a g space theory and a weakened weak w2 form for a unified formulation of compatible and incompatible methods part ii applications to solid mechanics problems in part i of this paper we have established the g space theory and fundamentals for w 2 formulation part ii focuses on the applications of the g space theory to formulate w 2 models for solid mechanics problems we first define a bilinear form prove some of the important properties and prove that the w 2 formulation will be spatially stable and convergent to exact solutions we then present examples of some of the possible w 2 models including the sfem ns fem es fem ns pim es pim and cs pim we show the major properties of these models 1 they are variationally consistent in a conventional sense if the solution is sought in a proper h space compatible cases 2 they pass the standard patch test when the solution is sought in a proper g space with discontinuous functions incompatible cases 3 the stiffness of the discretized model is reduced compared with the finite element method fem model and possibly to the exact model allowing us to obtain upper bound solutions with respect to both the fem and the exact solutions and 4 the w 2 models are less sensitive to the quality of the mesh and triangular meshes can be used without any accuracy problems these properties and theories have been confirmed numerically via examples solved using a number of w 2 models including compatible and incompatible cases we shall see that the g space theory and the w 2 forms can formulate a variety of stable and convergent numerical methods with the fem as one special case

a stabilized conforming nodal integration for galerkin mesh free methods domain integration by gauss quadrature in the galerkin mesh free methods adds considerable complexity to solution procedures direct nodal integration on the other hand leads to a numerical instability due to under integration and vanishing derivatives of shape functions at the nodes a strain smoothing stabilization for nodal integration is proposed to eliminate spatial instability in nodal integration for convergence an integration constraint ic is introduced as a necessary condition for a linear exactness in the mesh free galerkin approximation the gradient matrix of strain smoothing is shown to satisfy ic using a divergence theorem no numerical control parameter is involved in the proposed strain smoothing stabilization the numerical results show that the accuracy and convergent rates in the mesh free method with a direct nodal integration are improved considerably by the proposed stabilized conforming nodal integration method it is also demonstrated that the gauss integration method fails to meet ic in mesh free discretization for this reason the proposed method provides even better accuracy than gauss integration for galerkin mesh free method as presented in several numerical examples copyright 2001 john wiley sons ltd

hybrid smoothed finite element method for acoustic problems abstract it is well known that overly stiff finite element fe model fails to provide accurate results to the helmholtz equation with large wave numbers due to the well known pollution error caused by the numerical dispersion in this paper the hybrid smoothed finite element method hs fem using triangular 2d and tetrahedron 3d elements that can be generated automatically for any complicated domain is formulated to solve acoustic problems in order to overcome the shortcomings of standard finite element method fem in the formulation a parameter is equipped into hs fem and the strain field is further assumed to be the weighted average between compatible strains from standard fem and smoothed strains from node based smoothed finite element method ns fem the smoothing technique can provide a softening effect to the model and have a very close to exact stiffness of the continuous system and hence significantly improve the accuracy of solution in both structural and acoustic analyses intensive numerical studies have been conducted here to demonstrate the effectiveness of the hs fem

confidence intervals for probabilities and tolerance regions based on a generalization of the mann whitney statistic abstract inference procedures are proposed for any specified function of two random variables f x y assuming that independent random samples from the x and y populations are available a generalization of the mann whitney statistic is used to obtain point and interval estimates for the probability that f x y falls in a given interval one proposed confidence interval is a modification and improvement to the approach of halperin gilbert and lachin 1987 for estimating pr x y a thorough review is made of the literature on nonparametric confidence bounds for pr x y with emphasis on methods based on the central limit theorem in addition to the improvement of halperin et al s method bounds analogous to the clopper pearson confidence interval for a binomial parameter are proposed simulation results show the performance of the alternative procedures approximate nonparametric tolerance limits for f x y are also proposed the article closes by constructing a two sided tolerance interval for

time domain electromagnetic wave propagation analysis by edge based smoothed point interpolation methods in this work smoothed meshfree methods are firstly applied to numerically analyze two dimensional electromagnetic wave propagation models a weakened weak formulation based on the edges of triangular cells obtained by a delaunay triangulation is considered here framing the so called edge based smoothed domains the meshfree shape functions are computed by the radial point interpolation method rpim considering two schemes for the shape function support domains namely the t3 and the t6 scheme these schemes are based on the above mentioned triangular cells and they consider fixed numbers of nodes for the support domains a new procedure to compute the transient related matrices is discussed here aiming to be more consistent with the edge based smoothed point interpolation method in this new procedure finer local integration techniques are managed to be considered at lower computational costs rendering more accurate and efficient techniques at the end of the paper numerical examples are presented illustrating the effectiveness and potentialities of the proposed methodologies

high precision solution for thermo elastic equations using stable node based smoothed finite element method abstract the stable node based smoothed finite element method sns fem is presented to analyze thermo elastic equations with various boundary conditions the node based smoothing domains are constructed to implement numerical integrations and then the smoothed galerkin weak form is utilized to obtain the discretized system equations in the formulation both the smoothed strains and the strain variance items over the node based smoothing domains are used to perform the integration several numerical examples are studied in detail to investigate the performance of the sns fem by comparison with the original ns fem and traditional fem results show that the present sns fem can provide very high precision solution for thermo elastic equations in addition the sns fem is more efficient than original ns fem and the standard fem

a g space theory and a weakened weak w2 form for a unified formulation of compatible and incompatible methods part i theory this paper introduces a g space theory and a weakened weak form w2 using the generalized gradient smoothing technique for a unified formulation of a wide class of compatible and incompatible methods the w2 formulation works for both finite element method settings and mesh free settings and w2 models can have special properties including softened behavior upper bounds and ultra accuracy part i of this paper focuses on the theory and fundamentals for w2 formulations a normed g space is first defined to include both continuous and discontinuous functions allowing the use of much more types of methods techniques to create shape functions for numerical models important properties and a set of useful inequalities for g spaces are then proven in the theory and analyzed in detail these properties ensure that a numerical method developed based on the w2 formulation will be spatially stable and convergent to the exact solutions as long as the physical problem is well posed the theory is applicable to any problems to which the standard weak formulation is applicable and can offer numerical solutions with special properties including close to exact stiffness upper bounds and ultra accuracy copyright 2009 john wiley sons ltd

a stable nodal integration method for static and quasi static electromagnetic field computation a stable nodal integration method snim is presented to solve static and quasi static electromagnetic problems in this paper the analysis domain is firstly discretized into a set of triangular or tetrahedral elements and linear interpolation is adopted within each element a weakened weak formulation based on the nodes is further considered framing the so called node based smoothing domains equivalent smoothing domains are then acquired as circular or spherical regions where the gradient of shape function is expanded as the first order taylor form subsequently four or six temporary integration points on the region are picked to obtain items of the stiffness matrix and the external load vector by simplifying the equations the stiffness matrix can be received in quite concise form with one point integration and stabilization terms which are calculated on original node based smoothing domains the implementation of snim on electromagnetic problems is thus realized the proposed formulation is validated against both analytical solutions and traditional methods and its effectiveness and potentialities can be well represented and clarified by numerical examples

two sample tests and one way manova for multivariate biomarker data with nondetects testing whether the mean vector of a multivariate set of biomarkers differs between several populations is an increasingly common problem in medical research biomarker data is often left censored because some measurements fall below the laboratory s detection limit we investigate how such censoring affects multivariate two sample and one way multivariate analysis of variance tests type i error rates power and robustness to increasing censoring are studied under both normality and non normality parametric tests are found to perform better than non parametric alternatives indicating that the current recommendations for analysis of censored multivariate data may have to be revised copyright 2016 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

computer aided determination of stability robustness measure of linear discrete time systems abstract in this paper several upper bounds for parameter variations of a linear discrete time system that is expressed in either matrix or polynomial form are presented within these upper bounds the system remains asymptotically stable these upper bounds which are only a set of sufficient conditions are then used iteratively in a computer aided algorithm to reach to the largest numerical such upper bounds the largest numerical upper bound is called the stability robustness measure of the discrete time dynamic system

adaptive stabilization of time varying discrete time linear systems we develop an adaptive control technique for the regulation of a class of linear discrete time time varying system the only a priori knowledge required is a bound of the varying component of the parameters the result is concerned with global behaviour

immersed smoothed finite element method for two dimensional fluid structure interaction problems summary a novel method called immersed smoothed fem using three node triangular element is proposed for two dimensional fluid structure interaction fsi problems with largely deformable nonlinear solids placed within incompressible viscous fluid the fluid flows are solved using the semi implicit characteristic based split method smoothed fems are employed to calculate the transient responses of solids based on explicit time integration the fictitious fluid with two assumptions is introduced to achieve the continuous form of the fsi conditions the discrete formulations to calculate the fsi forces are obtained in terms of the characteristic based split scheme and the algorithm based on a set of fictitious fluid mesh is proposed for evaluating the fsi force exerted on the solid the accuracy stability and convergence properties of immersed smoothed fem are verified by numerical examples investigations on the mesh size ratio indicate that the stability is fairly independent of the wide range of the mesh size ratio no additional volume correction is required to satisfy the incompressible constraints copyright 2012 john wiley sons ltd

a thin plate formulation without rotation dofs based on the radial point interpolation method and triangular cells a formulation for thin plates with only the deflection as nodal variables has been proposed using the generalized gradient smoothing technique and the radial point interpolation method rpim the deflection fields are approximated using the rpim shape functions which possess the kronecker delta property for easy impositions of essential boundary conditions three types of smoothing domains which are also serving as the numerical integrations domains are constructed based on the background three node triangular cells and the generalized gradient smoothing operation is performed over each of them to obtain the smoothed curvatures the generalized smoothed galerkin weak form is then used to create the discretized system equations the essential boundary conditions of rotations are imposed in the process of constructing the curvature field and the translation boundary conditions are imposed as in the standard fem a number of numerical examples including both static and free vibration analysis are studied using the present methods and the numerical results are compared with the analytical ones and those in the open literatures the results show that the present formulation can obtain very stable and accurate solutions even for the extremely irregular background cells

a stable node based smoothed finite element method for acoustic problems abstract it is well known that the classical overly soft node based smoothed finite element method ns fem fails to provide reliable results to the helmholtz equation due to the temporal instability to cure the fatal drawback of ns fem and reduce the dispersion error in computational acoustics this paper proposed a stable node based smoothed finite element method sns fem for analyzing acoustic problems using linear triangular for 2d space and tetrahedral for 3d space elements that can be generated automatically for any complicated configurations in the present formulation the system stiffness matrix is computed using the smoothed acoustic pressure gradients together with the gradient variance items over the smoothing domains associated with nodes of element mesh it turns out the addition of stabilization term makes the sns fem possess an ideal stiffness thus successfully cures the temporal instability and significantly reduces the dispersion error in acoustic problems numerical examples including both benchmark cases and practical engineering problems demonstrate that the sns fem possesses the following important properties 1 temporal stability 2 super accuracy and super convergence 3 higher computational efficiency 4 insensitive to mesh distortion

estimation of the area under the roc curve the area under the receiver operating characteristic curve is frequently used as a measure for the effectiveness of diagnostic markers in this paper we discuss and compare estimation procedures for this area these are based on i the mann whitney statistic ii kernel smoothing iii normal assumptions iv empirical transformations to normality these are compared in terms of bias and root mean square error in a large variety of situations by means of an extensive simulation study overall we find that transforming to normality usually is to be preferred except for bimodal cases where kernel methods can be effective

an enhanced cell based smoothed finite element method for the analysis of reissner mindlin plate bending problems involving distorted mesh summary in this work an enhanced cell based smoothed finite element method fem is presented for the reissner mindlin plate bending analysis the smoothed curvature computed by a boundary integral along the boundaries of smoothing cells in original smoothed fem is reformulated and the relationship between the original approach and the present method in curvature smoothing is established to improve the accuracy of shear strain in a distorted mesh we span the shear strain space over the adjacent element this is performed by employing an edge based smoothing technique through a simple area weighted smoothing procedure on mitc4 assumed shear strain field a three field variational principle is utilized to develop the mixed formulation the resultant element formulation is further reduced to a displacement based formulation via an assumed strain method defined by the edge smoothing technique as the result a new formulation consisting of smoothed curvature and smoothed shear strain interpolated by the standard transverse displacement rotation fields and smoothing operators can be shown to improve the solution accuracy in cell based smoothed fem for reissner mindlin plate bending analysis several numerical examples are presented to demonstrate the accuracy of the proposed formulation copyright 2013 john wiley sons ltd

theoretical aspects of the smoothed finite element method sfem this paper examines the theoretical bases for the smoothed finite element method sfem which was formulated by incorporating cell wise strain smoothing operation into standard compatible finite element method fem the weak form of sfem can be derived from the hu washizu three field variational principle for elastic problems it is proved that 1d linear element and 2d linear triangle element in sfem are identical to their counterparts in fem while 2d bilinear quadrilateral elements in sfem are different from that of fem when the number of smoothing cells scs of the elements equals 1 the sfem solution is proved to be variationally consistent and has the same properties with those of fem using reduced integration when sc approaches infinity the sfem solution will approach the solution of the standard displacement compatible fem model when sc is a finite number larger than 1 the sfem solutions are not variationally consistent but energy consistent and will change monotonously from the solution of sfem sc 1 to that of sfem sc it is suggested that there exists an optimal number of sc such that the sfem solution is closest to the exact solution the properties of sfem are confirmed by numerical examples copyright 2006 john wiley sons ltd

an edge based smoothed finite element method for 3d analysis of solid mechanics problems summary the edge based smoothed finite element method es fem was proposed recently in liu nguyen thoi and lam to improve the accuracy of the fem for 2d problems this method belongs to the wider family of the smoothed fem for which smoothing cells are defined to perform the numerical integration over the domain later the face based smoothed fem fs fem was proposed to generalize the es fem to 3d problems according to this method the smoothing cells are centered along the faces of the tetrahedrons of the mesh in the present paper an alternative method for the extension of the es fem to 3d is investigated this method is based on an underlying mesh composed of tetrahedrons and the approximation of the field variables is associated with the tetrahedral elements however in contrast to the fs fem the smoothing cells of the proposed es fem are centered along the edges of the tetrahedrons of the mesh from selected numerical benchmark problems it is observed that the es fem is characterized by a higher accuracy and improved computational efficiency as compared with linear tetrahedral elements and to the fs fem for a given number of degrees of freedom copyright 2013 john wiley sons ltd

a rotation free shell formulation using nodal integration for static and dynamic analyses of structures summary this paper proposed a rotation free thin shell formulation with nodal integration for elastic static free vibration and explicit dynamic analyses of structures using three node triangular cells and linear interpolation functions the formulation is based on the classic kirchhoff plate theory in which only three translational displacements are treated as the filed variables based on each node the integration domains are further formed where the generalized gradient smoothing technique and green divergence theorem that can relax the continuity requirement for trial function are used to construct the curvature filed with the aid of strain smoothing operation and tensor transformation rule the smoothed strains in the integration domain can be finally expressed by constants the principle of virtual work is then used to establish the discretized system equations the translational boundary conditions are imposed same as the practice of standard finite element method while the rotational boundary conditions are constrained in the process of constructing the smoothed curvature filed to test the performance of the present formulation several numerical examples including both benchmark problems and practical engineering cases are studied the results demonstrate that the present method possesses better accuracy and higher efficiency for both static and dynamic problems copyright 2015 john wiley sons ltd

regression for skewed biomarker outcomes subject to pooling epidemiological studies involving biomarkers are often hindered by prohibitively expensive laboratory tests strategically pooling specimens prior to performing these lab assays has been shown to effectively reduce cost with minimal information loss in a logistic regression setting when the goal is to perform regression with a continuous biomarker as the outcome regression analysis of pooled specimens may not be straightforward particularly if the outcome is right skewed in such cases we demonstrate that a slight modification of a standard multiple linear regression model for poolwise data can provide valid and precise coefficient estimates when pools are formed by combining biospecimens from subjects with identical covariate values when these x homogeneous pools cannot be formed we propose a monte carlo expectation maximization mcem algorithm to compute maximum likelihood estimates mles simulation studies demonstrate that these analytical methods provide essentially unbiased estimates of coefficient parameters as well as their standard errors when appropriate assumptions are met furthermore we show how one can utilize the fully observed covariate data to inform the pooling strategy yielding a high level of statistical efficiency at a fraction of the total lab cost

a point interpolation method for two dimensional solids a point interpolation method pim is presented for stress analysis for two dimensional solids in the pim the problem domain is represented by properly scattered points a technique is proposed to construct polynomial interpolants with delta function property based only on a group of arbitrarily distributed points the pim equations are then derived using variational principles in the pim the essential boundary conditions can be implemented with ease as in the conventional finite element methods the present pim has been coded in fortran the validity and efficiency of the present pim formulation are demonstrated through example problems it is found that the present pim is very easy to implement and very flexible for obtained displacements and stresses of desired accuracy in solids as the elements are not used for meshing the problem domain the present pim opens new avenues to develop adaptive analysis codes for stress analysis in solids and structures copyright 2001 john wiley sons ltd

a face based smoothed finite element method fs fem for 3d linear and geometrically non linear solid mechanics problems using 4 node tetrahedral elements this paper presents a novel face based smoothed finite element method fs fem to improve the accuracy of the finite element method fem for three dimensional 3d problems the fs fem uses 4 node tetrahedral elements that can be generated automatically for complicated domains in the fs fem the system stiffness matrix is computed using strains smoothed over the smoothing domains associated with the faces of the tetrahedral elements the results demonstrated that the fs fem is significantly more accurate than the fem using tetrahedral elements for both linear and geometrically non linear solid mechanics problems in addition a novel domain based selective scheme is proposed leading to a combined fs ns fem model that is immune from volumetric locking and hence works well for nearly incompressible materials the implementation of the fs fem is straightforward and no penalty parameters or additional degrees of freedom are used the computational efficiency of the fs fem is found better than that of the fem copyright 2008 john wiley sons ltd

parameter space methods for robust control design a guided tour the results obtained in studies of robust stability and stabilizability of control systems with parametric structured uncertainties are reviewed both the algebraic methods based upon characteristic equations and the methods using lyapunov functions and riccati equations are discussed and compared in the context of algebraic methods most promising are the kharitonov type approach and the optimization procedure of embedding a geometric figure of some kind inside the stability regions of the parameter space maximizing its size using minimax or some other mathematical programming technique in the framework of lyapunov s direct method the dominant approach has been a quadratic function estimation of stability regions in the parameter space in large sale systems the concept of vector lyapunov functions has been used with the possibility of choosing quadratic forms norm like functions and their combinations

an edge based smoothed finite element method es fem for static free and forced vibration analyses of solids abstract this paper presents an edge based smoothed finite element method es fem to significantly improve the accuracy of the finite element method fem without much changing to the standard fem settings the es fem can use different shape of elements but prefers triangular elements that can be much easily generated automatically for complicated domains in the es fem the system stiffness matrix is computed using strains smoothed over the smoothing domains associated with the edges of the triangles intensive numerical results demonstrated that the es fem possesses the following excellent properties 1 the es fem model possesses a close to exact stiffness it is much softer than the overly stiff fem and much stiffer than the overly soft ns fem model 2 the results are often found superconvergence and ultra accurate much more accurate than the linear triangular elements of fem and even more accurate than those of the fem using quadrilateral elements with the same sets of nodes 3 there are no spurious non zeros energy modes found and hence the method is also temporally stable and works well for vibration analysis and 4 the implementation of the method is straightforward and no penalty parameter is used and the computational efficiency is better than the fem using the same sets of nodes in addition a novel domain based selective scheme is proposed leading to a combined es ns fem model that is immune from volumetric locking and hence works very well for nearly incompressible materials these properties of the es fem are confirmed using examples of static free and forced vibration analyses of solids

extended finite element method with edge based strain smoothing esm xfem for linear elastic crack growth abstract this paper presents a strain smoothing procedure for the extended finite element method xfem the resulting edge based smoothed extended finite element method esm xfem is tailored to linear elastic fracture mechanics and in this context to outperform the standard xfem in the xfem the displacement based approximation is enriched by the heaviside and asymptotic crack tip functions using the framework of partition of unity this eliminates the need for the mesh alignment with the crack and re meshing as the crack evolves edge based smoothing es relies on a generalized smoothing operation over smoothing domains associated with edges of simplex meshes and produces a softening effect leading to a close to exact stiffness super convergence and ultra accurate solutions the present method takes advantage of both the es fem and the xfem thanks to the use of strain smoothing the subdivision of elements intersected by discontinuities and of integrating the singular derivatives of the approximation functions is suppressed via transforming interior integration into boundary integration numerical examples show that the proposed method improves significantly the accuracy of stress intensity factors and achieves a near optimal convergence rate in the energy norm even without geometrical enrichment or blending correction

stability robustness analysis of discrete time systems with multiple large parameter variations abstract a method is presented to construct the largest set of parameter variations for any asymptotically stable convergent matrix whose corresponding set of perturbed matrices remains stable

a novel reduced basis method with upper and lower bounds for real time computation of linear elasticity problems abstract this paper presents a novel reduced basis method for analyzing problems of linear elasticity in a systematical rapid and reliable fashion for solutions with both upper and lower bounds to the exact solution in the form of energy norm or compliance output the lower bound of the solution output is obtained form the well known reduced basis method based on the galerkin projection used in the finite element method which is termed as gp rbm for the upper bound a new reduced basis approach is developed by the combination of the reduced basis method and a smoothed galerkin projection used in the linearly conforming point interpolation method and it is thus termed as sgp rbm to examine the present sgp rbm we first conduct a theoretical study on the very important upper bound property reduced basis models for both gp rbm and sgp rbm are constructed with the aid of an asymptotic error estimation and greedy adaptive procedure the gp rbm and the newly proposed sgp rbm are applied to analyze a cantilever beam with an oblique crack to verify the proposed rbm technique in terms of accuracy convergence bound properties and computational savings both theoretical analysis and numerical results have demonstrated that the present method is a very efficient method for real time solutions providing exact output bounds

proofs of the stability and convergence of a weakened weak method using pim shape functions recently the smoothed point interpolation method s pim regarded as a weakened weak w 2 formulation method has been developed for solving engineering mechanics problems it works well with distorted meshes the g space theory offers the theoretical base for all the w 2 methods that use smoothing operations in this paper we first prove mathematically that if a function is of lipschitz continuity and its interpolated function is established using pim shape functions then the interpolated function belongs to a g h 0 s space our proofs work for smoothing operations that are the node based cell based and a mixture of both smoothing domains in addition when mesh is refined under a given regularity condition a sufficiently smooth target function can be approximated by its interpolated function with arbitrary accuracy meaning that the interpolation error norm approaches to zero therefore the stability and convergence of a w 2 method using pim shape functions and g space theory can be ensured

technical communique robustness measures in nonlinear discrete time systems with delays and large parameter variations certain aspects of constructing the largest class of asymptotically convergent stable systems which surrounds a convergent system with nonlinearity and delays and subject to large parameter variations are presented both the magnitude and computational efficiency of generating these results which are based on the corresponding results from linear systems are presented here three numerical examples namely i linear systems with linear multiple parameter variations ii nonlinear systems with linear multipleparameter variations and multiple nonlinearities and iii linear systems with multiple nonlinear parameter variations are given to show applications of the underlying results these building blocks examples can be assembled to solve a complicated nonlinear discrete time system with delays involving all the above variations

a point interpolation meshless method based on radial basis functions a point interpolation meshless method is proposed based on combining radial and polynomial basis functions involvement of radial basis functions overcomes possible singularity associated with the meshless methods based on only the polynomial basis this non singularity is useful in constructing well performed shape functions furthermore the interpolation function obtained passes through all scattered points in an influence domain and thus shape functions are of delta function property this makes the implementation of essential boundary conditions much easier than the meshless methods based on the moving least squares approximation in addition the partial derivatives of shape functions are easily obtained thus improving computational efficiency examples on curve surface fittings and solid mechanics problems show that the accuracy and convergence rate of the present method is high copyright 2002 john wiley sons ltd

assessment of skewed exposure in case control studies with pooling pooling based strategies that combine samples from multiple participants for laboratory assays have been proposed for epidemiologic investigations of biomarkers to address issues including cost efficiency detection and when minimal sample volume is available a modification of the standard logistic regression model has been previously described to allow use with pooled data however this model makes assumptions regarding exposure distribution and logit linearity of risk i e constant odds ratio that can be violated in practice we were motivated by a nested case control study of miscarriage and inflammatory factors with highly skewed distributions to develop a more flexible model for analysis of pooled data using characteristics of the gamma distribution and the relation between models of binary outcome conditional on exposure and of exposure conditional on outcome we use a modified logistic regression to accommodate non linearity due to unequal shape parameters in gamma distributed exposure for cases and controls using simulations we compare our approach with existing methods for logistic regression for pooled data considering 1 constant and dose dependent effects 2 gamma and log normal distributed exposure 3 effect size and 4 the proportions of biospecimens pooled we show that our approach allows estimation of odds ratios that vary with exposure level yet has minimal loss of efficiency compared to existing approaches when exposure effects are dose invariant our model performed similarly to a maximum likelihood estimation approach in terms of bias and efficiency and provides an easily implemented approach for estimation with pooled biomarker data when effects may not be constant across exposure

dispersion error reduction for acoustic problems using the edge based smoothed finite element method es fem the paper reports a detailed analysis on the numerical dispersion error in solving 2d acoustic problems governed by the helmholtz equation using the edge based smoothed finite element method es fem in comparison with the standard fem it is found that the dispersion error of the standard fem for solving acoustic problems is essentially caused by the overly stiff feature of the discrete model in such an overly stiff fem model the wave propagates with an artificially higher numerical speed and hence the numerical wave number becomes significantly smaller than the actual exact one owing to the proper softening effects provided naturally by the edge based gradient smoothing operations the es fem model however behaves much softer than the standard fem model leading to the so called very close to exact stiffness therefore the es fem can naturally and effectively reduce the dispersion error in the numerical solution in solving acoustic problems results of both theoretical and numerical studies will support these important findings it is shown clearly that the es fem suits ideally well for solving acoustic problems governed by the helmholtz equations because of the crucial effectiveness in reducing the dispersion error in the discrete numerical model

a sub domain smoothed galerkin method for solid mechanics problems summary a sub domain smoothed galerkin method is proposed to integrate the advantages of mesh free galerkin method and fem arbitrarily shaped sub domains are predefined in problems domain with mesh free nodes in each sub domain based on mesh free galerkin weak formulation the local discrete equation can be obtained by using the moving kriging interpolation which is similar to the discretization of the high order finite elements strain smoothing technique is subsequently applied to the nodal integration of sub domain by dividing the sub domain into several smoothing cells moreover condensation of dof can also be introduced into the local discrete equations to improve the computational efficiency the global governing equations of present method are obtained on the basis of the scheme of fem by assembling all local discrete equations of the sub domains the mesh free properties of galerkin method are retained in each sub domain several 2d elastic problems have been solved on the basis of this newly proposed method to validate its computational performance these numerical examples proved that the newly proposed sub domain smoothed galerkin method is a robust technique to solve solid mechanics problems based on its characteristics of high computational efficiency good accuracy and convergence copyright 2014 john wiley sons ltd

a linearly conforming point interpolation method lc pim for three dimensional elasticity problems linearly conforming point interpolation method lc pim is formulated for three dimensional elasticity problems in this method shape functions are generated using point interpolation method by adopting polynomial basis functions and local supporting nodes are selected based on the background cells the shape functions so constructed have the kronecker delta functions property and it allows straightforward imposition of point essential boundary conditions galerkin weak form is used for creating discretized system equations and a nodal integration scheme with strain smoothing operation is used to perform the numerical integration the present lc pim can guarantee linear exactness and monotonic convergence for the numerical results numerical examples are used to examine the present method in terms of accuracy convergence and efficiency compared with the finite element method using linear elements the lc pim can achieve better efficiency and higher accuracy especially for stresses copyright 2007 john wiley sons ltd

upper bound solution to elasticity problems a unique property of the linearly conforming point interpolation method lc pim it is well known that the displacement based fully compatible finite element method fem provides a lower bound in energy norm for the exact solution to elasticity problems it is however much more difficult to bound the solution from above for general problems in elasticity and it has been a dream of many decades to find a systematical way to obtain such an upper bound this paper presents a very important and unique property of the linearly conforming point interpolation method lc pim it provides a general means to obtain an upper bound solution in energy norm for elasticity problems this paper conducts first a thorough theoretical study on the lc pim we derive its weak form based on variational principles study a number of properties of the lc pim and prove that lc pim is variationally consistent and that it produces upper bound solutions we then demonstrate these properties through intensive numerical studies with many examples of 1d 2d and 3d problems using the lc pim together with the fem we now have a systematical way to numerically obtain both upper and lower bounds of the exact solution to elasticity problems as shown in these example problems copyright 2007 john wiley sons ltd

a stabilized finite element method for certified solution with bounds in static and frequency analyses of piezoelectric structures abstract this paper develops a stabilization procedure in piezoelectric media to ensure the temporal stability of node based smoothed finite element method ns fem and applies it to obtain certified solution with bounds in both static and frequency analyses of piezoelectric structures using three node triangular elements for such stabilized ns fem two stabilization terms corresponding to squared residuals of two equilibrium equations i e mechanical stress equilibrium and electric displacement equilibrium are added into the smoothed potential energy functional of the original ns fem a gradient smoothing operation is then performed on second order derivatives of shape functions to achieve the stabilization terms due to the use of divergence theory the smoothing operation relaxes the requirement of shape functions so that the square residuals can be evaluated using linear elements the effectiveness of the present stabilized ns fem is demonstrated via numerical examples

an accurate and efficient scheme for acoustic structure interaction problems based on unstructured mesh abstract this paper focuses on the accurate and efficient numerical implementation of acoustic structure coupling formulations using the edge based smoothed finite element method for the flexible shell and the gradient weighted finite element method for the acoustic fluid field namely the es gw fem the shell is discretized using the simplest linear triangular elements and the edge based smoothing domain is then constructed by introducing an edge local coordinate system the edge based smoothing operation is performed on the smoothing domain as for the acoustic fluid domain the tetrahedron elements are adopted a compacted support domain is then constructed and the gradient weighted operation is performed on the support domain to model the exterior acoustic domain an artificial boundary is introduced and the dirichlet to neumann dtn boundary condition is imposed based on the appropriate compatibility and equilibrium conditions on the interface boundaries the coupled es gw fem formulation is finally obtained both the interior acoustic structure coupled problems and exterior acoustic structure coupled problems are available as the dtn boundary is considered numerical examples demonstrate that the coupled es gw fem achieves much higher accuracy and works more reliably compared with the coupled fem fem in solving practical engineering problems

a cell based smoothed finite element method for multi body contact analysis using linear complementarity formulation abstract in this paper the cell based smoothed finite element using quadrilateral elements cs fem is used for 2d contact problems which are converted into linear complementarity problems lcps which can be solved efficiently using the lemke method the modified coulomb friction contact model with tangential strength and normal adhesion is considered which models sticking slipping contacting departing and bonding debonding processes in a unified formulation smoothed galerkin weak form with contact boundary is deduced in which the stiffness is implemented using the cs fem with 1 smoothing domain 1sd 2sd 3sd 4sd 8sd and 16sd for each element contact interface equations are discretized through contact point pairs that are constructed using a master slave surface algorithm intensive numerical examples are given to investigate the effects of contact parameters on contact behaviors and examine the effectiveness of the proposed approach the numerical results of cs fem models are compared with that of fem q4 model which demonstrates that all cs fem models are softer than fem q4 model the strain energy solutions obtained using several cs fem models are monotonically decreasing with the number of the sds for each element increasing the upper bound solutions in strain energy can be obtained using a cs fem 1sd model in our examples while the lower bound solutions are obtained using cs fem 16sd model or fem q4 with fem q4 solution being the lowest

the meshless galerkin boundary node method for stokes problems in three dimensions the galerkin boundary node method gbnm is a boundary only meshless method that combines an equivalent variational formulation of boundary integral equations for governing equations and the moving least squares mls approximations for generating the trial and test functions in this approach boundary conditions can be implemented directly and easily despite of the fact that the mls shape functions lack the delta function property besides the resulting formulation inherits the symmetry and positive definiteness of the variational problems the gbnm is developed in this paper for solving three dimensional stationary incompressible stokes flows in primitive variables the numerical scheme is based on variational formulations for the first kind integral equations which are valid for both interior and exterior problems simultaneously a rigorous error analysis and convergence study of the method for both the velocity and the pressure is presented in sobolev spaces the capability of the method is also illustrated and assessed through some selected numerical examples copyright 2011 john wiley sons ltd

a fully smoothed xfem for analysis of axisymmetric problems with weak discontinuities in this paper we propose a fully smoothed extended finite element method for axisymmetric problems with weak discontinuities the salient feature of the proposed approach is that all the terms in the stiffness and mass matrices can be computed by smoothing technique this is accomplished by combining the gaussian divergence theorem with the evaluation of indefinite integral based on smoothing technique which is used to transform the domain integral into boundary integral the proposed technique completely eliminates the need for isoparametric mapping and the computing of jacobian matrix even for the mass matrix when employed over the enriched elements the proposed technique does not require sub triangulation for the purpose of numerical integration the accuracy and convergence properties of the proposed technique are demonstrated with a few problems in elastostatics and elastodynamics with weak discontinuities it can be seen that the proposed technique yields stable and accurate solutions and is less sensitive to mesh distortion

a stabilised mixed meshfree method for incompressible media application to linear elasticity and stokes flow abstract this paper addresses some problems of modelling incompressible media using meshfree methods with a stabilised mixed formulation the aims of this paper are twofold to avoid the volumetric locking that occurs at the incompressible limit and to circumvent the inf sup condition while approximating both displacement and pressure with the same set of nodes and shape functions we employ a modified polynomial pressure projection stabilisation method to stabilise and filter spurious pressure modes where the gradient is corrected as proposed by duan et al 2014 the gradient correction is used to counteract the lack of variational consistency when numerical integration of the rational shape functions is performed a threat that could undermine the stabilisation effort the resulting novel method passes the mixed patch tests and is demonstrated to be effective and optimally accurate in linear elasticity and stokes flow test cases

roc curve analysis for biomarkers based on pooled assessments interleukin 6 is a biomarker of inflammation which has been suggested as having potential discriminatory ability for myocardial infarction because of its high assaying cost it is very expensive to evaluate this marker in order to reduce this cost we propose pooling the specimens in this paper we examine the efficiency of roc curve analysis specifically the estimation of the area under the roc curve when dealing with pooled data we study the effect of pooling when there are only a fixed number of individuals available for testing and pooling is carried out to save on the number of assays alternatively we examine how many pooled assays of size g are necessary to provide essentially the same information as n individual assays we measure loss of information by means of the change in root mean square error of the estimate of the area under the roc curve and study the extent of this loss via a simulation study

an adaptive singular es fem for mechanics problems with singular field of arbitrary order this paper presents a singular edge based smoothed finite element method ses fem for mechanics problems with singular stress fields of arbitrary order the ses fem uses a basic mesh of three noded linear triangular t3 elements and a special layer of five noded singular triangular elements st5 connected to the singular point of the stress field the st5 element has an additional node on each of the two edges connected to the singular point it allows us to represent simple and efficient enrichment with desired terms for the displacement field near the singular point with the satisfaction of partition of unity property the stiffness matrix of the discretized system is then obtained using the assumed displacement values not the derivatives over smoothing domains associated with the edges of elements an adaptive procedure for the ses fem is proposed to enhance the quality of the solution with minimized number of nodes several numerical examples are provided to validate the reliability of the present ses fem method c 2012 elsevier b v all rights reserved

on stability convergence and accuracy of bes fem and bfs fem for nearly incompressible elasticity abstract we present in this paper a rigorous theoretical framework to show stability convergence and accuracy of improved edge based and face based smoothed finite element methods bes fem and bfs fem for nearly incompressible elasticity problems the crucial idea is that the space of piecewise linear polynomials used for the displacements is enriched with bubble functions on each element while the pressure is a piecewise constant function the meshes of triangular or tetrahedral elements required by these methods can be generated automatically the enrichment induces a softening in the bilinear form allowing the weakened weak w 2 procedure to produce a high quality solution free from locking and that does not oscillate we prove theoretically that both methods confirm the uniform inf sup and convergence conditions four numerical examples are given to validate the reliability of the bes fem and bfs fem

a strain constructed point interpolation method and strain field construction schemes for solid mechanics problems using triangular mesh abstract this paper presents a strain constructed point interpolation method sc pim for solid mechanics problems using three node triangular mesh in the sc pim the point interpolation method pim is used to construct both displacement and strain fields a total of 14 schemes are proposed to construct strain fields that are equivalent to the compatible strain fields in energy norm and therefore the strain constructed galerkin sc galerkin weak form can be used to form the discretized system equations in these schemes strains at critical points vertices of the triangular integration cells are first obtained using the generalized strain smoothing techniques over the node based and or edge based smoothing domains and constructed strain fields in the integration cells are then obtained using linear interpolations a sc pim model using any of the 14 schemes is stable and convergent but not necessarily to the exact solution standard numerical patch tests are conducted to find six linearly conforming schemes converging to the exact solution benchmark problems have been studied to investigate the performance and properties of the sc pim with all these six conforming schemes outstanding schemes have been identified with better accuracy and high convergence rates in terms of both displacement and energy norms

an element free smoothed radial point interpolation method efs rpim for 2d and 3d solid mechanics problems abstract this paper presents a novel element free smoothed radial point interpolation method efs rpim for solving 2d and 3d solid mechanics problems the idea of the present technique is that field nodes and smoothing cells scs used for smoothing operations are created independently and without using a background grid which saves tedious mesh generation efforts and makes the pre process more flexible in the formulation we use the generalized smoothed galerkin gs galerkin weak form that requires only discrete values of shape functions that can be created using the rpim by varying the amount of nodes and scs as well as their ratio the accuracy can be improved and upper bound or lower bound solutions can be obtained by design the scs can be of regular or irregular polygons in this work we tested triangular quadrangle n sided polygon and tetrahedron as examples stability condition is examined and some criteria are found to avoid the presence of spurious zero energy modes this paper is the first time to create gs galerkin weak form models without using a background mesh that tied with nodes and hence the efs rpim is a true meshfree approach the proposed efs rpim is so far the only technique that can offer both upper and lower bound solutions numerical results show that the efs rpim gives accurate results and desirable convergence rate when comparing with the standard finite element method fem and the cell based smoothed fem cs fem