniques are also presented to economize the computer time for connections with large number of bolts. Results are presented to compare the accuracy of several modeling strategies commonly used in practice. It is shown that for eccentric connections, the flexural bending largely affect the maximum tensile and compressive stresses within the joint. The difference may reach up to 54%. Finally, Experimental comparisons are made with the numerical procedures for typical connection model.     

On the one-commodity pickup-and-delivery traveling salesman problem with stochastic demands

This paper studies how to set the vehicle capacity for traveling Salesman Problems where some of the customer demands are stochastic. The analyses are done for the one-commodity pickup-and-delivery TSP, as this problem also includes the setting of the initial load. The paper first considers feasibility issues. This includes finding the smallest vehicle capacity and some initial load such that a given tour is feasible for all scenarios. Different variants are considered as a function of the time when information becomes available. The paper then analyzes the case where some penalties are paid for routing a tour unable to handle customer demands. Various types of penalties are considered. The paper studies properties of the minimal expected penalty of a given tour, which are then used to provide approaches to find near-optimal tours. Computational results are presented.     

Backward and forward recurrence times,and their interrelationships in Bellman-Harris branching processes

Random variables are constructed for a Bellman-Harris branching process which are the extensions of backward and forward recurrence times from an ordinary renewal process. The sum of the two extended random variables is also constructed, and then the distribution functions for all three random variables are developed. The asymptotic limits for all three time-dependent distributions are also obtained.