a nitsche stabilized finite element method for frictional sliding on embedded interfaces part ii intersecting interfaces abstract we extend the weighted nitsche s method proposed in the first part of this study to include multiple intersecting embedded interfaces these intersections arise either inside a computational domain where two internal interfaces intersect or on the boundary of the computational domain where an internal interface intersects with the external boundary we propose a variational treatment of both the interfacial kinematics and the external dirichlet constraints within nitsche s framework we modify the numerical analysis to account for these intersections and provide an explicit expression for the weights and the method parameters that arise in the nitsche variational form in the presence of junctions finally we demonstrate the performance of the method for both perfectly tied interfaces and perfectly plastic sliding interfaces through several benchmark examples

computational modeling of deformation bands in granular media ii numerical simulations development of accurate mathematical models of geomaterial behavior requires a more fundamental understanding of the localization phenomena in particular the important factors responsible for the inception and development of localized deformation the objective of this paper is to implement and test the mathematical formulations presented in a companion paper to better understand the different failure processes in granular media specifically the formation of deformation bands in geomaterials our approach revolves around the use of classical bifurcation theory combined with advanced constitutive modeling and state of the art computation to capture the end members of the failures modes described in the companion paper namely simple shear pure compaction and pure dilation bands as well as the combination modes described in the geological framework the paper revisits the notion of the critical hardening modulus as it applies to the entire range of failure modes elucidates the role of the third stress invariant and finite deformation effects on the localization properties and describes some useful properties of the constitutive and algorithmic tangent operators as they relate to the capture of the onset of deformation bands in geomaterials

hypothesis testing with multiterminal data compression the multiterminal hypothesis testing h xy against h xy is considered where x n x n and y n y n are separately encoded at rates r 1 and r 2 respectively the problem is to determine the minimum beta n of the second kind of error probability under the condition that the first kind of error probability alpha n leq epsilon for a prescribed 0 a good lower bound theta l r 1 r 2 on the power exponent theta r 1 r 2 epsilon lim inf n rightarrow infty 1 n log beta n is given and several interesting properties are revealed the lower bound is tighter than that of ahlswede and csiszar furthermore in the special case of testing against independence this bound turns out to coincide with that given by them the main arguments are devoted to the special case with r 2 infty corresponding to full side information for y n y n in particular the compact solution is established to the complete data compression cases which are useful in statistics from the practical point of view

level set topology optimization of structural problems with interface cohesion summary this paper presents a finite element topology optimization framework for the design of two phase structural systems considering contact and cohesion phenomena along the interface the geometry of the material interface is described by an explicit level set method and the structural response is predicted by the extended finite element method in this work the interface condition is described by a bilinear cohesive zone model on the basis of the traction separation constitutive relation the non penetration condition in the presence of compressive interface forces is enforced by a stabilized lagrange multiplier method the mechanical model assumes a linear elastic isotropic material infinitesimal strain theory and a quasi static response the optimization problem is solved by a nonlinear programming method and the design sensitivities are computed by the adjoint method the performance of the presented method is evaluated by 2d and 3d numerical examples the results obtained from topology optimization reveal distinct design characteristics for the various interface phenomena considered in addition 3d examples demonstrate optimal geometries that cannot be fully captured by reduced dimensionality the optimization framework presented is limited to two phase structural systems where the material interface is coincident in the undeformed configuration and to structural responses that remain valid considering small strain kinematics copyright 2017 john wiley sons ltd

a multiscale projection method for macro microcrack simulations we present a new multiscale method for crack simulations this approach is based on a two scale decomposition of the displacements and a projection to the coarse scale by using coarse scale test functions the extended finite element method xfem is used to take into account macrocracks as well as microcracks accurately the transition of the field variables between the different scales and the role of the microfield in the coarse scale formulation are emphasized the method is designed so that the fine scale computation can be done independently of the coarse scale computation which is very efficient and ideal for parallelization several examples involving microcracks and macrocracks are given it is shown that the effect of crack shielding and amplification for crack growth analyses can be captured efficiently copyright 2007 john wiley sons ltd

efficient modeling of localized material failure by means of a variationally consistent embedded strong discontinuity approach this paper is concerned with a novel embedded strong discontinuity approach suitable for the analysis of material failure at finite strains focus is on localized plastic deformation particularly relevant for slip bands in contrast to already existing models the proposed implementation allows to consider several interacting discontinuities in each finite element based on a proper re formulation of the kinematics an efficient parameterization of the deformation gradient is derived it permits to compute the strains explicitly that improves the performance significantly however the most important novel contribution of the present paper is the advocated variational constitutive update within this framework every aspect is naturally driven by energy minimization i e all unknown variables are jointly computed by minimizing the stress power the proposed update relies strongly on an extended principle of maximum dissipation this framework provides enough flexibility for different failure types and for a broad class of non associative evolution equations by discretizing the aforementioned continuous variational principle an efficient numerical implementation is obtained it shows in addition to its physical and mathematical elegance several practical advantages for instance the physical minimization principle itself specifies automatically and naturally the set of active strong discontinuities copyright 2011 john wiley sons ltd

the suboptimality of randomized tests in distributed and quantized detection systems the design of decentralized or quantized detection systems requires simultaneous optimization of quantizer mappings and ultimate fusion rule it is shown that if the likelihood ratios of the unquantized or raw observations are independent and contain no point masses of probability the optimal test does not randomize this is so despite the fact that the data to be fused can be considered discrete the result is a considerable simplification in the design search

classification error analysis in stereo vision abstract depth perception in humans is obtained by comparing images generated by the two eyes to each other given the highly stochastic nature of neurons in the brain this comparison requires maximizing the mutual information mi between the neuronal responses in the two eyes by distributing the coding information across a large number of neurons unfortunately mi is not an extensive quantity making it very difficult to predict how the accuracy of depth perception will vary with the number of neurons n in each eye to address this question we present a two arm distributed decentralized sensors detection model we demonstrate how the system can extract depth information from a pair of discrete valued stimuli represented here by a pair of random dot matrix stereograms using the theory of large deviations we calculated the rate at which the global average error probability of our detector and the mi between the two arms output vary with n we found that mi saturates exponentially with n at a rate which decays as 1 n the rate function approached the chernoff distance between the two probability distributions asymptotically our results may have implications in computer stereo vision that uses hebbian based algorithms for terrestrial navigation

computational modeling of deformation bands in granular media i geological and mathematical framework failure of granular media under natural and laboratory loading conditions involves a variety of micromechanical processes producing several geometrically kinematically and texturally distinct types of structures this paper provides a geological framework for failure processes as well as a mathematical model to analyze these processes of particular interest is the formation of tabular deformation bands in granular rocks which could exhibit distinct localized deformation features including simple shearing pure compaction dilation and various possible combinations thereof the analysis is carried out using classical bifurcation theory combined with non linear continuum mechanics and theoretical computational plasticity for granular media yielding and plastic flow are known to be influenced by all three stress invariants and thus we formulate a family of three invariant plasticity models with a compression cap to capture the entire spectrum of yielding of geomaterials we then utilize a return mapping algorithm in principal stress directions to integrate the stresses over discrete load increments allowing the solution to find the critical bifurcation point for a given loading path the formulation covers both the infinitesimal and finite deformation regimes and comparisons are made of the localization criteria in the two regimes in the accompanying paper we demonstrate with numerical examples the role that the constitutive model and finite deformation effects play on the prediction of the onset of deformation bands in geomaterials

an analysis of strong discontinuities in multiplicative finite strain plasticity and their relation with the numerical simulation of strain localization in solids abstract this paper presents an analysis of strong discontinuities in inelastic solids at finite strains solutions exhibiting this type of discontinuities characterized by a discontinuous displacement field are shown to make physical and mathematical sense in a classical multiplicative plasticity continuum model if the softening modulus is reinterpreted as a singular distribution physically the strainsoftening is localized along the discontinuity conditions for the appearance of strong discontinuities in the geometrically nonlinear range are characterized as it is the response of the material during localization in addition these analytical results are exploited in the design of a new class of finite element methods the proposed methods fall within the class of enhanced strain methods and lead to solutions independent of the mesh size and insensitive to mesh alignment without requiring any regularization of the solutions by numerical parameters like a characteristic length

a quasi static discontinuous galerkin configurational force crack propagation method for brittle materials summary this paper presents a framework for r adaptive quasi static configurational force cf brittle crack propagation cast within a discontinuous galerkin dg symmetric interior penalty sipg finite element scheme cracks are propagated in discrete steps with a staggered algorithm along element interfaces which align themselves with the predicted crack propagation direction the key novelty of the work is the exploitation of the dg face stiffness terms existing along element interfaces to propagate a crack in a mesh independent r adaptive quasi static fashion driven by the cf at the crack tip this adds no new degrees of freedom to the data structure additionally as dg methods have element specific degrees of freedom a geometry driven p adaptive algorithm is also easily included allowing for more accurate solutions of the cf on a moving crack front further for non determinant systems we introduce an average boundary condition that restrains rigid body motion leading to a determinant system to the authors knowledge this is first time such a boundary condition has been described the proposed formulation is validated against single and multiple crack problems with single and mixed mode cracks demonstrating the predictive capabilities of the method this article is protected by copyright all rights reserved

fine properties of functions with bounded deformation the paper is concerned with the fine properties of functions in the space of functions with bounded deformation we analyse the set of lebesgue points and the set where these functions have one sided approximate limits moreover following the analogy with we decompose the symmetric distributional derivative into an absolutely continuous part a jump part and a cantor part the main result of the paper is a structure theorem for functions showing that these parts of the derivative can be recovered from the corresponding ones of the one dimensional sections moreover we prove that functions are approximately differentiable in almost every point of their domain

new asymptotic results in parallel distributed detection the performance of a parallel distributed detection system is investigated as the number of sensors tends to infinity it is assumed that the i i d sensor data are quantized locally into m ary messages and transmitted to the fusion center for binary hypothesis testing the boundedness of the second moment of the postquantization log likelihood ratio is examined in relation to the asymptotic error exponent it is found that when that second moment is unbounded the neyman pearson error exponent can become a function of the test level whereas the bayes error exponent remains as previously conjectured by j n tsitsiklis 1986 unaffected large deviations techniques are also used to show that in bayes testing the equivalence of absolutely optimal and best identical quantizer systems is not limited to error exponents but extends to the actual bayes error probabilities up to a multiplicative constant

continuum discontinuum modelling of shear bands a methodology to model shear bands as strong discontinuities within a continuum mechanics context is presented the loss of hyperbolicity of the ibvp is used as the criterion for switching from a classical continuum description of the constitutive behaviour to a traction separation model acting at the discontinuity surface the extended finite element method xfem is employed for the spatial discretization of the governing equations this enables the shear bands to be arbitrarily positioned within the mesh examples that study the shear band progression within a rate independent material are presented copyright 2005 john wiley sons ltd

a bubble stabilized finite element method for dirichlet constraints on embedded interfaces we examine a bubble stabilized finite element method for enforcing dirichlet constraints on embedded interfaces by embedded we refer to problems of general interest wherein the geometry of the interface is assumed independent of some underlying bulk mesh as such the robust imposition of dirichlet constraints using a lagrange multiplier field is not trivial to focus issues we consider a simple one sided problem that is representative of a wide class of evolving interface problems the bulk field is decomposed into coarse and fine scales giving rise to coarse scale and fine scale one sided sub problems the fine scale solution is approximated with bubble functions permitting static condensation and giving rise to a stabilized form bearing strong analogy with a classical method importantly the method is simple to implement readily extends to multiple dimensions obviates the need to specify any free stabilization parameters and can lead to a symmetric positive definite system of equations the performance of the method is then examined through several numerical examples the accuracy of the lagrange multiplier is compared to results obtained using a local version of the domain integral method the variational multiscale approach proposed herein is shown to both stabilize the lagrange multiplier and improve the accuracy of the post processed fluxes copyright 2006 john wiley sons ltd

on some unresolved issues in finding optimum distributed detection schemes optimum distributed detection under the neyman pearson np criterion is considered for a general case with possibly dependent observations from sensor to sensor the focus is on the parallel architecture new necessary conditions are presented that relate the threshold used in the np optimum fusion rule to those used in the np optimum sensor rules these results clearly illustrate that the necessary conditions for np optimality have exactly the same form as those for bayes optimality based on these conditions a new algorithm for finding np optimum distributed detection schemes is developed the algorithm allows randomization at the fusion center which we show is generally needed to achieve optimality the algorithm allows one to attempt to optimize the fusion rule along with the sensor rules or to find the best schemes among those using each of a set of fixed possible fusion rules

domain integral formulation for stress intensity factor computation along curved three dimensional interface cracks new domain integrals for extracting mixed mode stress intensity factors along curved three dimensional bimaterial interface cracks are derived in the derivation the asymptotic auxiliary fields for the plane problem of a bimaterial interface crack are imposed along a curved crack front the general crack tip interaction integral a contour integral surrounding a point on the crack front which is evaluated in the limit as the contour is shrunk onto the crack tip is then expressed in domain form which is more suitable for numerical computation a consequence of imposing the auxiliary fields along a curved crack front is that the auxiliary stress fields do not satisfy equilibrium and the auxiliary strain fields do not satisfy compatibility the terms which arise due to the lack of equilibrium and compatibility are not sufficiently singular to contribute to the crack tip interaction integral or to affect its path independence however these terms become important when domain integral representations are introduced because they involve fields which are not asymptotically close to the crack tip in order to compute the pointwise stress intensity factors along the crack front the domain integrals are evaluated as a post processing step in the finite element method in the numerical results it is demonstrated that it is crucial to incorporate the terms that arise due to lack of equilibrium and compatibility of the auxiliary fields especially in regions where the local crack front curvature is high in the paper we present two numerical examples as a benchmark we first consider the problem of a penny shaped interface crack embedded in a cylinder the results for the complex stress intensity factor and phase angle are found to be in excellent agreement with the analytical solution the problem of an elliptical crack embedded between two dissimilar isotropic materials is also considered and the results are discussed

detection in sensor networks the saddlepoint approximation this paper presents a computationally simple and accurate method to compute the error probabilities in decentralized detection in sensor networks the cost of the direct computation of these probabilities e g the probability of false alarm the probability of a miss or the average error probability is combinatorial in the number of sensors and becomes infeasible even with small size networks the method is based on the theory of large deviations in particular the saddlepoint approximation and applies to generic parallel fusion sensor networks including networks with nonidentical sensors nonidentical observations and unreliable communication links the paper demonstrates with parallel fusion sensor network problems the accuracy of the saddlepoint methodology 1 computing the detection performance for a variety of small and large sensor network scenarios and 2 designing the local detection thresholds elsewhere we have used the saddlepoint approximation to study tradeoffs among parameters for networks of arbitrary size

the extended generalized finite element method an overview of the method and its applications an overview of the extended generalized finite element method gefm xfem with emphasis on methodological issues is presented this method enables the accurate approximation of solutions that involve jumps kinks singularities and other locally non smooth features within elements this is achieved by enriching the polynomial approximation space of the classical finite element method the gefm xfem has shown its potential in a variety of applications that involve non smooth solutions near interfaces among them are the simulation of cracks shear bands dislocations solidification and multi field problems copyright 2010 john wiley sons ltd

extended finite element method for plastic limit load computation of cracked structures summary the extended finite element method is extended to allow computation of the limit load of cracked structures in the paper it is demonstrated that the linear elastic tip enrichment basis with and without radial term r may be used in the framework of limit analysis but the six function enrichment basis based on the well known hutchinson rice rosengren asymptotic fields appears to be the best the discrete kinematic formulation is cast in the form of a second order cone problem which can be solved using highly efficient interior point solvers finally the proposed numerical procedure is applied to various benchmark problems showing that the present results are in good agreement with those in the literature copyright 2015 john wiley sons ltd

error estimates in weighted sobolev norms for finite element immersed interface methods abstract when solving elliptic partial differential equations in a region containing immersed interfaces possibly evolving in time it is often desirable to approximate the problem using an independent background discretisation not aligned with the interface itself optimal convergence rates are possible if the discretisation scheme is enriched by allowing the discrete solution to have jumps aligned with the surface at the cost of a higher complexity in the implementation a much simpler way to reformulate immersed interface problems consists in replacing the interface by a singular force field that produces the desired interface conditions as done in immersed boundary methods these methods are known to have inferior convergence properties depending on the global regularity of the solution across the interface when compared to enriched methods in this work we prove that this detrimental effect on the convergence properties of the approximate solution is only a local phenomenon restricted to a small neighbourhood of the interface in particular we show that optimal approximations can be constructed in a natural and inexpensive way simply by reformulating the problem in a distributionally consistent way and by resorting to weighted norms when computing the global error of the approximation

symmetric weak form integral equation method for three dimensional fracture analysis a symmetric galerkin boundary element method is developed for the analysis of linearly elastic isotropic three dimensional solids containing fractures the formulation is based upon a weak form displacement integral equation and a weak form traction integral equation recently developed by li and mear 1997 these integral equations are only weakly singular and their validity requires only that the boundary displacement data be continuous hence allowing standard co elements to be employed as part of the numerical implementation a special crack tip element is developed which has a novel feature in that there exist degrees of freedom associated with the nodes at the crack front as a result a higher degree of approximation is achieved for the relevant displacement data on the crack and further the stress intensity factors are obtained directly in terms of the crack front nodal data various examples are treated for cracks in unbounded domains and for cracks in finite domains including both embedded and surface breaking cracks and it is demonstrated that highly accurate results can be achieved using relatively coarse meshes

on strategies for enforcing interfacial constraints and evaluating jump conditions with the extended finite element method we consider a problem stemming from recent models of phase transitions in stimulus responsive hydrogels wherein a sharp interface separates swelled and collapsed phases extended finite element methods that approximate the local solution with an enriched basis such that the mesh need not explicitly fit the interface geometry are emphasized attention is focused on the weak enforcement of the normal configurational force balance and various options for evaluating the jump in the normal component of the solute flux at the interface we show that as the reciprocal interfacial mobility vanishes it plays the role of a penalty parameter enforcing a pure dirichlet constraint eventually triggering oscillations in the interfacial velocity we also examine alternative formulations employing a lagrange multiplier to enforce this constraint it is shown that the most convenient choice of basis for the lagrange multiplier results in oscillations in the multiplier field and a decrease in accuracy and rate of convergence in local error norms suggesting a lack of stability in the discrete formulation under such conditions neither the direct evaluation of the gradient of the approximation at the phase interface nor the interpretation of the lagrange multiplier field provide a robust means to obtain the jump in the normal component of solute flux fortunately the adaptation and use of local domain integral methodologies considerably improves the flux evaluations several example problems are presented to compare and contrast the various techniques and methods

dynamic crack propagation based on loss of hyperbolicity and a new discontinuous enrichment summary a methodology is developed for switching from a continuum to a discrete discontinuity where the governing partial dierential equation loses hyperbolicity the approach is limited to rate independent materials so that the transition occurs on a set of measure zero the discrete discontinuity is treated by the extendednite element method xfem whereby arbitrary discontinuities can be incorporated in the model without remeshing loss of hyperbolicity is tracked by a hyperbolicity indicator that enables both the crack speed and crack direction to be determined for a given material model a new method was developed for the case when the discontinuity ends within an element it facilitates the modelling of crack tips that occur within an element in a dynamic setting the method is applied to several dynamic crack growth problems including the branching of cracks copyright 2003 john wiley sons ltd

assumed enhanced strain and the extended finite element methods a unification of concepts abstract we present strong and weak forms of boundary value problems for a solid with a cohesive frictional crack two commonly used techniques for enhancing the finite element fe interpolation are considered the assumed enhanced strain aes and the extended fe methods we compare and contrast the fe approximations involved in these techniques the aes method employs a piecewise constant interpolation of slip that is discontinuous across element boundaries in contrast the extended fe method interpolates slip continuously across element boundaries through numerical examples we discuss the implications of these approximations to the calculated overall deformation field in the regime of infinitesimal deformation with only a heaviside enrichment we find the aes method to predict larger slip i e softer response compared to the extended fe solution we ascribe the discrepancy to the lack of higher order crack tip enhancement in the extended fe solution finally we compare the slip predicted by the above fe enhancement techniques to that calculated by classical nonlinear contact mechanics algorithm for the case where the crack traverses the element sides

modeling holes and inclusions by level sets in the extended finite element method a methodology to model arbitrary holes and material interfaces inclusions without meshing the internal boundaries is proposed the numerical method couples the level set method s osher j a sethian j comput phys 79 1 1988 12 to the extended finite element method x fem n moes j dolbow t belytschko int j numer methods engrg 46 1 1999 131 in the x fem the finite element approximation is enriched by additional functions through the notion of partition of unity the level set method is used for representing the location of holes and material interfaces and in addition the level set function is used to develop the local enrichment for material interfaces numerical examples in two dimensional linear elastostatics are presented to demonstrate the accuracy and potential of the new technique

a recovery type error estimator for the extended finite element method based on singular smooth stress field splitting a new stress recovery procedure that provides accurate estimations of the discretization error for linear elastic fracture mechanic problems analyzed with the extended finite element method xfem is presented the procedure is an adaptation of the superconvergent patch recovery spr technique for the xfem framework it is based on three fundamental aspects a the use of a singular smooth stress field decomposition technique involving the use of different recovery methods for each field standard spr for the smooth field and reconstruction of the recovered singular field using the stress intensity factor k for the singular field b direct calculation of smoothed stresses at integration points using conjoint polynomial enhancement and c assembly of patches with elements intersected by the crack using different stress interpolation polynomials at each side of the crack the method was validated by testing it on problems with an exact solution in mode i mode ii and mixed mode and on a problem without analytical solution the results obtained showed the accuracy of the proposed error estimator copyright 2008 john wiley sons ltd

on the optimality of finite level quantizations for distributed signal detection distributed multiple sensor detection problems with quantized observations are investigated for cases of nonbinary hypothesis and possibly statistically dependent observations from sensor to sensor conditioned on the hypothesis the observations available at each sensor are quantized to produce a multiple digit sensor decision which is sent to a fusion center at the fusion center the sensor decisions are combined to form a final decision using a predetermined fusion rule first it is demonstrated that there is a maximum number of digits that should be used to communicate the sensor decision from a given sensor to the fusion center this maximum is based on the number of digits used to communicate the decisions from all the other sensors to the fusion center if more than this maximum number of digits is used the performance of the optimum scheme will not be improved in some special cases of great interest the upper bound on the number of digits that should be used can be made significantly smaller secondly the optimum way to allocate a fixed overall number of digits across sensors is investigated illustrative numerical results are also presented in this correspondence

modeling quasi static crack growth with the extended finite element method part i computer implementation abstract the extended finite element method x fem is a numerical method for modeling strong displacement as well as weak strain discontinuities within a standard finite element framework in the x fem special functions are added to the finite element approximation using the framework of partition of unity for crack modeling in isotropic linear elasticity a discontinuous function and the two dimensional asymptotic crack tip displacement fields are used to account for the crack this enables the domain to be modeled by finite elements without explicitly meshing the crack surfaces and hence quasi static crack propagation simulations can be carried out without remeshing in this paper we discuss some of the key issues in the x fem and describe its implementation within a general purpose finite element code the finite element program dynaflow is considered in this study and the implementation for modeling 2 d cracks in isotropic and bimaterial media is described in particular the array allocation for enriched degrees of freedom use of geometric based queries for carrying out nodal enrichment and mesh partitioning and the assembly procedure for the discrete equations are presented we place particular emphasis on the design of a computer code to enable the modeling of discontinuous phenomena within a finite element framework

a continuum based finite element formulation for the implicit solution of multibody large deformation frictional contact problems in this paper a formulation is presented for the finite element treatment of multibody large deformation frictional contact problems the term multibody is used to mean that when two bodies mechanically contact both may be deformable a novel aspect of the approach advocated is that the equations governing contact are developed in the continuum setting first before deriving the corresponding finite element equations this feature distinguishes the current work from many earlier treatments of contact problems and renders it considerably more general in particular the approach yields a characterization of the frictional constraint assuming a coulomb law suitable for arbitrary discretizations in either two or three dimensions a geometric framework is constructed within which both frictionless and frictional response are naturally described making subsequent finite element discretization a straightforward substitution of finite dimensional solution spaces for their continuum counterparts to our knowledge this general formulation and implementation of the frictional contact problem in a finite element setting has not been reported previously in the literature the development includes exact linearization of the statement of virtual work which enables optimal convergence properties for newton raphson solution strategies and which appears to be highly desirable if not essential for the general robustness of implicit finite element techniques since the theory and subsequent linearization require no limitations on the amount of deformation or relative sliding that can occur the resulting treatment of frictional contact is suitable for a wide range of examples displaying significant non linear behaviour this assertion is substantiated through presentation of a variety of examples in both two and three dimensions

a weighted nitsche stabilized method for small sliding contact on frictional surfaces abstract we propose a weighted nitsche framework for small sliding frictional contact problems on three dimensional interfaces the proposed method inherits the advantages of both augmented lagrange multiplier and penalty methods while also addressing their shortcomings algorithmic details of the traction update and consistent linearization in the presence of nitsche terms are provided several benchmark numerical experiments are conducted and the results are compared with existing studies the results are encouraging and indicate accurate satisfaction of the non interpenetration constraint stable tractions and asymptotic quadratic convergence of the newton raphson method

bayesian detection in bounded height tree networks we study the detection performance of large scale sensor networks configured as trees with bounded height in which information is progressively compressed as it moves towards the root of the tree we show that under a bayesian formulation the error probability decays exponentially fast and we provide bounds for the error exponent we then focus on the case where the tree has certain symmetry properties we derive the form of the optimal exponent within a restricted class of easily implementable strategies as well as optimal strategies within that class we also find conditions under which suitably defined majority rules are optimal finally we provide evidence that in designing a network it is preferable to keep the branching factor small for nodes other than the neighbors of the leaves

shear band capturing using a multiscale extended digital image correlation technique abstract finite elements have been used recently to solve the optical flow conservation principle invoked to determine displacement fields by digital image correlation inspired by these recent advances and by the computational effort that has been accomplished during the past 10 years for the simulation of discontinuities by the extended finite element method xfem an extended correlation technique is introduced for capturing shear band like discontinuities from images of real mechanical tests because of the specific information at hand i e gray level images this extended finite element approach is included in a non linear multi grid solver the performances of the proposed approach are discussed on two examples namely the analysis of a bolted assembly and the formation of piobert luders bands

a contact algorithm for frictional crack propagation with the extended finite element method we present an incremental quasi static contact algorithm for path dependent frictional crack propagation in the framework of the extended finite element fe method the discrete formulation allows for the modeling of frictional contact independent of the fe mesh standard coulomb plasticity model is introduced to model the frictional contact on the surface of discontinuity the contact constraint is borrowed from non linear contact mechanics and embedded within a localized element by penalty method newton raphson iteration with consistent linearization is used to advance the solution we show the superior convergence performance of the proposed iterative method compared with a previously published algorithm called latin for frictional crack propagation numerical examples include simulation of crack initiation and propagation in 2d plane strain with and without bulk plasticity in the presence of bulk plasticity the problem is also solved using an augmented lagrangian procedure to demonstrate the efficacy and adequacy of the standard penalty solution copyright 2008 john wiley sons ltd

embedded localization band in undrained soil based on regularized strong discontinuity theory and fe analysis abstract the paper presents a novel approach to the analysis of a developing localization zone in undrained soil considered as a mixture of a solid skeleton and fluid filled pores where the solid phase is considered as elastic plastic the basic feature is the concept of regularized displacement and pore pressure discontinuities which are assumed to occur across an internal discontinuity surface in this respect the present developments are extensions of those suggested by simo et al 1993 comput mech 12 277 296 and more recently by larsson and runesson 1995 j engng mech asce in press a finite element formulation is proposed on the basis of a mixed variational formulation in the spirit of the enhanced strain concept by simo and rifai 1990 int j numer meth engng 29 1595 1638 in this fashion the localization zone is embedded into a base element for the ordinary analysis of the non localized mixture problem

strain localization in frictional materials exhibiting displacement jumps abstract this paper presents a mathematical model for analyzing strain localization in frictional solids exhibiting displacement jumps precise conditions for the appearance of slip lines including their initiation and evolution are outlined for a rate independent strain softening drucker prager model and explicit analytical expressions are used to describe the orientation of the slip line a stress displacement relation obtained through the consistency condition is also formulated to describe the quasi static response in the post localization regime the mathematical model which is cast within the framework of finite element analysis employing the assumed enhanced strain method circumvents mesh dependence issues often associated with rate independent plasticity models it is shown that the enhancement equation is nothing else but the consistency condition imposed on the band numerical examples involving plane strain compression are described to demonstrate objectivity with respect to mesh refinement and insensitivity to mesh alignment of finite element solutions

enriched element free galerkin methods for crack tip fields summary the element free galerkin efg method is a meshless method for solving partial di erential equations which uses only a set of nodal points and a cad like description of the body to formulate the discrete model it has been used extensively for fracture problems and has yielded good results when adequate refinement is used near the crack tip but stresses tend to be oscillatatory near the crack tip unless substantial refinement is used an enriched efg formulation for fracture problems is proposed two methods are used 1 adding the asymptotic fields to the trial function and 2 augmenting the basis by the asymptotic fields a local mapping of the enriched fields for curved cracks is also described results show that both methods greatly reduce stress oscillations and allow the calculation of accurate stress intensity factors with far fewer degrees of freedom 1997 by john wiley sons ltd

extended finite element method for three dimensional crack modelling an extended finite element method x fem for three dimensional crack modelling is described a discontinuous function and the two dimensional asymptotic crack tip displacement fields are added to the finite element approximation to account for the crack using the notion of partition of unity this enables the domain to be modelled by finite elements with no explicit meshing of the crack surfaces computational geometry issues associated with the representation of the crack and the enrichment of the finite element approximation are discussed stress intensity factors sifs for planar three dimensional cracks are presented which are found to be in good agreement with benchmark solutions copyright 2000 john wiley sons ltd

topological complexity of symplectic manifolds open access via springer compact agreement the authors wish to thank ay se borat michael farber jarek kedra and john oprea for helpful comments regarding an earlier draft of this paper

randomized fusion rules can be optimal in distributed neyman pearson detectors we show that randomized fusion rules can be locally optimal in distributed detection systems under the neyman pearson criterion this result is contrary to common belief we first formulate conditions for a randomized fusion rule to be locally optimal then we present distribution functions of local observations that satisfy these conditions

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

capturing strain localization in dense sands with random density summary this paper presents a three invariant constitutive framework suitable for the numerical analyses of localization instabilities in granular materials exhibiting unstructured random density a recently proposed elastoplastic model for sands based on critical state plasticity is enhanced with the third stress invariant to capture the difference in the compressive and extensional yield strengths commonly observed in geomaterials undergoing plastic deformation the new three invariant constitutive model similar to its two invariant predecessor is capable of accounting for meso scale inhomogeneities as well as material and geometric nonlinearities details regarding the numerical implementation of the model into a fully nonlinear finite element framework are presented and a closed form expression for the consistent tangent operator whose spectral form is used in the strain localization analyses is derived an algorithm based on the spectral form of the so called acoustic tensor is proposed to search for the necessary conditions for deformation bands to develop the aforementioned framework is utilized in a series of boundary value problems on dense sand specimens whose density fields are modelled as exponentially distributed unstructured random fields to account for the effect of inhomogeneities at the meso scale and the intrinsic uncertainty associated with them copyright 2006 john wiley sons ltd

aes for multiscale localization modeling in granular media this work presents a multiscale strong discontinuity approach to tackle key challenges in modeling localization behavior in granular media accommodation of discontinuities in the kinematic fields and direct linkage to the underlying grain scale information assumed enhanced strain aes concepts are borrowed to enhance elements for post localization analysis but are reformulated within a recently proposed hierarchical multiscale computational framework unlike classical aes methods where material properties are usually constants or assumed to evolve with some arbitrary phenomenological laws this framework provides a bridge to extract evolutions of key material parameters such as friction and dilatancy based on grain scale computational or experimental data more importantly the phenomenological softening modulus typically used in aes methods is no longer required numerical examples of plane strain compression tests are presented to illustrate the applicability of this method and to analyze its numerical performance

quantization in multisensor random signal detection optimum detection schemes based on quantized data are of great interest in radar and sonar applications the design and properties of multisensor schemes are considered here for detection of weak random signals in additive possibly non gaussian noise signal to noise ratios are assumed unknown and the signals at the different sensors may be statistically dependent analytical expressions describing the best way to fuse the quantized observations for cases with any given observation sample size are provided the best schemes for originally quantizing the observations are also studied for the case of asymptotically large observation sample sizes these schemes are shown to minimize the mean squared error between the best weak signal test statistic based on unquantized observations and the best weak signal test statistic based on quantized observations under signal absent numerical results indicate it is sometimes best for each quantizer to use different size alphabets when a quantizer is located at each sensor

fundamental structures and asymptotic performance criteria in decentralized binary hypothesis testing two fundamental distributed decision network structures are considered the first system consists of finite number of sensors each collecting asymptotically many data while the second one employs asymptotically many sensors each collecting a single datum for binary hypothesis testing the neyman pearson criterion is utilized and justified via information theoretic arguments an asymptotic relative efficiency performance measure is used to establish tradeoffs between the two structures by comparing the performance characteristics of the decentralized detection systems to their centralized counterparts

distributed signal detection under the neyman pearson criterion a procedure for finding the neyman pearson optimum distributed sensor detectors for cases with statistically dependent observations is described this is the first valid procedure we have seen for this case this procedure is based on a theorem proven in this paper these results clarify and correct a number of possibly misleading discussions in the existing literature cases with networks of sensors in fairly general configurations are considered along with cases where the sensor detectors make multiple bit sensor decisions

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

finite element simulation of strain localization with large deformation capturing strong discontinuity using a petrov galerkin multiscale formulation the finite element model for strain localization analysis developed in a previous work is generalized to the finite deformation regime strain enhancements via jumps in the displacement field are captured and condensed on the material level leading to a formulation that does not require static condensation to be performed on the element level a general evolution condition is first formulated laying out conditions for the continued activation of a strong discontinuity then a multiscale finite element model is formulated to describe the post bifurcation behavior highlighting the key roles played by the continuous and conforming deformation maps on the characterization of the finite deformation kinematics of a localized element traced by a strong discontinuity the resulting finite element equation exhibits the features of a petrov galerkin formulation in which the gradient of the weighting function is evaluated over the continuous part of the deformation map whereas the gradient of the trial function is evaluated over the conforming part of the same map in the limit of infinitesimal deformations the formulation reduces to the standard galerkin approximation described in a previous work numerical examples are presented demonstrating absolute objectivity with respect to mesh refinement and insensitivity to mesh alignment of finite element solutions 2002 elsevier science b v all rights reserved

finite deformation formulation for embedded frictional crack with the extended finite element method we reformulate an extended finite element fe framework for embedded frictional cracks in elastoplastic solids to accommodate finite deformation including finite stretching and rotation for the fe representation we consider a galerkin approximation in which both the trial and weighting functions adapt to the current contact configuration contact and frictional constraints employ two kuhn tucker conditions a contact separation constraint nesting over a stick slip constraint for the case when the crack faces are in frictional sliding mode we integrate finite deformation bulk plasticity into the formulation using the multiplicative decomposition technique of nonlinear continuum mechanics we then present plane strain simulations demonstrating various aspects of the extended fe solutions the mechanisms considered include combined opening and frictional sliding in initially straight curved and s shaped cracks with and without bulk plasticity to gain further insight into the extended fe solutions we perform mesh convergence studies focusing on both the global and the local responses of structures with cracks including the distribution of the normal component of traction on the crack faces copyright 2009 john wiley sons ltd

necessary conditions for optimum distributed sensor detectors under the neyman pearson criterion distributed signal detection schemes that are optimum under the neyman pearson criterion continue to be of interest the functional forms of these schemes can be difficult to specify especially for cases with dependent observations from sensor to sensor for cases with dependent observations from sensor to sensor the optimum sensor test statistics are generally not the likelihood ratios of the sensor observations equations expressing the forms of the optimum sensor test statistics in terms of the other optimum test statistics and the optimum fusion rule are given detailed proofs of these results are given in this correspondence and have not been given previously in some communication radar and sonar system problems the amplitude of the received signal may be unknown but the signal may be known to be weak equations expressing the forms of the optimum sensor test statistics for such cases are given these expressions have already been shown to be useful for interpreting and finding optimum distributed detection schemes but detailed proofs of the type given here have not yet been given

an interface enriched generalized fem for problems with discontinuous gradient fields summary a new generalized fem is introduced for solving problems with discontinuous gradient fields the method relies on enrichment functions associated with generalized degrees of freedom at the nodes generated from the intersection of the phase interface with element edges the proposed approach has several advantages over conventional generalized fem formulations such as a lower computational cost easier implementation and straightforward handling of dirichlet boundary conditions a detailed convergence study of the proposed method and a comparison with the standard fem are presented for heat transfer problems the method achieves the optimal rate of convergence using meshes that do not conform to the interfaces present in the domain while achieving a level of accuracy comparable to that of the standard fem with conforming meshes various application problems are presented including the conjugate heat transfer problem encountered in microvascular materials copyright 2011 john wiley sons ltd

on the construction of blending elements for local partition of unity enriched finite elements for computational efficiency partition of unity enrichments are preferably localized to the sub domains where they are needed it is shown that an appropriate construction of the elements in the blending area the regionwhere the enriched elements blend to unenriched elements is often crucial for good performance of local partition of unity enrichments an enhanced strain formulation is developed which leads to good performance the optimal rate of convergence is achieved for polynomial enrichments it is shown that a proper choice of the finite element shape functions and partition of unity shape functions also improves the accuracy and convergence the methods are illustrated by several examples the examples deal primarily with the signed distance function enrichment for treating discontinuous derivatives inside an element but other enrichments are also considered results show that both methods provide optimal rates of convergence

a new fast finite element method for dislocations based on interior discontinuities a new technique for the modelling of multiple dislocations based on introducing interior discontinuities is presented in contrast to existing methods the superposition of infinite domain solutions is avoided interior discontinuities are specified on the dislocation slip surfaces and the resulting boundary value problem is solved by a finite element method the accuracy of the proposed method is verified and its efficiency for multi dislocation problems is illustrated bounded core energies are incorporated into the method through regularization of the discontinuities at their edges though the method is applied to edge dislocations here its extension to other types of dislocations is straightforward copyright 2006 john wiley sons ltd

stabilized low order finite elements for frictional contact with the extended finite element method abstract contact problem suffers from a numerical instability similar to that encountered in incompressible elasticity in which the normal contact pressure exhibits spurious oscillation this oscillation does not go away with mesh refinement and in some cases it even gets worse as the mesh is refined using a lagrange multipliers formulation we trace this problem to non satisfaction of the lbb condition associated with equal order interpolation of slip and normal component of traction in this paper we employ a stabilized finite element formulation based on the polynomial pressure projection ppp technique which was used successfully for stokes equation and for coupled solid deformation fluid diffusion using low order mixed finite elements for the frictional contact problem the polynomial pressure projection approach is applied to the normal contact pressure in the framework of the extended finite element method we use low order linear triangular elements tetrahedral elements for 3d for both slip and normal pressure degrees of freedom and show the efficacy of the stabilized formulation on a variety of plane strain plane stress and three dimensional problems

a finite element model for strain localization analysis of strongly discontinuous fields based on standard galerkin approximation abstract this paper presents a finite element model for strain localization analysis of elastoplastic solids subjected to discontinuous displacement fields based on standard galerkin approximation strain enhancements via jumps in the displacement field are captured and condensed on the material level leading to a formulation that does not require static condensation to be performed on the element level the mathematical formulation revolves around the dual response of a macroscopic point cut by a shear band which requires the satisfaction of the yield condition on the band as the same stress point unloads elastically just outside the band precise conditions for the appearance of slip lines including their initiation and evolution are outlined for a rate independent strain softening drucker prager model and explicit analytical expressions are used to describe the orientation of the slip line in a plane strain setting at post localization the stress point integration algorithm along the band is exact and amenable to consistent linearization numerical examples involving simple shearing of elastoplastic solids with deviatoric plastic flow as well as plane strain compression of dilatant cohesive frictional materials are presented to demonstrate absolute objectivity with respect to mesh refinement and insensitivity to mesh alignment of finite element solutions

plane strain finite element analysis of pressure sensitive plasticity with strong discontinuity numerical simulations of localized deformation in solids should capture the structural phenomenon of localization and associated loss of material body strength in a manner independent of spatial discretization many regularization techniques have been proposed to address the ill posedness associated with rate independent softening plasticity that leads to mesh dependent numerical simulations one approach to alleviating mesh dependence is the strong discontinuity approach which represents localized deformation as a slip surface within a plasticity model a strong discontinuity is a discontinuous displacement field this approach is used in this paper to formulate a plane strain pressure sensitive nonassociative plasticity model with strong discontinuity and to implement the model along with an enhanced bilinear quadrilateral element via an assumed enhanced strain method numerical examples demonstrate mesh independence of the method for pressure sensitive materials

a multiple level set approach to prevent numerical artefacts in complex microstructures with nearby inclusions within xfem in this paper we highlight that when the extended finite element method xfem is employed to model a microstructure in which inclusions are involved and the distance between two inclusions is small enough to be comparable with the mesh size three numerical artefacts are induced significantly affecting the convergence and accuracy of the numerical solution to the problem with such a microstructure these artefacts are a an artificial percolation of nearby inclusions b an artificial distortion of phase domains c an enrichment deficiency we propose to improve the xfem levelset method so as to avoid these artefacts the new technique leading to this improvement uses one level set function for each inclusion and adds additional enrichment in an element whose support is cut by several interfaces a local description of the multiple level sets is provided to avoid the storage of all level set functions a simple integration rule is employed for numerical quadrature in elements cut by several interfaces we show that the artefacts mentioned hereinbefore are circumvented in this framework the performances of the method are demonstrated through benchmarks and examples applied to the homogenization of concrete materials in 2d and 3d cases

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

discontinuous modelling of shear bands using adaptive meshfree methods a simple methodology to model shear bands as strong displacement discontinuities in an adaptive meshfree method is presented the shear band is represented by a displacement jump at discrete particle positions the displacement jump in normal direction is suppressed with penalty method loss of material stability is used as transition criterion from continuum to discontinuum the method is two and three dimensional examples of complicated shear banding including transition from brittle to ductile failure are studied and compared to experimental data and other examples from the literature

error probability bounds for balanced binary relay trees we study the detection error probability associated with a balanced binary relay tree where the leaves of the tree correspond to n identical and independent sensors the root of the tree represents a fusion center that makes the overall detection decision each of the other nodes in the tree is a relay node that combines two binary messages to form a single output binary message only the leaves are sensors in this way the information from the sensors is aggregated into the fusion center via the relay nodes in this context we describe the evolution of the type i and type ii error probabilities of the binary data as it propagates from the leaves toward the root tight upper and lower bounds for the total error probability at the fusion center as functions of n are derived these characterize how fast the total error probability converges to 0 with respect to n even if the individual sensors have error probabilities that converge to 1 2

the generalized finite element method an example of its implementation and illustration of its performance the generalized finite element method gfem was introduced in reference 1 as a combination of the standard fem and the partition of unity method the standard mapped polynomial finite element spaces are augmented by adding special functions which reflect the known information about the boundary value problem and the input data the geometry of the domain the loads and the boundary conditions the special functions are multiplied with the partition of unity corresponding to the standard linear vertex shape functions and are pasted to the existing finite element basis to construct a conforming approximation the essential boundary conditions can be imposed exactly as in the standard fem adaptive numerical quadrature is used to ensure that the errors in integration do not affect the accuracy of the approximation this paper gives an example of how the gfem can be developed for the laplacian in domains with multiple elliptical voids and illustrates implementation issues and the superior accuracy of the gfem versus the standard fem copyright 2000 john wiley sons ltd

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

data fusion trees for detection does architecture matter we consider the problem of decentralized detection in a network consisting of a large number of nodes arranged as a tree of bounded height under the assumption of conditionally independent and identically distributed i i d observations we characterize the optimal error exponent under a neyman pearson formulation we show that the type ii error probability decays exponentially fast with the number of nodes and the optimal error exponent is often the same as that corresponding to a parallel configuration we provide sufficient as well as necessary conditions for this to happen for those networks satisfying the sufficient conditions we propose a simple strategy that nearly achieves the optimal error exponent and in which all non leaf nodes need only send 1 bit messages

two scale shear band evolution by local partition of unity we introduce a methodology to model shear band evolution in the quasi static regime using the extended finite element method we enrich the finite element polynomial displacement field with a fine scale function which models the high displacement gradient in the shear band for this purpose we use a local partition of unity and a parameterized displacement enrichment based on closed form solutions for one dimensional shear bands a stabilized consistent penalty method is used to circumvent locking in the regularized elasto viscoplastic plane strain regime and to guarantee element stability the loss of stability of the boundary value problem is used as an indicator of shear band initiation point and direction shear band development examples are shown illustrating the capabilities of the method to track shear band evolution and strains as high as 1000 copyright 2005 john wiley sons ltd

calculation of fracture mechanics parameters for an arbitrary three dimensional crack by the equivalent domain integral method summary in this paper an equivalent domain integral edi method and the attendant numerical algorithms arc presented for the computation of a near crack tip field parameter the vector je integral and its variation along the front of an arbitrary three dimensional crack in a structural component account is taken of possible non elastic strains present in the structure in this case the near tip je values may be significantly different from the far field values jf especially under non proportional loading

theory of the stochastic resonance effect in signal detection part ii variable detectors in part i of this paper ldquotheory of the stochastic resonance effect in signal detection part i fixed detectors rdquo ieee transactions on signal processing vol 55 no 7 pt 1 pp 3172 3184 the mechanism of the stochastic resonance sr effect for a fixed detector has been examined this paper analyzes the stochastic resonance sr effect under the condition that the detector structure or its parameters can also be changed the detector optimization problem with sr noise under both neyman pearson and bayesian criteria is examined in the bayesian approach when the prior probabilities are unknown the minimax approach is adopted the form of the optimal noise pdf along with the corresponding detector as well as the maximum achievable performance are determined the developed theory is then applied to a general class of weak signal detection problems under the assumptions that the sample size n is large enough and the test statistics satisfies the conditions of central limit theorem the optimal sr noise is shown to be a constant vector and independent of the signal strength for both neyman pearson and bayesian criteria illustrative examples are presented where performance comparisons are made between the original detector and the optimal sr noise modified detector for different types of sr noise

a mixed augmented lagrangian extended finite element method for modelling elastic plastic fatigue crack growth with unilateral contact the complete modelling of fatigue crack growth is still an industrial challenging issue for numerical methods a new technique for the finite element modelling of elastic plastic fatigue crack growth with unilateral contact on the crack faces is presented the extended finite element method x fem is used to discretize the equations allowing for the modelling of arbitrary cracks whose geometries are independent of the finite element mesh this paper presents an augmented lagrangian formulation in the x fem framework that is able to deal with elastic plastic crack growth with treatment of contact an original formulation which takes advantages of two powerful numerical methods is presented next the numerical issues such as contact treatment and numerical integration are addressed and finally numerical examples are shown to validate the method copyright 2007 john wiley sons ltd