analysis of three dimensional fracture mechanics problems a two scale approach using coarse generalized fem meshes this paper presents a generalized finite element method gfem based on the solution of interdependent global structural and local crack scale problems the local problems focus on the resolution of fine scale features of the solution in the vicinity of three dimensional cracks while the global problem addresses the macro scale structural behavior the local solutions are embedded into the solution space for the global problem using the partition of unity method the local problems are accurately solved using an hp gfem and thus the proposed method does not rely on analytical solutions the proposed methodology enables accurate modeling of three dimensional cracks on meshes with elements that are orders of magnitude larger than the process zone along crack fronts the boundary conditions for the local problems are provided by the coarse global mesh solution and can be of dirichlet neumann or cauchy type the effect of the type of local boundary conditions on the performance of the proposed gfem is analyzed several three dimensional fracture mechanics problems aimed at investigating the accuracy of the method and its computational performance both in terms of problem size and cpu time are presented copyright 2009 john wiley sons ltd

robustness and information levels in case based multiple criteria sorting abstract case based preference elicitation methods for multiple criteria sorting problems have the advantage of posing rather small cognitive demands on a decision maker but they may lead to ambiguous results when preference parameters are not uniquely determined we use a simulation approach to determine the extent of this problem and to study the impact of additional case information on the quality of results our experiments compare two decision analysis tools case based distance sorting and the simple additive weighting method in terms of the effects of additional case information on sorting performance depending on problem dimension number of groups number of criteria etc our results confirm the expected benefit of additional case information on the precision of estimates of the decision maker s preferences problem dimension however has some unexpected effects

value minimization in circumscription abstract minimization in circumscription has focussed on minimizing the extent of a set of predicates with or without priorities among them or of a formula although functions and other constants may be left varying during circumscription no earlier formalism to the best of our knowledge minimized functions in this paper we introduce and motivate the notion of value minimizing a function in circumscription intuitively value minimizing a function consists in choosing those models where the value of the function is minimal relative to an ordering on its range we first give the formulation of value minimization of a single function based on a syntactic transformation and then give a formulation in model theoretic terms we then discuss value minimization of a set of functions with and without priorities we show how lifschitz s nested abnormality theories can be used to express value minimization and discuss the prospect of its use for knowledge representation particularly in formalizing reasoning about actions

on the strong discontinuity approach in finite deformation settings taking the strong discontinuity approach as a framework for modelling displacement discontinuities and strain localization phenomena this work extends previous results in infinitesimal strain settings to finite deformation scenarios by means of the strong discontinuity analysis and taking isotropic damage models as target continuum stress strain constitutive equation projected discrete tractions displacement jumps constitutive models are derived together with the strong discontinuity conditions that restrict the stress states at the discontinuous regime a variable bandwidth model to automatically induce those strong discontinuity conditions and a discontinuous bifurcation procedure to determine the initiation and propagation of the discontinuity are briefly sketched the large strain counterpart of a non symmetric finite element with embedded discontinuities frequently considered in the strong discontinuity approach for infinitesimal strains is then presented finally some numerical experiments display the theoretical issues and emphasize the role of the large strain kinematics in the obtained results copyright 2003 john wiley sons ltd

deriving rankings from incomplete preference information a comparison of different approaches abstract volume based methods for decision making under incomplete information like the smaa family of methods provide rich probabilistic information to support decision making however they usually do not directly generate a unique ranking of alternatives methods to create such a unique ranking from incomplete preference information typically select one parameter vector either by mathematical programming approaches or by averaging and then apply a preference model using this parameter vector in the present paper we develop several models to infer a complete ranking or a complete preorder of alternatives directly from the probabilistic information provided by volume based methods without singling out a specific parameter vector we compare the results obtained by these models to those obtained with a single parameter approach in a computational study results indicate small but significant differences in the performance of methods as well as in the probability that additional preference information might worsen rather than improve the results

two counterexamples related to baker s approach to the frame problem abstract andrew baker s approach to reasoning about actions is the most robust circumscriptive approach currently known investigation of its applicability to nondeterministic actions reveals that this approach does not allow us to draw some intuitively plausible conclusions also it does not always generate the proper existence of situations axiom the limitations are traced to an unexpected interference of the axioms encoding observations with the minimization a modification that avoids the shortcomings is suggested

a refined global local finite element analysis method a refined global local method was proposed to improve the efficiency of finite element analysis the proposed method was based on the regular finite element method in conjunction with three basic step i e the global analysis the local analysis and the refined global analysis in the first two steps a coarse finite element mesh was used to analyse the entire structure to obtain the nodal displacements which were subsequently used as displacement boundary conditions for local regions of interest these local regions with the prescribed boundary conditions were then analysed with refined meshes to obtain more accurate stresses in the third step a new global displacement distribution based on the results of the previous two steps was assumed for the analysis from which much improved solutions for both stresses and displacements were produced numerical examples showed that the proposed method yielded accurate solutions with significant savings in computing time compared with the regular finite element method further this method is suitable for parallel computation

towards a general theory of topological maps we present a general theory of topological maps whereby sensory input topological and local metrical information are combined to define the topological maps explaining such information topological maps correspond to the minimal models of an axiomatic theory describing the relationships between the different sources of information explained by a map we use a circumscriptive theory to specify the minimal models associated with this representation the theory here proposed is independent of the exploration strategy the agent follows when building a map we provide an algorithm to calculate the models of the theory this algorithm supports different exploration strategies and facilitates map disambiguation when perceptual aliasing arises

canonical analysis of two convex polyhedral cones and applications canonical analysis of two convex polyhedral cones consists in looking for two vectors one in each cone whose square cosine is a maximum this paper presents new results about the properties of the optimal solution to this problem and also discusses in detail the convergence of an alternating least squares algorithm the set of scalings of an ordinal variable is a convex polyhedral cone which thus plays an important role in optimal scaling methods for the analysis of ordinal data monotone analysis of variance and correspondence analysis subject to an ordinal constraint on one of the factors are both canonical analyses of a convex polyhedral cone and a subspace optimal multiple regression of a dependent ordinal variable on a set of independent ordinal variables is a canonical analysis of two convex polyhedral cones as long as the signs of the regression coefficients are given we discuss these three situations and illustrate them by examples

nested abnormality theories we propose a new approach to the use of circumscription for representing knowledge nested abnormality theories are similar to simple abnormality theories introduced by mccarthy except that their axioms may have a nested structure with each level corresponding to another application of the circumscription operator the new style of applying circumscription sometimes leads to more economical and elegant formalizations mathematical properties of nested abnormality theories may be easier to investigate these advantages are demonstrated by recasting several familiar applications of circumscription in the new format including some examples of inheritance hierarchies the domain closure assumption and causal minimization nested abnormality theories provide also a convenient representation for the explanation closure approach to the frame problem developed by schubert

reasoning under minimal upper bounds in propositional logic reasoning from the minimal models of a theory as fostered by circumscription is in the area of artificial intelligence an important method to formalize common sense reasoning however as it appears minimal models may not always be suitable to capture the intuitive semantics of a knowledge base aiming intuitively at an exclusive interpretation of disjunctions of atoms i e if possible then assign at most one of the disjuncts the value true in a model in this paper we consider an approach which is more lenient and also admits non minimal models such that inclusive interpretation of disjunction also may be possible in cases where minimal model reasoning adopts an exclusive interpretation nonetheless in the spirit of minimization the approach aims at including only positive information that is necessary this is achieved by closing the set of admissible models of a theory under minimal upper bounds in the set of models of the theory which we refer to as curbing we demonstrate this method on some examples and investigate its semantical and computational properties we establish that curbing is an expressive reasoning method since the main reasoning tasks are shown to be pspace complete on the other hand we also present cases of lower complexity and in particular cases in which the complexity is located just as for ordinary minimal model reasoning at the second level of the polynomial hierarchy or even below

a multiscale strategy for structural optimization this paper presents a multiscale strategy dedicated to structural optimization the applications concern the study of geometric details such as holes surface profiles etc within the structures with frictional contacts the first characteristic of the method is that it uses a micro macro approach this approach is based on a domain decomposition into substructures and interfaces which involves the resolution of independent micro problems in each substructure and transfers macro information only through the interfaces the second characteristic is the use of a multiresolution strategy in order to reduce the computation cost for problems with evolving design parameters the last characteristic is the capability to model the geometry of details without remeshing thanks to two features the use of a local enrichment method and the use of level set functions to easily modify the boundary of the detail during the optimization process

selection of a representative value function in robust multiple criteria ranking and choice we introduce the concept of a representative value function in robust ordinal regression applied to multiple criteria ranking and choice problems the proposed method can be seen as a new interactive uta like procedure which extends the utagms and grip methods the preference information supplied by the decision maker dm is composed of a partial preorder and intensities of preference on a subset of reference alternatives robust ordinal regression builds a set of general additive value functions which are compatible with the preference information and returns two binary preference relations necessary and possible they identify recommendations which are compatible with all or at least one compatible value function respectively in this paper we propose a general framework for selection of a representative value function from among the set of compatibles ones there are a few targets which build on results of robust ordinal regression and could be attained by a representative value function in general according to the interactively elicited preferences of the dm the representative value function may emphasize the advantage of some alternatives over the others when all compatible value functions acknowledge this advantage or reduce the ambiguity in the advantage of some alternatives over the others when some compatible value functions acknowledge an advantage and other ones acknowledge a disadvantage the basic procedure is refined by few extensions they enable emphasizing the advantage of alternatives that could be considered as potential best options accounting for intensities of preference or obtaining a desired type of the marginal value functions

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

global maximization of uta functions in multi objective optimization abstract the utas utilite additives type methods for constructing nondecreasing additive utility functions were first proposed by jacquet lagreze and siskos in 1982 for handling decision problems of multicriteria ranking in this article by uta functions we mean functions which are constructed by the uta type methods our purpose is to propose an algorithm for globally maximizing uta functions of a class of linear convex multiple objective programming problems the algorithm is established based on a branch and bound scheme in which the branching procedure is performed by a so called i rectangular bisection in the objective outcome space and the bounding procedure by some convex or linear programs preliminary computational experiments show that this algorithm can work well for the case where the number of objective functions in the multiple objective optimization problem under consideration is much smaller than the number of variables

the light beam search approach an overview of methodology applications the paper gives a general overview of the light beam search lbs methodology and applications lbs enables an interactive analysis of multiple objective decision problems due to presentation of samples of a large set of non dominated points to the decision maker dm in each iteration a local preference model in the form of an outranking relation is used to define the neighborhood of a current non dominated point the sample comes from the first current point is obtained by projection of an aspiration point onto the non dominated set in the direction of a reservation point the dm can control the search by either modifying the aspiration and reservation points or by shifting the current point to a selected better point from its neighborhood the paper describes applications of the approach to several real life problems and discusses observations made while working on these problems the lbs approach is compared to other existing methods and the class of problems suitable to this methodology is defined

representing action indeterminacy and ramifications abstract we define and study a high level language for describing actions more expressive than the action language a introduced by gelfond and lifschitz the new language ar allows us to describe actions with indirect effects ramifications nondeterministic actions and actions that may be impossible to execute it has symbols for nonpropositional fluents and for the fluents that are exempt from the commonsense law of inertia temporal projection problems specified using the language ar can be represented as nested abnormality theories based on the situation calculus

assessing a set of additive utility functions for multicriteria decision making the uta method abstract the purpose of the method presented in this paper is to assess additive utility functions which aggregate multiple criteria in a composite criterion using the information given by a subjective ranking on a set of stimuli or actions weak order comparison judgments and the multicriteria evaluations of these actions it is an ordinal regression method using linear programming to estimate the parameters of the utility function stability and sensitivity analysis leads to the assessment of a set of utility functions by means of post optimality analysis techniques in linear programming finally a simple illustrative example is presented and some extensions of the method are proposed

multiple objective linear fractional programming this paper presents a simplex based solution procedure for the multiple objective linear fractional programming problem by 1 departing slightly from the traditional notion of efficiency and 2 augmenting the feasible region as in goal programming the solution procedure solves for all weakly efficient vertices of the augmented feasible region the article discusses the difficulties that must be addressed in multiple objective linear fractional programming and motivates the solution algorithm that is developed

on the discrete constitutive models induced by strong discontinuity kinematics and continuum constitutive equations on the basis of continuum constitutive models stress vs strain the introduction of strong discontinuity kinematics considering jumps in the displacement fields across a discontinuity interface induces projected discrete constitutive models traction displacement jumps in a consistent manner therefore this projection provides possible links between the classical continuum strain localization analysis and the non linear decohesive fracture mechanics techniques the strong discontinuity analysis shows that bandwidth based regularization of the hardening softening parameter is the crucial modification to be done on the continuum model to achieve such a projection and it also provides the strong discontinuity conditions that set restrictions on the stress state compatible with bifurcations in a strong discontinuity format the methodology is illustrated on the basis of two classical families of non linear constitutive models scalar continuum damage and elasto plasticity for which the corresponding discrete constitutive models and the strong discontinuity conditions are derived

a multiscale extended finite element method for crack propagation in this paper we propose a multiscale strategy for crack propagation which enables one to use a refined mesh only in the crack s vicinity where it is required two techniques are used in synergy a multiscale strategy based on a domain decomposition method to account for the crack s global and local effects efficiently and a local enrichment technique the x fem to describe the geometry of the crack independently of the mesh the focus of this study is the avoidance of meshing difficulties and the choice of an appropriate scale separation to make the strategy efficient we show that the introduction of the crack s discontinuity both on the microscale and on the macroscale is essential for the numerical scalability of the domain decomposition method to remain unaffected by the presence of a crack thus the convergence rate of the iterative solver is the same throughout the crack s propagation

size effect and localization in j2 plasticity this paper studies the phenomenon of structural size effect and strain localization in j2 plasticity size effect is here understood as the change in the response of a given structure when the spatial dimensions are scaled up or down while the geometry and other relevant properties of the structure are preserved the work exploits the advantages of the mixed displacement pressure formulation in incompressible or quasi incompressible situations elasto j2 plastic constitutive behaviour with regularized softening is considered stability issues are discussed to ensure existence and uniqueness of the solution of the corresponding discrete finite element formulation numerical examples show that the formulation derived is able to solve a wide range of structural scales including real life engineering applications the results obtained do not suffer from spurious mesh dependence furthermore the formulation includes the classical theories of perfect plasticity and linear fracture mechanics as limit cases

cut a multicriteria approach for concavifiable preferences we consider the problem of helping a decision maker dm choose from a set of multiattributed objects when her preferences are concavifiable i e representable by a concave value function we establish conditions under which preferences or preference intensities are concavifiable we also derive a characterization for the family of concave value functions compatible with a set of such preference statements expressed by the dm this can be used to validate dominance relations over discrete sets of alternatives and forms the basis of an interactive procedure we report on the practical use of this procedure with several dms for a flat choice problem and its computational performance on a set of project portfolio selection problem instances the use of preference intensities is found to provide significant improvements to the performance of the procedure

error estimates for the three field formulation with bubble stabilization in this paper we prove convergence and error estimates for the so called 3 field formulation using piecewise linear finite elements stabilized with boundary bubbles optimal error bounds are proved in l 2 and in the broken h 1 norm for the internal variable u and in suitable weighted l 2 norms for the other variables a and

a pgd based homogenization technique for the resolution of nonlinear multiscale problems abstract this paper deals with the offline resolution of nonlinear multiscale problems leading to a pgd reduced model from which one can derive microinformation which is suitable for design here we focus on an improvement to the proper generalized decomposition pgd technique which is used for the calculation of the homogenized operator and which plays a central role in our multiscale computational strategy this homogenized behavior is calculated offline using the latin multiscale strategy and pgd leads to a drastic reduction in cpu cost indeed the multiscale aspect of the latin method is based on splitting the unknowns between a macroscale and a microcomplement this macroscale is used to capture the homogenized behavior of the structure and then to accelerate the convergence of the iterative algorithm the novelty of this work lies in the reduction of the computation cost of building the homogenized operator in order to do that the problems defined within each subdomain are solved using a new pgd representation of the unknowns in which the separation of the unknowns is performed not only in time and in space but also in terms of the interface macrodisplacements the numerical example presented shows that the convergence rate of the approach is not affected by this new representation and that a significant reduction in computation cost can be achieved particularly in the case of nonlinear behavior the technique used herein is then particularly important to enhance the performances of the latin strategy but is not limited to this method the more general path which is followed in this paper is to solve the microproblems arising in the homogenization for all the configurations that can be encountered in the calculation an additional and novel benefit of this approach is that it includes the calculation of the homogenized tangent operator which gives over the whole time interval and for any cell the relation between the perturbation in terms of macroforces and the perturbation in terms of macrodisplacements in linear viscoelasticity this operator represents the homogenized behavior of the structure exactly

hierarchical enrichment for bridging scales and mesh free boundary conditions the finite element method when used with a basis made up of piecewise polynomials often requires the generation of a very fine computational mesh in order to capture localized solution phenomena such as boundary layers or near singularities enrichment of the basis with additional functions obtained through analytical or experimental means can allow for a coarser mesh and more accurate solution we introduce an enrichment scheme in which an interaction or bridging scale term is used to separate the basis formed by the enrichment functions from the original set of basis functions in effect making the enrichment hierarchical this separation of scales allows the simple application of essential boundary conditions it also allows a quantification of the effects of the enrichment leading to strategies for error estimation and control of the stiffness matrix condition number we also find that this formulation allows for the simple application of essential boundary conditions for mesh free shape functions which are notoriously problematic we find that for multiple dimensions care must be taken to derive a weak form which is truly consistent with the strong form on the essential boundary copyright 2001 john wiley sons ltd

enabling fast stable and accurate peridynamic computations using multi time step integration abstract peridynamics is a nonlocal extension of classical continuum mechanics that is well suited for solving problems with discontinuities such as cracks this paper extends the peridynamic formulation to decompose a problem domain into a number of smaller overlapping subdomains and to enable the use of different time steps in different subdomains this approach allows regions of interest to be isolated and solved at a small time step for increased accuracy while the rest of the problem domain can be solved at a larger time step for greater computational efficiency performance of the proposed method in terms of stability accuracy and computational cost is examined and several numerical examples are presented to corroborate the findings

a multiscale computational approach for contact problems we introduce a two scale computational strategy for the resolution of contact problems with friction possibly with numerous contact surfaces the structure studied may also be highly heterogeneous the description of micro and macro quantities is performed on the interfaces arising from the decomposition of the structure studied into an assembly of substructures and interfaces the efficiency and robustness of the method are illustrated on several examples this iterative computational strategy is suitable for parallel computing it can be interpreted as a mixed multilevel domain decomposition method its scalability has been demonstrated and comparisons with other domain decomposition methods are also given

a two scale approximation of the schur complement and its use for non intrusive coupling this paper presents a two scale approximation of the schur complement of a subdomain s stiffness matrix obtained by combining local ie element strips and global ie homogenized contributions this approximation is used in the context of a coupling strategy that is designed to embed local plasticity and geometric details into a small region of a large linear elastic structure the strategy consists in creating a local model which contains the desired features of the concerned region and then substituting it into the global problem by the means of a non intrusive solver coupling technique adapted from domain decomposition methods using the two scale approximation of the schur complement as a robin condition on the local model enables to reach high efficiency examples include a large 3d problem provided by our industrial partner snecma

the generalized finite element method this paper describes a pilot design and implementation of the generalized finite element method gfem as a direct extension of the standard finite element method sfem or fem which makes possible the accurate solution of engineering problems in complex domains which may be practically impossible to solve using the fem the development of the gfem is illustrated for the laplacian in two space dimensions in domains which may include several hundreds of voids and or cracks for which the construction of meshes used by the fem is practically impossible the two main capabilities are 1 it can construct the approximation using meshes which may overlap part or all of the domain boundary 2 it can incorporate into the approximation handbook functions which are known analytically or are generated numerically and approximate well the solution of the boundary value problem in the neighborhood of corner points voids cracks etc the main tool is a special integration algorithm which we call the fast remeshing approach which is robust and works for any domain with arbitrary complexity the incorporation of the handbook functions into the gfem is done by employing the partition of unity method pum the presented formulations and implementations can be easily extended to the multi material medium where the voids are replaced by inclusions of various shapes and sizes and to the case of the elasticity problem this work can also be understood as a pilot study for the feasibility and demonstration of the capabilities of the gfem which is needed before analogous implementations are attempted in the three dmensional and nonlinear cases which are the cases of main interest for future work

formalizing sensing actions a transition function based approach abstract in presence of incomplete information about the world we need to distinguish between the state of the world and the state of the agent s knowledge about the world in such a case the agent may need to have at its disposal sensing actions that change its state of knowledge about the world and may need to construct more general plans consisting of sensing actions and conditional statements to achieve its goal in this paper we first develop a high level action description language that allows specification of sensing actions and their effects in its domain description and allows queries with conditional plans we give provably correct translations of domain description in our language to axioms in first order logic and relate our formulation to several earlier formulations in the literature we then analyze the state space of our formulation and develop several sound approximations that have much smaller state spaces finally we define regression of knowledge formulas over conditional plans

arbitrary branched and intersecting cracks with the extended finite element method summary extensions of a new technique for the nite element modelling of cracks with multiple branches multiple holes and cracks emanating from holes are presented this extended nite element method x fem allows the representation of crack discontinuities and voids independently of the mesh a standard displacementbased approximation is enriched by incorporating discontinuous elds through a partition of unity method a methodology that constructs the enriched approximation based on the interaction of the discontinuous geometric features with the mesh is developed computation of the stress intensity factors sif in dierent examples involving branched and intersecting cracks as well as cracks emanating from holes are presented to demonstrate the accuracy and the robustness of the proposed technique copyright 2000 john wiley sons ltd

nonmonotonic reasoning in the framework of situation calculus abstract most of the solutions proposed to the yale shooting problem have either introduced new nonmonotonic reasoning methods generally involving temporal priorities or completely reformulated the domain axioms to represent causality explicitly this paper presents a new solution based on the idea that since the abnormality predicate takes a situational argument it is important for the meanings of the situations to be held constant across the various models being compared this is accomplished by a simple change in circumscription policy when ab is circumscribed result rather than holds is allowed to vary in addition we need an axiom ensuring that every consistent situation is included in the domain of discourse ordinary circumscription will then produce the intuitively correct answer beyond its conceptual simplicity the solution proposed here has additional advantages over the previous approaches unlike the approach that uses temporal priorities it can support reasoning backward in time as well as forward and unlike the causal approach it can handle ramifications in a natural manner

the design and analysis of the generalized finite element method abstract in this paper we introduce the generalized finite element method gfem as a combination of the classical finite element method fem and the partition of unity method pum the standard finite element spaces are augmented by adding special functions which reflect the known information about the boundary value problem and the input data e g the singular functions obtained from the local asymptotic expansion of the exact solution in the neighborhood of a corner point etc the special functions are multiplied with the partition of unity corresponding to the standard linear vertex shape functions and pasted together with the existing finite element basis to construct an augmented conforming finite element space in this way the local approximability afforded by the special functions is included in the approximation while maintaining the existing infrastructure of finite element codes the major features of the gfem are 1 the essential boundary conditions can be imposed exactly as in the standard fem unlike other partition of unity based methods where this is a major issue 2 the accuracy of the numerical integration of the entries of the stiffness matrix and load vector is controlled adaptively so that the errors in integration of the special functions do not affect the accuracy of the constructed approximation this issue also has not been sufficiently addressed in other implementations of partition of unity or meshless methods and 3 linear dependencies in the system of equations are resolved by employing an easy modification of the direct linear solver the power of the gfem for solving problems in domains with complex geometry with less error and less computer resources than the standard fem is illustrated by numerical examples

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

direct estimation of generalized stress intensity factors using a three scale concurrent multigrid x fem a concurrent multigrid method is devised for the direct estimation of stress intensity factors and higher order coefficients of the elastic crack tip asymptotic field the proposed method bridges three characteristic length scales that can be present in fracture mechanics the structure the crack and the singularity at the crack tip for each of them a relevant model is proposed first a truncated analytical reduced order model based on williams expansion is used to describe the singularity at the tip then it is coupled with a standard extended finite element fe method model which is known to be suitable for the scale of the crack a multigrid solver finally bridges the scale of the crack to that of the structure for which a standard fe model is often accurate enough dedicated coupling algorithms are presented and the effects of their parameters are discussed the efficiency and accuracy of this new approach are exemplified using three benchmarks

molp with an interactive assessment of a piecewise linear utility function the paper presents a methodology for multi objective linear programming molp problems it relies on three steps 1 generation of a subset of feasible efficient solutions from 10 to 50 as representative as possible of the efficient set 2 assessment of an additive utility function using an interactive method prefcalc 3 optimization of the additive utility function on the original set of feasible alternatives following this methodology enables the user to find compromise solutions which can be different from the vertices it is particularly adapted for large scale linear programs where traditional multiobjective methods would be too costly to use since the interactive phase is limited to step 2 using prefcalc on a micro computer a micro computer version of the method prefchat is available

using assignment examples to infer weights for electre tri method some experimental results given a finite set of alternatives a the sorting or assignment problem consists in the assignment of each alternative to one of the pre defined categories in this paper we are interested in multiple criteria sorting problems and more precisely in the existing method electre tri this method requires the elicitation of preferential parameters weights thresholds category limits in order to construct a preference model which the decision maker dm accepts as a working hypothesis in the decision aid study a direct elicitation of these parameters requiring a high cognitive effort from the dm v mosseau r slowinski journal of global optimization 12 2 1998 174 proposed an interactive aggregation disaggregation approach that infers electre tri parameters indirectly from holistic information i e assignment examples in this approach the determination of electre tri parameters that best restore the assignment examples is formulated through a nonlinear optimization program in this paper we consider the subproblem of the determination of the weights only the thresholds and category limits being fixed this subproblem leads to solve a linear program rather than nonlinear in the global inference model numerical experiments were conducted so as to check the behaviour of this disaggregation tool results showed that this tool is able to infer weights that restores in a stable way the assignment examples and that it is able to identify inconsistencies in the assignment examples

the second generation feti methods and their application to the parallel solution of large scale linear and geometrically non linear structural analysis problems the feti algorithms are a family of numerically scalable domain decomposition methods they have been designed in the early 1990s for solving iteratively and on parallel machines large scale systems of equations arising from the finite element discretization of solid mechanics structural engineering structural dynamics and acoustic scattering problems and for analyzing complex structures obtained from the assembly of substructures with incompatible discrete interfaces in this paper we present the second generation of these methods that operate more efficiently on large numbers of subdomains offer greater robustness better performance and more flexibility for implementation on a wider variety of computational platforms we also report on the application and performance of these methods for the solution of geometrically non linear structural analysis problems we discuss key aspects of their implementation on shared and distributed memory parallel processors benchmark them against optimized direct sparse solvers and highlight their potential with the solution of large scale structural mechanics problems with several million degrees of freedom

a two scale extended finite element method for modelling 3d crack growth with interfacial contact 3d fatigue crack growth problems are nowadays handled using x fem coupled with level set techniques it is also well established that such an approach allows mesh independent crack modelling and no remeshing during crack propagation however when contact and friction occur along the crack faces a discretization of the internal variables linked to the interface law is necessary the interface discretization is generally constructed from the finite elements cut by the crack as a consequence a mesh dependency between the bulk discretization and the interface discretization is introduced however the dimension of the possible non linearities arising at the crack interface like confined plasticity or unilateral contact with friction may be several orders of magnitude finer than the crack size a finer discretization is thus required to accurately capture these non linearities the aim of the present paper is to develop a method considering the 3d cracked structure and the crack interface as two independent global and local problems characterized by different length scales and different behaviors here the interface is seen as an autonomous entity with its own discretization variables and constitutive law a formulation involving three fields is used the interface is linked to the global problem in a weak sense in order to avoid instabilities in the contact solution two iterative strategies are considered to solve the contact problem two dimensional and three dimensional numerical examples are presented to demonstrate the ability of the model to solve the contact at the crack interface with or without propagation at a given level of accuracy

two scale approach to predict multi site cracking potential in 3 d structures using the generalized finite element method this research utilized the novel computational framework of the generalized finite element method gfem to predict the potential for crack propagation in concrete slabs a two scale approach using the global local concept within the gfem framework gfemg l is applied to multi site cracking problems msc where different crack geometries are placed simultaneously at different positions in a three dimensional airfield slab loaded by new generation aircraft gears the gfemg l approach efficiently simulated multiple cracks without discretization in the global mesh but only in the local domain the gfemg l enrichment functions allow the displacements of the local problem to be represented in the global domain through enrichment functions from the local problems rather than explicitly modeling each crack discretely in the global domain the main contribution of this work was extension of the gfemg l approach to a class of three dimensional msc problems involving realistic boundaries conditions and existence of multiple cracks spanning different orders of magnitude in size scales within the domain for the linear elastic structure bottom and surface initiated cracks with small dimensions were considered in conjunction with a larger macro crack unlike traditional numerical methods the proposed gfemg l made it possible to tackle this class of problems by avoiding refined crack front meshes in the global domain as well as numerical round off errors furthermore the two scale approach significantly reduces the computational cost for large scale 3 d msc problems

decision making with incomplete information abstract decision situations with incomplete information are characterized by a decision maker without a precisely defined stable preference structure by probability distributions not known completely or by an inexact evaluation of consequences within the paper a general framework for decision making with incomplete information is presented which shows how to solve problems from descriptive as well as prescriptive decision theory based on this framework an overview of existing methods which are particularly suitable for handling incomplete information is given

the expressive power of circumscription abstract circumscription is a form of nonmonotonic reasoning introduced by mccarthy 1997 as a way of characterizing defaults using second order logic the consequences of circumscription are those formulas true in the minimal models under a pre order on models in the case of domain circumscription the pre order was the sub model relation formula circumscription mccarthy 1980 1986 is characterized by minimizing a set of formulas one model is preferred to another model when the extensions of the minimized formulas in the first are subsets of the extensions in the second we show that the propositional version of formula circumscription can capture all pre orders on valuations of finite languages we consider the question of infinite languages and give the corresponding representation theorems we further show that there are natural defaults inertia in temporal projection captured by inductive definitions that cannot be captured by circumscription in the first order case finally contrary to previous claims we show that propositional formula circumscription can capture all preferential consequence relations over finite propositional languages as defined by kraus et al 1990 thus in the finite propositional case there is no restriction on the kinds of preferential defaults that circumscription can describe

non planar 3d crack growth by the extended finite element and level sets part i mechanical model a methodology for solving three dimensional crack problems with geometries that are independent of the mesh is described the method is based on the extended finite element method in which the crack discontinuity is introduced as a heaviside step function via a partition of unity in addition branch functions are introduced for all elements containing the crack front the branch functions include asymptotic near tip fields that improve the accuracy of the method the crack geometry is described by two signed distance functions which in turn can be defined by nodal values consequently no explicit representation of the crack is needed examples for three dimensional elastostatic problems are given and compared to analytic and benchmark solutions the method is readily extendable to inelastic fracture problems copyright 2002 john wiley sons ltd

a simple method for crack growth in mixed mode with x fem abstract in this paper a new method for level set update is proposed in the context of crack propagation modeling with the extended finite element method x fem and level sets compared with the existing methods such as the resolution of the hamilton jacobi equations this new method is much simpler because it does not required complex manipulations of the level sets this method called the projection method uses both a classical discretization of the surface of the crack segments for 2d cracks and triangles for 3d cracks and a level set representation of the crack this discretization is updated with respect to the position of the new crack front then the level sets are re computed using the true distance to the new crack by an orthogonal projection of each node of the structure onto the new crack surface then numerical illustrations are given on 2d and 3d academic examples finally three illustrations are given on 3d industrial applications

learning lexicographic orders the purpose of this paper is to learn the order of criteria of lexicographic decision under various reasonable assumptions we give a sample evaluation and an oracle based algorithm in the worst case analysis we are dealing with the adversarial models we show that if the distances of the samples are less than 4 then it is not learnable but 4 distance samples are polynomial learnable

non additive robust ordinal regression a multiple criteria decision model based on the choquet integral abstract within the multicriteria aggregation disaggregation framework ordinal regression aims at inducing the parameters of a decision model for example those of a utility function which have to represent some holistic preference comparisons of a decision maker dm usually among the many utility functions representing the dm s preference information only one utility function is selected since such a choice is arbitrary to some extent recently robust ordinal regression has been proposed with the purpose of taking into account all the sets of parameters compatible with the dm s preference information until now robust ordinal regression has been implemented to additive utility functions under the assumption of criteria independence in this paper we propose a non additive robust ordinal regression on a set of alternatives a whose utility is evaluated in terms of the choquet integral which permits to represent the interaction among criteria modelled by the fuzzy measures parameterizing our approach in our methodology besides holistic pairwise preference comparisons of alternatives from a subset of reference alternatives a a the dm is also requested to express the intensity of preference on pairs of alternatives from a and to supply pairwise comparisons on the importance of criteria and the sign and intensity of interaction among pairs of criteria the output of our approach defines a set of fuzzy measures capacities such that the corresponding choquet integral is compatible with the dm s preference information moreover using linear programming our decision model establishes two preference relations for any a b a the necessary weak preference relation if for all compatible fuzzy measures the utility of a is not smaller than the utility of b and the possible weak preference relation if for at least one compatible fuzzy measure the utility of a is not smaller than the utility of b

a way to deal with fuzzy preferences in multi criteria decision problems this paper presents a special multiple criteria decision making approach for solving problems in context with fuzzy individual preferences at first we briefly expose the proposed methodology the individual preferences are explicitly given by a complete transitive relation r on a set of reference actions the modelling of the decision maker s preferences is obtained by means of fuzzy outranking relations these fuzzy relations are based on a system of additive utility functions which are estimated by means of ordinal regression methods analysing the preference relation r this is followed by a presentation of two real multicriteria problems which the proposed methodology has been applied to i e a highway plan choice problem and a problem in marketing research dealing with the launching of a new product in each application we tried to specify this method according to the specific structure of the problem considered

applications of circumscription to formalizing common sense knowledge we present a new and more symmetric version of the circumscription method of nonmonotonic reasoning first described in mccarthy 1980 and some applications to formalizing common sense knowledge the applications in this paper are mostly based on minimizing the abnormality of different aspects of various entities included are nonmonotonic treatments of is a hierarchies the unique names hypothesis and the frame problem the new circumscription may be called formula circumscription to distinguish it from the previously defined domain circumscription and predicate circumscription a still more general formalism called prioritized circumscription is briefly explored

non planar 3d crack growth by the extended finite element and level sets part ii level set update we present a level set method for treating the growth of non planar three dimensional cracks the crack is defined by two almost orthogonal level sets signed distance functions one of them describes the crack as a two dimensional surface in a three dimensional space and the second is used to describe the one dimensional crack front which is the intersection of the two level sets a hamilton jacobi equation is used to update the level sets a velocity extension is developed that preserves the old crack surface and can accurately generate the growing surface the technique is coupled with the extended finite element method which approximates the displacement field with a discontinuous partition of unity this displacement field is constructed directly in terms of the level sets so the discretization by finite elements requires no explicit representation of the crack surface numerical experiments show the robustness of the method both in accuracy and in treating cracks with significant changes in topology copyright 2002 john wiley sons ltd

preference modelling by estimating local utility functions for multiobjective optimization abstract this paper is intended to design goal programming models for capturing the decision maker s dm s preference information and for supporting the search for the best compromise solutions in multiobjective optimization at first a linear goal programming model is built to estimate piecewise linear local utility functions based on pairwise comparisons of efficient solutions as well as objectives the interactive step trade off method istm is employed to generate a typical subset of efficient solutions of a multiobjective problem another general goal programming model is then constructed to embed the estimated utility functions in the original multiobjective problem for utility optimization using ordinary nonlinear programming algorithms this technique consisting of the istm method and the newly investigated search process facilitates the identification and elimination of possible inconsistent information which may exist in the dm s preferences it also provides various ways to carry out post optimality analysis to test the robustness of the obtained best solutions a modified nonlinear multiobjective management problem is taken as example to demonstrate the technique

functional anova ultramodularity and monotonicity applications in multiattribute utility theory abstract utility function properties as monotonicity and concavity play a fundamental role in reflecting a decision maker s preference structure these properties are usually characterized via partial derivatives however elicitation methods do not necessarily lead to twice differentiable utility functions furthermore while in a single attribute context concavity fully reflects risk aversion in multiattribute problems such correspondence is not one to one we show that tsetlin and winkler s multivariate risk attitudes imply ultramodularity of the utility function we demonstrate that geometric properties of a multivariate utility function can be successfully studied by utilizing an integral function expansion functional anova the necessary and sufficient conditions under which monotonicity and or ultramodularity of single attribute functions imply the monotonicity and or ultramodularity of the corresponding multiattribute function under additive preferential and mutual utility independence are then established without reliance on the utility function differentiability we also investigate the relationship between the presence of interactions among the attributes of a multiattribute utility function and the decision maker s multivariate risk attitudes

a stable and optimally convergent latin cutfem algorithm for multiple unilateral contact problems in this paper we propose a novel unfitted finite element method for the simulation of multiple body contact the computational mesh is generated independently of the geometry of the interacting solids which can be arbitrarily complex the key novelty of the approach is the combination of elements of the cutfem technology namely the enrichment of the solution field via the definition of overlapping fictitious domains with a dedicated penalty type regularisation of discrete operators and the latin hybrid mixed formulation of complex interface conditions furthermore the novel p1 p1 discretisation scheme that we propose for the unfitted latin solver is shown to be stable robust and optimally convergent with mesh refinement finally the paper introduces a high performance 3d level set cutfem framework for the versatile and robust solution of contact problems involving multiple bodies of complex geometries with more than two bodies interacting at a single point

a variational multiscale method to model crack propagation at finite strains this contribution presents a hierarchical variational multiscale framework to model propagating discontinuities at finite strains thereby the deformation map is decomposed into coarse scale and fine scale displacements which results in a decoupled system of coarse scale and fine scale equations both are solved numerically by means of the finite element method whereby crack propagation is taken into account at the fine scale growing cracks are numerically handled by the introduction of discontinuous elements a locality assumption on the fine scale solution and an adaptive scheme to resize the fine scale domain are introduced and demonstrated to increase the efficiency of the method copyright 2009 john wiley sons ltd

an interactive multiobjective nonlinear programming procedure abstract this paper develops a method for interactive multiobjective nonlinear programming procedure monlp it provides a detailed description of an efficient algorithm and reports on promising computational results it also discusses several alternative strategies for implementing grg code generalized reduced gradient which is known as one of the best methods for solving nonlinear optimization problems abadie 1978 the method relies on three steps 1 generation of a subset of feasible efficient solutions 2 interactive definition by decision maker dm of his preference structure according to desired outcome 3 determination of a compromise solution using nonlinear optimization a global analysis based on reference point search procedure is performed in the criteria space following this methodology it is possible for the dm to find his final solution a microcomputer version for medium problems of the method is available

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