stability analysis of particle methods with corrected derivatives abstract the stability of discretizations by particle methods with corrected derivatives is analyzed it is shown that the standard particle method which is equivalent to the element free galerkin method with an eulerian kernel and nodal quadrature has two sources of instability 1 rank deficiency of the discrete equations and 2 distortion of the material instability the latter leads to the so called tensile instability it is shown that a lagrangian kernel with the addition of stress points eliminates both instabilities examples that verify the stability of the new formulation are given

meshfree and finite element nodal integration methods nodal integration can be applied to the galerkin weak form to yield a particle type method where stress and material history are located exclusively at the nodes and can be employed when using meshless or finite element shape functions this particle feature of nodal integration is desirable for large deformation settings because it avoids the remapping or advection of the state variables required in other methods to a lesser degree nodal integration can be desirable because it relies on fewer stress point evaluations than most other methods in this work aspects regarding stability consistency efficiency and explicit time integration are explored within the context of nodal integration both small and large deformation numerical examples are provided copyright 2007 john wiley sons ltd

extended finite element method coupled with face based strain smoothing technique for three dimensional fracture problems summary in this work the extended finite element method xfem is for the first time coupled with face based strain smoothing technique to solve three dimensional fracture problems this proposed method which is called face based smoothed xfem here is expected to combine both the advantages of xfem and strain smoothing technique in xfem arbitrary crack geometry can be modeled and crack advance can be simulated without remeshing strain smoothing technique can eliminate the integration of singular term over the volume around the crack front thanks to the transformation of volume integration into area integration special smoothing scheme is implemented in the crack front smoothing domain three examples are presented to test the accuracy efficiency and convergence rate of the face based smoothed xfem from the results it is clear that smoothing technique can improve the performance of xfem for three dimensional fracture problems copyright 2015 john wiley sons ltd

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

embedded crack vs smeared crack models a comparison of elementwise discontinuous crack path approaches with emphasis on mesh bias this paper is concerned with an analysis of the mesh dependence of results from numerical failure analyses using the strong discontinuity approach sda based on an analytical and numerical comparison with a standard plasticity model pertaining to the classical fracture energy based smeared crack concept using a consistent characteristic length the sda is characterized by incorporating the kinematics of fractured solids locally within the finite element the resulting jumps in the displacement field are captured by their corresponding singularly distributed strains for the analytical and numerical study of the mesh dependence only mode i failure is considered analogies and differences of both finite element formulations are investigated and evaluated

cracking node method for dynamic fracture with finite elements a new method for modeling discrete cracks based on the extended finite element method is described in the method the growth of the actual crack is tracked and approximated with contiguous discrete crack segments that lie on finite element nodes and span only two adjacent elements the method can deal with complicated fracture patterns because it needs no explicit representation of the topology of the actual crack path a set of effective rules for injection of crack segments is presented so that fracture behavior beginning from arbitrary crack nucleations to macroscopic crack propagation is seamlessly modeled the effectiveness of the method is demonstrated with several dynamic fracture problems that involve complicated crack patterns such as fragmentation and crack branching copyright 2008 john wiley sons ltd

locally geodesically quasiconvex functions on complete riemannian manifolds on etudie la structure topologique des varietes de riemann completes admettant des fonctions localement geodesiquement quasi convexes dont la famille inclut toutes les fonctions geodesiquement convexes

adaptivity for structured meshfree particle methods in 2d and 3d the implementation of h adaptivity for meshfree particle methods within a structured framework is described in this framework the initial particle arrangement is structured along with a background mesh and outside boundaries and interior interfaces are described by implicit functions the advantage of meshfree approximations in this framework lies in the ease of implementing h adaptivity and the simplicity of the data structures particles can easily be added and removed without complications in the data structure although there are some issues in the quadrature an a posteriori error estimation is used for the adaptive refinement an adaptive refinement strategy is applied to several linear elastic problems with high stress and strain gradients and singularities several non linear examples are also given copyright 2005 john wiley sons ltd

longitudinal data analysis using generalized linear models summary this paper proposes an extension of generalized linear models to the analysis of longitudinal data we introduce a class of estimating equations that give consistent estimates of the regression parameters and of their variance under mild assumptions about the time dependence the estimating equations are derived without specifying the joint distribution of a subject s observations yet they reduce to the score equations for multivariate gaussian outcomes asymptotic theory is presented for the general class of estimators specific cases in which we assume independence m dependence and exchangeable correlation structures from each subject are discussed efficiency of the proposed estimators in two simple situations is considered the approach is closely related to quasi likelih ood some key ironh estimating equation generalized linear model longitudinal data quasi likelihood repeated measures

a unified stability analysis of meshless particle methods a uni ed stability analysis of meshless methods with eulerian and lagrangian kernels is presented three types of instabilities were identi ed in one dimension an instability due to rank de ciency a tensile instability and a material instability which is also found in continua the stability of particle methods with eulerian and lagrangian kernels is markedly di erent lagrangian kernels do not exhibit the tensile instability in both kernels the instability due to rank de ciency can be suppressed by stress points in two dimensions the stabilizing e ect of stress points is dependent on their locations it was found that the best approach to stable particle discretizations is to use lagrangian kernels with stress points the stability of the least squares stabilization was also studied copyright 2000 john wiley sons ltd

composite conditional likelihood for sparse clustered data summary sparse clustered data arise in finely stratified genetic and epidemiologic studies and pose at least two challenges to inference first it is difficult to model and interpret the full joint probability of dependent discrete data which limits the utility of full likelihood methods second standard methods for clustered data such as pairwise likelihood and the generalized estimating function approach are unsuitable when the data are sparse owing to the presence of many nuisance parameters we present a composite conditional likelihood for use with sparse clustered data that provides valid inferences about covariate effects on both the marginal response probabilities and the intracluster pairwise association our primary focus is on sparse clustered binary data in which case the method proposed utilizes doubly discordant quadruplets drawn from each stratum to conduct inference about the intracluster pairwise odds ratios

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

element free galerkin methods for static and dynamic fracture abstract element free galerkin efg methods are presented and applied to static and dynamic fracture problems efg methods which are based on moving least square mls interpolants require only nodal data no element connectivity is needed the description of the geometry and numerical model of the problem consists only of a set of nodes and a description of exterior boundaries and interior boundaries from any cracks this makes the method particularly attractive for growing crack problems since only minimal remeshing is needed to follow crack growth in moving least square interpolants the dependent variable at any point is obtained by minimizing a function in terms of the nodal values of the dependent variable in the domain of influence of the point numerical examples involving fatigue crack growth and dynamic crack propagation are presented to illustrate the performance and potential of this method

dynamic fracture using element free galerkin methods the element free galerkin method for dynamic crack propagation is described and applied to several problems this method is a gridless method which facilitates the modelling of growing crack problems because it does not require remeshing the growth of the crack is modelled by extending its surfaces the essential feature of the method is the use of moving least squares interpolants for the trial and test functions in these interpolants the dependent variable is obtained at any point by minimizing a weighted quadratic form involving the nodal variables within a small domain surrounding the point the discrete equations are obtained by a galerkin method the procedures for modelling dynamic crack propagation based on dynamic stress intensity factors are also described

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

marginally specified logistic normal models for longitudinal binary data summary likelihood based inference for longitudinal binary data can be obtained using a generalized linear mixed model breslow n and clayton d g 1993 journal of the american statistical association88 9 25 wolfinger r and o connell m 1993 journal of statistical computation and simulation48 233 243 given the recent improvements in computational approaches alternatively fitzmaurice and laird 1993 biometrika80 141 151 molenberghs and lesaffre 1994 journal of the american statistical association89 633 644 and heagerty and zeger 1996 journal of the american statistical association91 1024 1036 have developed a likelihood based inference that adopts a marginal mean regression parameter and completes full specification of the joint multivariate distribution through either canonical and or marginal higher moment assumptions each of these marginal approaches is computationally intense and currently limited to small cluster sizes in this manuscript an alternative parameterization of the logistic normal random effects model is adopted and both likelihood and estimating equation approaches to parameter estimation are studied a key feature of the proposed approach is that marginal regression parameters are adopted that still permit individual level predictions or contrasts an example is presented where scientific interest is in both the mean response and the covariance among repeated measurements

approximate inference in generalized linear mixed models statistical approaches to overdispersion correlated errors shrinkage estimation and smoothing of regression relationships may be encompassed within the framework of the generalized linear mixed model glmm given an unobserved vector of random effects observations are assumed to be conditionally independent with means that depend on the linear predictor through a specified link function and conditional variances that are specified by a variance function known prior weights and a scale factor the random effects are assumed to be normally distributed with mean zero and dispersion matrix depending on unknown variance components for problems involving time series spatial aggregation and smoothing the dispersion may be specified in terms of a rank deficient inverse covariance matrix approximation of the marginal quasi likelihood using laplace s method leads eventually to estimating equations based on penalized quasilikelihood or pql for the mean parameters and pseudo likelihood for the variances im

finite element analysis on implicitly defined domains an accurate representation based on arbitrary parametric surfaces in this paper we present some novel results and ideas for robust and accurate implicit representation of geometric surfaces in finite element analysis the novel contributions of this paper are threefold 1 describe and validate a method to represent arbitrary parametric surfaces implicitly 2 represent arbitrary solids implicitly including sharp features using level sets and boolean operations 3 impose arbitrary dirichlet and neumann boundary conditions on the resulting implicitly defined boundaries the methods proposed do not require local refinement of the finite element mesh in regions of high curvature ensure the independence of the domain s volume on the mesh do not rely on boundary regularization and are well suited to methods based on fixed grids such as the extended finite element method xfem numerical examples are presented to demonstrate the robustness and effectiveness of the proposed approach and show that it is possible to achieve optimal convergence rates using a fully implicit representation of object boundaries this approach is one step in the desired direction of tying numerical simulations to computer aided design cad similarly to the isogeometric analysis paradigm

generalization of the mantel haenszel estimating function for sparse clustered binary data we extend the mantel haenszel estimating function to estimate both the intra cluster pairwise correlation and the main effects for sparse clustered binary data we propose both a composite likelihood approach and an estimating function approach for the analysis of such data the proposed estimators are consistent and asymptotically normally distributed simulation results demonstrate that the two approaches are comparable in terms of bias and efficiency however the estimating equation approach is computationally simpler analysis of the georgia high blood pressure survey is used for illustration

a likelihood based method for analysing longitudinal binary responses summary in this paper we discuss a likelihood based method for analysing correlated binary responses based on a multivariate model it is related to the pseudo maximum likelihood approach suggested recently by zhao prentice 1990 their parameterization results in a simple pairwise model in which the association between responses is modelled in terms of correlations while the present paper uses conditional log odds ratios with this approach higher order associations can be incorporated in a natural way one important advantage of this parameterization is that the maximum likelihood estimates of the marginal mean parameters are robust to misspecification of the time dependence we describe an iterative two stage procedure for obtaining the maximum likelihood estimates two examples are presented to illustrate this methodology

a parametric model for cluster correlated categorical data summary a fully parametric copula model for symmetric dependent clustered categorical data is discussed the model accommodates any marginal regression models of interest and admits a broad range of within cluster association the form of the distribution is independent of cluster size and may be used to model data with varying cluster sizes the model contains an association parameter that is estimated from the data to give a measure of the strength of the within cluster association and also a test of independence two examples are given to illustrate the methods

a simple and robust three dimensional cracking particle method without enrichment abstract a new robust and efficient approach for modeling discrete cracks in meshfree methods is described the method is motivated by the cracking particle method rabczuk t belytschko t international journal for numerical methods in engineering 2004 where the crack is modeled by a set of cracked segments however in contrast to the above mentioned paper we do not introduce additional unknowns in the variational formulation to capture the displacement discontinuity instead the crack is modeled by splitting particles located on opposite sides of the associated crack segments and we make use of the visibility method in order to describe the crack kinematics we apply this method to several two and three dimensional problems in statics and dynamics and show through several numerical examples that the method does not show any mesh orientation bias

smoothing and accelerated computations in the element free galerkin method two topics in the formulation and implementation of meshless methods are considered the smoothing of the approximating functions at concave boundaries and the speedup of the calculation of the approximating functions and their derivatives these techniques are described in the context of the element free galerkin method but they are applicable to other meshless methods results are presented for some elastostatic problems which show a moderate improvement in the accuracy of the smoothed interpolant the speedup in calculating the shape functions is about a factor of two

marginal modeling of correlated ordinal data using a multivariate plackett distribution abstract an extension of the bivariate model suggested by dale is proposed for the analysis of dependent ordinal categorical data the so called multivariate dale model is constructed by first generalizing the bivariate plackett distribution to any dimensions because the approach is likelihood based it satisfies properties that are not fulfilled by other popular methods such as the generalized estimating equations approach the proposed method models both the marginal and the association structure in a flexible way the attractiveness of the multivariate dale model is illustrated in three key examples covering areas such as crossover trials longitudinal studies with patients dropping out from the study and discriminant analysis applications the differences and similarities with the generalized estimating approach are highlighted

extended mantel haenszel estimating procedure for multivariate logistic regression models a class of estimating functions is proposed for the estimation of multivariate relative risk in stratified case control studies it reduces to the well known mantel haenszel estimator when there is a single binary risk factor large sample properties of the solutions to the proposed estimating equations are established for two distinct situations efficiency calculations suggest that the proposed estimators are nearly fully efficient relative to the conditional maximum likelihood estimator for the parameters considered application of the proposed method to family data and longitudinal data where the conditional likelihood approach fails is discussed two examples from case control studies and one example from a study on familial aggregation are presented

models for longitudinal data a generalized estimating equation approach this article discusses extensions of generalized linear models for the analysis of longitudinal data two approaches are considered subject specific ss models in which heterogeneity in regression parameters is explicitly modelled and population averaged pa models in which the aggregate response for the population is the focus we use a generalized estimating equation approach to fit both classes of models for discrete and continuous outcomes when the subject specific parameters are assumed to follow a gaussian distribution simple relationships between the pa and ss parameters are available the methods are illustrated with an analysis of data on mother s smoking and children s respiratory disease

stable particle methods based on lagrangian kernels abstract a large deformation particle method based on the krongauz belytschko corrected gradient meshfree method with lagrangian kernels is developed in this form the gradient is corrected by a linear transformation so that linear completeness is satisfied for the test functions shepard functions are used this guarantees that the patch test is met lagrangian kernels are introduced to eliminate spurious distortions of the domain of material stability a mass allocation scheme is developed that captures correct reflection of waves without any explicit application of traction boundary conditions in addition the lagrangian kernel versions of various forms of smooth particle methods sph including the standard forms and the randles libersky modification are presented and studied results are obtained for a variety of problems that compare this method to standard forms of sph the randles libersky correction and large deformation versions of the element free galerkin method

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 family of multivariate binary distributions for simulating correlated binary variables with specified marginal means and correlations summary we introduce a family of multivariate binary distributions with certain conditional linear property this family is particularly useful for efficient and easy simulation of correlated binary variables with a given marginal mean vector and correlation matrix

a comparative study on finite elements for capturing strong discontinuities e fem vs x fem a comparative study on finite elements for capturing strong discontinuities by means of elemental e fem or nodal enrichments x fem is presented based on the same constitutive model continuum damage and linear elements triangles and tetrahedra optimized implementations of both types of enrichments in the same non linear code are tested for a representative set of 2d and 3d crack propagation examples it is shown that both methods provide the same qualitative and quantitative results for enough refined meshes for the performed tests e fem exhibited in general a higher accuracy mostly for coarse meshes whereas convergence rate with mesh refinement which is super linear showed slightly higher for x fem as for the computational costs for single crack modelling x fem showed depending on the case from 1 1 to about 2 5 times more expensive than e fem for multiple cracks the computational cost of e fem keeps constant whereas the cost associated to x fem increases linearly with the number of modelled cracks