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

variational and projection methods for the volume constraint in finite deformation elasto plasticity this paper focuses on the treatment of volume constraints which in the context of elasto plasticity typically arise as a result of assuming volume preserving plastic flow projection methods based on the modification of the discrete gradient operator b often proposed on an ad hoc basis are systematically obtained in the variational context furnished by a three field hu washizu principle the fully nonlinear formulation proposed here is based on a local multiplicative split of the deformation gradient into volume preserving and dilatational parts without relying on rate forms of the weak form of momentum balance this approach fits naturally in a formulation of plasticity based on the multiplicative decomposition of the deformation gradient and enables one to exactly enforce the condition of volume preserving plastic flow within the framework proposed in this paper rate forms and incrementally objective algorithms are entirely bypassed

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

discrete gradient method over polygon mesh this paper presents a discrete method over domains originally discretized by polygons including triangle quadrilateral and general n sided polygon elements in this method the domain is re partitioned into node based cells at each node the gradient of a physical variable is approximated using a linearly exact discrete operator that involves a set of neighboring nodes the discrete gradient is subsequently substituted into a weak form to yield a nodal integration galerkin formulation a unified geometric approach is provided for constructing the gradient operators over an arbitrary polygon mesh the method does not introduce continuous approximation of the unknown variable therefore the numerical computation is very simple the linear displacement patch test is satisfied by construction numerical tests show that the method has comparable accuracy and convergence rate as the displacement finite element method examples are also included to illustrate the ability to resist numerical locking in the incompressibility limit and the thin element limit copyright 2008 john wiley sons ltd

design of simple low order finite elements for large strain analysis of nearly incompressible solids a simple four node quadrilateral and an eight node hexahedron for large strain analysis of nearly incompressible solids are proposed based on the concept of deviatoric volumetric split and the replacement of the compatible deformation gradient with an assumed modified counterpart the formulation developed is applicable to arbitrary material models the closed form of the corresponding exact tangent stiffnesses which have a particularly simple structure is derived it ensures asymptotically quadratic rates of convergence of the newton raphson scheme employed in the solution of the implicit finite element equilibrium equations from a practical point of view the incorporation of the proposed elements into existing codes is straightforward it requires only small changes in the routines of the standard displacement based 4 node quadrilateral and 8 node brick a comprehensive set of numerical examples involving hyperelasticity as well as multiplicative elasto plasticity is provided it illustrates the performance of the proposed elements over a wide range of applications including strain localisation problems metal forming simulation and adaptive analysis

patch averaged assumed strain finite elements for stress analysis summary a finite element model for linear elastic small deformation problems is presented the formulation is based on a weighted residual that requires a priori the satisfaction of the kinematic equation in this approach an averaged strain displacement matrix is constructed for each node of the mesh by defining an appropriate patch of elements yielding a smooth representation of strain and stress fields connections with traditional and similar procedure are explored linear quadrilateral four node and linear hexahedral eight node elements are derived various numerical tests show the accuracy and convergence properties of the proposed elements in comparison with extant finite elements and analytic solutions specific examples are also included to illustrate the ability to resist numerical locking in the incompressible limit and insensitive response in the presence of shape distortion furthermore the numerical inf sup test is applied to a selection of problems to show the stability of the present formulation copyright 2012 john wiley sons ltd

second order statistics of logarithmic quantization noise in qam data communication when a qam quadrature amplitude modulation data signal is transmitted over a channel that includes pcm codecs it has frequently been observed and shown that the resulting noise around the final received constellation points grows with the distance of the point from the origin the authors extend the analysis of this effect and further show that the noise distribution about each point is elliptical with greater variance in the radial direction formulas giving the signal dependent noise components as a function of the channel characteristics of the analog transmit and receive access legs are derived experimental results confirm the analysis

non linear version of stabilized conforming nodal integration for galerkin mesh free methods a stabilized conforming sc nodal integration which meets the integration constraint in the galerkin meshfree approximation is generalized for nonlinear problems in sc nodal integration a strain smoothing stabilization is introduced and applied to the deformation gradient using a lagrangian meshfree discretization the assumed strain method expressed in terms of deformation gradient is employed to formulate an efficient meshfree discrete equation for nonlinear problems a significant gain in computational efficiency is achieved as well as enhanced accuracy in comparison to the solution of meshfree method using gauss integration method the performance of the proposed method appears to be quite robust when dealing with irregular discretization

asymptotic iterated bootstrap confidence intervals an iterated bootstrap confidence interval requires an additive correction to be made to the nominal coverage level of an uncorrected interval such correction is usually performed using a computationally intensive monte carlo simulation involving two nested levels of bootstrap sampling asymptotic expansions of the required correction and the iterated interval endpoints are used to provide two new computationally efficient methods for constructing an approximation to the iterated bootstrap confidence interval the first asymptotic interval replaces the need for a second level of bootstrap sampling with a series of preliminary analytic calculations which are readily automated and from which an approximation to the coverage correction is easily obtained the second interval directly approximates the endpoints of the iterated interval and yields for the first time the possibility of constructing an approximation to an iterated bootstrap confidence interval which does not require any resampling the theoretical properties of the two intervals are considered the computation required for their construction is detailed and has been coded in a fully automatic user friendly fortran program which may be obtained by anonymous ftp a simulation study which illustrates their effectiveness on three examples is presented

consistent pseudo derivatives in meshless methods a meshless petrov galerkin formulation is developed in which derivatives of the trial functions are obtained as a linear combination of derivatives of shepard functions a key contribution is the development of conditions on test functions and trial functions for nonintegrable pseudo derivatives for petrov galerkin method which pass the patch test numerical results show that the resulting method is substantially more accurate than the galerkin method with shepard approximants and exceeds the rate of convergence of linear finite elements

calibrating confidence coefficients abstract two approaches for dealing with the problem of poor coverage probabilities of certain standard confidence intervals are proposed the first is a recommendation that the actual coverage be estimated directly from the data and its value reported in addition to the nominal level this is achieved through a combination of computer simulation and density estimation the asymptotic validity of the procedure is proved for a number of common situations a classical example is the nonparametric estimation of the variance of a population using the normal theory interval here it is shown that the estimated coverage probability consistently estimates the true coverage probability if the population distribution possesses a finite sixth moment the second approach is more traditional it is a procedure for modifying an interval to yield improved coverage properties given a confidence interval its estimated coverage probability obtained in the first approach is used to alter the nominal level of the interval

a stabilized nodally integrated tetrahedral a stabilized nodally integrated linear tetrahedral is formulated and analysed it is well known that linear tetrahedral elements perform poorly in problems with plasticity nearly incompressible materials and acute bending for a variety of reasons low order tetrahedral elements are preferable to quadratic tetrahedral elements particularly for nonlinear problems but the severe locking problems of tetrahedrals have forced analysts to employ hexahedral formulations for most nonlinear problems on the other hand automatic mesh generation is often not feasible for building many 3d hexahedral meshes a stabilized nodally integrated linear tetrahedral is developed and shown to perform very well in problems with plasticity nearly incompressible materials and acute bending the formulation is analytically and numerically shown to be stable and optimally convergent for the compressible case provided sufficient smoothness of the exact solution u c2 h1 3 future work may extend the formulation to the incompressible regime and relax the regularity requirements nonetheless the results demonstrate that the method is not susceptible to locking and performs quite well in several standard linear and nonlinear benchmarks published in 2006 by john wiley sons ltd

conforming polygonal finite elements summary in this paper conforming finite elements on polygon meshes are developed polygonal finite elements provide greater flexibility in mesh generation and are better suited for applications in solid mechanics which involve a significant change in the topology of the material domain in this study recent advances in meshfree approximations computational geometry and computer graphics are used to construct different trial and test approximations on polygonal elements a particular and notable contribution is the use of meshfree natural neighbour nn basis functions on a canonical element combined with an affine map to construct conforming approximations on convex polygons this numerical formulation enables the construction of conforming approximation on n gons n 3 and hence extends the potential applications of finite elements to convex polygons of arbitrary order numerical experiments on second order elliptic boundary value problems are presented to demonstrate the accuracy and convergence of the proposed method copyright 2004 john wiley sons ltd

fast and accurate approximate double bootstrap confidence intervals we propose two new methods for the construction of approximate iterated bootstrap confidence intervals our methods follow a saddlepoint approach but employ approximate rather than exact solutions to the nonlinear saddlepoint equations that arise in applying that technique the main advantages of the new techniques are that they yield confidence intervals with high coverage accuracy in small to moderately sized samples and that they achieve this accuracy with very substantial reductions in computation time compared to other methods

nodal integration of the element free galerkin method abstract spatial integration of the element free galerkin efg method is achieved by evaluating the integrals of the weak form only at the nodes in previous efg formulations a grid of cells was used to perform gaussian quadrature over the domain the absence of a cell structure for nodal integration results in a completely meshless method similar in simplicity to particle methods such as smooth particle hydrodynamics sph it is shown that nodal integration like sph suffers from spurious singular modes this spatial instability results from underintegration of the weak form and it is treated by the addition to the potential energy functional of a stabilization term which contains the square of the residual of the equilibrium equation example problems illustrate the effect of the stabilization and provide the basis for convergence studies

the patch test a condition for assessing fem convergence this paper discusses various forms of the irons patch test and shows again that its satisfaction is a necessary convergence condition being equivalent to consistency further it is shown that the test can be applied for verification of stability requirements thus providing also a sufficient condition of convergence the patch test is useful in testing the order of asymptotic convergence and the satisfaction of the test gives a guide for development of certain incompatible element forms

stabilized conforming nodal integration in the natural element method a stabilized conforming nodal integration scheme is implemented in the natural neighbour method in conjunction with non sibsonian interpolation in this approach both the shape functions and the integration scheme are defined through use of first order voronoi diagrams the method illustrates improved performance and significant advantages over previous natural neighbour formulations the method also shows substantial promise for problems with large deformations and for the computation of higher order gradients copyright 2004 john wiley sons ltd

a class of mixed assumed strain methods and the method of incompatible modes a three field mixed formulation in terms of displacements stresses and an enhanced strain field is presented which encompasses as a particular case the classical method of incompatible modes within this frame work incompatible elements arise as particular compatible mixed approximations of the enhanced strain field the conditions that the stress interpolation contain piece wise constant functions and be l2 ortho gonal to the enhanced strain interpolation ensure satisfaction of the patch test and allow the elimination of the stress field from the formulation the preceding conditions are formulated in a form particularly convenient for element design as an illustration of the methodology three new elements are developed and shown to exhibit good performance a plane 3d elastic plastic quad an axisymmetric element and a thick plate bending quad the formulation described herein is suitable for non linear analysis

locking free continuum displacement finite elements with nodal integration summary an assumed strain flnite element technique is presented for linear elastic small deformation models weighted residual method reminiscent of the strain displacement functional is used to enforce weakly the balance equation with the natural boundary condition and the kinematic equation the strain displacement relationship a priori satisfaction of the kinematic weighted residual serves as a condition from which strain displacement operators are derived via nodal integration a variety of element shapes is treated linear triangles quadrilaterals tetrahedra hexahedra and furthermore quadratic six node triangles and 27 node hexahedra the degrees of freedom are only the primitive variables displacements at the nodes the formulation allows for general anisotropic materials a straightforward constraint count can partially explain the insensitivity of the resulting flnite element models to locking in the incompressible limit furthermore the numerical inf sup test is applied in select problems and several variants of the proposed formulations linear triangles quadrilaterals tetrahedra hexahedra and 27 node hexahedra pass the test examples are used to illustrate the performance with with respect to sensitivity to shape distortion and ability to resist volumetric locking copyright c 2007 john wiley sons ltd