Network topology and the theory of rubber elasticity

The earliest investigations on rubber elasticity, commencing in the 19th century, were necessarily limited to phenomenological interpretations. The realisation that polymers consist of very long molecular chains. commencing c. 1930, gave impetus to the molecular theory of rubber elasticity (1932-). according to which the high deformability of an elastomer, and the elastic force generated by deformation, stem from the configurations accessible to long molecular chains. Theories of rubber elasticity put forward from 1934-1946 relied on the assumption that the junctions of the rubber network undergo displacements that are affine in macroscopic strain. The theory of James and Guth (1947) dispensed with this premise, and demonstrated instead that the mean positions of the junctions of a ‘phantom’ network consisting of Gaussian chains devoid of material properties are affine in the strain. The vital significance of the distinction between the actual distribution of chain vectors in a network and their distribution if the junctions would be fixed at their mean positions went unnoticed for nearly 30 years. Experimental investigations, commencing with the incisive work of Gee in 1946. revealed large departures from the relationship of stress to strain predicted by the theories cited. This discrepancy prompted extensive studies, theoretical and experimental, during succeeding years. Inquiry into the fundamentals of polymer networks, formed for example by interlinking very long polymer molecules, exposed the need to take account of network imperfections, typically consisting of chains attached at only one end to a network junction. Various means were advocated to make corrections for these imperfections. The cycle rank ζ of the network has been shown (1976) to be the fundamental measure of its connectivity, regardless of the junction functionality and pattern of imperfections. Often overlooked is the copious interpenetration of the chains comprising typical elastomeric networks. Theories that attempt to represent such networks on a lattice are incompatible with this universal feature. Moreover, the dense interpenetration of chains may limit the ability of junctions in real networks to accommodate the fluctuations envisaged in the theory of phantom networks. It was suggested in 1975 that departures from the form predicted for the elastic equation of state are due to constraints on the fluctuations of junctions whose effect diminishes with deformation and with dilation. Formulation of a self-consistent theory based on this suggestion required recognition of the non-affine connection between the chain vector distribution function and the macroscopic strain in a real network, which may partake of characteristics of a phantom network in some degree. Implementation of the idea was achieved through postulation of domains of constraint affecting the equilibrium distribution of fluctuations of network junctions from their mean positions. This led in due course to a theory that accounts for the relationship of stress to strain virtually throughout the ranges of strain accessible to measurement. The theory establishes connections between structure and elastic properties. This is achieved with utmost frugality in arbitrary parameters.     

Issues in nonlinear stochastic grey box identification

Grey box identification refers to the practice of identifying dynamical systems in model structures exploiting partial prior information. This contribution reviews a method for stochastic grey box identification and surveys experiences and lessons of applying it to a number of industrial processes. Issues to be addressed include advantages and costs of introducing stochastics into the model, the question of what contribution must be expected from the model designer as opposed to what can be formalized in computer algorithms, and an outlook on future plans to resolve present shortcomings.     

The effect of additives on the thermal stability of poly(vinyl chloride)

The effect of a range of organic additives on the thermal stability of poly(vinyl chloride), both with and without a chloroparaffin extender, was studied using a number of experimental techniques. Of the additives used the best overall balance was provided by pentaerythritol, which increased stability when the extender was present and had no effect when it was absent. The congo red test emerged as the most suitable technique, being consistent and inexpensive and able to screen several additives simultaneously. Isothermal differential thermal analysis correlated with the congo red test but required more expensive equipment, was time-consuming and demanded good mixing of the poly(vinyl chloride) compound to give reproducible results. Thermogravimetry was not sufficiently sensitive and the heat stability test was the least useful of all.     

Application of boundary element method to 3-D problems of coupled thermoelasticity

This paper deals with a new boundary element method for analysis of the quasistatic problems in coupled thermoelasticity. Through some mathematical manipulation of the Navier equation in elasticity, the heat conduction equation is transformed into a simpler form, similar to the uncoupled-type equation with the modified thermal conductivity which shows the coupling effects. This procedure enables us to treat the coupled thermoelastic problems as an uncoupled one, A few examples are computed by the proposed BEM, and the results obtained are compared with the analytical ones available in the literature, whereby the accuracy and versatility of the proposed method are demonstrated.     

利用Liapanov直接方法判定差分方程稳定性

研究差分方程稳定性的强有力的方法是Liapanov直接方法,这一方法的核心思想是针对所研究的方程,构造出其相应的Liapanov函数,利用它来判定方程的稳定性．     

小波变换在求解重力测定反问题中的应用

针对重力测定反问题,提出将其离散为线性不适定问题,利用小波变换方法进行数值求解.该方法将小波变换和正则化方法相结合,选取小波函数作为一组基底,将原不适定问题转化为粗子空间上的适定问题,并给出选取粗子空间基的方法.通过数值模拟已有方法和小波变换方法求解结果的比较,表明了小波变换方法的可行性和有效性.     

Sampling average approximation method for a class of stochastic Nash equilibrium problems

We consider a class of stochastic Nash equilibrium problems (SNEP). Under some mild conditions, we reformulate the SNEP as a stochastic mixed complementarity problem (SMCP). We apply the well-known sample average approximation (SAA) method to solve the SMCP. We further introduce a semismooth Newton method to solve the SAA problems. The comprehensive convergence analysis is given as well. In addition, we demonstrate the proposed approach on a stochastic Nash equilibrium model in the wholesale gas–oil markets.     

Limit load and shakedown analysis of plastic structures under stochastic uncertainty

Problems from plastic analysis are based on the convex, linear or linearised yield/strength condition and the linear equilibrium equation for the stress (state) vector. In practice one has to take into account stochastic variations of several model parameters. Hence, in order to get robust maximum load factors, the structural analysis problem with random parameters must be replaced by an appropriate deterministic substitute problem. A direct approach is proposed based on the primary costs for missing carrying capacity and the recourse costs (e.g. costs for repair, compensation for weakness within the structure, damage, failure, etc.). Based on the mechanical survival conditions of plasticity theory, a quadratic error/loss criterion is developed. The minimum recourse costs can be determined then by solving an optimisation problem having a quadratic objective function and linear constraints. For each vector a(·) of model parameters and each design vector x, one obtains then an explicit representation of the “best” internal load distribution F^∗. Moreover, also the expected recourse costs can be determined explicitly. Consequently, an explicit stochastic nonlinear program results for finding a robust maximal load factor μ^∗. The analytical properties and possible solution procedures are discussed.     

An ant direction hybrid differential evolution heuristic for the large-scale passive harmonic filters planning problem

This article presents a heuristic which combines the orthogonal array experiment technique and an ant direction hybrid differential evolution algorithm (ADHDEOA) for planning of a large-scale passive harmonic filters problem. The addressed problem has a multi-bus and under abundant harmonic current sources in the system. In this study, an orthogonal array is first conducted to obtain the initial solution. Next, an ant direction hybrid differential evolution (ADHDE) is applied to search for a near optimum solution. The objective is to minimize the cost of the filter, the total demand distortion of harmonic currents and the total harmonic distortion of voltages at each bus simultaneously. In order to determine a set of weights of each term in the objective function, the simplest and most efficient form of triangular membership functions has been considered. The designed heuristic ADHDEOA is applied to a practical harmonic problem in a steel plant, and three design schemes are compared to demonstrate the performance of the ADHDEOA.