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Microplane Model M7 for Plain Concrete. I: Formulation

JOURNAL OF ENGINEERING MECHANICS 2013年第12期139卷 1714-1723页

作者： Caner, Ferhun C. Bazant, Zdenek P. Univ Politecn Cataluna Sch Ind Engn Inst Energy Technol Barcelona 08028 Spain Northwestern Univ Dept Civil & Environm Engn Evanston IL 60208 USA McCormick Inst Evanston IL 60208 USA Northwestern Univ Evanston IL 60208 USA

Mathematical modeling of the nonlinear triaxial behavior and damage of such a complex material as concrete has been a long-standing challenge in which progress has been made only in gradual increments. The goal of this study is a realistic and robust material model for explicit finite-element programs for concrete structures that computes the stress tensor from the given strain tensor and some history variables. The microplane models, which use a constitutive equation in a vectorial rather than tensorial form and are semimultiscale by virtue of capturing interactions among phenomena of different orientation, can serve this goal effectively. This paper presents a new concrete microplane model, M7, which achieves this goal much better than the previous versions M1-M6 developed at Northwestern University since 1985. The basic mathematical structure of M7 is logically correlated to thermodynamic potentials for the elastic regime, the tensile and compressive damage regimes, and the frictional slip regime. Given that the volumetric-deviatoric (V-D) split of strains is inevitable for distinguishing between compression failures at low and high confinement, the key idea is to apply the V-D split only to the microplane compressive stress-strain boundaries (or strain-dependent yield limits), the sum of which is compared with the total normal stress from the microplane constitutive relation. This avoids the use of the V-D split of the elastic strains and of the tensile stress-strain boundary, which caused various troubles in M3-M6 such as excessive lateral strains and stress locking in far postpeak uniaxial extension, poor representation of unloading and loading cycles, and inability to represent high dilatancy under postpeak compression in lower-strength concretes. Moreover, the differences between high hydrostatic compression and compressive uniaxial strain are accurately captured by considering the compressive volumetric boundary as dependent on the principal strain differen

关键词： Constitutive modeling Inelastic behavior Cracking damage Yield limits Softening Concrete numerical algorithm Thermodynamic potentials Unloading

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Conditional parameter identification with different losses of under- and overestimation

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APPLIED MATHEMATICAL MODELLING 2013年第4期37卷 2166-2177页

作者： Kulczycki, Piotr Charytanowicz, Malgorzata Polish Acad Sci Syst Res Inst Ctr Informat Technol Data Anal Methods PL-00901 Warsaw Poland Cracow Univ Technol Dept Automat Control & Informat Technol Krakow Poland Catholic Univ Lublin Inst Math & Comp Sci Lublin Poland

In many scientific and practical tasks, the classical concepts for parameter identification are satisfactory and generally applied with success, although many specialized problems necessitate the use of methods created with specifically defined assumptions and conditions. This paper investigates the method of parameter identification for the case where losses resulting from estimation errors can be described in polynomial form with additional asymmetry representing different results of under- and overestimation. Most importantly, the method presented here considers the conditionality of this parameter, which in practice means its significant dependence on other quantities whose values can be obtained metrologically. To solve a problem in this form the Bayes approach was used, allowing a minimum expected value of losses to be achieved. The methodology was based on the nonparametric technique of statistical kernel estimators, which freed the investigated procedure from forms of probability distributions characterizing both the parameter under investigation and conditioning quantities. As a result an algorithm is presented, ready for direct use without further intensive research and calculations. (C) 2012 Elsevier Inc. All rights reserved.

关键词： Parameter identification Asymmetrical losses of estimation errors Conditional factors Nonparametric estimation Statistical kernel estimators numerical algorithm

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Simple algorithms for solving steady-state frictional rolling contact problems in two and three dimensions

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INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES 2013年第6期50卷 843-852页

作者： Zehil, Gerard-Philippe Gavin, Henri P. Duke Univ Dept Civil & Environm Engn Durham NC 27708 USA

This paper presents simple, yet robust and efficient algorithms for solving steady-state, frictional, rolling/sliding contact problems, in two and three dimensions. These are alternatives to powerful, well established, but in particular instances, possibly 'cumbersome' general-purpose numerical techniques, such as finite-element approaches based on constrained optimization. The cores of the solvers rely on very general principles: (i) resolving motional conflicts, and (ii) eliminating unacceptable surface tractions. The proposed algorithms are formulated in the context of small deformations and applied to the cases of a rigid cylinder and a rigid sphere rolling on a linear viscoelastic layer of finite thickness, in two and three dimensions, respectively. The underlying principles are elucidated, relevant mathematical expressions derived and details given about corresponding implementation techniques. The proposed contact algorithms can be extended to more general settings involving a deformable indenter, material nonlinearities and large deformations. (C) 2012 Elsevier Ltd. All rights reserved.

关键词： Rolling contact Cylinder Sphere Viscoelastic layer Coulomb's friction Stick/slip contact numerical algorithm

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Non-symbolic algorithms for the inversion of tridiagonal matrices

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2013年 252卷 3-11页

作者： Abderraman Marrero, J. Rachidi, M. Tomeo, V. Tech Univ Madrid ETSIT UPM Telecommun Engn Sch Dept Math Appl Informat Technol Madrid 28040 Spain Univ Moulay Ismail Fac Sci Dept Math & Informat Grp DEFA Beni Mhamed Meknes Morocco Univ Complutense EUE UCM Sch Stat Dept Algebra E-28040 Madrid Spain

A representation for the entries of the inverse of general tridiagonal matrices is based on the determinants of their principal submatrices. It enables us to introduce, through the linear recurrence relations satisfied by such determinants, a simple algorithm for the entries of the inverse of any tridiagonal nonsingular matrix, reduced as well as unreduced. The numerical approach is preserved here, without invoking the symbolic computation. For tridiagonal diagonally dominant matrices, a scaling transformation on the recurrences allows us to give another algorithm to avoid overflow and underflow. (C) 2012 Elsevier B.V. All rights reserved.

关键词： Computational complexity Difference equation Inverse matrix numerical algorithm Tridiagonal matrix

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An analytic approach for optimal coordination of overcurrent relays

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IET GENERATION TRANSMISSION & DISTRIBUTION 2013年第7期7卷 674-680页

作者： Mahari, Arash Seyedi, Heresh Univ Tabriz Fac Elect & Comp Engn Tabriz Iran

This study presents a new analytic approach to optimal coordination of directional overcurrent relays. This approach is based on the selection of optimum pickup current and time dial setting, in order to obtain minimum operating time for the relays, while satisfying various coordination and boundary constraints. Based on the new optimal relay setting procedure, an iterative numerical solution is proposed. The proposed numerical algorithm converges to the global optimum values, which are independent of initial values and the order of relay setting. The proposed method is applied to three different test systems. The new method is compared with some previously proposed analytic and evolutionary approaches. The results demonstrate the advantages of the proposed method over the previous works.

关键词： evolutionary computation iterative methods overcurrent protection relay protection directional overcurrent relay optimal coordination optimum pickup current selection boundary constraints iterative numerical algorithm numerical algorithm evolutionary approaches analytic approach overcurrent relay protection time dial setting selection

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Encoder based online motion planning and feedback control of redundant manipulators

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CONTROL ENGINEERING PRACTICE 2013年第10期21卷 1277-1289页

作者： Zhang, Yunong Li, Weibing Yu, Xiaotian Wu, Huarong Li, Jun Sun Yat Sen Univ Sch Informat Sci & Technol Guangzhou 510006 Guangdong Peoples R China Sun Yat Sen Univ Res Inst Shenzhen 518057 Peoples R China

This paper proposes and investigates an online motion planning and feedback control (OMPFC) scheme for redundant manipulators via techniques of quadratic programming and rotary encoder. The proposed OMPFC scheme is performed on a planar six degrees-of-freedom (DOF) manipulator. This robotic scheme incorporates the feedback of task-space position error. The joint state is obtained in real time via rotary encoders equipped on the physical manipulator. The original scheme is finally reformulated as a unified quadratic program (QP). The QP is solved online during the joint motion by employing an efficient numerical algorithm. Simulation and experimental results validate the physical realizability, online property, and efficacy of the proposed OMPFC scheme (including the employed numerical algorithm). (C) 2013 Elsevier Ltd. All rights reserved.

关键词： Online motion planning and control Rotary encoder feedback numerical algorithm Global linear convergence Redundancy resolution

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Interval optimal control problem in a Hilbert space

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COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS 2013年第4期53卷 389-395页

作者： Olegovna, Victoria O. Far East Fed Univ Vladivostok 690950 Russia Russian Acad Sci Far East Branch Inst Appl Math Vladivostok 690041 Russia

An optimal control problem for a system involving an interval parameter is considered. The concepts of a universal optimal state and a universal optimal control are introduced. The existence and uniqueness of a universal solution to the interval optimal control problem is proved, and an algorithm for its determination is presented. The interval optimal control problem for a system described by the boundary value problem for a second-order ordinary differential equation is solved as an example.

关键词： interval problems optimal control in Hilbert space Lagrange principle numerical algorithm existence and uniqueness theorem

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Solving an Inverse Problem for Maxwell's Equations numerically with Laguerre Functions

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numerical ANALYSIS AND APPLICATIONS 2013年第4期6卷 279-288页

作者： Mastryukov, A. F. Russian Acad Sci Siberian Branch Inst Computat Math & Math Geophys Pr Akad Lavrenteva 6 Novosibirsk 630090 Russia

An inverse problem is solved by an optimization method using Laguerre functions. numerical simulations are carried out for one-dimensional Maxwell's equations in the wave and diffusion approximations. The spatial distributions of permittivity and conductivity in a medium are determined from a known solution at a certain point. A Laguerre harmonics function is minimized. The minimization is performed by the conjugate gradient method. The results of determining permittivity and conductivity are presented. The influence of the shape and spectrum of a source of electromagnetic waves on the solution accuracy of the inverse problem is investigated. The solutions with broadband and harmonic sources of electromagnetic waves are compared in accuracy.

关键词： numerical algorithm Maxwell's equations electromagnetic wave conductivity inverse problem Laguerre method finite difference linear equations accuracy

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Computing matrix symmetrizers, finally possible via the Huang and Nong algorithm

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LINEAR & MULTILINEAR ALGEBRA 2013年第7期61卷 954-969页

作者： Uhlig, Frank Auburn Univ Dept Math & Stat Auburn AL 36849 USA

By a theorem of Frobenius (F.G. Frobenius, uber die mit einer Matrix vertauschbaren Matrizen, Sitzungsberichte der Koniglich Preu ss ischen Akademie der Wissenschaften zu Berlin (1910), pp. 3-15 (also in Gesammelte Abhandlungen, Band 3, Springer 1968. pp. 415-427)), every matrix A(n,n) over any field ? is the product of two symmetric ones. Using the algorithm of Huang and Nong (J. Huang and L. Nong, An iterative algorithm for solving finite-dimensional linear operator equations T(x)=f with applications, Linear Algebra Appl. 432 (2010), pp. 1176-1188) for linear systems, we develop an algorithm to compute a symmetric matrix S=S-T?(n,n) for which SA is symmetric for any given square matrix A?(n,n) where ?= or C. The algorithm is implemented and tested in MATLAB.

关键词： matrix factorization symmetrizer linear matrix system numerical algorithm MATLAB code

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Determining the Cutoff Based on a Continuous Variable to Define Two Populations with Application to Vaccines

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JOURNAL OF BIOPHARMACEUTICAL STATISTICS 2013年第3期23卷 662-680页

作者： Li, Shu Parnes, Milton Chan, Ivan S. F. Johnson & Johnson Pharmaceut Res & Dev Clin Biostat Wayne PA 19087 USA Temple Univ Dept Stat Philadelphia PA 19122 USA Merck Res Labs Late Dev Stat N Wales PA USA

In clinical research, it is sometimes desirable to dichotomize a continuous variable so that the information expressed using a dichotomous variable is more straightforward for clinicians to interpret and communicate with patients. The distribution of the continuous variable can differ between two populations defined by a disease case status. Under such a scenario, the dichotomization process can be based on distributions of the continuous variable in two distinct populations. The resulting dichotomous variable can be used as an endpoint in future studies. Even though dichotomization has not been extensively studied, dichotomization has been commonly carried out in clinical trials. We developed a methodology for determining the optimal cutoff point based on maximizing the correlation between the two populations and the dichotomous variable. In some real-world scenarios where outcome status in samples from two populations is not completely identified, we recommend using EM method to first estimate the parameters associated with the two populations before applying the proposed method to find the optimal cutoff point. In addition, we have investigated the performance of the proposed method for several common distributions (e.g., normal, log-normal and exponential distribution) of the continuous variable. Finally, we applied the proposed methods to a varicella vaccine example.

关键词： Continuous variable Cutoff point Dichotomization Dichotomous variable EM method Maximization of correlation numerical algorithm

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