refinable bounds for large markov chains a method to bound the steady state solution of large markov chains is presented it integrates the concepts of eigen vector polyhedron and of aggregation and is iterative in nature the bounds are obtained by considering a subset only of the system state space this makes the method specially attractive for problems which are too large to be dealt with by traditional methods the quality of the bounds depends on the locality of the system which is studied when the system spends most of its time in a small subset of states tight bounds can be obtained by considering this subset only finally the bounds are refinable in the sense that the tightness of the bounds can be improved by enlarging the subset of states which is considered the method is illustrated on a model of a repairable fault tolerant system with 16 million states tight bounds on its availability are obtained by considering less than 0 1 percent of its state space

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

assumed strain stabilization of the eight node hexahedral element an accurate and robust stabilization based on the assumed strain method and an operator orthogonal to constant strain fields is presented for an eight node hexahedral element with uniform reduced integration the stabilization forces depend only on the element geometry and material properties user specified parameters are not needed yet the assumed strain stabilization is nearly as fast as perturbation type hourglass control in an explicit code it has excellent coarse mesh accuracy for linear elastic bending and is easily incorporated into a nonlinear program the assumed strain field is also used with four point integration which does not require stabilization in addition two forms of the b matrix are studied and it is shown that the mean form is more efficient since it passes the patch test in a simplified form

on polyhedra of perron frobenius eigenvectors abstract this paper deals with the positive eigenvectors of nonnegative irreducible matrices which are merely characterized by a given upper bound u on their spectral radius and by a given matrix l of lower bounds for their elements for any such matrix the normalized positive left right eigenvector is shown to belong to the polyhedron the vertices of which are given by the normalized rows columns of the matrix u i l 1 this polyhedron is proven to be also the smallest closed set which is guaranteed to contain the positive left right normalized eigenvector its vertices are therefore the best componentwise bounds one can obtain on the positive eigenvectors of these matrices a less general result has also been obtained for the symmetrical case when the matrices are only characterized by a given lower bound l on their spectral radius and by a given matrix u of upper bounds for their elements

a mixed finite element for the analysis of large inelastic strains a 4 node element with 1 integration point is developed for the analysis of elastoplastic large strains it is based on the hu washizu principle and uses a co rotational formulation special care is taken to avoid spurious zero energy modes and incompressibility locking this element successfully passes the large strain patch test it proves to be accurate and computationally very cheap

a locking free meshfree method for the simulation of shear deformable plates based on a mixed variational formulation abstract the problem of shear locking in the thin plate limit is a well known issue that must be overcome when discretising the reissner mindlin plate equations in this paper we present a shear locking free method utilising meshfree maximum entropy basis functions and rotated raviart thomas nedelec elements within a mixed variational formulation the formulation draws upon well known techniques in the finite element literature due to the inherent properties of the maximum entropy basis functions our method allows for the direct imposition of dirichlet essential boundary conditions in contrast to methods based on moving least squares basis functions we present benchmark problems that demonstrate the accuracy and performance of the proposed method

geometry independent field approximation cad analysis integration geometrical exactness and adaptivity in isogeometric analysis iga the same spline representation is employed for both the geometry of the domain and approximation of the unknown fields over this domain this identity of the geometry and field approximation spaces was put forward in the now classic 2005 paper 20 as a key advantage on the way to the integration of computer aided design cad and subsequent analysis in computer aided engineering cae 20 claims indeed that any change to the geometry of the domain is automatically inherited by the approximation of the field variables without requiring the regeneration of the mesh at each change of the domain geometry yet in finite element versions of iga a parameterization of the interior of the domain must still be constructed since cad only provides information about the boundary the identity of the boundary and field representation decreases the flexibility in which this parameterization can be generated and somewhat constrains the modeling and simulation process because an approximation able to represent the domain geometry accurately need not be adequate to also approximate the field variables accurately in particular when the solution is not smooth we propose here a new paradigm called geometry independent field approximation gift where the spline spaces used for the geometry and the field variables can be chosen and adapted independently while preserving geometric exactness and tight cad integration gift has the following features 1 it is possible to flexibly

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

comparing markov chains aggregation and precedence relations applied to sets of states with applications to assemble to order systems solving markov chains is in general difficult if the state space of the chain is very large or infinite and lacking a simple repeating structure one alternative to solving such chains is to construct models that are simple to analyze and provide bounds for a reward function of interest we present a new bounding method for markov chains inspired by markov reward theory our method constructs bounds by redirecting selected sets of transitions facilitating an intuitive interpretation of the modifications of the original system we show that our method is compatible with strong aggregation of markov chains thus we can obtain bounds for an initial chain by analyzing a much smaller chain we illustrate our method by using it to prove monotonicity results and bounds for assemble to order systems

an iterative method for the calculation of narrow solitary excitations on atomic chains abstract we discuss the quasicontinuum approximation of collins and give a general condition for its validity for the solution of the difference differential equations of the full discrete model we develop an iteration procedure in fourier space the method is tested for solitary excitations with widths of the order of the lattice constant by a comparison with both exact results and computer simulations an additional result of the new mwthod is a simple derivation of the collins approximation which allows several generalizations

stationary breather modes of generalized nonlinear klein gordon lattices this paper studies the form of stationary breather modes in discrete generalized nonlinear klein gordon equations with symmetric and non symmetric potential energy functions in the case of static breathers the discrete nature of the spatial dimension has a much more subtle effect on the breather than the moving breather mode this effect is analysed using a variety of approximating partial differential equations whose solutions are found by using an extended multiple scales asymptotic approach to reduce the equation to a nonlinear schrodinger equation at leading order and more complex equations at higher order where secularity conditions are required to fully specify the solution as well as the much studied discrete sine gordon equation the methods are demonstrated on a discrete nonlinear klein gordon equation with second neighbour interactions and non symmetric on site potential new partial differential equations which approximate these lattice systems are also proposed and analysed

discrete lattice solitons properties and stability the authors present a detailed numerical study of the dynamics of high energy kink excitations in monatomic chains with a simple description using a microscopic model of the narrow kink core they present velocity amplitude and energy momentum curves for the kink which fit well the numerical results kink kink collisions are slightly inelastic depending on the velocities and point of collision within a lattice spacing

derivatives of maximum entropy basis functions on the boundary theory and computations summary in this paper we obtain explicit expressions to evaluate the derivatives of maximum entropy max ent basis function on the boundary of a convex domain in the max ent formulation the basis functions are obtained by maximizing a concave functional subjected to linear constraints reproducing conditions in doing so it is found that the lagrange multipliers blow up when x and the expressions for the derivatives of the max ent basis functions in are of an indeterminate form for points on we appeal to l hopital s rule to derive expressions to determine the derivatives of the basis functions we consider the shannon entropy functional and the relative entropy functional with different choices of the prior weight function the first order derivatives of all basis functions are bounded in contrast on an irregular grid with a certain nodal spacing some of the second derivatives of the basis functions are unbounded on the boundary necessary and sufficient conditions on the priors to obtain bounded lagrange multipliers are established optimal convergence rates for fourth order problems are demonstrated for a galerkin approach with a quadratically complete partition of unity enriched max ent approximation copyright 2013 john wiley sons ltd

gradient bounds for wachspress coordinates on polytopes we derive upper and lower bounds on the gradients of wachspress coordinates defined over any simple convex d dimensional polytope p the bounds are in terms of a single geometric quantity h ast which denotes the minimum distance between a vertex of p and any hyperplane containing a nonincident face we prove that the upper bound is sharp for d 2 and analyze the bounds in the special cases of hypercubes and simplices additionally we provide an implementation of the wachspress coordinates on convex polyhedra using matlab and employ them in a three dimensional finite element solution of the poisson equation on a nontrivial polyhedral mesh as expected from the upper bound derivation the h 1 norm of the error in the method converges at a linear rate with respect to the size of the mesh elements

physically based dirac s delta functions in the static analysis of multi cracked euler bernoulli and timoshenko beams abstract dirac s delta functions enable simple and effective representations of point loads and singularities in a variety of structural problems leading very often to elegant and otherwise unworkable closed form solutions this is the case of cracked beams under static loads whose theoretical and practical significance has attracted in recent years the interest of many researchers nevertheless analytical formulations currently available for this problem are not completely satisfactory either in terms of computational efficiency when the continuity conditions must be enforced with auxiliary equations or in terms of physical consistency when the singularities in the beam s flexural rigidity are represented with dirac s delta functions having a questionable negative sign these considerations motivate the present study which offers a novel and physically based modelling of slender euler bernoulli beams and short timoshenko beams with any number and severity of cracks conducing in both cases to exact closed form solutions for validation purposes a standard finite element code is used along with two nascent deltas uniform and gaussian density functions to describe a smeared increase in the bending flexibility around the abscissa of the crack

existence theorem for solitary waves on lattices in this article we give an existence theorem for localized travelling wave solutions on one dimensional lattices with hamiltonian h sum limits n in mathbb z left tfrac 1 2 p n 2 v q n 1 q n right wherev is the potential energy due to nearest neighbour interactions until now apart from rare integrable lattices like the toda latticev ab 1 e b b 1 the only evidence for existence of such solutions has been numerical our result in particular recovers existence of solitary waves in the toda lattice establishes for the first time existence of solitary waves in the nonintegrable cubic and quartic latticesv 1 2 2 1 3a 3 v 1 2 2 1 4b 4 thereby confirming the numerical findings in 1 and shedding new light on the recurrence phenomena in these systems observed first by fermi pasta and ulam 2 and shows that contrary to widespread belief the presence of exact solitary waves is not a peculiarity of integrable systems but generic in this class of nonlinear lattices the approach presented here is new and quite general and should also be applicable to other forms of lattice equations the travelling waves are sought as minimisers of a naturally associated variational problem obtained via hamilton s principle and existence of minimisers is then established using modern methods in the calculus of variations the concentration compactness principle of p l lions 3

a paradigm for higher order polygonal elements in finite elasticity using a gradient correction scheme abstract recent studies have demonstrated that polygonal elements possess great potential in the study of nonlinear elastic materials under finite deformations on the one hand these elements are well suited to model complex microstructures e g particulate microstructures and microstructures involving different length scales and incorporating periodic boundary conditions on the other hand polygonal elements are found to be more tolerant to large localized deformations than the standard finite elements and to produce more accurate results in bending and shear with mixed formulations lower order mixed polygonal elements are also shown to be numerically stable on voronoi type meshes without any additional stabilization treatment however polygonal elements generally suffer from persistent consistency errors under mesh refinement with the commonly used numerical integration schemes as a result non convergent finite element results typically occur which severely limit their applications in this work a general gradient correction scheme is adopted that restores the polynomial consistency by adding a minimal perturbation to the gradient of the displacement field with the correction scheme the recovery of optimal convergence for solutions of displacement based and mixed formulations with both linear and quadratic displacement interpolants is confirmed by numerical studies of several boundary value problems in finite elasticity in addition for mixed polygonal elements the various choices of the pressure field approximations are discussed and their performance on stability and accuracy are numerically investigated we present applications of those elements in physically based examples including a study of filled elastomers with interphasial effect and a qualitative comparison with cavitation experiments for fiber reinforced elastomers

surfaces generated by moving least squares methods an analysis of moving least squares m l s methods for smoothing and interpolating scattered data is presented in particular theorems are proved concerning the smoothness of interpolants and the description of m l s processes as projection methods some properties of compositions of the m l s projector with projectors associated with finiteelement schemes are also considered the analysis is accompanied by examples of univariate and bivariate problems

a unified formulation of small strain corotational finite elements i theory this paper presents a unified theoretical framework for the corotational cr formulation of finite elements in geometrically nonlinear structural analysis the key assumptions behind cr are i strains from a corotated configuration are small while ii the magnitude of rotations from a base configuration is not restricted following a historical outline the basic steps of the element independent cr formulation are presented the element internal force and consistent tangent stiffness matrix are derived by taking variations of the internal energy with respect to nodal freedoms it is shown that this framework permits the derivation of a set of cr variants through selective simplifications this set includes some previously used by other investigators the different variants are compared with respect to a set of desirable qualities including self equilibrium in the deformed configuration tangent stiffness consistency invariance symmetrizability and element independence we discuss the main benefits of the cr formulation as well as its modeling limitations

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

a return mapping algorithm for plane stress elastoplasticity an unconditionally stable algorithm for plane stress elastoplasticity is developed based upon the notion of elastic predictor return mapping plastic corrector enforcement of the consistency condition is shown to reduce to the solution of a simple nonlinear equation consistent elastoplastic tangent moduli are obtained by exact linearization of the algorithm use of these moduli is essential in order to preserve the asymptotic rate of quadratic convergence of newton methods the accuracy of the algorithm is assessed by means of iso error maps the excellent performance of the algorithm for large time steps is illustrated in numerical experiments

asymptotic analysis of combined breather kink modes in a fermi pasta ulam chain we find approximations to travelling breather solutions of the one dimensional fermi pasta ulam fpu lattice both bright breather and dark breather solutions are found we find that the existence of localised bright solutions depends upon the coefficients of cubic and quartic terms of the potential energy generalising an earlier inequality derived by james cr acad sci paris 332 581 2001 we use the method of multiple scales to reduce the equations of motion for the lattice to a nonlinear schr o dinger equation at leading order and hence construct an asymptotic form for the breather we show that in the absence of a cubic potential energy term the lattice supports combined breathing kink waveforms the amplitude of breathing kinks can be arbitrarily small as opposed to traditional monotone kinks which have a nonzero minimum amplitude in such systems we also present numerical simulations of the lattice verifying the shape and velocity of the travelling waveforms and confirming the long lived nature of all such modes

superconvergent gradient smoothing meshfree collocation method abstract a superconvergent meshfree collocation method with smoothed nodal gradients is presented in this method the first order smoothed gradients of meshfree shape function are constructed through a meshfree interpolation of the standard derivatives of meshfree shape function while the second order smoothed gradients are computed through directly differentiating the first order smoothed gradients it is noted that the second order smoothed gradients evaluated at meshfree nodes can be conveniently expressed as two successive first order gradient smoothing operations on the meshfree shape function which facilitates a trivial numerical implementation subsequently an employment of the second order smoothed gradients in the strong form of a given problem leads to the gradient smoothing meshfree collocation method purely using nodes as the collocation points based upon a local truncation error analysis it is systematically shown that the proposed meshfree collocation method yields superconvergent solutions for odd degree basis functions a key ingredient attributed to this superconvergence property is that the second order smoothed gradients meet the consistency conditions which go one order beyond the original basis degree of meshfree approximation another interesting fact is that the present formulation enables a convergent collocation scheme when the linear basis function is used in meshfree approximation which is non feasible in the conventional collocation formulation the effectiveness of the proposed methodology is validated by numerical examples for both potential and elasticity problems numerical results well demonstrate the superconvergence and higher efficiency of the present gradient smoothing meshfree collocation method

a study of incremental iterative strategies for non linear analyses the paper describes a study of incremental iterative solution techniques for geometrically non linear analyses the solution methods documented are based on a modified newton raphson approach meaning that the tangent stiffness matrix is computed at the commencement of each load step but is then held constant throughout the equilibrium iterations a consistent mathematical notation is employed in the description of the iterative and load incrementation strategies enabling the simple inclusion of several solution options in a computer program the iterative strategies investigated are iteration at constant load iteration at constant displacement iteration at constant arc length iteration at constant external work iteration at minimum unbalanced displacement norm iteration at minimum unbalanced force norm and iteration at constant weighted response the load incrementation schemes investigated include strategies based on the number of iterations required to achieve convergence in the previous load step strategies based on the current stiffness parameter and a strategy based on a parabolic approximation to the load deflection response criteria for detecting when the applied external load increment should reverse sign are described a challenging example of a circular arch exhibiting snap through load limit point behaviour and snap back displacement limit point behaviour is solved using several different iterative and load incrementation strategies the performance of the solution schemes is evaluated and conclusions are drawn

quasi continuum approximations to lattice equations arising from the discrete nonlinear telegraph equation we show how quasi continuum methods can be used to construct approximate solutions of nonlinear differential delay equations derived from symmetry reductions of the discrete nonlinear telegraph equation travelling wave solutions are proven to exist and the existence of solutions to two other symmetry reductions are studied two of the less familiar reductions are studied the first supports both a one parameter family of single pulse solitary wave type solutions and a one parameter family of periodic waves the size and shape of these waves are examined using the quasi continuum technique this approximates the differential difference equation with a higher order differential equation which is integrated and analysed using phase plane techniques in the large amplitude limit the shape of the pulse approaches a limiting form which has a corner at its peak the manner of this approach is elucidated using matched asymptotic expansions the second reduction though differing only by the addition of a single term appears not to support the solitary wave type of solution even in the limit where the additional term is premultiplied by an asymptotically small constant

new six node and seven node hexagonal finite elements abstract in this paper we introduce a six node and a seven node hexagonal elements both elements are based on the rotated trilinear interpolation in terms of the three directional coordinates optimal a priori error estimates are provided for the new elements by decomposing the consistency error into two parts that both can be estimated using the f e m test some numerical tests are carried out to verify the theoretical analysis comparisons to both the previously studied edge oriented hexagonal elements and the traditional linear triangular elements are also provided to show the efficiency and superiority of the new six node and seven node hexagonal elements

consistent and stable meshfree galerkin methods using the virtual element decomposition summary over the past two decades meshfree methods have undergone significant development as a numerical tool to solve partial differential equations pdes in contrast to finite elements the basis functions in meshfree methods are smooth nonpolynomial functions and they do not rely on an underlying mesh structure for their construction these features render meshfree methods to be particularly appealing for higher order pdes and for large deformation simulations of solid continua however a deficiency that still persists in meshfree galerkin methods is the inaccuracies in numerical integration which affects the consistency and stability of the method several previous contributions have tackled the issue of integration errors with an eye on consistency but without explicitly ensuring stability in this paper we draw on the recently proposed virtual element method to present a formulation that guarantees both the consistency and stability of the approximate bilinear form we adopt maximum entropy meshfree basis functions but other meshfree basis functions can also be used within this framework numerical results for several two dimensional and three dimensional elliptic poisson and linear elastostatic boundary value problems that demonstrate the effectiveness of the proposed formulation are presented copyright 2017 john wiley sons ltd

overview and construction of meshfree basis functions from moving least squares to entropy approximants in this paper an overview of the construction of meshfree basis functions is presented with particular emphasis on moving least squares approximants natural neighbour based polygonal interpolants and entropy approximants the use of information theoretic variational principles to derive approximation schemes is a recent development in this setting data approximation is viewed as an inductive inference problem with the basis functions being synonymous with a discrete probability distribution and the polynomial reproducing conditions acting as the linear constraints the maximization minimization of the shannon jaynes entropy functional relative entropy functional is used to unify the construction of globally and locally supported convex approximation schemes a java applet is used to visualize the meshfree basis functions and comparisons and links between different meshfree approximation schemes are presented copyright 2006 john wiley sons ltd

local maximum entropy approximation schemes a seamless bridge between finite elements and meshfree methods we present a one parameter family of approximation schemes which we refer to as local maximum entropy approximation schemes that bridges continuously two important limits delaunay triangulation and maximum entropy max ent statistical inference local max ent approximation schemes represent a compromise in the sense of pareto optimality between the competing objectives of unbiased statistical inference from the nodal data and the definition of local shape functions of least width local max ent approximation schemes are entirely defined by the node set and the domain of analysis and the shape functions are positive interpolate affine functions exactly and have a weak kronecker delta property at the boundary local max ent approximation may be regarded as a regularization or thermalization of delaunay triangulation which effectively resolves the degenerate cases resulting from the lack or uniqueness of the triangulation local max ent approximation schemes can be taken as a convenient basis for the numerical solution of pdes in the style of meshfree galerkin methods in test cases characterized by smooth solutions we find that the accuracy of local max ent approximation schemes is vastly superior to that of finite elements

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

construction of polygonal interpolants a maximum entropy approach in this paper we establish a link between maximizing information theoretic entropy and the construction of polygonal interpolants the determination of shape functions on n gons n 3 leads to a non unique under determined system of linear equations the barycentric co ordinates i which form a partition of unity are associated with discrete probability measures and the linear reproducing conditions are the counterpart of the expectations of a linear function the i are computed by maximizing the uncertainty h 1 2 n i log i subject to the above constraints the description is expository in nature and the numerical results via the maximum entropy maxent formulation are compared to those obtained from a few distinct polygonal interpolants the maximum entropy formulation leads to a feasible solution for i in any convex or non convex polygon this study is an instance of the application of the maximum entropy principle wherein least biased inference is made on the basis of incomplete information copyright 2004 john wiley sons ltd

trefftz difference schemes on irregular stencils the recently developed flexible local approximation method flame produces accurate difference schemes by replacing the usual taylor expansion with trefftz functions local solutions of the underlying differential equation this paper advances and casts in a general form a significant modification of flame proposed recently by pinheiro and webb a least squares fit instead of the exact match of the approximate solution at the stencil nodes as a consequence of that flame schemes can now be generated on irregular stencils with the number of nodes substantially greater than the number of approximating functions the accuracy of the method is preserved but its robustness is improved for demonstration the paper presents a number of numerical examples in 2d and 3d electrostatic magnetostatic particle interactions scattering of electromagnetic acoustic waves and wave propagation in a photonic crystal the examples explore the role of the grid and stencil size of the number of approximating functions and of the irregularity of the stencils

quasi continuum approximations for travelling kinks in diatomic lattices we extend the quasi continuum method of approximation to the case of a diatomic lattice this is illustrated by a lattice in which both small and large atoms interact with first and second nearest neighbours we show that highly accurate quasi continuum techniques may be generalized to determine the shape of nontopological kinks many previous analyses of such systems have found travelling wave solutions only for one particular speed using a second order continuum theory we show i how wave shapes can be found for arbitrary speeds and ii how solution profiles can be calculated from fourth order partial differential equations which approximate the lattice alongside the theoretical analysis we also present numerical simulations of the lattice which demonstrate propagation of the predicted waves through the lattice we show that the particular speed for which solutions have been found in previous studies is a special speed for waves in the lattice but waves can travel for long periods of time at faster or slower speeds whilst slowly relaxing to this critical speed

a multiple quadrature eight node hexahedral finite element for large deformation elastoplastic analysis abstract a multiple quadrature underintegrated hexahedral finite element which is free of volumetric and shear locking and has no spurious singular modes is described and implemented for nonlinear analysis finite element formulations are derived in the corotational coordinate system the use of consistent tangent operators for large deformation elastoplasticity with nonlinear isotropic kinematic hardening rules preserves the quadratic rate of convergence of the newton s iteration method in static analysis test problems studied demonstrate the efficiency and effectiveness of this element in solving a wide variety of problems including sheet metal forming processes

floating stress point integration meshfree method for large deformation analysis of elastic and elastoplastic materials summary a new meshfree formulation of stress point integration called the floating stress point integration meshfree method is proposed for the large deformation analysis of elastic and elastoplastic materials this method is a galerkin meshfree method with an updated lagrangian procedure and a quasi implicit time advancing scheme without any background cell for domain integration its new formulation is based on incremental equilibrium equations derived from the incremental virtual work equation which is not generally used in meshfree formulations hence this technique allows the temporal continuity of the mechanical equilibrium to be naturally achieved the details of the new formulation and several examples of the large deformation analysis of elastic and elastoplastic materials are presented to show the validity and accuracy of the proposed method in comparison with those of the finite element method copyright 2012 john wiley sons ltd

approximations to solitary waves on lattices iii the monatomic lattice with second neighbour interactions we find new behaviour in a lattice with second neighbour interactions first we find solitary waves with oscillatory spatial decay this is something that cannot occur in lattices with nearest neighbour interactions alone this is found by standard asymptotic analysis which leads to an exact curve in parameter space where this behaviour starts a number of highly accurate quasi continuum approximations are derived and solved one of these suggests a possible method for subsonic solitary waves to cease existing an alternative method of approximation elegantly reveals the differences in shape between subsonic and supersonic solitary waves this is based on the weak form of the differential delay equation for the travelling wave and is derived using the calculus of variations

bounds for the positive eigenvectors of nonnegative matrices and for their approximations by decomposition cet article traite des vecteurs propres positifs des matrices irreductibles non reparties qui sont simplement caracterisees par une limite superieure donnee sur leur rayon spectral et par une matrice l donnee de limites inferieures pour leurs elements analyse du cas particulier des matrices stochastiques et on donne un exemple numerique

meshfree co rotational formulation for two dimensional continua in this paper a meshfree co rotational formulation for two dimensional continua is proposed in a co rotational formulation the motion of a body is separated into rigid motion and strain producing deformation traditionally this has been done in the setting of finite elements for beams and shell type elements in the present work every node in a meshfree discretized domain has its own co rotating coordinate system three key ingredients are established in order to apply the co rotational formulation i the relationship between global and local variables ii the angle of rotation of a typical co rotating coordinate system and iii a variationally consistent tangent stiffness matrix an algorithm for the co rotational formulation based on load control is provided maximum entropy basis functions are used to discretize the domain and stabilized nodal integration is implemented to construct the global system of equations numerical examples are presented to demonstrate the validity of the meshfree co rotational formulation copyright 2009 john wiley sons ltd

cell based maximum entropy approximants in this paper we devise cell based maximum entropy max ent basis functions that are used in a galerkin method for the solution of partial differential equations the motivation behind this work is the construction of smooth approximants with controllable support on unstructured meshes in the variational scheme to obtain max ent basis functions the nodal prior weight function is constructed from an approximate distance function to a polygonal curve in r2 more precisely we take powers of the composition of r functions via boolean operations the basis functions so constructed are nonnegative smooth linearly complete and compactly supported in a neighbor ring of segments that enclose each node the smoothness is controlled by two positive integer parameters the normalization order of the approximation of the distance function and the power to which it is raised the properties and mathematical foundations of the new compactly supported approximants are described and its use to solve two dimensional elliptic boundary value problems poisson equation and linear elasticity is demonstrated the sound accuracy and the optimal rates of convergence of the method in sobolev norms are established

second order convex maximum entropy approximants with applications to high order pde we present a new approach for second order maximum entropy max ent meshfree approximants that produces positive and smooth basis functions of uniform aspect ratio even for non uniform node sets and prescribes robustly feasible constraints for the entropy maximization program defining the approximants we examine the performance of the proposed approximation scheme in the numerical solution by a direct galerkin method of a number of partial differential equations pdes including structural vibrations elliptic second order pdes and fourth order pdes for kirchhoff love thin shells and for a phase field model describing the mechanics of biomembranes the examples highlight the ability of the method to deal with non uniform node distributions and the high accuracy of the solutions surprisingly the first order meshfree max ent approximants with large supports are competitive when compared to the proposed second order approach in all the tested examples even in the higher order pdes

gradient and dilatational stabilizations for stress point integration in the element free galerkin method stabilized stress point integration schemes based on gradient stabilization and dilatational stabilization methods are presented for linear elastostaticity problems in the framework of element free galerkin efg method the instability in stress fields associated with the stress point integration is treated by the addition to the galerkin weak form of stabilization terms which contain product of the gradient of the residual or the trace of the gradient of the residual the latter is called dilatational stabilization numerical results show that the oscillations in the stress fields are successfully removed by the presented stabilization methods and that the convergence and stability properties of direct stress point integration are greatly improved these stabilization methods are particularly suitable for the solution of non linear continua with explicit time integration methods copyright 2008 john wiley sons ltd

approximations to solitary waves on lattices ii quasi continuum methods for fast and slow waves a number of highly accurate analytic approximations to solitary waves on lattices are detailed and the results of numerical tests presented two types of approximation are considered the first set of approximations are generalizations of the continuum approximation based around various pade expansions of the operator these are convergent to the exact solution in the limit of wavespeed c to 1 or a dense lattice the author also considers ways of constructing approximations to fast solitary waves from a continuum type theory the two types are closely related in both cases significant improvements are made on existing approximations a symplectic hamiltonian integration scheme is used to perform computer simulations a new method of measuring the accuracy of a predicted waveform is also used on new and old approximations alike to compare the various methods considered

bounding availability of repairable systems markov models are widely used for the analysis of availability of computer communication systems realistic models often involve state space cardinalities that are so large that it is impractical to generate the transition rate matrix let alone solve for availability measures an approximation technique is presented for determining steady state availability of particular interest is that the method also provides bounds on the error examples are given to illustrate the method

approximations to large amplitude solitary waves on nonlinear electrical lattices abstract in this paper we describe an approximate method to characterise solitary wave solutions of nonlinear lattice equations it is based upon one and two point pade approximations to a series of the real exponential travelling wave solutions of the underlying dispersive system the theory is applied to an example of a lattice system which models an experimental nonlinear transmission line and the results obtained are consistent with numerical simulations even for relatively large amplitude solitary waves the speed amplitude relation is investigated and compared with the derived using quasi continuum methods