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non-linear programming in shakedown analysis with plasticity and friction

JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS 2017年 104卷 71-83页

作者： Spagnoli, A. Terzano, M. Barber, J. R. Klarbring, A. Univ Parma Dept Engn & Architecture Viale Usberti 181-A I-43124 Parma Italy Univ Michigan Dept Mech Engn Ann Arbor MI 48109 USA Linkoping Univ Dept Mech Engn S-58183 Linkoping Sweden

Complete frictional contacts, when subjected to cyclic loading, may sometimes develop a favourable situation where slip ceases after a few cycles, an occurrence commonly known as frictional shakedown. Its resemblance to shakedown in plasticity has prompted scholars to apply direct methods, derived from the classical theorems of limit analysis, in order to assess a safe limit to the external loads applied on the system. In circumstances where zones of plastic deformation develop in the material (e.g., because of the large stress concentrations near the sharp edges of a complete contact), it is reasonable to expect an effect of mutual interaction of frictional slip and plastic strains on the load limit below which the global behaviour is non dissipative, i.e., both slip and plastic strains go to zero after some dissipative load cycles. In this paper, shakedown of general two-dimensional discrete systems, involving both friction and plasticity, is discussed and the shakedown limit load is calculated using a non-linear programming algorithm based on the static theorem of limit analysis. An illustrative example related to an elastic-plastic solid containing a frictional crack is provided. (C) 2017 Elsevier Ltd. All rights reserved.

关键词： Limit analysis Shakedown Complete contact Friction non-linear programming

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non-linear programming for the optimization of machine repair problems in fuzzy environments

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ENGINEERING OPTIMIZATION 2006年第7期38卷 789-799页

作者： Chen, Shih-Pin Natl Chung Cheng Univ Dept Business Adm Chiayi 621 Taiwan

Machine repair models have wide applications in many systems such as production line systems and maintenance operations. A procedure is developed to derive the fuzzy objective value of the cost-based machine repair optimization problem, in that the cost coefficients and the machine breakdown rate are fuzzy numbers. On the basis of the extension principle, a pair of non-linear programs are formulated to calculate the lower and upper bounds of the fuzzy minimum expected total cost at the possibility level alpha. The membership function of the minimum expected total cost is constructed by enumerating different values of alpha. A numerical example is solved successfully to demonstrate the validity of the proposed method. Since the minimum expected total cost is completely expressed by a membership function rather than by a crisp value, the fuzziness of the input data is conserved, and more information is provided for decision-making. Furthermore, since the optimum repair rate obtained is fuzzy, a crisp optimum repair rate based on the Yager ranking indices is recommended for practical use.

关键词： machine repair machine interference fuzzy sets non-linear programming

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non-linear programming Method for Buffer Allocation in Unreliable Production Lines

Non-linear Programming Method for Buffer Allocation in Unrel...

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21st International Conference on Analytical and Stochastic Modelling Techniques and Applications (ASMTA)

作者： Ouazene, Yassine Yalaoui, Alice Yalaoui, Farouk Chehade, Hicham Univ Technol Troyes Inst Charles Delaunay Lab Optimisat Syst Ind UMR CNRS 6281 F-10004 Troyes France

ISBN: (纸本)9783319082196;9783319082189

This paper proposes a new algorithm based on a non-linear programming approach to deal with the buffer allocation problem in the case of unreliable production lines. Processing, failure and repair times are assumed to be random variables exponentially distributed. The proposed approach can be used to solve the different versions of the buffer allocation problem: primal, dual and generalized. This method is based on the modeling and the analysis of the serial production line using an equivalent machines method. The idea is to model the different possible states of each buffer using dedicated birth-death Markov processes to calculate the blockage and starvation probabilities of each machine. Then, each original machine is replaced by an equivalent one taking into account these probabilities. A comparative study based on different test instances issued from the literature is presented and discussed. The obtained results show the effectiveness and the accuracy of the proposed approach.

关键词： Buffer allocation Unreliable production lines Equivalent Machine Method non-linear programming Birth-death processes

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non-linear programming in groundwater decontamination problems

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Engineering Optimization 1991年第1-3期18卷 121-136页

作者： Merckx, Christian Universitaires Notre-Dame de la Paix Department of Mathematics B-5000 Namur Belgium

The contaminant distribution into an aquifer is simulated through steady slate groundwater flow and transient convective-dispersive transport. A minimal cost pumpage strategy for groundwater decontamination is found as the solution of a non-linearly constrained optimization problem. The exact gradient of the constrains is computed at a minimal cost through the introduction of the discrete sensitivity equations or the discrete adjoint sensitivity equations. We propose a new initialization procedure of the Lagrangian function Hessian for the Sequential Quadratic programming method (SQP). For this peculiar application, it appears to be very efficient when combined with the SQP implementation of Schittkowski and the discrete gradient computation. Numerical experiments with problems with up to thirty-five extraction wells have been solved in a computer time equivalent to less than one hundred state equations simulations. © 1991, Taylor & Francis Group, LLC. All Rights Reserved.

关键词： advective-dispersive transport Groundwater flow non-linear programming optimal control sensitivity analysis sequential quadratic programming

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Constrained non-linear programming: A minimum cross-entropy algorithm

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ENGINEERING OPTIMIZATION 1999年第4期31卷 479-487页

作者： Das, NC Mazumder, SK De, K Bengal Engn Coll DU Dept Math Howrah 711103 W Bengal India Univ Calcutta Dept Math Kolkata 700073 W Bengal India Vidyasagar Univ Dept Math Midnapore W Bengal India

The paper presents an information-theoretic algorithm for solving constrained non-linear programming problems based upon the principle of minimum cross-entropy and surrogate mathematical programming. It is an alternative to the earlier work by Templeman and Li [4-6] based on the maximum entropy principle and so far as the rate of convergence of the solution is concerned it is an improvement upon it. The merit of the present technique is illustrated with two numerical examples.

关键词： entropy cross-entropy non-linear programming surrogate constraints minimum-cross entropy principle

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Transmission-expansion planning based on a non-linear programming algorithm

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APPLIED ENERGY 2003年第1-3期76卷 169-177页

作者： Al-Hamouz, ZM Al-Faraj, AS King Fahd Univ Petr & Minerals Dept Elect Engn Dhahran 31261 Saudi Arabia

In this formulation, the objective function and operating constraints include the corona power-loss term. The objective function consists of three terms: cost of investment of new transmission lines, ohmic power loss of new and existing lines, and corona-power loss of new lines. This combination of terms results in a non-linear objective function. The non-linear programming or the non-convex optimization technique is used to solve such large-scale practical problem. The new formulation has been applied to the 28-bus Jordanian high-voltage transmission network in order to test and justify its applicability. (C) 2003 Elsevier Ltd. All rights reserved.

关键词： corona power loss expansion non-linear programming planning transmission lines

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Investigating the Utility of Water Cycle Optimization and non-linear programming Techniques in Electric Vehicle Stations Smart Planning

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IETE JOURNAL OF RESEARCH 2024年第1期70卷 597-609页

作者： Elkasrawy, M. A. Besadap, Peter Makeen Abdullatif, Sameh O. Memon, Saim Ghali, Hani A. British Univ Egypt BUE Fac Engn Ctr Emerging Learning Technol CELT FabLab El Sherouk 11837 Egypt British Univ Egypt BUE Fac Engn Renewable Energy Postgrad Programme El Sherouk 11837 Egypt London South Bank Univ London Ctr Energy Engn Sch Engn Div Elect & Elect Engn London SE1 0AA England Univ Huddersfield Ctr Efficiency & Performance Engn CEPE Sch Comp & Engn Dept Engn & Technol Huddersfield HD1 3DH W Yorkshire England

Transportation electrification shows enormous prospects regarding the global environmental pollution issue. However, the penetration of electric vehicles (EVs) is not massive in the global market. We attribute this to the long AC charging time and the limitations of the charging topologies at home. Accordingly, the need for a centralized electrical vehicle station (EVS) becomes a must to enlarge the contribution of the EVs industry market. Intelligent decision-making is essential in enhancing the EVS performance by optimizing the charging time and minimizing the queuing delay, especially during peak hours. In the current study, we propose an entire scenario for an EVS with a maximum of 14 EVs at peak hours. Multiple charging methodologies have been provided, including DC constant current constant voltage, DC multistage constant currents, AC 110/120 V, and AC 220/240 V. In addition, four various photovoltaic/grid integration scenarios have been introduced seeking the optimum EVS operation concerning;Levelized cost of energy, charging time and capacity. Finally, two charging schemes have been demonstrated, targeting a minimum total charging time and queuing delay, where the water cycle optimization technique has been enrolled in parallel with non-linear programming. A significant reduction in the total charging time, nearly 90%, has been reached concerning the overnight in-home AC charging time.

关键词： Electric vehicles LCOE meta-heuristic optimization non-linear programming photovoltaic system queuing delay optimization

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A non-linear programming-based similarity reasoning scheme for modelling of monotonicity-preserving multi-input fuzzy inference systems

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JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2012年第2-3期23卷 71-92页

作者： Tay, Kai Meng Jee, Tze Ling Lim, Chee Peng Univ Malaysia Sarawak Dept Elect Engn Fac Engn Kuching Malaysia Univ Sci Malaysia Sch Comp Sci Petaling Jaya Malaysia

In this paper, the zero-order Sugeno Fuzzy Inference System (FIS) that preserves the monotonicity property is studied. The sufficient conditions for the zero-order Sugeno FIS model to satisfy the monotonicity property are exploited as a set of useful governing equations to facilitate the FIS modelling process. The sufficient conditions suggest a fuzzy partition (at the rule antecedent part) and a monotonically-ordered rule base (at the rule consequent part) that can preserve the monotonicity property. The investigation focuses on the use of two Similarity Reasoning (SR)-based methods, i.e., Analogical Reasoning (AR) and Fuzzy Rule Interpolation (FRI), to deduce each conclusion separately. It is shown that AR and FRI may not be a direct solution to modelling of a multi-input FIS model that fulfils the monotonicity property, owing to the difficulty in getting a set of monotonically-ordered conclusions. As such, a non-linear programming (NLP)-based SR scheme for constructing a monotonicity-preserving multi-input FIS model is proposed. In the proposed scheme, AR or FRI is first used to predict the rule conclusion of each observation. Then, a search algorithm is adopted to look for a set of consequents with minimized root means square errors as compared with the predicted conclusions. A constraint imposed by the sufficient conditions is also included in the search process. Applicability of the proposed scheme to undertaking fuzzy Failure Mode and Effect Analysis (FMEA) tasks is demonstrated. The results indicate that the proposed NLP-based SR scheme is useful for preserving the monotonicity property for building a multi-input FIS model with an incomplete rule base.

关键词： Fuzzy inference system similarity reasoning analogical reasoning fuzzy rule interpolation non-linear programming monotonicity property failure mode and effect analysis

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Best proximity point theorems: resolution of an important non-linear programming problem

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OPTIMIZATION LETTERS 2013年第6期7卷 1167-1177页

作者： Basha, S. Sadiq Anna Univ Dept Math Madras 600025 Tamil Nadu India

The purpose of this article is to resolve the non-linear programming problem of globally minimizing the real valued function where S is a non-self-mapping in the setting of a metric space with the distance function 'd'. An iterative algorithm is also furnished to find a solution of such global optimization problems. As a consequence, one can determine an optimal approximate solution to some equations of the form Sx = x.

关键词： Global optimization non-linear programming Optimal approximate solution Best proximity point Fixed point Weak contraction Contraction Proximal contraction Generalized proximal contraction Proximal cyclic contraction Generalized proximal cyclic contraction

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Lower bound shakedown analysis by using the element free Galerkin method and non-linear programming

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COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 2008年第45-48期197卷 3911-3921页

作者： Chen, Shenshen Liu, Yinghua Cen, Zhangzhi Tsinghua Univ Dept Engn Mech Beijing 100084 Peoples R China

Shakedown analysis is a powerful tool for assessing the safety of structures under variable repeated loads. By using the element free Galerkin (EFG) method and non-linear programming, a novel numerical solution procedure is developed to perform lower bound shakedown analysis of structures made up of elastoperfectly plastic material. 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 here 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 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 the non-linear programming and determine the lower bound of shakedown load. The proposed numerical method is verified by using several numerical examples and the results show good agreement with other available solutions. (C) 2008 Elsevier B.V. All rights reserved.

关键词： shakedown analysis EFG method self-equilibrium stress reduced-basis technique non-linear programming

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