On the stability of periodic trajectories of a planar Birkhoff billiard

The inertial motion of a material point is analyzed in a plane domain bounded by two curves that are coaxial segments of an ellipse. The collisions of the point with the boundary curves are assumed to be absolutely elastic. There exists a periodic motion of the point that is described by a two-link trajectory lying on a straight line segment passed twice within the period. This segment is orthogonal to both boundary curves at its endpoints. The nonlinear problem of stability of this trajectory is analyzed. The stability and instability conditions are obtained for almost all values of two dimensionless parameters of the problem.     

Experimental investigation of a moored floating system

Floating structures are generally excited by a more or less irregular sea state. Therefore the structure undergoes a nonlinear dynamical behaviour which results from hydrodynamic effects or the kinematic coupling of different components. The motions of these structures have been analysed intensively with numerical techniques which predict a wide range of nonlinear effects. On the other hand, experiments are still important when it comes to verifying these theoretical findings. Investigating such a floating structure experimentally requires a complex setup: A wave generator needs to be driven in an appropriate way to yield waves with the required characteristics at the structure. The structure itself is usually designed similar to a real–world system and it has to allow for a comparison with numerical analyses. Sensors which measure the tracks of the individual components not only have to reach a prescribed precision but also need to ensure that the motion is not perturbed as a result of the measurements. Lastly, unwanted disturbances have to be avoided. For experiments in a wave tank this includes that reflections have to be minimized. This talk addresses the development of an experimental setup for the investigation of a floating structure. It highlights components which are found to be critical for the obtained accuracy and proposes techniques to reduce experimental errors. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On a periodic motion of a rigid body carrying a material point in the presence of impacts with a horizontal plane

A material system consisting of an outer rigid body (a shell) and an inner body (a material point) is considered. The system moves in a uniform field of gravity over a fixed absolutely smooth horizontal plane. The central ellipsoid of inertia of the shell is an ellipsoid of rotation. The material point moves according to the harmonic law along a straight-line segment rigidly attached to the shell and lying on its axis of dynamical symmetry. During its motion, the shell may collide with the plane. The coefficient of restitution for an impact is supposed to be arbitrary. The periodic motion of the shell is found when its symmetry axis is situated along a fixed vertical, and the shell rotates around this vertical with an arbitrary constant angular velocity. The conditions for existence of this periodic motion are obtained, and its linear stability is studied.     

Obtaining Cosserat material parameters by homogenization of a Cauchy continuum

An increasing importance of composites with sandwich architecture and fibre-reinforced components is recognizable especially in aerospace and light weight industry. Due to the inner structure such materials often exhibit a complex behavior. If the ratio of micro- and macroscopic length scales, l and L, violates the condition l/L ≪ 1, a higher order continuum should be used to describe the macroscopic material behavior correctly. The numerical simulation requires reliable material constants, for which the experimental determination is laborious and sometimes impossible. Alternatively homogenization methods can be used for the numerical identification of overall material parameters. A short introduction to the linear Cosserat theory is followed by an extended homogenization procedure to derive the macroscopic material constants of a linear Cosserat continuum. The parameters obtained with a heterogeneous cell are used to simulate different bending load cases. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A statistical approach to the determination of stability for dynamical systems modelling physiological processes

One of the questions involved in the formulation of a new model for a physiological phenomenon, when the model represents a dynamical system, is that concerning its qualitative behavior. The determination of the stability of a particular dynamical system is usually made analytically, from a linearization of the system around an equilibrium point. This analytic proof may often be very complex or impossible, leading to the imposition of conditions on the relative magnitude of the structural model parameters or to other partial results. We discuss a general technique whereby a probabilistic judgment is made on the stability of a dynamical system, and we apply it to the study of a particular delay differential system modelling the relationship between insulin secretion and glucose uptake. This technique is applicable in case experimental material is available from which to estimate the dispersion of the model parameters. A stability criterion is obtained via the usual linearization around an equilibrium point, it is approximated as a Taylor series in the parameters truncated after the first term, and its variance is then computed from the dispersion of the parameters. While the conclusion is probabilistic in nature, it can be obtained for a wide class of models and from either sample or individual experimental subject's parameter estimates.     

Dynamic inversion method for the material parameters of a high arch dam and its foundation

The overall mechanical behavior of the structure of an arch dam is comprehensively reflected by the vibration modal information included in measured vibration response. Hence, the results obtained from inverting material parameters based on measured vibration data are often superior to those based on static monitoring data. In this study, a dynamic inversion method for the material parameters of a high arch dam and its foundation is proposed on the basis of the measured vibration response. First, an arch dam prototype test is conducted to obtain the measured dynamic displacement response as input. Then, a stochastic subspace identification method based on singular entropy is formulated to determine the modal parameters. Second, a dynamic elastic modulus (DEM) with a great influence on the modal parameters is selected as the material parameter to be inverted. Then, a response surface model (RSM), which reflects the nonlinear relationship between the material and modal parameters of each zone, is constructed. Latin hypercube sampling is used to generate the sample library of the DEM. The RSM is fitted by modal parameters calculated on the basis of the arch dam finite element model (FEM) and is applied to replace the FEM. Finally, the optimization mathematical model of the inversion of the DEM is established. Then, the objective function is optimized through a genetic algorithm, and the optimal combination of the DEM in each zone is inverted. The modal parameters of the arch dam calculated by inversion results are consistent with those measured by variation law and values. Therefore, the inversion results are reasonable and reliable. This method provides a new idea for determining the material parameters of a high arch dam and its foundation during the operation period.     

The significance of reducing setup times/setup costs

Scheduling with setup times or setup costs plays a crucial role in todays modern manufacturing and service environments where reliable products/services are to be delivered on time. Scheduling activities profoundly depend on the times/costs required to prepare the facility for performing the activities. However, the vast majority of existing scheduling literature ignores this fact. We define and emphasize the importance, applications, and benefits of explicitly considering setup times/costs in scheduling research. Moreover, a review of the latest research on scheduling problems with setup times/costs is provided.     

基于EM算法的混合模型中子总体个数的研究

混合模型已成为数据分析中最流行的技术之一,由于拥有数学模型,它通常比聚类分析中的传统的方法产生的结果更精确,而关键因素是混合模型中子总体个数,它决定了数据分析的最终结果。期望最大化(EM)算法常用在混合模型的参数估计,以及机器学习和聚类领域中的参数估计中,是一种从不完全数据或者是有缺失值的数据中求解参数极大似然估计的迭代算法。学者们往往采用AIC和BIC的方法来确定子总体的个数,而这两种方法在实际的应用中的效果并不稳定,甚至可能会产生错误的结果。针对此问题,本文提出了一种利用似然函数的碎石图来确定混合模型中子总体的个数的新方法。实验结果表明,本文方法确定的子总体的个数在大部分理想的情况下可以得到与AIC、BIC方法确定的聚类个数相同的结果,而在一般的实际数据中或条件不理想的状态下,碎石图方法也可以得到更可靠的结果。随后,本文将新方法在选取的黄石公园喷泉数据的参数估计中进行了实际的应用。     

Exact Analysis of the State-Dependent Polling Model

We consider a polling model in which a number of queues are served, in cyclic order, by a single server. Each queue has its own distinct Poisson arrival stream, service time, and switchover time (the server's travel time from that queue to the next) distribution. A setup time is incurred if the polled queue has one or more customers present. This is the polling model with State-Dependent service (the SD model). The SD model is inherently complex; hence, it has often been approximated by the much simpler model with State-Independent service (the SI model) in which the server always sets up for a service at the polled queue, regardless of whether it has customers or not. We provide an exact analysis of the SD model and obtain the probability generating function of the joint queue length distribution at a polling epoch, from which the moments of the waiting times at the various queues are obtained. A number of numerical examples are presented, to reveal conditions under which the SD model could perform worse than the corresponding SI model or, alternately, conditions under which the SD model performs better than a corresponding model in which all setup times are zero. We also present expressions for a variant of the SD model, namely, the SD model with a patient server.     

Nonlinear dynamic response of a simply-supported Kelvin-Voigt viscoelastic beam, additionally supported by a nonlinear spring

The free and forced vibrations of a Kelvin-Voigt viscoelastic beam, supported by a nonlinear spring are analytically investigated in this paper. The governing equations of motion along with the compatibility conditions are obtained employing Newton’s second law of motion and constitutive relations. The viscoelastic beam material is constituted by the Kelvin-Voigt rheological model, which is a two-parameter energy dissipation model. The method of multiple timescales, a perturbation technique, is employed which ultimately leads to approximate analytical expressions for vibration response, and provides better insight into how the system parameters influence the vibration response. Finally, the effect of system parameters on the linear and nonlinear natural frequencies, vibration responses and frequency-response curves of the system is characterized.     

An MIP-based interval heuristic for the capacitated multi-level lot-sizing problem with setup times

This paper considers the capacitated multi-level lot-sizing problem with setup times, a class of difficult problems often faced in practical production planning settings. In the literature, relax-and-fix is a technique commonly applied to solve this problem due to the fact that setup decisions in later periods of the planning horizon are sensitive to setup decisions in the early periods but not vice versa. However, the weakness of this method is that setup decisions are optimized only on a small subset of periods in each iteration, and setup decisions fixed in early iterations might adversely affect setup decisions in later periods. In order to avoid these weaknesses, this paper proposes an extended relax-and-fix based heuristic that systematically uses domain knowledge derived from several strategies of relax-and-fix and a linear programming relaxation technique. Computational results show that the proposed heuristic is superior to other well-known approaches on solution qualities, in particular on hard test instances.     

Multiscale modelling of skeletal muscle tissue by incorporating microstructural effects

The macroscopic mechanical response of skeletal muscle tissue is mainly influenced by the properties and arrangement of microstructural elements, such as, for example, sarcomeres and connective tissue. Like for many biological materials, the mechanical properties of skeletal muscle tissue can vary quite significantly between different specimens like, for example, different persons or muscle types. Current state-of-the-art continuum-mechanical muscle models often lack the ability to take into account such variations in a natural way. Further, phenomenological constitutive laws face the challenge that appropriate material parameter sets need to be found for each tissue variation. Thus, the present work aims to identify the microstructural features and parameters governing the overall mechanical response and to incorporate them into a macroscopic material model by applying suitable homogenisation methods. The motivation hereby is that the estimation of material parameters for microstructures, such as collagen fibres, can be done in a more reliable and general way and that fluctuations between specimens are included by, for example, adapting the alignment of the collagen fibres inside the muscle. Moreover, instead of computationally expensive homogenisation methods like FE², this work proceeds from well-founded analytical homogenisation techniques in order to keep the model as simple as possible. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Interfacial model for crash resistant adhesives of ductile-modified epoxy resins

Debonding in adhesive joints is modelled and analyzed with the concept of interfacial mechanics. Material equations are presented for the inelastic behaviour of ductile-modified epoxy resins. A two surface function for the onset of yielding is advantageously expressed in terms of the stress vector on the interface. The theory may be extended to material softening due to damage and to rate dependency. This simple constitutive model is not stable in the sense of Drucker's postulate. Therefore, the non-associated flow rule is modified with a quadratic stress-dependent plastic potential. The material parameters are identified by means of the finite-element simulation of the experimental setup for a bluntly glued double steel tube sample. The numerical performance of this modified model is tested at an adhesively bonded joint in the form of a T-intersection. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Estimating parameters of proportional hazards model based on expert knowledge and statistical data

Proportional hazards model (PHM) is a convenient statistical tool that can be successfully applied in industrial problems, such as in accelerated life testing and condition-based maintenance, or in biomedical sciences. Estimation of PHM requires lifetime data, as well as condition monitoring data, which often is incomplete or missing, and necessitates the use of expert knowledge to compensate for it. This paper describes the methodology for elicitation of expert's beliefs and experience necessary to estimate the parameters of a PHM with time-dependent covariates. The paper gives a background of PHM and review of the literature related to the knowledge elicitation problem and gives a foundation for the proposed methodology. The knowledge elicitation process is based on case analyses and comparisons. This method results in a set of inequalities, which in turn define a feasible space for the parameters of the PHM. By sampling from the feasible space an empirical prior distribution of the parameters can be estimated. Then, using Bayes rule and statistical data the posterior distribution can be obtained. This technique can also provide reliable outcomes when no statistical data are available. The technique has been tested several times in laboratory experiments and in a real industrial case and has shown promising results.     

A genetic algorithm approach for solving a closed loop supply chain model: A case of battery recycling

Due to the implementation of government legislation, social responsibility, environmental concern, economic benefits and customer awareness the industries are under a great pressure not only to provide environmentally friendly products but also to take back the product after its use. The issue in reverse logistics is to take back the used products, either under warranty or at the end of use or at the end of lease, so that the products or its parts are appropriately disposed, recycled, reused or remanufactured. In order to overcome this issue, it is necessary to setup a logistics network for arising goods flow from end users to manufacturers. In this study, the optimum usage of secondary lead recovered from the spent lead–acid batteries for producing new battery is presented. The disposal in surface or sewage water or land of liquid content of the lead–acid batteries is strictly restricted. Because of the need for environmental protection and the lack of considerable lead resources, the spent batteries treatment and lead recovery are becoming crucial now-a-days. The objective of this paper is to develop a multi echelon, multi period, multi product closed loop supply chain network model for product returns and the decisions are made regarding material procurement, production, distribution, recycling and disposal. The proposed heuristics based genetic algorithm (GA) is applied as a solution methodology to solve mixed integer linear programming model (MILP). Finally the computational results obtained through GA are compared with the solutions obtained by GAMS optimization software. The solution reveals that the proposed methodology performs very well in terms of both quality of solutions obtained and computational time.     

Influence of friction in material characterization in microindentation measurement

A comprehensive computational study is undertaken to identify the influence of friction in material characterization by indentation measurement based on elasto- plastic solids. The impacts of friction on load versus indentation depth curve, and the values of calculated hardness and Young’s modulus in conical and spherical indentations are shown in this paper. The results clearly demonstrate that, for some elasto-plastic materials, the curves of load versus indentation depth obtained either by spherical or conical indenters with different friction coefficients, cannot be distinguished. However, if utilizing the parameter β (see text for details), to quantify the deformation of piling-up or sinking-in, it is easy to find that the influence of friction on piling-up or sinking-in in indentation is significant. Therefore, the material parameters which are related to the projected area will also have a large error caused by the influence of friction. The maximum differences on hardness and Young’s modulus can reach 14.59% and 6.78%, respectively, for some elastic materials shown in this paper. These results do not agree with those from researchers who stated that the instrumented indentation experiments are not significantly affected by friction.     

Parameter identification based on multiple inhomogeneous experiments of practical relevance

Existing procedures to identify material parameters are based on experiments with simple specimens. Additionally, the load distribution is approximately homogeneous. But there are only few feasible experiments which produce homogeneous or almost homogeneous load distributions. Furthermore, deviations from homogeneity and their consequences cannot be avoided, but are often ignored. We present a solution algorithm which takes several different experimental results into account. Thereby, the experiments are performed on specimens which respond with inhomogeneous distributions of strains and stresses. The restriction to homogeneous loads is not necessary. Thus, it is possible to use different measured data of multiple load cases on one and the same test specimen. The component-oriented design of the specimen permits to consider the specific properties of product groups, the load types and the effect of the manufacturing process on the final material properties already during the identification process. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Investigation of elastoplastic effects of cables under large spatial deformation

Cables are complex components consisting of a multi-layer structure and various materials. The structural setup includes for example conducting wires, isolating shields and protecting sheaths. This leads to several inelastic effects under large deformations like pull-out of wires, delamination of layers or friction between the constituents. The materials used in cables belong to different material classes and consequently show different behavior under load. Elastoplastic behavior has to be expected for metallic wires, whereas polymer layers behave viscoelastically. The combination of these inelastic effects caused by the structure and constituents of cables motivates the inclusion of inelasticity in the material model on a phenomenological level. Since cables are flexible, slender structures, they can be described physically correctly by the theory of Cosserat rods. In this context, the constitutive equations are formulated in terms of the sectional quantities. The related model parameters have to be determined in suitable experiments. As cables undergo large multiaxial deformations in applications, uniaxial experiments are not sufficient for their characterization. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the Effect of Product Variety in Production–Inventory Systems

In this paper, we examine the effect of product variety on inventory costs in a production–inventory system with finite capacity where products are made to stock and share the same manufacturing facility. The facility incurs a setup time whenever it switches from producing one product type to another. The production facility has a finite production rate and stochastic production times. In order to mitigate the effect of setups, products are produced in batches. In contrast to inventory systems with exogenous lead times, we show that inventory costs increase almost linearly in the number of products. More importantly, we show that the rate of increase is sensitive to system parameters including demand and process variability, demand and capacity levels, and setup times. The effect of these parameters can be counterintuitive. For example, we show that the relative increase in cost due to higher product variety is decreasing in demand and process variability. We also show that it is decreasing in expected production time. On the other hand, we find that the relative cost is increasing in expected setup time, setup time variability and aggregate demand rate. Furthermore, we show that the effect of product variety on optimal base stock levels is not monotonic. We use the model to draw several managerial insights regarding the value of variety-reducing strategies such as product consolidation and delayed differentiation.     

具有缺陷的不可压缩neo-Hookean球壳的动力学行为的定性分析

研究了一类具有缺陷的不可压缩超弹性材料球壳的径向对称运动问题,该类材料可以看作是带有径向摄动的均匀各向同性不可压缩的neo-Hookean材料．得到了描述球壳内表面运动的二阶非线性常微分方程,并给出了方程的首次积分．通过对微分方程的解的动力学行为的分析,讨论了材料的缺陷参数和球壳变形前的内外半径的比值对解的定性性质的影响,并给出了相应的数值算例．特别地,对于一些给定的参数,证明了存在一个正的临界值,当内压与外压之差小于临界值时,球壳内表面随时间的演化是非线性周期振动;当内压与外压之差大于临界值时,球壳的内表面半径随时间的演化将无限增大,即球壳最终将被破坏．