boosting the margin a new explanation for the effectiveness of voting methods one of the surprising recurring phenomena observed in experiments with boosting is that the test error of the generated classifier usually does not increase as its size becomes very large and often is observed to decrease even after the training error reaches zero in this paper we show that this phenomenon is related to the distribution of margins of the training examples with respect to the generated voting classification rule where the margin of an example is simply the difference between the number of correct votes and the maximum number of votes received by any incorrect label we show that techniques used in the analysis of vapnik s support vector classifiers and of neural networks with small weights can be applied to voting methods to relate the margin distribution to the test error we also show theoretically and experimentally that boosting is especially effective at increasing the margins of the training examples finally we compare our explanation to those based on the bias variance decomposition

homogenization of two phase elasto plastic composite materials and structures study of tangent operators cyclic plasticity and numerical algorithms we develop homogenization schemes and numerical algorithms for two phase elasto plastic composite materials and structures a hill type incremental formulation enables the simulation of unloading and cyclic loadings it also allows to handle any rate independent model for each phase we study the crucial issue of tangent operators elasto plastic or continuum versus algorithmic or consistent and anisotropic versus isotropic we apply two methods of extraction of isotropic tangent moduli we compare mathematically the stiffnesses of various tangent operators all rate equations are discretized in time using implicit integration we implemented two homogenization schemes mori tanaka and a double inclusion model and two plasticity models classical j 2 plasticity and chaboche s model with non linear kinematic and isotropic hardenings we consider composites with different properties and present several discriminating numerical simulations in many cases the results are validated against finite element fe or experimental data we integrated our homogenization code into the fe program abaqus using a user material interface umat a two scale procedure allows to compute realistic structures made of non linear composite materials within reasonable cpu time and memory usage examples are shown c 2002 elsevier science ltd all rights reserved

canonical fuzzy numbers of dimension two abstract recently several authors have dealt with interactive fuzzy numbers this paper proposes a new approach to interactions between fuzzy numbers by using canonical fuzzy numbers of dimension two

a review of some methods for ranking fuzzy subsets this paper deals with the problem of ranking n fuzzy subsets of the unit interval a number of methods suggested in the literature is reviewed and tested on a group of selected examples where the fuzzy sets can be nonnormal and or nonconvex the ranking is obtained from i the index of strict preference defined by watson ii three indexes proposed by yager iii the algorithm used by chang iv three versions of the a preference index suggested by adamo v the index defined by baas and kwakernaak vi three modified versions used by baldwin and guild vii the method proposed by kerre viii three forms of the index suggested by jain ix the four grades of dominance studied by dubois and prade in simple cases the results are good for all the methods with some exceptions in questionable cases where the decision must be probably modelled in accordance with the context in which it is imbedded the best indexes seem to be the dominances suggested by dubois and prade these indexes do not force any particular choice but clearly describe the situation hence allowing the decision maker himself to make his best choice

robust principal component analysis with adaptive selection for tuning parameters the present paper discusses robustness against outliers in a principal component analysis pca we propose a class of procedures for pca based on the minimum psi principle which unifies various approaches including the classical procedure and recently proposed procedures the reweighted matrix algorithm for off line data and the gradient algorithm for on line data are both investigated with respect to robustness the reweighted matrix algorithm is shown to satisfy a desirable property with local convergence and the on line gradient algorithm is shown to satisfy an asymptotical stability of convergence some procedures in the class involve tuning parameters which control sensitivity to outliers we propose a shape adaptive selection rule for tuning parameters using k fold cross validation

effective properties of composite materials with periodic microstructure a computational approach abstract this study reviews several problems which are specific of composites with periodic microstructure composed of linear or nonlinear constituents the theoretical background of the method is recalled first two different families of numerical methods are considered to solve the problem the first is based on the finite element method the concept of macroscopic degrees of freedom is presented the implementation of periodicity conditions is discussed a general framework permitting either a strain or stress control is proposed the second numerical method is based on fast fourier transforms it considers first the problem of a homogeneous linear reference material undergoing a nonhomogeneous periodic eigenstrain the solution of this problem is based on the explicit form of the periodic green s function of the reference medium the relative merits of the two methods are compared and several examples are discussed both methods give very comparable results on test examples and their domains of applications appear to be complementary

two scale analysis of heterogeneous elastic plastic materials with asymptotic homogenization and voronoi cell finite element model in this paper a multiple scale finite element model vcfem homo has been developed for elastic plastic analysis of heterogeneous porous and composite materials by combining asymptotic homogenization theory with the voronoi cell finite element model vcfem vcfem for microstructural modeling originates from dirichlet tessellation of representative material elements at sampling points in the structure structural modeling is done by the general purpose finite element code abaqus and interfacing with the microscale vcfem analysis is done through the user subroutine in abaqus for material constitutive relation umat asymptotic homogenization in umat generates macroscopic material parameters for abaqus following the macroscopic analysis a local vcfem analysis is invoked to depict the true evolution of microstructural state variables various numerical examples are executed for validating the effectiveness of vcfem homo and the effect of size shape and distribution of heterogeneities on local and global response is examined

finite elements for materials with strain gradient effects a finite element implementation is reported of the fleck hutchinson phenomenological strain gradient theory this theory fits within the toupin mindlin framework and deals with first order strain gradients and the associated work conjugate higher order stresses in conventional displacement based approaches the interpolation of displacement requires c1 continuity in order to ensure convergence of the finite element procedure for higher order theories mixed type finite elements are developed herein for the fleck hutchinson theory these elements use standard c0 continuous shape functions and can achieve the same convergence as c1 elements these c0 elements use displacements and displacement gradients as nodal degrees of freedom kinematic constraints between displacement gradients are enforced via the lagrange multiplier method the elements developed all pass a patch test the resulting finite element scheme is used to solve some representative linear elastic boundary value problems and the comparative accuracy of various types of element is evaluated copyright 1999 john wiley sons ltd

a continuum model for nonlinear lattices under large deformations abstract a continuum model is developed for hexagonal lattices composed of a set of masses connected by linear axial and angular springs with nonlinearity arising solely from geometric effects for a set of lattice parameters these lattices exhibit complex deformation patterns under uniform loading conditions due to instabilities a continuum model accounting for these instabilities is developed from explicit expressions of the potential energy functional of a unit cell this functional is non convex it captures the bistable nature of the lattice and is used to derive its effective constitutive behavior finite element simulations of continuum medium illustrate the formation of microstructural patterns with discontinuous displacement gradients similar to the features observed in nonlinear elasticity and finite deformation plasticity a comparison of discrete lattice simulations and finite element analysis under general loading conditions illustrates that the continuum model captures the effective behavior due to instabilities within the lattice

asymptotic analysis of heterogeneous cosserat media abstract the present work deals with the development of homogenization procedures for periodic heterogeneous linear elastic cosserat media it is resorted to asymptotic methods classically used in periodic homogenization it is shown that the nature of the homogeneous equivalent medium depends on the hierarchy of three characteristic lengths the size l of the heterogeneities the cosserat intrinsic lengths l c of the constituents and the typical size l of the considered structure when l and l c are comparable and much smaller than l the effective medium is proved to be a cauchy continuum with volume couples whereas the case l c l leads to a cosserat effective medium finite element simulations are provided in the case of a fiber matrix composite for a large range of characteristic lengths l c and for two different volume fractions reference calculations involving every heterogeneity are compared to the response obtained using a homogeneous equivalent medium the results confirm the predicted hierarchy of models and also show that a cosserat effective medium still provide a good estimation when all characteristic lengths have the same order of magnitude

on a multiscale computational strategy with time and space homogenization for structural mechanics a new multiscale computational strategy was recently proposed for the analysis of structures described both on a fine space scale and a fine time scale this strategy which involves homogenization in space as well as in time could replace in several domains of application the standard homogenization techniques which are generally limited to the space domain it is an iterative strategy which calls for the resolution of problems on both a micro fine scale and a macro homogenized scale in this paper we review the bases of this approach and present improved approximation techniques to solve the micro and macro problems

gradient enhanced damage for quasi brittle materials summary conventional continuum damage descriptions of material degeneration suffer from loss of well posedness beyond a certain level of accumulated damage as a consequence numerical solutions are obtained which are unacceptable from a physical point of view the introduction of higher order deformation gradients in the constitutive model is demonstrated to be an adequate remedy to this deficiency of standard damage models a consistent numerical solution procedure of the governing partial differential equations is presented which is shown to be capable of properly simulating localization phenomena

stable splitting scheme for general form of associated plasticity including different scales of space and time an efficient implementation of the operator split procedure for boundary value solution with plastic flow computation is presented for a general form of associated plasticity model we start with the general form of phenomenological model of plasticity where the yield criterion is not restricted to a simple quadratic form and the elasticity tensor does not have constant entries we then turn to the multi scale model of plasticity which employs the fine scale representation of the plastic deformation along with the homogenization procedure for stress computation we also visit the plasticity model with rate sensitive plastic response where plastic flow computation is carried out at fine scale in time we proved herein the sufficient and necessary conditions for the proposed operator split procedure to converge for any such general form of associated plasticity moreover we presented a systematic manner for constructing the main ingredients for the plastic flow computation and the global newton s iteration such as the consistent elastoplastic tangent

multiscale computational homogenization methods with a gradient enhanced scheme based on the discontinuous galerkin formulation abstract when considering problems of dimensions close to the characteristic length of the material the size effects can not be neglected and the classical so called first order multiscale computational homogenization scheme fmch looses accuracy motivating the use of a second order multiscale computational homogenization smch scheme this second order scheme uses the classical continuum at the micro scale while considering a second order continuum at the macro scale although the theoretical background of the second order continuum is increasing the implementation into a finite element code is not straightforward because of the lack of high order continuity of the shape functions in this work we propose a smch scheme relying on the discontinuous galerkin dg method at the macro scale which simplifies the implementation of the method indeed the dg method is a generalization of weak formulations allowing for inter element discontinuities either at the c 0 level or at the c 1 level and it can thus be used to constrain weakly the c 1 continuity at the macro scale the c 0 continuity can be either weakly constrained by using the dg method or strongly constrained by using usual c 0 displacement based finite elements therefore two formulations can be used at the macro scale i the full discontinuous galerkin formulation fdg with weak c 0 and c 1 continuity enforcements and ii the enriched discontinuous galerkin formulation edg with high order term enrichment into the conventional c 0 finite element framework the micro problem is formulated in terms of standard equilibrium and periodic boundary conditions a parallel implementation in three dimensions for non linear finite deformation problems is developed showing that the proposed method can be integrated into conventional finite element codes in a straightforward and efficient way

an enhanced multi scale approach for masonry wall computations with localization of damage this contribution presents a multi scale framework for the computational study of masonry structures in order to overcome the need for excessively complex closed form constitutive equations a first order computational homogenization framework is applied to infer the non linear material behaviour of brick masonry in the presence of quasi brittle damage a localization analysis is carried out based on the macroscopic homogenized tangent stiffness it is shown that localization is detected along preferential orientations which are consistent with the underlying mesostructural failure patterns and with the applied loading the macroscopic description is enhanced with a finite width damage band model in order to allow the treatment of macroscopic localization resulting from damage growth in the constituents as a result of the use of homogenization techniques on finite volumes and the presence of quasi brittle constituents mesostructural snap back may occur in the homogenized material response a methodology to introduce this type of response in the multi scale technique is proposed the numerical implementation of the multi scale solution scheme using a finite element method is outlined the results obtained by the framework are illustrated by means of elementary examples and by an example of a structural wall computation

numerical multiscale solution strategy for fracturing heterogeneous materials abstract this paper presents a numerical multiscale modelling strategy for simulating fracturing in materials where the fine scale heterogeneities are fully resolved with a particular focus on concrete the fine scale is modelled using a hybrid trefftz stress formulation for modelling propagating cohesive cracks the very large system of algebraic equations that emerges from detailed resolution of the fine scale structure requires an efficient iterative solver with a preconditioner that is appropriate for fracturing heterogeneous materials this paper proposes a two grid strategy for construction of the preconditioner that utilizes scale transition techniques derived for computational homogenization and represents an adaptation of the work of miehe and bayreuther 2 and its extension to fracturing heterogeneous materials for the coarse scale this paper investigates both classical c 0 continuous displacement based finite elements as well as c 1 continuous elements the preconditioned gmres krylov iterative solver with dynamic convergence tolerance is integrated with a constrained newton method with local arc length control and line searches the convergence properties and performance of the parallel implementation of the proposed solution strategy is illustrated on two numerical examples

a multi level computational model for multi scale damage analysis in composite and porous materials abstract an adaptive multi level methodology is developed in this paper to create a hierarchy of computational sub domains with varying resolution for multiple scale problems it is intended to concurrently predict evolution of variables at the structural and microstructural scales as well as to track the incidence and propagation of microstructural damage in composite and porous materials the microstructural analysis is conducted with the voronoi cell finite element model vcfem while a conventional displacement based fem code executes the macroscopic analysis the model introduces three levels in the computational domain which include macro macro micro and microscopic analysis it differentiates between non critical and critical regions and ranges from macroscopic computations using continuum constitutive relations to zooming in at hotspots for pure microscopic simulations coupling between the scales in regions of periodic microstructure is accomplished through asymptotic homogenization an adaptive process significantly increases the efficiency while retaining appropriate level of accuracy for each region numerical examples are conducted for composite and porous materials with a variety of microscopic architectures to demonstrate the potential of the model

gradient elasticity in statics and dynamics an overview of formulations length scale identification procedures finite element implementations and new results in this paper we discuss various formats of gradient elasticity and their performance in static and dynamic applications gradient elasticity theories provide extensions of the classical equations of elasticity with additional higher order spatial derivatives of strains stresses and or accelerations we focus on the versatile class of gradient elasticity theories whereby the higher order terms are the laplacian of the corresponding lower order terms one of the challenges of formulating gradient elasticity theories is to keep the number of additional constitutive parameters to a minimum we start with discussing the general mindlin theory that in its most general form has 903 constitutive elastic parameters but which were reduced by mindlin to three independent material length scales further simplifications are often possible in particular the aifantis theory has only one additional parameter in statics and opens up a whole new field of analytical and numerical solution procedures we also address how this can be extended to dynamics an overview of length scale identification and quantification procedures is given finite element implementations of the most commonly used versions of gradient elasticity are discussed together with the variationally consistent boundary conditions details are provided for particular formats of gradient elasticity that can be implemented with simple linear finite element shape functions new numerical results show the removal of singularities in statics and dynamics as well as the size dependent mechanical response predicted by gradient elasticity

identification of elastoplastic microscopic material parameters within a homogenization scheme summary a two scale parameter identification approach is investigated the microscopic material parameters of a two scale model are identified by comparing macroscopic simulation data with macroscopic full field measurements of the micro structured specimen gradient based solution strategies are employed for the optimization problem of the two scale parameter identification in particular two approaches for the gradient calculation are investigated the finite difference method is compared with a newly introduced semi analytical scheme the focus lies on the identification of microscopic elastoplastic material parameters the presented identification example with artificial data confirms a reduced computational effort and advantageous convergence for the semi analytical approach within the two scale parameter identification a drawback is the increase in memory requirement copyright 2015 john wiley sons ltd

a support vector machine formulation to pca analysis and its kernel version in this paper we present a simple and straightforward primal dual support vector machine formulation to the problem of principal component analysis pca in dual variables by considering a mapping to a high dimensional feature space and application of the kernel trick mercer theorem kernel pca is obtained as introduced by scholkopf et al 2002 while least squares support vector machine classifiers have a natural link with the kernel fisher discriminant analysis minimizing the within class scatter around targets 1 and 1 for pca analysis one can take the interpretation of a one class modeling problem with zero target value around which one maximizes the variance the score variables are interpreted as error variables within the problem formulation in this way primal dual constrained optimization problem interpretations to the linear and kernel pca analysis are obtained in a similar style as for least square support vector machine classifiers

two scale kinematics and linearization for simultaneous two scale analysis of periodic heterogeneous solids at finite strain abstract we introduce the notion of two scale kinematics and the procedure of two scale linearization which are indispensable to the simultaneous two scale analysis method for the mechanical behavior of periodic heterogeneous solids at finite strain these are accomplished by formulating the two scale boundary value problem in both material and spatial descriptions with reference to the two scale modeling strategy developed in comput methods appl mech engrg 190 40 41 2001 5427 that utilized the convergence results of mathematical homogenization the formulation brings the intimate relationship between micro and macro scale kinematics in describing the micro macro coupling behavior inherent in heterogeneous media it is also shown that the two scale linearization necessitates the strict consistency with the micro scale equilibrated state and naturally invites the tangential homogenization process for both material and spatial descriptions several numerical examples of simultaneous two scale computations are presented to illustrate the two scale nature of the deformation of a heterogeneous solid at finite strain

homogenization based multiscale crack modelling from micro diffusive damage to macro cracks the existence of a representative volume element rve for a class of quasi brittle materials having a random heterogeneous microstructure in tensile shear and mixed mode loading is demonstrated by deriving traction separation relations which are objective with respect to rve size a computational homogenization based multiscale crack modelling framework implemented in an fe2 setting for quasi brittle solids with complex random microstructure is presented the objectivity of the macroscopic response to the micro sample size is shown by numerical simulations therefore a homogenization scheme which is objective with respect to macroscopic discretization and microscopic sample size is devised numerical examples including a comparison with direct numerical simulation are given to demonstrate the performance of the proposed method

a new maximum margin algorithm for one class problems and its boosting implementation in this paper each one class problem is regarded as trying to estimate a function that is positive on a desired slab and negative on the complement the main advantage of this viewpoint is that the loss function and the expected risk can be defined to ensure that the slab can contain as many samples as possible inspired by the nature of svms the intuitive margin is also defined as a result a new linear optimization problem to maximize the margin and some theoretically motivated learning algorithms are obtained moreover the proposed algorithms can be implemented by boosting techniques to solve nonlinear one class classifications

nonlinear component analysis as a kernel eigenvalue problem a new method for performing a nonlinear form of principal component analysis is proposed by the use of integral operator kernel functions one can efficiently compute principal components in high dimensional feature spaces related to input space by some nonlinear map for instance the space of all possible five pixel products in 16 16 images we give the derivation of the method and present experimental results on polynomial feature extraction for pattern recognition

a class of general algorithms for multi scale analyses of heterogeneous media abstract a class of computational algorithms for multi scale analyses is developed in this paper the two scale modeling scheme for the analysis of heterogeneous media with fine periodic microstructures is generalized by using relevant variational statements instead of the method of two scale asymptotic expansion the mathematical results on the generalized convergence are utilized in the two scale variational descriptions accordingly the global local type computational schemes can be unified in association with the homogenization procedure for general nonlinear problems after formulating the problem in linear elastostatics that with local contact condition and the elastoplastic problem we present representative numerical examples along with the computational algorithm consistent with our two scale modeling strategy as well as some direct approaches

principal component analysis based on robust estimators of the covariance or correlation matrix influence functions and efficiencies a robust principal component analysis can be easily performed by computing the eigenvalues and eigenvectors of a robust estimator of the covariance or correlation matrix in this paper we derive the influence functions and the corresponding asymptotic variances for these robust estimators of eigenvalues and eigenvectors the behaviour of several of these estimators is investigated by a simulation study it turns out that the theoretical results and simulations favour the use of s estimators since they combine a high efficiency with appealing robustness properties 2000 biometrika trust

a class of fuzzy random optimization expected value models fuzzy random variable is a measurable mapping from a probability space to a collection of fuzzy variables this concept may be regard as an extension of both random variable and fuzzy variable in this paper the linearity of a scalar value expected value operator of fuzzy random variable is discussed and a fuzzy random simulation approach is suggested to evaluate the expected value of a fuzzy random variable in addition three types of fuzzy random expected value models are presented to model fuzzy random decision systems moreover a hybrid intelligent algorithm which incorporates simulation neural network and genetic algorithm is designed in order to solve general fuzzy random expected value models at the end of this paper the effectiveness of this algorithm is showed via three numerical examples

novel formulations of microscopic boundary value problems in continuous multiscale finite element methods abstract this article explores the use of a homogenization method inspired by the classical irving kirkwood procedure in the continuous multiscale modeling of elastic solids within the context of the finite element method this homogenization method gives rise to a broad range of allowable boundary conditions for the rve which in turn yield a rich spectrum of estimates of the macroscopic stress response for two representative problems involving heterogeneous elastic bodies

a general model for fuzzy linear programming abstract in the current literature there are several models of fuzzy linear programming problems the aim of this paper is first to describe the more important problems in fuzzy linear programming and second to give a general model of fuzzy linear programming problems involving all of the above ones finally a resolution method for that general model is proposed

computational homogenization of cellular materials abstract in this work we propose to study the behavior of cellular materials using a second order multi scale computational homogenization approach during the macroscopic loading micro buckling of thin components such as cell walls or cell struts can occur even if the behavior of the materials of which the micro structure is made remains elliptic the homogenized behavior can lose its ellipticity in that case a localization band is formed and propagates at the macro scale when the localization occurs the assumption of local action in the standard approach for which the stress state on a material point depends only on the strain state at that point is no longer suitable which motivates the use of the second order multi scale computational homogenization scheme at the macro scale of this scheme the discontinuous galerkin method is chosen to solve the mindlin strain gradient continuum at the microscopic scale the classical finite element resolutions of representative volume elements are considered since the meshes generated from cellular materials exhibit voids on the boundaries and are not conforming in general the periodic boundary conditions are reformulated and are enforced by a polynomial interpolation method with the presence of instability phenomena at both scales the arc length path following technique is adopted to solve both macroscopic and microscopic problems

inequality relation between fuzzy numbers and its use in fuzzy optimization the inequality relation between two fuzzy numbers is investigated a certain type of such a relation motivated by practical interpretation is proposed and its correspondence with the usual lattice type relation generated by the extended maximum and minimum operators and its possible interpretation are discussed the concept of r l fuzzy number is introduced the class of all r l fuzzy numbers covering practically the whole set of normal convex fuzzy numbers comparing two r l fuzzy numbers of the same type the relation introduced in the paper may be replaced by four ordinary inequalities this fact may be taken advantage of in optimization problems with linear fuzzy constraints

computational homogenization of mesoscale gradient viscoplasticity variationally consistent selective homogenization is applied to a class of gradient enhanced dissipative materials which is adopted for the mesoscale modeling the adopted standard first order homogenization assumption results in the classical equilibrium equation for a local continuum on the macroscale while the internal variables live on the mesoscale only among the issues considered in the paper we note i the variationally consistent setting of homogenization of gradient theory on the mesoscale ii the variational basis of the sve problem sve statistical volume element in the time incremental setting the sve problem is formulated for the classical boundary conditions dirichlet and neumann pertinent to the standard momentum balance as well as the micro momentum balance the weak format of the sve problem constitutes the stationarity condition of an incremental sve potential which represents an extension of the situation for a single phase continuum model the macroscale stress in a given time increment is derivable from an incremental macroscale pseudo elastic strain energy moreover the saddle point properties of the sve potential are shown to form the basis for establishing upper and lower bounds on the pseudo elastic strain energy bingham viscoplasticity with gradient enhanced hardening is chosen as the prototype model problem for the numerical evaluation the computed stress strain response relations confirm the theoretical predictions of the influence of different combinations of boundary conditions on the sve

continuum damage model for orthotropic materials application to masonry this paper contributes to the formulation of continuum damage models for orthotropic materials under plane stress conditions two stress transformation tensors related to tensile and compressive stress states respectively are used to establish a one to one mapping relationship between the orthotropic behaviour and an auxiliary model this allows the consideration of two individual damage criteria according to different failure mechanisms i e cracking and crushing the constitutive model adopted in the mapped space makes use of two scalar variables which monitor the local damage under tension and compression respectively the model affords the simulation of orthotropic induced damage while also accounting for unilateral effects thanks to a stress tensor split into tensile and compressive contributions the fundamentals of the method are presented together with the procedure utilized to adjust the model in order to study the mechanical behaviour of masonry material the validation of the model is carried out by means of comparisons with experimental results on different types of orthotropic masonry at the material level

bounds and estimates for the overall plastic behaviour of composites with strain gradient effects the macroscopic plastic response is estimated for a composite with each phase satisfying a strain gradient constitutive description in a j 2 deformation theory of strain gradient plasticity the strain energy function is assumed to depend on both the von mises strain invariant epsilon e and on a curvature invariant chi e for a general coupling between epsilon e and chi e a nonlinear variational principle is formulated generalizing that of ponte castaneda 1992 j mech phys solids 40 1757 the minimum principle is used to derive bounds and estimates for the overall plastic response of statistically homogeneous and isotropic strain gradient composites an essential ingredient of the strategy is the use of previous results of the authors 1994 j mech phys solids 42 1851 for a linear comparison composite for a particular coupling between epsilon e and chi e suggested earlier by fleck hutchinson 1993 the hashin shtrikman upper bounds and lower estimates are calculated for a power law hardening solid including the rigid perfectly plastic limit the results demonstrate a size effect

a micromechanics based approach for the derivation of constitutive elastic coefficients of strain gradient media a micromechanics based approach for the derivation of the effective properties of periodic linear elastic composites which exhibit strain gradient effects at the macroscopic level is presented at the local scale all phases of the composite obey the classic equations of three dimensional elasticity but since the assumption of strict separation of scales is not verified the macroscopic behavior is described by the equations of strain gradient elasticity the methodology uses the series expansions at the local scale for which higher order terms which are generally neglected in standard homogenization framework are kept in order to take into account the microstructural effects an energy based micro macro transition is then proposed for upscaling and constitutes in fact a generalization of the hill mandel lemma to the case of higher order homogenization problems the constitutive relations and the definitions for higher order elasticity tensors are retrieved by means of the state law associated to the derived macroscopic potential as an illustration purpose we derive the closed form expressions for the components of the gradient elasticity tensors in the particular case of a stratified periodic composite for handling the problems with an arbitrary microstructure a fft based computational iterative scheme is proposed in the last part of the paper its efficiency is shown in the particular case of composites reinforced by long fibers

fuzzy mathematical programming based on some new inequality relations abstract this paper deals with inequality relations in fuzzy mathematical programming problem fmp not necessarily linear moreover fuzzy parameters may have nonlinear membership functions a new approach for comparing fuzzy sets is proposed which is more general than the well known proposals in the literature

new support vector algorithms we propose a new class of support vector algorithms for regression and classification in these algorithms a parameter lets one effectively control the number of support vectors while this can be useful in its own right the parameterization has the additional benefit of enabling us to eliminate one of the other free parameters of the algorithm the accuracy parameter epsilon in the regression case and the regularization constant c in the classification case we describe the algorithms give some theoretical results concerning the meaning and the choice of and report experimental results

possibilistic linear programming a brief review of fuzzy mathematical programming and a comparison with stochastic programming in portfolio selection problem in this paper we review some fuzzy linear programming methods and techniques from a practical point of view in the rst part the general history and the approach of fuzzy mathematical programming are introduced using a numerical example some models of fuzzy linear programming are described in the second part of the paper fuzzy mathematical programming approaches are compared to stochastic programming ones the advantages and disadvantages of fuzzy mathematical programming approaches are exemplied in the setting of an optimal portfolio selection problem finally some newly developed ideas and techniques in fuzzy mathematical programming are briey reviewed c 2000 elsevier science b v all rights reserved

an adaptive sub incremental strategy for the solution of homogenization based multi scale problems abstract in this contribution several schemes for the solution of homogenization based multi scale constitutive problems undergoing finite strains with inelastic material behavior are investigated these schemes are aimed at improving the robustness and efficiency of the newton raphson method in the multilevel finite element ml fem framework an adaptive sub incremental strategy is proposed for the discrete representative volume element rve boundary value problem the procedure is able to ensure the convergence of the solution algorithm in the presence of several sources of non linearity and obtains improved initial guesses for the newton raphson scheme in the ml fem framework the enlargement of the convergence bowl of the newton raphson procedure at the micro scale allows larger macroscopic deformation gradients to be prescribed and significantly reduces the overall computational cost of ml fem analyses the proposed strategy preserves the quadratic rates of asymptotic convergence that characterize the newton raphson scheme at the macroscopic level numerical examples of both micro scale and two scale finite element simulations are presented to demonstrate the improved robustness and efficiency of the solution procedures proposed

measuring the satisfaction of constraints in fuzzy linear programming the paper proposes a new kind of method for solving fuzzy linear programming problems based on the satisfaction or fulfillment degree of the constraints using a new ranking method of fuzzy numbers the fulfillment of the constraints can be measured then the properties of the ranking index are discussed with this ranking index the decision maker can make the constraints tight or loose based on his optimistic or pessimistic attitude and get the optimal solution from the fuzzy constraint space the corresponding value of objective distribution function can be obtained a numerical example illustrates the merits of the approach

a new generalized finite element method for two scale simulations of propagating cohesive fractures in 3 d summary this paper presents a novel numerical framework based on the generalized finite element method with global local enrichments gfemgl for two scale simulations of propagating fractures in three dimensions a non linear cohesive law is adopted to capture objectively the dissipated energy during the process of material degradation without the need of adaptive remeshing at the macro scale or artificial regularization parameters the cohesive crack is capable of propagating through the interior of finite elements in virtue of the partition of unity concept provided by the generalized extended finite element method and thus eliminating the need of interfacial surface elements to represent the geometry of discontinuities and the requirement of finite element meshes fitting the cohesive crack surface the proposed method employs fine scale solutions of non linear local boundary value problems extracted from the original global problem in order to not only construct scale bridging enrichment functions but also to identify damaged states in the global problem thus enabling accurate global solutions on coarse meshes this is in contrast with the available gfemgl in which the local solution field contributes only to the kinematic description of global solutions the robustness efficiency and accuracy of this approach are demonstrated by results obtained from representative numerical examples copyright 2015 john wiley sons ltd

application of fuzzy minimum cost flow problems to network design under uncertainty this paper deals with fuzzy quantities and relations in multi objective minimum cost flow problem when t norms and t conorms are available the goal programming is applied to minimize the deviation among the multiple costs of fuzzy flows and the given targets when the fuzzy supplies and demands are satisfied to obtain the most optimistic and the most pessimistic satisficing solutions of this problem two polynomial time algorithms are introduced applying some network transformations to demonstrate the performance of this approach in actual substances network design under fuzziness is considered and an efficient scheme is proposed including genetic algorithm together with fuzzy minimum cost flow problem this scheme is applied on a pilot network for more description

large scale optimization of eigenvalues optimization problems involving eigenvalues arise in many applications let x be a vector of real parameters and let a x be a continuously differentiable symmetric matrix function of x we consi

efficient methods for implicit geometrical representation of complex material microstructures summary we present two methods for initializing distance functions on adaptively refined finite element meshes to represent complex material microstructures from segmented x ray tomographic data implicit microstructure representation combined with the extended fem allows modelers to represent complex material microstructures with consistent mesh quality and accuracy in the first method a level set evolution equation is formulated and solved by the galerkin method on an adaptively refined mesh we show that the convergence and stability of this method is optimal for the order of elements used in the second approach we initialize the distance field by the fast marching method on a uniform grid and then project the solution onto the finite element mesh by least squares we show that this latter approach is superior in speed and accuracy as an example problem both methods are demonstrated in the initialization of distance fields for two inclusion phases within a al 7075 alloy copyright 2014 john wiley sons ltd

multiple scale analysis of heterogeneous elastic structures using homogenization theory and voronoi cell finite element method abstract this paper deals with the development of a multiple scale finite element method by combining the asymptotic homogenization theory with voronoi cell vcfem for microstructural modeling the voronoi cell finite element model originates from dirichlet tessellation of a representative material element or a base cell in the microstructure homogenized material coefficients for a global displacement finite element model are generated by vcfem analysis using periodic boundary conditions on the base cell following the macroscopic analysis the local vcfem analysis is implemented to depict the true evolution of microstructural stresses and strains various numerical examples are executed for validating the effectiveness of vcfem macro micro modeling of elastic materials the effect of size shape orientation and distribution of heterogeneities on the local and global response are examined

an energetically consistent concurrent multiscale method for heterogeneous heat transfer and phase transition applications abstract a concurrent multiscale method is developed to model time dependent heat transfer and phase transitions in heterogeneous media and is formulated in a way such that the energy being exchanged between scales is conserved ensuring this energetic consistency among scales enables the implementation of high fidelity physics based models at critical locations within the coarse scale to temporally and spatially resolve highly complex and localized phenomena to achieve this only neumann boundary conditions are applied over the fine scale domain ensuring a conservative formulation the coarse scale solution is used to reconstruct these neumann boundary conditions on the fine scale which are then used to evolve a separate system of governing equations the results on the fine scale are then sent back to the coarse scale through an energy based homogenization scheme transient simulations for the heat equation are implemented with the proposed method to demonstrate its accuracy in energy conservation and effectiveness including the coupling of a phase field model at the fine scale to a coarse scale heat equation

learning linear pca with convex semi definite programming the aim of this paper is to learn a linear principal component using the nature of support vector machines svms to this end a complete svm like framework of linear pca svpca for deciding the projection direction is constructed where new expected risk and margin are introduced within this framework a new semi definite programming problem for maximizing the margin is formulated and a new definition of support vectors is established as a weighted case of regular pca our svpca coincides with the regular pca if all the samples play the same part in data compression theoretical explanation indicates that svpca is based on a margin based generalization bound and thus good prediction ability is ensured furthermore the robust form of svpca with a interpretable parameter is achieved using the soft idea in svms the great advantage lies in the fact that svpca is a learning algorithm without local minima because of the convexity of the semi definite optimization problems to validate the performance of svpca several experiments are conducted and numerical results have demonstrated that their generalization ability is better than that of regular pca finally some existing problems are also discussed

mesoscopic modelling of masonry using weak and strong discontinuities a mesoscopic masonry model is presented in which joints are modelled by weak and strong discontinuities through the partition of unity property of finite element shape functions a drucker prager damage model describes joint degradation whereas the bricks remain linear elastic throughout the simulations analogies and differences amongst strong and weak discontinuity models are discussed with special emphasis on kinematic description and implementation mesh sensitivity and performance of the presented models are illustrated by two brick three point bending and shear wall tests

computational homogenization based on a weak format of micro periodicity for rve problems computational homogenization with a priori assumed scale separation is considered whereby the macroscale stress is obtained via averaging on representative volume elements rve s a novel variational formulation of the rve problem based on the assumption of weak micro periodicity of the displacement fluctuation field is proposed notably independent fe discretization of boundary tractions lagrange multipliers allows for a parameterized transition between the conventional strong periodicity and neumann boundary conditions in this paper the standard situation of macroscale strain control is considered numerical results demonstrate the convergence properties with respect to 1 the approximation of displacement and tractions and 2 the rve size for random realizations of the microstructure

a multicriteria fuzzy linear programming method for water supply system development planning abstract a method is presented for solving a multicriteria linear program where the coefficients of the objective functions and the constraints are fuzzy numbers of the l r type assuming the aspiration levels for particular criteria to be fuzzy and basing on comparison of fuzzy numbers the original problem is transformed into a multicriteria linear fractional program the latter is solved using an interactive technique involving a linear programming procedure in the calculation phase this method has been elaborated with a view to the application to the development of a water supply system

linear programming problems and ranking of fuzzy numbers abstract in this paper linear programming problems with fuzzy constraints and fuzzy coefficients in both matrix and right hand side of the constraint set are considered because of fuzzy coefficients in both members of each constraint ranking methods for fuzzy numbers must be considered the diversity of such methods provides a lot of different models of conventional linear programming problems from which fuzzy solutions to the former problem can be obtained

nearest piecewise linear approximation of fuzzy numbers abstract the problem of the nearest approximation of fuzzy numbers by piecewise linear 1 knot fuzzy numbers is discussed by using 1 knot fuzzy numbers one may obtain approximations which are simple enough and flexible to reconstruct the input fuzzy concepts under study they might be also perceived as a generalization of the trapezoidal approximations moreover these approximations possess some desirable properties apart from theoretical considerations approximation algorithms that can be applied in practice are also given

a formulation for the micromorphic continuum at finite inelastic strains the paper presents a generalized theory of deformation which can capture scale effects also in a homogenously deforming body scale effects are relevant when the dimensions of the specimen or structure themselves are in the micron and submicron scale but also when it comes to high strain concentrations as in the case of localised shear bands or at crack tips etc in this context so called generalized continuum formulations have been proven to provide remedy as they allow for the incorporation of internal length scale parameters which reflect the micro structural influence on the macroscopic material response here we want to adopt a generalized continuum framework which is based on the mathematical description of a combined macro and micro space sansour 1998b the approach introduces additional degrees of freedom which constitute a so called micromorphic deformation first the treatment presented is general in nature but will be specified for the sake of an example and the number of extra degrees of freedom will be reduced to four based on the generalized deformation description new strain and stress measures are defined which lead to the formulation of a corresponding generalized variational principle the theory is completed by dirichlet boundary conditions for the displacement field of great advantage is the fact that the constitutive law is defined in the generalized space but can be classical otherwise this limits the number of the extra material parameters necessary to those needed for the specification of the micro space in the example presented to only one an example of scale effects in a homogenously deforming specimen and a further example of shearband formation are presented where the constitutive law is a classical viscoplastic one

a single and a multi valued order on fuzzy numbers and its use in linear programming with fuzzy coefficients abstract this paper deals with inequality relations in fuzzy linear programming problem flp the coefficients are trapezoidal fuzzy numbers or even more simple left or right trapezoidal numbers two new approaches for comparing left and right hand sides of constraints in flp problems are investigated an example demonstrating the two approaches is supplied

a micromechanically based couple stress model of an elastic two phase composite abstract the study reported in this paper concerns the determination of couple stress moduli and characteristic lengths of heterogeneous materials the study is set in the context of a planar two dimensional two phase composite with linear non couple stress classical elastic constituents with a single microstructural length scale inclusion spacing in an equilateral triangular array we use an approach which allows a replacement of this composite by an approximating couple stress continuum we determine the effective material parameters from the response of a unit cell under either displacement displacement periodic or traction boundary conditions we carry out computations of all the moduli by varying the stiffness ratio of both phases so as to cover a range of very different materials from porous solids through composites with rigid inclusions it is found that the three boundary conditions result in hierarchies of couple stress moduli in addition we observe from our numerical computations that these three boundary conditions also result in a hierarchy of characteristic lengths

multi scale constitutive modelling of heterogeneous materials with a gradient enhanced computational homogenization scheme a gradient enhanced computational homogenization procedure that allows for the modelling of microstructural size effects is proposed within a general non linear framework in this approach the macroscopic deformation gradient tensor and its gradient are imposed on a microstructural representative volume element rve this enables us to incorporate the microstructural size and to account for non uniform macroscopic deformation fields within the microstructural cell every microstructural constituent is modelled as a classical continuum and the rve problem is formulated in terms of standard equilibrium and boundary conditions from the solution of the microstructural boundary value problem the macroscopic stress tensor and the higher order stress tensor are derived based on an extension of the hill mandel condition this automatically delivers the microstructurally based constitutive response of the higher order macro continuum and deals with the microstructural size in a natural way several examples illustrate the approach particularly the microstructural size effects

learning the kernel matrix with semidefinite programming kernel based learning algorithms work by embedding the data into a euclidean space and then searching for linear relations among the embedded data points the embedding is performed implicitly by specifying the inner products between each pair of points in the embedding space this information is contained in the so called kernel matrix a symmetric and positive semidefinite matrix that encodes the relative positions of all points specifying this matrix amounts to specifying the geometry of the embedding space and inducing a notion of similarity in the input space classical model selection problems in machine learning in this paper we show how the kernel matrix can be learned from data via semidefinite programming sdp techniques when applied to a kernel matrix associated with both training and test data this gives a powerful transductive algorithm using the labeled part of the data one can learn an embedding also for the unlabeled part the similarity between test points is inferred from training points and their labels importantly these learning problems are convex so we obtain a method for learning both the model class and the function without local minima furthermore this approach leads directly to a convex method for learning the 2 norm soft margin parameter in support vector machines solving an important open problem

simulation of the multi scale convergence in computational homogenization approaches although the asymptotic homogenization is known to explicitly predict the thermo mechanical behaviors of an overall structure as well as the microstructures the current developments in engineering fields introduce some kinds of approximation about the microstructural geometry in order for the homogenization method for periodic media to apply for general heterogeneous ones the problems arising from mathematical modeling are examined in the framework of representative volume element rve analyses here the notion of homogenization convergence allows us to eliminate the geometrical periodicity requirement when the size of rve is sufficiently large then the numerical studies in this paper realize the multi scale nature of the convergence of overall material properties as the unit cell size is increased in addition to such dependency of the macroscopic field variables on the selected size of unit cells the convergence nature of microscopic stress values is also studied quantitatively via the computational homogenization method similar discussions are made for the elastoplastic mechanical responses in both macro and microscopic levels in these multi scale numerical analyses the specific effects of the microstructural morphology are reflected by using the digital image based dib finite element fe modeling technique which enables the construction of accurate microstructural models

prediction of the mechanical behavior of nonlinear heterogeneous systems by multi level finite element modeling an accurate homogenization method that accounts for large deformations and viscoelastic material behavior on microscopic and macroscopic levels is presented this method is based on the classical homogenization theory assuming local spatial periodicity of the microstructure consequently the microstructure is identified by a representative volume element rve with conformity of opposite boundaries at any stage of the deformation process the local macroscopic stress is obtained by applying the local macroscopic deformation represented by the deformation tensor on a unique rve through imposing appropriate boundary conditions and averaging the resulting rve stress field if the assumption of local periodicity of the morphology is valid this homogenization procedure supplies a consistent objective relationship between the local macroscopic deformation and the microstructural deformation the homogenization method was implemented in a multi level finite element program with meshes on macroscopic level mesh of entire structure and microscopic level meshes of rves the performance was successfully verified by the comparison of the deformation of a perforated macroscopic sheet to the response of a homogenized sheet

on micro to macro connections in domain decomposition multiscale methods abstract micro to macro connection techniques constitute a key ingredient in the formulation of multiscale strategies in this contribution several connection methods are explored for the concurrent multiscale analysis of brittle heterogeneous materials particularly these techniques are investigated in a domain decomposition strong coupling multiscale framework the structural component under analysis is partitioned into a number of non overlapping domains and a fine scale resolution is assigned therein in an adaptive manner exploiting a zoom in technique mesh refinement is employed in the domains where crack coalescence and growth take place the original contribution presented in this manuscript consists in the study of different strong and weak locality constraints that connect coarse and fine resolution domains standard collocation and average compatibility are considered and serve as a basis for the development of two new interscale links the influence of different locality constraints is studied in terms of the mechanical response and the error distribution is compared to a full fine scale analysis

multiscale aggregating discontinuities a method for circumventing loss of material stability new methods for the analysis of failure by multiscale methods that invoke unit cells to obtain the subscale response are described these methods called multiscale aggregating discontinuities are based on the concept of perforated unit cells which exclude subdomains that are unstable i e exhibit loss of material stability using this concept it is possible to compute an equivalent discontinuity at the coarser scale including both the direction of the discontinuity and the magnitude of the jump these variables are then passed to the coarse scale model along with the stress in the unit cell the discontinuity is injected at the coarser scale by the extended finite element method analysis of the procedure shows that the method is consistent in power and yields a bulk stress strain response that is stable applications of this procedure to crack growth in heterogeneous materials are given copyright 2007 john wiley sons ltd

bridging multiple structural scales with a generalized finite element method summary this paper presents a generalized fem based on the solution of interdependent coarse scale global and fine scale local problems in order to resolve multiscale effects due to fine scale heterogeneities overall structural behavior is captured by the global problem while local problems focus on the resolution of fine scale solution features in regions where material heterogeneities may govern the structural response fine scale problems are accurately solved in parallel and to address the intrinsic coupling of scales these solutions are embedded into the global solution space using a partition of unity approach this method is demonstrated on representative heat transfer examples in order to examine its accuracy efficiency and flexibility copyright 2014 john wiley sons ltd

regularized principal manifolds many settings of unsupervised learning can be viewed as quantization problems the minimization of the expected quantization error subject to some restrictions this allows the use of tools such as regularization from the theory of supervised risk minimization for unsupervised learning this setting turns out to be closely related to principal curves the generative topographic map and robust coding we explore this connection in two ways 1 we propose an algorithm for finding principal manifolds that can be regularized in a variety of ways and 2 we derive uniform convergence bounds and hence bounds on the learning rates of the algorithm in particular we give bounds on the covering numbers which allows us to obtain nearly optimal learning rates for certain types of regularization operators experimental results demonstrate the feasibility of the approach