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Selected AbstractsThe ,-reliable minimax and maximin location problems on a network with probabilistic weightsNETWORKS: AN INTERNATIONAL JOURNAL, Issue 2 2010Jiamin Wang Abstract We study the ,-reliable minimax and maximin location problems on a network when the weights associated with the nodal points are random variables. In the ,-reliable minimax (maximin) problem, we locate a single facility so as to minimize (maximize) the upper (lower) bound on the maximum (minimum) weighted distance from the nodes to the facility with a probability greater than or equal to a pre-specified level ,. It is shown that under some conditions the two probabilistic models are equivalent to their deterministic counterparts. Solution procedures are developed to solve the problems with weights of continuous and discrete probability distributions. © 2009 Wiley Periodicals, Inc. NETWORKS, 2010 [source] Steady-State Analysis of Water Distribution Networks Including Pressure-Reducing ValvesCOMPUTER-AIDED CIVIL AND INFRASTRUCTURE ENGINEERING, Issue 4 2001L. Khezzar Hydraulic networks that contain controlling elements such as pressure-reducing valves (PRVs) are difficult to simulate. Limited literature exists on the explicit modeling of PRVs in a general solution procedure for steady-state analysis of water distribution systems. It is also known that inclusion of PRVs may lead to numerical difficulties. The objective of this article is to develop and present in sufficient detail the modeling of PRVs in combination with the linear theory method for steady-state analysis of water distribution networks. The presentation is explicit enough and leads to a robust algorithm that can be directly implemented in a computer program. The general methodology for simulating water distribution networks that embodies graph theoretic concepts, hydraulic theory, and numerical algorithms is reviewed. [source] Coordinated Capacitated Lot-Sizing Problem with Dynamic Demand: A Lagrangian HeuristicDECISION SCIENCES, Issue 1 2004E. Powell Robinson Jr. ABSTRACT Coordinated replenishment problems are common in manufacturing and distribution when a family of items shares a common production line, supplier, or a mode of transportation. In these situations the coordination of shared, and often limited, resources across items is economically attractive. This paper describes a mixed-integer programming formulation and Lagrangian relaxation solution procedure for the single-family coordinated capacitated lot-sizing problem with dynamic demand. The problem extends both the multi-item capacitated dynamic demand lot-sizing problem and the uncapacitated coordinated dynamic demand lot-sizing problem. We provide the results of computational experiments investigating the mathematical properties of the formulation and the performance of the Lagrangian procedures. The results indicate the superiority of the dual-based heuristic over linear programming-based approaches to the problem. The quality of the Lagrangian heuristic solution improved in most instances with increases in problem size. Heuristic solutions averaged 2.52% above optimal. The procedures were applied to an industry test problem yielding a 22.5% reduction in total costs. [source] The analysis of thermoelastic isopachic data from crack tip stress fieldsFATIGUE & FRACTURE OF ENGINEERING MATERIALS AND STRUCTURES, Issue 4 2000Dulieu-Barton A computer program,FACTUS (fracture analysis of crack tips using SPATE),has been developed for the efficient analysis of thermoelastic data obtained from around a crack tip. The program is based on earlier work for the determination of stress intensity factors (SIFs), and also includes a novel solution procedure for the derivation of the non-singular stress term ,0x,. The program has been used in the analysis of a series of large plate specimens with central or edge slots/cracks. The derived SIFs are compared with independent values. Issues, e.g. crack closure and the extent and effect of the plastic zone, are discussed. [source] An efficient time-domain damping solvent extraction algorithm and its application to arch dam,foundation interaction analysisINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 9 2008Hong Zhong Abstract The dynamic structure,unbounded foundation interaction plays an important role in the seismic response of structures. The damping solvent extraction (DSE) method put forward by Wolf and Song has a great advantage of simplicity, with no singular integrals to be evaluated, no fundamental solution required and convolution integrals avoided. However, implementation of DSE in the time domain to large-scale engineering problems is associated with enormous difficulties in evaluating interaction forces on the structure,unbounded foundation interface, because the displacement on the corresponding interface is an unknown vector to be found. Three sets of interrelated large algebraic equations have to be solved simultaneously. To overcome these difficulties, an efficient algorithm is presented, such that the solution procedure can be greatly simplified and computational effort considerably saved. To verify its accuracy, two examples with analytical solutions were investigated, each with a parameter analysis on the domain size and amount of artificial damping. Then with the parameters suggested in the parameter study, the complex frequency,response functions and earthquake time history analysis of Morrow Point dam were presented to demonstrate the applicability and efficiency of DSE approach. Copyright © 2007 John Wiley & Sons, Ltd. [source] Laminar and turbulent flow calculations through a model human upper airway using unstructured meshesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 12 2007P. Nithiarasu Abstract In this paper, numerical investigation of airflow through a human upper airway is presented using an unstructured-based characteristic-based split (CBS) scheme. The CBS scheme used in the present study employs a fully explicit matrix-free solution procedure along with artificial compressibility. A one equation Spalrat,Allmaras (SA) turbulence model is employed to study low and moderate Reynolds number flows. A detailed discussion of the qualitative and quantitative results is presented. The results show a strong influence of the Reynolds number on the flow pattern and quantities of interest, pressure drop and wall shear stress. It is also apparent that SA model can be employed on unstructured meshes to predict the steady flow with good accuracy. Thus, the novelties of the present paper are: use of the unstructured mesh-based solution algorithm and the successful application of the SA model to a typical human upper airway. Copyright © 2006 John Wiley & Sons, Ltd. [source] Failure of heterogeneous materials: 3D meso-scale FE models with embedded discontinuitiesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 13 2010N. Benkemoun Abstract We present a meso-scale model for failure of heterogeneous quasi-brittle materials. The model problem of heterogeneous materials that is addressed in detail is based on two-phase 3D representation of reinforced heterogeneous materials, such as concrete, where the inclusions are melt within the matrix. The quasi-brittle failure mechanisms are described by the spatial truss representation, which is defined by the chosen Voronoi mesh. In order to explicitly incorporate heterogeneities with no need to change this mesh, some bar elements are cut by the phase-interface and must be split into two parts. Any such element is enhanced using both weak and strong discontinuities, based upon the Incompatible Mode Method. Furthermore, a dedicated operator split solution procedure is proposed to keep local any additional computation on elements with embedded discontinuities. The results for several numerical simulations are presented to illustrate the capabilities of the proposed model to provide an excellent representation of failure mechanisms for any different macroscopic loading path. Copyright © 2010 John Wiley & Sons, Ltd. [source] Analysis of the block Gauss,Seidel solution procedure for a strongly coupled model problem with reference to fluid,structure interactionINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 7 2009M. M. Joosten Abstract The block Gauss,Seidel procedure is widely used for the resolution of the strong coupling in the computer simulation of fluid,structure interaction. Based on a simple model problem, this work presents a detailed analysis of the convergence behaviour of the method. In particular, the model problem is used to highlight some aspects that arise in the context of the application of the block Gauss,Seidel method to FSI problems. Thus, the effects of the time integration schemes chosen, of relaxation techniques, of physical constraints and non-linearities on the convergence of the iterations are investigated. Copyright © 2008 John Wiley & Sons, Ltd. [source] Lower-bound limit analysis by using the EFG method and non-linear programmingINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 3 2008Shenshen Chen Abstract Intended to avoid the complicated computations of elasto-plastic incremental analysis, limit analysis is an appealing direct method for determining the load-carrying capacity of structures. On the basis of the static limit analysis theorem, a solution procedure for lower-bound limit analysis is presented firstly, making use of the element-free Galerkin (EFG) method rather than traditional numerical methods such as the finite element method and boundary element method. The numerical implementation is very simple and convenient because it is only necessary to construct an array of nodes in the domain under consideration. The reduced-basis technique is adopted to solve the mathematical programming iteratively in a sequence of reduced self-equilibrium stress subspaces with very low dimensions. The self-equilibrium stress field is expressed by a linear combination of several self-equilibrium stress basis vectors with parameters to be determined. These self-equilibrium stress basis vectors are generated by performing an equilibrium iteration procedure during elasto-plastic incremental analysis. The Complex method is used to solve these non-linear programming sub-problems and determine the maximal load amplifier. Numerical examples show that it is feasible and effective to solve the problems of limit analysis by using the EFG method and non-linear programming. Copyright © 2007 John Wiley & Sons, Ltd. [source] An efficient co-rotational formulation for curved triangular shell elementINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 9 2007Zhongxue Li Abstract A 6-node curved triangular shell element formulation based on a co-rotational framework is proposed to solve large-displacement and large-rotation problems, in which part of the rigid-body translations and all rigid-body rotations in the global co-ordinate system are excluded in calculating the element strain energy. Thus, an element-independent formulation is achieved. Besides three translational displacement variables, two components of the mid-surface normal vector at each node are defined as vectorial rotational variables; these two additional variables render all nodal variables additive in an incremental solution procedure. To alleviate the membrane and shear locking phenomena, the membrane strains and the out-of-plane shear strains are replaced with assumed strains in calculating the element strain energy. The strategy used in the mixed interpolation of tensorial components approach is employed in defining the assumed strains. The internal force vector and the element tangent stiffness matrix are obtained from calculating directly the first derivative and second derivative of the element strain energy with respect to the nodal variables, respectively. Different from most other existing co-rotational element formulations, all nodal variables in the present curved triangular shell formulation are commutative in calculating the second derivative of the strain energy; as a result, the element tangent stiffness matrix is symmetric and is updated by using the total values of the nodal variables in an incremental solution procedure. Such update procedure is advantageous in solving dynamic problems. Finally, several elastic plate and shell problems are solved to demonstrate the reliability, efficiency, and convergence of the present formulation. Copyright © 2007 John Wiley & Sons, Ltd. [source] An unconditionally convergent algorithm for the evaluation of the ultimate limit state of RC sections subject to axial force and biaxial bendingINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 8 2007G. Alfano Abstract We present a numerical procedure, based upon a tangent approach, for evaluating the ultimate limit state (ULS) of reinforced concrete (RC) sections subject to axial force and biaxial bending. The RC sections are assumed to be of arbitrary polygonal shape and degree of connection; furthermore, it is possible to keep fixed a given amount of the total load and to find the ULS associated only with the remaining part which can be increased by means of a load multiplier. The solution procedure adopts two nested iterative schemes which, in turn, update the current value of the tentative ultimate load and the associated strain parameters. In this second scheme an effective integration procedure is used for evaluating in closed form, as explicit functions of the position vectors of the vertices of the section, the domain integrals appearing in the definition of the tangent matrix and of the stress resultants. Under mild hypotheses, which are practically satisfied for all cases of engineering interest, the existence and uniqueness of the ULS load multiplier is ensured and the global convergence of the proposed solution algorithm to such value is proved. An extensive set of numerical tests, carried out for rectangular, L-shaped and multicell sections shows the effectiveness of the proposed solution procedure. Copyright © 2007 John Wiley & Sons, Ltd. [source] Trefftz solutions for piezoelectricity by Lekhnitskii's formalism and boundary-collocation methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 13 2006N. Sheng Abstract In this paper, a solution procedure for plane piezoelectricity is developed by Trefftz boundary-collocation method. Starting with the general plane piezoelectricity solution derived by Lekhnitskii's formalism, the basic sets of Trefftz functions which satisfy the homogeneous governing equations are derived. Moreover, special sets of Trefftz functions are derived for impermeable elliptical voids, impermeable sharp cracks and permeable sharp cracks with arbitrary orientations with respect to the material poling direction. The functions in the special sets satisfy not only the homogeneous governing equations but also the boundary conditions at the peripheries of the pertinent defects. By adopting Trefftz functions as the trial functions, multi-domain Trefftz boundary-collocation method is formulated. Numerical examples are presented to illustrate the efficacy of the formulation. Copyright © 2005 John Wiley & Sons, Ltd. [source] Optimal design and optimal control of structures undergoing finite rotations and elastic deformationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 14 2004A. Ibrahimbegovic Abstract In this work, we deal with the optimal design and optimal control of structures undergoing large rotations and large elastic deformations. In other words, we show how to find the corresponding initial configuration through optimal design or the corresponding set of multiple load parameters through optimal control, in order to recover a desired deformed configuration or some desirable features of the deformed configuration as specified more precisely by the objective or cost function. The model problem chosen to illustrate the proposed optimal design and optimal control methodologies is the one of geometrically exact beam. First, we present a non-standard formulation of the optimal design and optimal control problems, relying on the method of Lagrange multipliers in order to make the mechanics state variables independent from either design or control variables and thus provide the most general basis for developing the best possible solution procedure. Two different solution procedures are then explored, one based on the diffuse approximation of response function and gradient method and the other one based on genetic algorithm. A number of numerical examples are given in order to illustrate both the advantages and potential drawbacks of each of the presented procedures. Copyright © 2004 John Wiley & Sons, Ltd. [source] An accurate scheme for mixed-mode fracture analysis of functionally graded materials using the interaction integral and micromechanics modelsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 10 2003Jeong-Ho Kim Abstract The interaction integral is a conservation integral that relies on two admissible mechanical states for evaluating mixed-mode stress intensity factors (SIFs). The present paper extends this integral to functionally graded materials in which the material properties are determined by means of either continuum functions (e.g. exponentially graded materials) or micromechanics models (e.g. self-consistent, Mori,Tanaka, or three-phase model). In the latter case, there is no closed-form expression for the material-property variation, and thus several quantities, such as the explicit derivative of the strain energy density, need to be evaluated numerically (this leads to several implications in the numerical implementation). The SIFs are determined using conservation integrals involving known auxiliary solutions. The choice of such auxiliary fields and their implications on the solution procedure are discussed in detail. The computational implementation is done using the finite element method and thus the interaction energy contour integral is converted to an equivalent domain integral over a finite region surrounding the crack tip. Several examples are given which show that the proposed method is convenient, accurate, and computationally efficient. Copyright © 2003 John Wiley & Sons, Ltd. [source] A ,-coordinate three-dimensional numerical model for surface wave propagationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 11 2002Pengzhi Lin Abstract A three-dimensional numerical model based on the full Navier,Stokes equations (NSE) in , -coordinate is developed in this study. The , -coordinate transformation is first introduced to map the irregular physical domain with the wavy free surface and uneven bottom to the regular computational domain with the shape of a rectangular prism. Using the chain rule of partial differentiation, a new set of governing equations is derived in the , -coordinate from the original NSE defined in the Cartesian coordinate. The operator splitting method (Li and Yu, Int. J. Num. Meth. Fluids 1996; 23: 485,501), which splits the solution procedure into the advection, diffusion, and propagation steps, is used to solve the modified NSE. The model is first tested for mass and energy conservation as well as mesh convergence by using an example of water sloshing in a confined tank. Excellent agreements between numerical results and analytical solutions are obtained. The model is then used to simulate two- and three-dimensional solitary waves propagating in constant depth. Very good agreements between numerical results and analytical solutions are obtained for both free surface displacements and velocities. Finally, a more realistic case of periodic wave train passing through a submerged breakwater is simulated. Comparisons between numerical results and experimental data are promising. The model is proven to be an accurate tool for consequent studies of wave-structure interaction. Copyright © 2002 John Wiley & Sons, Ltd. [source] Algorithms for the circular two-dimensional open dimension problemINTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH, Issue 6 2008Hakim Akeb Abstract In this paper, we propose three heuristics for the circular two-dimensional open dimension problem, also known as the circular strip cutting/packing problem. We first propose an open strip generation solution procedure that uses the best local position rule into the open strip. Second, we propose a simple augmented version of the first heuristic by introducing an exchange-order strategy. Third, we propose a hybrid heuristic that combines beam search and a series of target values belonging to a predetermined interval search. We evaluate the performance of these heuristics on several instances varying from small to large ones. Encouraging results have been obtained. [source] Sensitivity analysis of the knapsack sharing problem: perturbation of the profit of an itemINTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH, Issue 1 2008T. Belgacem Abstract In this paper, we study the sensitivity of the optimum of a max,min combinatorial optimization problem, namely the knapsack sharing problem, to the perturbation of the profit of an arbitrary item. We mainly establish the interval limits of each perturbed item by applying a reduction of the original problem into a series of single knapsack problems. We propose a solution procedure in order to establish these interval limits. The principle of the method is to stabilize the optimal solution in the perturbed problem, following two cases: (i) when the item belongs to an optimal class and (ii) when the item belongs to a non-optimal class. We also consider either the problem admits a unique or multiple optimal classes. Finally, we evaluate the effectiveness of the proposed method on several problem instances in the literature. [source] Determination of ,, solution temperature in Re-rich Ni-base superalloy by small-angle neutron scatteringJOURNAL OF APPLIED CRYSTALLOGRAPHY, Issue 5 2001Pavel Strunz A harmful segregation of heavy elements (e.g. W, Mo, Re) during solidification of Ni-base superalloys can only be eliminated by using a homogenizing heat treatment, which needs to be carried out in the single-phase (,) field above the ,, solvus temperature but below the solidus temperature. Small-angle neutron scattering (SANS) was employed for in situ observation of the dissolution of precipitates in an Re-rich superalloy. The temperature dependence of the relative volume fraction and the size distribution of smaller ,, precipitates, and the specific surface of large inhomogeneities as well as some other parameters were determined from the two-dimensional scattering curves measured for as-cast and heat-treated samples. Overlap of the incipient melting region with the region where a certain amount of precipitates remained undissolved was observed, thus complicating a determination of the temperature at which all ,, precipitates are already dissolved. Nevertheless, conclusions about the temperature at which the precipitates dissolve and about the temperature at which the incipient melting starts could be formulated. The total scattering probability is suggested as the measure of the overall homogeneity of the distribution of elements in the sample. The temperature dependence of this parameter indicates the optimum solution procedure. [source] Optimal design and planning of sustainable chemical supply chains under uncertaintyAICHE JOURNAL, Issue 1 2009Gonzalo Guillén-Gosálbez Abstract This article addresses the design of sustainable chemical supply chains in the presence of uncertainty in the life cycle inventory associated with the network operation. The design task is mathematically formulated as a bi-criterion stochastic mixed-integer nonlinear program (MINLP) that simultaneously accounts for the maximization of the net present value and the minimization of the environmental impact for a given probability level. The environmental performance is measured through the Eco-indicator 99, which incorporates the recent advances made in Life Cycle Assessment. The stochastic model is converted into its deterministic equivalent by reformulating the probabilistic constraint required to calculate the environmental impact in the space of uncertain parameters. The resulting deterministic bi-criterion MINLP problem is further reformulated as a parametric MINLP, which is solved by decomposing it into two sub-problems and iterating between them. The capabilities of the proposed model and solution procedure are illustrated through two case studies for which the set of Pareto optimal, or efficient solutions that trade-off environmental impact and profit, are calculated. These solutions provide valuable insights into the design problem and are intended to guide the decision maker towards the adoption of more sustainable design alternatives. © 2008 American Institute of Chemical Engineers AIChE J, 2009 [source] DECISION SUPPORT FOR ALLOCATION OF WATERSHED POLLUTION LOAD USING GREY FUZZY MULTIOBJECTIVE PROGRAMMING,JOURNAL OF THE AMERICAN WATER RESOURCES ASSOCIATION, Issue 3 2006Ho-Wen Chen ABSTRACT: This paper uses the grey fuzzy multiobjective programming to aid in decision making for the allocation of waste load in a river system under versatile uncertainties and risks. It differs from previous studies by considering a multicriteria objective function with combined grey and fuzzy messages under a cost benefit analysis framework. Such analysis technically integrates the prior information of water quality models, water quality standards, wastewater treatment costs, and potential benefits gained via in-stream water quality improvement. While fuzzy sets are characterized based on semantic and cognitive vagueness in decision making, grey numbers can delineate measurement errors in data collection. By employing three distinct set theoretic fuzzy operators, the synergy of grey and fuzzy implications may smoothly characterize the prescribed management complexity. With the aid of genetic algorithm in the solution procedure, the modeling outputs contribute to the development of an effective waste load allocation and reduction scheme for tributaries in this subwatershed located in the lower Tseng-Wen River Basin, South Taiwan. Research findings indicate that the inclusion of three fuzzy set theoretic operators in decision analysis may delineate different tradeoffs in decision making due to varying changes, transformations, and movements of waste load in association with land use pattern within the watershed. [source] Capacitated lot-sizing and scheduling with parallel machines, back-orders, and setup carry-overNAVAL RESEARCH LOGISTICS: AN INTERNATIONAL JOURNAL, Issue 4 2009Daniel Quadt Abstract We address the capacitated lot-sizing and scheduling problem with setup times, setup carry-over, back-orders, and parallel machines as it appears in a semiconductor assembly facility. The problem can be formulated as an extension of the capacitated lot-sizing problem with linked lot-sizes (CLSPL). We present a mixed integer (MIP) formulation of the problem and a new solution procedure. The solution procedure is based on a novel "aggregate model," which uses integer instead of binary variables. The model is embedded in a period-by-period heuristic and is solved to optimality or near-optimality in each iteration using standard procedures (CPLEX). A subsequent scheduling routine loads and sequences the products on the parallel machines. Six variants of the heuristic are presented and tested in an extensive computational study. © 2009 Wiley Periodicals, Inc. Naval Research Logistics 2009 [source] Optimal production and maintenance policy for imperfect production systemsNAVAL RESEARCH LOGISTICS: AN INTERNATIONAL JOURNAL, Issue 2 2006Chih-Hsiung Wang Abstract A joint optimization of the production run length and preventive maintenance (PM) policy is studied for a deteriorating production system where the in-control period follows a general probability distribution with non-decreasing failure rate. In the literature, the sufficient conditions for the optimality of the equal-interval PM schedule is explored to derive an optimal production run length and an optimal number of PM actions. Nevertheless, an exhaustive search may arise. In this study, based on the assumption that the conditions for the optimality of the equal-interval PM schedule hold, we derive some structural properties for the optimal production/PM policy, which increases the efficiency of the solution procedure. These analyses have implications for the practical application of the production/PM model to be more available in practice. A numerical example of gamma shift distribution with non-decreasing failure rates is used to illustrate the solution procedure, leading to some insight into the management process. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2006 [source] Bicriteria product design optimization: An efficient solution procedure using AND/OR treesNAVAL RESEARCH LOGISTICS: AN INTERNATIONAL JOURNAL, Issue 6 2002S. Raghavan Competitive imperatives are causing manufacturing firms to consider multiple criteria when designing products. However, current methods to deal with multiple criteria in product design are ad hoc in nature. In this paper we present a systematic procedure to efficiently solve bicriteria product design optimization problems. We first present a modeling framework, the AND/OR tree, which permits a simplified representation of product design optimization problems. We then show how product design optimization problems on AND/OR trees can be framed as network design problems on a special graph,a directed series-parallel graph. We develop an enumerative solution algorithm for the bicriteria problem that requires as a subroutine the solution of the parametric shortest path problem. Although this parametric problem is hard on general graphs, we show that it is polynomially solvable on the series-parallel graph. As a result we develop an efficient solution algorithm for the product design optimization problem that does not require the use of complex and expensive linear/integer programming solvers. As a byproduct of the solution algorithm, sensitivity analysis for product design optimization is also efficiently performed under this framework. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 574,592, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10031 [source] Low-connectivity network design on series-parallel graphsNETWORKS: AN INTERNATIONAL JOURNAL, Issue 3 2004S. Raghavan Abstract Network survivability is a critical issue for modern fiber-optic telecommunication networks. Networks with alternate routes between pairs of nodes permit users to communicate in the face of equipment failure. In this paper, we consider the following low-connectivity network design (LCND) problem: Given a graph G = (N, E) and a connectivity requirement di , {0, 1, 2} for each node and edge costs ce for each edge e , E, design a minimum-cost network that contains at least dst = min{ds, dt} disjoint paths between nodes s and t. We present linear-time algorithms for both node- and edge-connectivity versions of the problem on series-parallel graphs. Due to the sparsity of telecommunications networks, this algorithm can be applied to obtain partial solutions and decompositions that may be embedded in a heuristic solution procedure as well as exact solution algorithms for the problem on general graphs. © 2004 Wiley Periodicals, Inc. [source] The particular solutions for thin plates resting on Pasternak foundations under arbitrary loadingsNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 1 2010Chia-Cheng Tsai Abstract Analytical particular solutions of splines and monomials are obtained for problems of thin plate resting on Pasternak foundation under arbitrary loadings, which are governed by a fourth-order partial differential equation (PDEs). These analytical particular solutions are valuable when the arbitrary loadings are approximated by augmented polyharmonic splines (APS) constructed by splines and monomials. In our derivations, the real coefficient operator in the governing equation is decomposed into two complex coefficient operators whose particular solutions are known in literature. Then, we use the difference trick to recover the analytical particular solutions of the original operator. In addition, we show that the derived particular solution of spline with its first few directional derivatives are bounded as r , 0. This solution procedure may have the potential in obtaining analytical particular solutions of higher order PDEs constructed by products of Helmholtz-type operators. Furthermore, we demonstrate the usages of these analytical particular solutions by few numerical cases in which the homogeneous solutions are complementarily solved by the method of fundamental solutions (MFS). © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010 [source] Two Parallel Computing Methods for Coupled Thermohydromechanical ProblemsCOMPUTER-AIDED CIVIL AND INFRASTRUCTURE ENGINEERING, Issue 3 2000B. A. Schrefler Two different approaches are presented for the parallel implementation of computer programs for the solution of coupled thermohydromechanical problems. One is an asynchronous method in connection with staggered and monolithic solution procedures. The second one is a domain decomposition method making use of substructuring techniques and a Newton-Raphson procedure. The advantages of the proposed methods are illustrated by examples. Both methods are promising, but we actually have no comparison between the two because one works on a linear program with only two interacting fields and the other on a full nonlinear set of (multifield) equations. [source] Quantitative Comparison of Approximate Solution Sets for Bi-criteria Optimization Problems,DECISION SCIENCES, Issue 1 2003W. Matthew Carlyle ABSTRACT We present the Integrated Preference Functional (IPF) for comparing the quality of proposed sets of near-pareto-optimal solutions to bi-criteria optimization problems. Evaluating the quality of such solution sets is one of the key issues in developing and comparing heuristics for multiple objective combinatorial optimization problems. The IPF is a set functional that, given a weight density function provided by a decision maker and a discrete set of solutions for a particular problem, assigns a numerical value to that solution set. This value can be used to compare the quality of different sets of solutions, and therefore provides a robust, quantitative approach for comparing different heuristic, a posteriori solution procedures for difficult multiple objective optimization problems. We provide specific examples of decision maker preference functions and illustrate the calculation of the resulting IPF for specific solution sets and a simple family of combined objectives. [source] On the boundary conditions in slope stability analysisINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 11 2003Ashok K. Chugh Abstract Boundary conditions can affect computed factor of safety results in two- and three-dimensional stability analyses of slopes. Commonly used boundary conditions in two- and three-dimensional slope stability analyses via limit-equilibrium and continuum-mechanics based solution procedures are described. A sample problem is included to illustrate the importance of boundary conditions in slope stability analyses. The sample problem is solved using two- and three-dimensional numerical models commonly used in engineering practice. Copyright © 2003 John Wiley & Sons, Ltd. [source] Optimal design and optimal control of structures undergoing finite rotations and elastic deformationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 14 2004A. Ibrahimbegovic Abstract In this work, we deal with the optimal design and optimal control of structures undergoing large rotations and large elastic deformations. In other words, we show how to find the corresponding initial configuration through optimal design or the corresponding set of multiple load parameters through optimal control, in order to recover a desired deformed configuration or some desirable features of the deformed configuration as specified more precisely by the objective or cost function. The model problem chosen to illustrate the proposed optimal design and optimal control methodologies is the one of geometrically exact beam. First, we present a non-standard formulation of the optimal design and optimal control problems, relying on the method of Lagrange multipliers in order to make the mechanics state variables independent from either design or control variables and thus provide the most general basis for developing the best possible solution procedure. Two different solution procedures are then explored, one based on the diffuse approximation of response function and gradient method and the other one based on genetic algorithm. A number of numerical examples are given in order to illustrate both the advantages and potential drawbacks of each of the presented procedures. Copyright © 2004 John Wiley & Sons, Ltd. [source] Design of distributed controllers with constrained and noisy linksINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 18 2006Shengxiang Jiang Abstract In this paper we consider some design aspects of distributed controllers that guarantee a ,, performance level. In particular, we consider two design problems. First, is the case where, without loss of generality, there are two distributed subcontrollers connected to a (generalized) plant and the interest is placed in minimizing the number of noise-free (and dynamics free) communication channels between the subcontrollers needed to provide a given performance. The second is the case where, given a distributed controller designed in the first case, communication noise is present and we seek an optimal choice of the communication signals to guarantee a performance level while keeping the communication signal to noise power limited. We take a linear matrix inequality (LMI) approach to provide solution procedures to these problems and present examples that demonstrate their efficiency. Copyright © 2006 John Wiley & Sons, Ltd. [source] | ||||||||||||||||||||||