Starting-point strategy for interior-point algorithms for lower-bound shakedown analysis

Shakedown analysis by using the lower-bound theorem leads to computationally intensive nonlinear convex optimization problems with a large number of unknowns and constraints. Interior-point algorithms such as recently developed by the authors have proven to be efficient for the solution of these problems. For convergence and efficiency of the iterative process of these algorithms the choice of the starting-point is crucial. It should be inside of the feasible region and well-centered for fast convergence. No general method exists for the construction of optimum starting-points and only few investigations have been published on this issue. In this paper the physical meaning of the involved variables in shakedown problems is used to optimize starting-points. The efficiency of the new method is illustrated by a numerical examples and comparison with an alternative approach. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

An approximation algorithm for identical parallel machine scheduling with resource dependent processing times

We present a (3.5+?)-approximation algorithm for a scheduling problem on identical parallel machines with the objective to mimimize the makespan. The processing times depend on the usage of a single renewable resource where at any point of time at most k units from the resource are available.     

Random yield supply chain with a yield dependent secondary market

This paper considers a simple supply chain with one supplier and one retailer where the supplier’s production is subject to random yield and the retailer faces uncertain demand. There exists a secondary market for acquiring or disposing products by the supplier. We study both the centralized and decentralized systems. In the decentralized system, a no risk sharing contract and a risk sharing minimum commitment contract are analyzed. The supply chain with the risk sharing contract is further analyzed with a constant secondary market price and a yield dependent secondary market price. We present both the supplier’s and the retailer’s optimal strategies and provide insights for managers when making decisions under random yield risk and demand uncertainty. We find that the secondary market generally has a positive impact on supply chain performance and the actual effect of random yield risk on the supply chain performance depends on cost parameters and supply chain contract settings. Under certain conditions, reducing yield randomness may weaken the double marginalization effect and improve the chain performance. From the numerical study, we also show that there exists an optimal commitment level for the supply chain.     

Extremum theorems for large displacement analysis of discrete elastoplastic structures with piecewise linear yield surfaces

Discrete or discretized structures are considered in the range of large displacements. Elastic plastic behavior is assumed, under the hypothesis that both yield functions and hardening rules are piecewise linear. The structural response to a single finite loading step is assumed to involve regularly progressive yielding (no local unloading). An extremum property of this structural response is established, by recognizing that the relations governing the configuration change coincide with the Kuhn-Tucker conditions of a particular nonlinear constrained optimization problem, subject to sign constraints alone. This extremum property can be regarded as an extension of the theorem of minimum potential energy. Other properties, even if computationally less attractive, broaden the theory developed, so that some results previously obtained are derived as special cases.     

An accelerated differential evolution algorithm with new operators for multi-damage detection in plate-like structures

This paper proposes an Accelerated Differential Evolution (ADE) algorithm for damage localization and quantification in plate-like structures. In this study, the inverse damage detection problem is formulated as a nonlinear optimization problem. The objective function is established through the alterations of the structure flexibility matrix weighted with a penalty-function, used specifically to prevent the detection of false alarms. The ADE algorithm is designed via the introduction of three modifications in the standard differential evolution algorithm. Firstly, the initial population is created using knowledge we usually have about the damage scenario of a structure. Such initialization technique assists the algorithm to converge promptly. Secondly, in the mutation phase, a new difference vector, created based on the dispersion of individuals through the search space, is used to ensure the automatic balance between global and local searching abilities. Thirdly, a new exchange operator is designed and used to avoid the untimely convergence to local optima. Finite-element models of isotropic and laminated composite plates are considered as numerical examples to test the efficiency of the proposed approach. Numerical results validate the performance of the ADE method, in terms of both solution accuracy and computational cost and highlight its ability to locate and assess damage, even for large-scale problems and noise-contaminated data.     

Modified base-stock policies for semiconductor production system with dependent yield rates

We consider a two-stage production system faced by semiconductor manufacturing which produces a hierarchy of multiple grades of outputs. In the first stage, a single type of input (wafer) is used to produce multiple types of semi-finished parts with dependent yield rates, and in the second stage, each type of semi-finished parts can be transformed into a corresponding type of final products, or downgraded to a type of lower grade final products. Random customer demands are faced on the final products, and demands of different types of final products are not allowed to be substituted. The advantage of this production system is that it can prevent unhealthy ordering from customers who intentionally send out false demand signals for high grade products and revise the orders to lower grade products when the delivery time is close, which was observed in semiconductor manufacturing. The objective of the study is to plan the quantity of the input at the first stage and the respective downgrade quantities at the second stage so as to meet the required service level at the minimum cost. With some common assumptions, we propose a modified base-stock policy for this two-stage production system and show that the occurrence of nil excess inventory above the base-stock level follows a renewal process. We further extend the modified base-stock policy to a better policy that invokes risk pooling over multiple grade products. The performance of these two polices are evaluated via simulation to provide managerial insights.     

An algorithm and efficient data structures for the binary knapsack problem

A branch-and-bound algorithm for the binary knapsack problem is presented which uses a combined stack and deque for storing the tree and the corresponding LP-relaxation. A reduction scheme is used to reduce the problem size. The algorithm was implemented in FORTRAN. Computational experience is based on 600 randomly generated test problems with up to 9000 zero-one variables. The average solution times (excluding an initial sorting step) increase linearly with problem size and compare favorably with other codes designed to solve binary knapsack problems.     

Thermoelastic problem for an isotropic sphere with temperature dependent properties

Zusammenfassung Es werden Wärmespannungen infolge polarsymmetrischer stationärer Temperaturfelder in einer isotropen Kugel mit temperaturabhängigen Stoffwerten untersucht. Das Material wird als inkompressibel vorausgesetzt, was einem oberen Grenzwert der viskoelastischen Spannungen in einem Maxwellschen Körper entspricht. Diese Annahme erlaubt, die Lösung in einer geschlossenen Form und für jede Temperaturverteilung und Temperaturabhängigkeit der Materialkonstanten und des Wärmeausdehnungskoeffizienten aufzustellen. Es werden allgemeine Formeln für die Spannungs- und Verschiebungsfelder in einer vollen Kugel und in einer kugelförmigen Schale gegeben und die Einwirkung der variablen Wärmeleitzahl auf das Temperaturfeld untersucht. Ein numerisches Beispiel für lineare Temperaturabhängigkeit des Elastizitätsmoduls und des Wärmeausdehnungskoeffizienten wird berechnet.

---

---

This research was sponsored by the United States Army under Contract No. DA-11-022-ORD-2059     

The Poiseuille solution with temperature dependent viscosity

This article studies the Poiseuille flow in a cylindrical channel of arbitrary section and finite length of a fluid with temperature dependent viscosity and internal dissipation. A theorem of existence of solution is proved and a special case is examined in detail.     

An algorithm for computing the stable coalition structures in tree-graph communication games

We construct an algorithm which provides in finite steps the stable coalition structure(s) of tree-graph communication games and an allocation of the core: the restricted marginal contribution allocation. This paper has been presented at the St. Petersburg Institute for Economics and Mathematics (Russian Academy of Sciences), University of Santiago de Compostela (International Workshop on Game Theory), Universidad Autónoma de Barcelona, and Universidad de Sevilla. This research has been supported partially by: DGICYT PB94-1372 and UPV 035.321-HB146/96     

An algorithm for least squares analysis of spectroscopic data

This paper describes a variant of the Gauss-Newton-Hartley algorithm for nonlinear least squares, in which aQR implementation is used to solve the linear least squares problem. We follow Grey's idea of updating variables at intermediate stages of the orthogonalization. This technique, applied in partitions identified with known or suspected spectral lines, appears to be especially suited to the analysis of spectroscopic data. We suggest that this algorithm is an attractive candidate for the optimization role in Ekenberg's interactive computer graphics curve fitting program.     

Spectral numerical schemes for time-dependent convection with viscosity dependent on temperature

This article proposes spectral numerical methods to solve the time evolution of convection problems with viscosity strongly dependent on temperature at infinite Prandtl number. Although we verify the proposed techniques solely for viscosities that depend exponentially on temperature, the methods are extensible to other dependence laws. The set-up is a 2D domain with periodic boundary conditions along the horizontal coordinate which introduces a symmetry in the problem. This is the O(2) symmetry, which is particularly well described by spectral methods and motivates the use of these methods in this context. We examine the scope of our techniques by exploring transitions from stationary regimes towards time dependent regimes. At a given aspect ratio, stable stationary solutions become unstable through a Hopf bifurcation, after which the time-dependent regime is solved by the spectral techniques proposed in this article.     

Semidefinite optimization models for limit and shakedown analysis problems involving matrix spreads

Limit and shakedown analysis problems of Computational Mechanics lead to convex optimization problems, characterized by linear objective functions, linear equality constraints and constraints expressing the restrictions imposed by the material strength. It is shown that two important strength criteria, the Mohr–Coulomb and the Tresca criterion, can be represented as systems of semidefinite constraints, leading this way to semidefinite programming problems.     

Investigations of yield stress in ferrofluids with a stress controlled rheometer

One of the most important properties of ferrofluids is the strong change of viscosity when subject to an applied magnetic field – the so called magnetoviscous effect. The rheological experiments as well as theoretical studies correlate this effect with the appearance of chain-like structures of magnetic particles due to the strong interparticle interaction in presence of a magnetic field. Furthermore, viscoelastic effects or other non-Newtonian features, like yield stress in ferrofluids, can theoretically be described with these structures under the influence of the magnetic field. In earlier experiments, when a shear rate controlled rheometer has been used, yield stress could not be investigated directly. A field dependent yield stress could only be estimated in ferrofluids. For direct yield stress investigations, a dedicated stress controlled rheometer is needed, so that the yield stress and its dependence on the magnetic field can be investigated directly. This paper presents investigations of yield stress and its dependence on the magnetic field strength as well as on volume concentration of large magnetic particles. In order to get more information about the structure formed by the particles, variation of gap thickness of the shear cell for the yield stress experiments has been used. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

An analysis of the shiftedLR algorithm

Summary We introduce and analyze generalized shift strategies for theLR algorithm and prove that these strategies are generalizations of classical iterations for non-linear equations. We also study how certain matrix functions transform under theLR algorithm.This paper is based on work done while T. J. Dekker was visiting Bell Telephone Laboratories, Incorporated.Some of the material in this paper was presented by J. F. Traub in an invited talk at the Gatlinburg Symposium on Numerical Algebra, April 1969.     

An approximate waves-bordering algorithm for adaptive finite elements analysis

In this paper an Approximate Waves-Bordering algorithm (AWB) is presented. It computes the finite elements linear system solution-update after a refinement/unrefinement step. This is done taking into consideration only the equations that correspond to the nodes whose solution is modified above a certain tolerance and it appears to be very efficient. The algorithm considers an increasing set of equations that updates recursively and stops when the norm of the residual has gone under a user-defined threshold. This revised version was published online in June 2006 with corrections to the Cover Date.     

Thermoelastic rolling contact problem with temperature dependent friction

The paper is concerned with the numerical solution of a thermoelastic rolling contact problem with wear. The friction between the bodies is governed by Coulomb law. A frictional heat generation and heat transfer across the contact surface as well as Archard's law of wear in contact zone are assumed. The friction coefficient is assumed to depend on temperature. In the paper quasistatic approach to solve this contact problem is employed. This approach is based on the assumption that for the observer moving with the rolling body the displacement of the supporting foundation is independent on time. The original thermoelastic contact problem described by the hyperbolic inequality governing the displacement and the parabolic equation governing the heat flow is transformed into elliptic inequality and elliptic equation, respectively. In order to solve numerically this system we decouple it into mechanical and thermal parts. Finite element method is used as a discretization method. Numerical examples showing the influence of the temperature dependent friction coefficient on the temperature distribution and the length of the contact zone are provided. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

An analysis of turbulent film condensation on a sphere with variable wall temperature under the effect of local shear stress

This paper presents an investigation into turbulent film condensation on a sphere with variable wall temperature. Under the wide range of vapor velocity, the wall temperature and the local film shear stress were considered. The result shows that under the high velocity vapor, the increase of the temperature amplitude will bring out a larger Nusselt number, and the increase is about 2.7–5.6%. Besides, under the effect of the local film shear stress, the mean Nusselt number will decrease about 0.65–0.8%. Furthermore, the paper then discusses the influence of shears and temperature amplitudes on the local dimensionless film thickness and heat transfer characteristics. Finally, the results developed in the current study are compared with those generated by previous theoretical results.     

One-dimensional viscous radiative gas with temperature dependent viscosity

This paper is concerned with the construction of global, large amplitude solutions to the Cauchy problem of the one-dimensional compressible Navier–Stokes system for a viscous radiative gas when the viscosity and heat conductivity coefficients depend on both specific volume and absolute temperature. The data are assumed to be without vacuum,mass concentrations, or vanishing temperatures, and the same is shown to be hold for the global solution constructed. The proof is based on some detailed analysis on uniform positive lower and upper bounds of the specific volume and absolute temperature.     

An efficient backcalculation algorithm of time domain for large-scale pavement structures using Ritz vectors

This paper describes a backcalculation algorithm to determine the layer moduli and damping coefficients in the time domain for large-scale pavement structures. Pavement is modeled by three-dimensional finite element (3D FE). The parameter identification procedure makes use of Ritz vectors to reduce the size of matrices involved in the forward dynamic response analysis and the deflection sensitivity analysis. An exact complex mode superposition technique is used to obtain the dynamic response of the reduced equation system in the time domain. This method is more efficient, accurate and stable. The parameter estimates are improved iteratively by means of an algorithm that calls the finite element program of dynamic response analysis as a subroutine combining truncated singular value decomposition (TSVD) method. Simulation of a numerical solution validates the efficiency of the proposed method. Finally, the method is implemented for two experimentally tested sections of semiflexible pavement. All parameters are determined using the surface deflections of pavement experimentally recorded at the sensor locations of falling weight deflectometer (FWD).