dynamic shakedown analysis and bounds for elastoplastic structures with nonassociative internal variable constitutive laws abstract reference is made to discrete finite element structural models formulated in terms of generalized variables the constitutive laws adopted are elastic plastic nonlinear hardening with internal variables and generally nonassociative the notion of reduced domain is employed as a generalization of a similar concept introduced in earlier developments of shakedown theory on this basis a unified theory is presented which encompasses necessary and separately sufficient conditions for shakedown by a static approach as a further generalization of classical melan s theorem bounds on various post shakedown quantities sufficient and necessary shakedown criteria by a kinematic approach as a further extension of neal symonds koiter theorem by suitable specializations and relaxations of the achievable results the criteria and bounding inequalities established here are formulated as mathematical programming problems in view of numerical applications

localization and regularization behavior of mixed finite elements for 2d structural problems with damaging material abstract a class of lagrangian mixed finite elements is presented for applications to 2d structural problems based on a damage constitutive model attention is focused on localization and regularization issues as compared with the correspondent behavior of lagrangian displacement based elements a non local regularization procedure of integral type is adopted a predictor corrector technique is used to solve the evolution problem of the damage variable the proposed elements show superior performances for typical structural applications

kinematical shakedown analysis with temperature dependent yield stress summary this paper describes a direct shakedown analysis of structures subjected to variable thermal and mechanical loading the classical kinematical shakedown theorem is modied to be implemented with any displacementbased nite elements the plastic incompressibility condition is imposed by the penalty function method the shakedown limit is found via a non linear mathematical programming procedure two numerical shakedown methods are developed and implemented to provide alternative numerical means the temperature dependent material model is included in theoretical and numerical calculation in a simple way its eect on shakedown limit is investigated the numerical examination for some pressure vessel structures subjected to thermal and mechanical loading shows a satisfying precision and eciency of the methods presented copyright 2001 john wiley sons ltd

fade statistics in nakagami lognormal channels new expressions for the average level crossing rate lcr and average time fade duration afd of the signal envelope in microcellular mobile radio channels characterized by nakagami 1960 fading and lognormal shadowing so called nakagami lognormal nln channels are derived new lcr and afd are computed and the effects of the nakagami m factor and shadowing spread spl sigma sub s on these fade statistics are discussed the generality of the nln model is demonstrated by matching some lcr curves with previously reported measurement for the land mobile satellite channel commonly described as the rice lognormal channels

variationally consistent modeling of finite strain plasticity theory with non linear kinematic hardening abstract variational constitutive updates provide a physically and mathematically sound framework for the numerical implementation of material models in contrast to conventional schemes such as the return mapping algorithm they are directly and naturally based on the underlying variational principle hence the resulting numerical scheme inherits all properties of that principle in the present paper focus is on a certain class of those variational methods which relies on energy minimization consequently the algorithmic formulation is governed by energy minimization as well accordingly standard optimization algorithms can be applied to solve the numerical problem a further advantage compared to conventional approaches is the existence of a natural distance semi metric induced by the minimization principle such a distance is the foundation for error estimation and as a result for adaptive finite elements methods though variational constitutive updates are relatively well developed for so called standard dissipative solids i e solids characterized by the normality rule the more general case i e generalized standard materials is far from being understood more precisely int j sol struct 2009 46 1676 1684 represents the first step towards this goal in the present paper a variational constitutive update suitable for a class of nonlinear kinematic hardening models at finite strains is presented two different prototypes of armstrong frederick type are re formulated into the aforementioned variationally consistent framework numerical tests demonstrate the consistency of the resulting implementation

linear and strong convergence of algorithms involving averaged nonexpansive operators abstract we introduce regularity notions for averaged nonexpansive operators combined with regularity notions of their fixed point sets we obtain linear and strong convergence results for quasicyclic cyclic and random iterations new convergence results on the borwein tam method btm and on the cyclically anchored douglas rachford algorithm cadra are also presented finally we provide a numerical comparison of btm cadra and the classical method of cyclic projections for solving convex feasibility problems

a direct method to predict cyclic steady states of elastoplastic structures the asymptotic steady state behavior of an elastic perfectly plastic structure under cyclic loading may be determined by time consuming incremental time stepping calculations direct methods alternatively have a big computational advantage as they attempt to find the characteristics of the cyclic state right from the start of the calculations most of these methods address an elastic shakedown state through the shakedown theorems and on the basis of mathematical programming algorithms in the present paper a novel direct method that has a more physical basis and may predict any cyclic stress state of a structure under a given loading is presented the method exploits the cyclic nature of the expected residual stress distribution at the steady cycle thus after equilibrating the elastic part of the total stress with the external load the unknown residual stress part is decomposed into fourier series whose coefficients are evaluated iteratively by satisfying compatibility and equilibrium with zero loads at time points inside the cycle and then integrating over the cycle a computationally simple way to account for plasticity is proposed the procedure converges uniformly to the true cyclic residual stress for a loading below the elastic shakedown limit or to an unsafe cyclic total stress which may be used to mark the regions with plastic straining inside the cycle the method then continues to determine whether the applied loading would lead the structure to ratcheting or to regions that alternate plastically the procedure is formulated within the finite element method a von mises yield surface is typically used examples of application of one and two dimensional structures are included

an algorithm for shakedown analysis with nonlinear yield functions abstract this paper is devoted to propose an algorithm to solve the discrete form of the shakedown analysis problem with a nonlinear yield function firstly variational formulations for shakedown analysis of structures under variable loads are considered secondly the corresponding discrete forms are briefly recalled then the algorithm is derived by combining a newton formula based on the discrete equality conditions with a return mapping procedure focusing plastic admissibility the proposed numerical procedure can be applied to finite element models with large number of degrees of freedom because the algorithm is specially designed to take advantage of the structure of such models the numerical procedure is applied to a square plate with a circular hole under variable traction in two directions and the obtained approximations are compared with available results finally a rectangular plate with two small holes is considered in both plane strain and plane stress conditions all application use the mises condition without linearization

a comparison between analytical calculations of the shakedown load by the bipotential approach and step by step computations for elastoplastic materials with nonlinear kinematic hardening abstract the class of generalized standard materials is not relevant to model the nonassociative constitutive equations the bipotential approach based on a possible generalization of fenchel s inequality allows the recovery of the flow rule normality in a weak form of an implicit relation this defines the class of implicit standard materials for such behaviours this leads to a weak extension of the classical bound theorems of the shakedown analysis in the present paper we recall the relevant features of this theory considering an elastoplastic material with nonlinear kinematic hardening rule we apply it to the problem of a sample in plane strain conditions under constant traction and alternating torsion in order to determine analytically the interaction curve bounding the shakedown domain the aim of the paper is to prove the exactness of the solution for this example by comparing it to step by step computations of the elastoplastic response of the body under repeated cyclic loads of increasing level a reliable criterion to stop the computations is proposed the analytical and numerical solutions are compared and found to be closed one of each other moreover the method allows uncovering an additional 2 cycle shakedown curve that could be useful for the shakedown design of structure

computation of collapse states with von mises type yield condition a new computational approach to the problem of limit analysis with quadratic yield condition is developed and tested the problem is solved with the exact convex yield condition and the general case of unbounded yield set corresponding to unrestricted hydrostatic pressure is treated the solution method simultaneously approximates the collapse fields for stresses and flow the approach consists of two separate steps first the continuous problem is discretized by the finite element method into a finite dimensional optimization problem which turns out to be of a very specific form then this problem is solved by a suitable optimization method this way it is not necessary to be an expert in optimization in order to solve collapse problems and we can take advantage of the rapid development in optimization methods for large sparse problems without changing the discretization program the efficiency and accuracy of the method for large problems is demonstrated by solving a classical problem in the plane strain model approximately 90000 finite element nodes with 3 stress components and 2 velocity components at each node in two space dimensions this may be overkill but it shows that we are able to solve problems in three space dimensions

strong conical hull intersection property bounded linear regularity jameson s property g and error bounds in convex optimization the strong conical hull intersection property and bounded linear regularity are properties of a collection of finitely many closed convex intersecting sets in euclidean space these fundamental notions occur in various branches of convex optimization constrained approximation convex feasibility problems linear inequalities for instance it is shown that the standard constraint qualification from convex analysis implies bounded linear regularity which in turn yields the strong conical hull intersection property jameson s duality for two cones which relates bounded linear regularity to property g is re derived and refined for polyhedral cones a statement dual to hoffman s error bound result is obtained a sharpening of a result on error bounds for convex inequalities by auslender and crouzeix is presented finally for two subspaces property g is quantified by the angle between the subspaces

unified framework for the effective rate analysis of wireless communication systems over miso fading channels this paper proposes a unified framework for the effective rate analysis over arbitrary correlated and not necessarily identical multiple input single output miso fading channels which uses the moment generating function mgf based approach and h transform representation the proposed framework has the potential to simplify the cumbersome analysis procedure compared with the probability density function based approach moreover the effective rates over two specific fading scenarios are investigated namely independent but not necessarily identical distributed i n i d miso hyper fox s h fading channels and arbitrary correlated generalized k fading channels the exact analytical representations for these two scenarios are also presented by substituting corresponding parameters the effective rates in various practical fading scenarios such as rayleigh nakagami m weibull gamma and generalized k fading channels are readily available in addition asymptotic approximations are provided for the proposed h transform and mgf based approach as well as for the effective rate over i n i d miso hyper fox s h fading channels simulations under various fading scenarios are also presented which support the validity of the proposed method

bounds to shakedown loads the shakedown analysis of structures under variable loads is considered and the corresponding variational principles are presented separate formulations for elastic or classical shakedown plastic shakedown and incremental collapse are compared two upper bounds for classical safety factors are presented and interpreted as the result of separate analysis concerning alternating plasticity and prevention of simple mechanisms of incremental collapse as a first application exact solutions are obtained for a closed tube under variable pressure and temperature this example is the bree problem with logarithmic temperature variation across the wall a finite element procedure for shakedown analysis of tubes is then presented this numerical procedure is validated by comparison with the exact solutions for the closed tube finally the numerical method is applied to a restrained tube under variable pressure and logarithmic temperature

amplify and forward two way relay networks error exponents and resource allocation in a two way relay network two terminals exchange information over a shared wireless half duplex channel with the help of a relay due to its fundamental and practical importance there has been an increasing interest in this channel however there has been little work that characterizes the fundamental tradeoff between the communication reliability and transmission rate across all signal to noise ratios in this paper we consider amplify and forward af two way relaying due to its simplicity we first derive the random coding error exponent for the link in each direction from the exponent expression the capacity and cutoff rate for each link are also deduced we then put forth the notion of bottleneck error exponent which is the worst exponent decay between the two links to give us insight into the fundamental tradeoff between the rate pair and information exchange reliability in the two way relay network as applications of the error exponent analysis to design a reliable af two way relay network we present two optimization framework to maximize the bottleneck error exponent namely i the optimal rate allocation under a sum rate constraint and its closed form quasi optimal solution that requires only knowledge of the capacity and cutoff rate of each link and ii the optimal power allocation under a total power constraint and perfect global channel state information which is shown equivalently to a quasi convex optimization problem numerical results verify our analysis and the effectiveness of the optimal rate and power allocations in maximizing the bottleneck error exponent i e the network information exchange reliability

a cell based smoothed finite element method for kinematic limit analysis this paper presents a new numerical procedure for kinematic limit analysis problems which incorporates the cell based smoothed finite element method with second order cone programming the application of a strain smoothing technique to the standard displacement finite element both rules out volumetric locking and also results in an efficient method that can provide accurate solutions with minimal computational effort the non smooth optimization problem is formulated as a problem of minimizing a sum of euclidean norms ensuring that the resulting optimization problem can be solved by an efficient second order cone programming algorithm plane stress and plane strain problems governed by the von mises criterion are considered but extensions to problems with other yield criteria having a similar conic quadratic form or 3d problems can be envisaged

duality preserving discretization of the large time increment methods abstract the large time increment method is a well established iterative computational method for time dependent non linear structural analyses which has the peculiarity to produce at each iteration an approximation of the complete structural response over the whole considered history of loading the method establishes a converging iterative sequence by exploiting the specific structure of the equations governing the continuum problem the relatively large body of literature on the subject has been mostly concerned with assessing conceptual and practical properties of the method by referring to the continuum problem so far computer implementations where based on heuristic considerations and standard finite element technology in the present paper a different approach is followed a space and time discretization which preserves the duality structure of the continuum problem is introduced first then the method is reformulated for the discrete problem it is shown how the so called generalized variable modelling preserves the fundamental duality structure of the continuum problem a proof of convergence of the iterative scheme to the solution of the discrete problem is also outlined

on the implementation of rate independent standard dissipative solids at finite strain variational constitutive updates this paper is concerned with an efficient variationally consistent implementation for rate independent dissipative solids at finite strain more precisely focus is on finite strain plasticity theory based on a multiplicative decomposition of the deformation gradient adopting the formalism of standard dissipative solids which allows to describe constitutive models by means of only two potentials being the helmholtz energy and the yield function or equivalently a dissipation functional finite strain plasticity is recast into an equivalent minimization problem in contrast to previous models the presented framework covers isotropic and kinematic hardening as well as isotropic and anisotropic elasticity and yield functions based on this approach a novel numerical implementation representing the main contribution of the paper is given in sharp contrast to by now classical approaches such as the return mapping algorithm and analogously to the theoretical part the numerical formulation is variationally consistent i e all unknown variables follow naturally from minimizing the energy of the considered system consequently several different numerically efficient and robust optimization schemes can be directly employed for solving the resulting minimization problem extending previously published works on variational constitutive updates the advocated model does not rely on any material symmetry and therefore it can be applied to a broad range of different plasticity theories as two examples an anisotropic hill type and a barlat type model are implemented numerical examples demonstrate the applicability and the performance of the proposed implementation

alternative ways for formulation of hybrid stress elements an element stiffness matrix can be derived by the conventional potential energy principle and indirectly also by generalized variational principles such as the hu washizu principle and the hellinger reissner principle the present investigation has the objective to show an approach which is concerned with the formulation of incompatible elements for solid continuum and for plate bending problems by the hellinger reissner principle it is found that the resulting scheme is equivalent to that considered by tong 1982 for the construction of hybrid stress elements in tong s scheme the inversion of a large flexibility matrix can be avoided it is concluded that the introduction of additional internal displacement modes in mixed finite element formulations by the hellinger reissner principle and the hu washizu principle can lead to element stiffness matrices which are equivalent to the assumed stress hybrid method

an internal variable variational formulation of viscoplasticity in the paper evolutive processes and variational principles in viscoplasticity are examined in detail the treatment is faced by the recourse to an internal variable formulation and by taking advantage of the appropriate tools in order to deal with multivalued operators this general framework enables the development of a consistent variational formulation for viscoplastic models for this purpose the problem at hand is set in operational form by encompassing into a unique expression the field equations and the constitutive equations the viscoplastic structural operator in all variables is accordingly integrated a family of viscoplastic potentials is deduced and the relevant sequence of extremum properties in one or more unknown variables is derived

variationally consistent state determination algorithms for nonlinear mixed beam finite elements abstract this paper presents and evaluates several variationally consistent state determination algorithms for geometric and material nonlinear beam finite elements based on the hellinger reissner hr assumed stress variational principle the specifically targeted element type is derived from the two field displacement and generalized stress form of this principle momentum balance and strain compatibility are expressed in a weak form and the constitutive equations are satisfied directly at each integration point i e section along the element length a specific formulation of one element of this type is presented in a companion paper interelement compatibility is not enforced in the dual stress resultant variables for this element and thus various state determination algorithms can be formulated at the local i e element and section levels four state determination algorithms referred to as the l l l n n l and n n procedures are considered the first symbol in these names indicates the element level and the second denotes the section level furthermore the symbol n indicates that local nonlinear iteration is performed prior to returning to the higher level whereas the symbol l indicates that only the linearized equations are satisfied at the corresponding local level the l l algorithm corresponds to conventional newton iteration on both the element and section levels whereas the n n algorithm entails the iterative satisfaction of the nonlinear element compatibility and section constitutive equations for each global iteration the performance of these algorithms is evaluated and compared it is found that the algorithms in which the local nonlinear strain displacement compatibility conditions are solved iteratively at the element level for every global iteration lead to fewer global iterations at the expense of iterations at the element level in particular the n n algorithm is overall the most efficient of the four algorithms for the problems tested also the n n algorithm has substantially smaller element storage requirements the n n algorithm is expected to be particularly advantageous for cases in which a large number of elements remain elastic and inelasticity is concentrated in a few elements

finite element shakedown analysis of two dimensional structures in the present paper the formulation proposed by casciaro and garcea comput meth appl mech eng 2002 191 5761 5792 and applied to the shakedown analysis of plane frames is extended to the analysis of two dimensional flat structures in both the cases of plane stress and plane strain the discrete formulation is obtained using a mixed finite element in which both stress and displacement fields are interpolated the material is assumed to be elasto plastic and a linearization of the elastic domain is performed the result is a versatile iterative scheme well suited to implementation in general purpose fem codes an extensive series of numerical tests is presented showing the reliability of the proposed formulation copyright 2005 john wiley sons ltd

development and testing of stable invariant isoparametric curvilinear 2 and 3 d hybrid stress elements abstract linear and quadratic serendipity hybrid stress elements are examined in respect of stability coordinate invariance and optimality a formulation based upon symmetry group theory successfully addresses these issues in undistorted geometries and is fully detailed for plane elements the resulting least order stable invariant stress polynomials can be applied as astute approximations in distorted cases through a variety of tensor components and variational principles a distortion sensitivity study for two and three dimensional elements provides favourable numerical comparisons with the assumed displacement method

accelerated variance reduction stochastic admm for large scale machine learning recently many stochastic variance reduced alternating direction methods of multipliers admms e g sag admm and svrg admm have made exciting progress such as linear convergence rate for strongly convex sc problems however their best known convergence rate for non strongly convex non sc problems is o 1 t as opposed to o 1 t 2 of accelerated deterministic algorithms where t is the number of iterations thus there remains a gap in the convergence rates of existing stochastic admm and deterministic algorithms to bridge this gap we introduce a new momentum acceleration trick into stochastic variance reduced admm and propose a novel accelerated svrg admm method called asvrg admm for the machine learning problems with the constraint ax by c then we design a linearized proximal update rule and a simple proximal one for the two classes of admm style problems with b i and b i respectively where i is an identity matrix and is an arbitrary bounded constant note that our linearized proximal update rule can avoid solving sub problems iteratively moreover we prove that asvrg admm converges linearly for sc problems in particular asvrg admm improves the convergence rate from o 1 t to o 1 t 2 for non sc problems finally we apply asvrg admm to various machine learning problems and show that asvrg admm consistently converges faster than the state of the art methods

on uniqueness of the dynamic finite step problem in gradient dependent softening plasticity the dynamic evolution of an elastoplastic softening solid is considered a material model including in the yield function the laplacian of the plastic multiplier is used to regularize the problem the dynamic finite step problem is formulated according to a generalized mid point integration scheme space discretization is carried out by a mixed finite element technique based on generalized variables a sufficient uniqueness condition of the finite step solution is proved for a one dimensional problem also a necessary and sufficient condition is presented a simple numerical test shows the regularizing properties mesh independence of the proposed model and the positive influence of the gradient term also on the time step amplitude ensuring uniqueness of solution

robust multicategory support matrix machines we consider the classification problem when the input features are represented as matrices rather than vectors to preserve the intrinsic structures for classification a successful method is the support matrix machine smm in 19 which optimizes an objective function with a hinge loss plus a so called spectral elastic net penalty however the issues of extending smm to multicategory classification still remain moreover in practice it is common to see the training data contaminated by outlying observations which can affect the robustness of existing matrix classification methods in this paper we address these issues by introducing a robust angle based classifier which boils down binary and multicategory problems to a unified framework benefitting from the use of truncated hinge loss functions the proposed classifier achieves certain robustness to outliers the underlying optimization model becomes nonconvex but admits a natural dc difference of two convex functions representation we develop a new and efficient algorithm by incorporating the dc algorithm and primal dual first order methods together the proposed dc algorithm adaptively chooses the accuracy of the subproblem at each iteration while guaranteeing the overall convergence of the algorithm the use of primal dual methods removes a natural complexity of the linear operator in the subproblems and enables us to use the proximal operator of the objective functions and matrix vector operations this advantage allows us to solve large scale problems efficiently theoretical and numerical results indicate that for problems with potential outliers our method can be highly competitive among existing methods

incremental shakedown analysis in the case of thermal effects a new method of performing the shakedown analysis of structures subjected to variable repeated loads and temperature fields is presented the method employs the standard incremental elastic plastic finite element algorithm and is based upon a cyclic repetition of piecewise proportional paths that contain all the vertices of the load temperature variation domain a numerical example illustrates the approach

implicit dynamics in the material point method abstract a time implicit discretization is derived and validated for the material point method mpm the resulting non linear discrete equations are solved using newton s method combined with either the conjugate gradient method or the generalized minimum residual method these newton krylov solvers are implemented in a matrix free fashion for numerical efficiency a description of the algorithms and evaluation of their performance is presented on all test problems if the time step is chosen appropriately the implicit solution technique is more efficient than an explicit method without loss of desired features in the solutions in a dramatic example time steps 10 000 times the explicit step size are possible for the large deformation compression of a cylindrical billet at 1 2 the computational cost

complementarity framework for non linear dynamic analysis of skeletal structures with softening plastic hinges in this paper we describe an algorithm for the incremental state update of elasto plastic systems with softening the algorithm uses a complementary pivoting technique and is based on casting the incremental state update as a complementarity problem in developing the algorithm we take advantage of the special features of solid and structural mechanics problems to achieve good computational performance and hence the ability to compute numerical solutions to practical size problems for example the notion of a tangent stiffness matrix arises numerical examples using models of skeletal structures are presented to demonstrate the practicability of the algorithm the numerical examples also raise some interesting questions about multiplicity of the solutions copyright 2010 john wiley sons ltd

random coding error exponents for two dimensional flat fading channels with complete channel state information in this correspondence we consider the random coding error exponent for nondispersive two dimensional 2 d quadrature fading channels for which the channel state information csi is perfectly known at the receiver and the input to the transmitter is constrained in its average power also the effect of space diversity on improving the performance is demonstrated the results obtained in this correspondence shed light on the effect of fading on communications reliability as well as the amount of coding complexity required to achieve a certain decoding error rate a treatment for the random coding error exponent for time correlated flat fading channels with rayleigh fading and bessel function correlation the jake s model is also provided

on projection algorithms for solving convex feasibility problems due to their extraordinary utility and broad applicability in many areas of classical mathematics and modern physical sciences most notably computerized tomography algorithms for solving convex feasibility problems continue to receive great attention to unify generalize and review some of these algorithms a very broad and flexible framework is investigated several crucial new concepts which allow a systematic discussion of questions on behaviour in general hilbert spaces and on the quality of convergence are brought out numerous examples are given

strain driven homogenization of inelastic microstructures and composites based on an incremental variational formulation the paper investigates computational procedures for the treatment of a homogenized macro continuum with locally attached micro structures of inelastic constituents undergoing small strains the point of departure is a general internal variable formulation that determines the inelastic response of the constituents of a typical micro structure as a generalized standard medium in terms of an energy storage and a dissipation function consistent with this type of inelasticity we develop a new incremental variational formulation of the local constitutive response where a quasi hyperelastic micro stress potential is obtained from a local minimization problem with respect to the internal variables it is shown that this local minimization problem determines the internal state of the material for finite increments of time we specify the local variational formulation for a setting of smooth single surface inelasticity and discuss its numerical solution based on a time discretization of the internal variables the existence of the quasi hyperelastic stress potential allows the extension of homogenization approaches of elasticity to the incremental setting of inelasticity focusing on macro strain driven micro structures we develop a new incremental variational formulation of the global homogenization problem where a quasi hyperelastic macro stress potential is obtained from a global minimization problem with respect to the fine scale displacement fluctuation field it is shown that this global minimization problem determines the state of the micro structure for finite increments of time we consider three different settings of the global variational problem for prescribed linear displacements periodic fluctuations and constant stresses on the boundary of the micro structure and discuss their numerical solutions based on a spatial discretization of the fine scale displacement fluctuation field the performance of the proposed methods is demonstrated for the model problem of von mises type elasto visco plasticity of the constituents and applied to a comparative study of micro to macro transitions of inelastic composites copyright 2002 john wiley sons ltd

faster convergence rates of relaxed peaceman rachford and admm under regularity assumptions in this paper we provide a comprehensive convergence rate analysis of the douglas rachford splitting drs peaceman rachford splitting prs and alternating direction method of multipliers admm algorithms under various regularity assumptions including strong convexity lipschitz differentiability and bounded linear regularity the main consequence of this work is that relaxed prs and admm automatically adapt to the regularity of the problem and achieve convergence rates that improve upon the tight worst case rates that hold in the absence of such regularity all of the results are obtained using simple techniques

a displacement like finite element model for j2 elastoplasticity variational formulation and finite step solution abstract the displacement like finite element formulation for finite step j2 elastoplasticity is revisited in this paper the classical computational strategy according to which plastic loading is tested at the gauss points of each element and an independent return mapping algorithm is performed for given incremental displacements is consistently derived from a suitably discretized version of a min max variational principle the sequence of solution phases to be performed within each load step adopting a full newton s method is illustrated in detail and the importance of a correct update of the plastic strains is emphasized it is further shown that in order to increase the rate of convergence and the stability properties of the newton s method the consistent elastoplastic tangent operator must be exploited even at the first iteration of each load step subsequent to the first yielding of the structural model this is in contrast with the traditional implementation according to which the elastic operator is used at the first iteration of each load step the effectiveness of the present approach is shown by a set of numerical examples referred to plane strain problems

a high performance element for the analysis of 2d elastoplastic continua abstract the paper presents a four node element for the analysis of 2d continua described by elastic perfectly plastic von mises laws its formulation is based on the assumed stress approach which has been widely tested in the elastic field the elastoplastic formulation of the element is obtained by enriching its variational basis with the weak enforcement of the plastic loading unloading conditions in this way the elastoplastic problem is formulated with respect to the stress parameters of the element consistently with the weak statement of the compatibility condition

treatment of internal constraints by mixed finite element methods unification of concepts a general method to generate assumed stress and strain fields within the context of mixed finite element methods is presented the assumed fields are constructed in such a way that internal constraints are satisfied a priori consequently the locking behaviour commonly observed in finite element solutions of problems with internal constraints is avoided to this end the assumed stress and strain fields are constructed to satisfy a priori the homogeneous part of the equilibrium equations thus avoiding fraeijs de veubeke s limitation principle results obtained using the proposed methodology on a nearly incompressible plane strain problem and thin plate application using a shear deformable theory are indicated

a variational constitutive update algorithm for a set of isotropic hyperelastic viscoplastic material models abstract in three dimensional formulations of plasticity the rate of plastic deformation is usually decomposed in direction and amplitude in the most simple cases of von mises type flows this allows to assume a known radial flow direction and computations are reduced to the determination of the amplitude of the plastification in the context of a variational formulation of finite plasticity it is verified that this decomposition between constitutive and kinematic aspects is accomplished by the choice of a quadratic elastic potential hencky model the aim of this paper is to show that a wide set of simple hyperelastic plastic isotropic models not restricted to quadratic elastic behavior can be constructed by relaxing the classical decomposition amplitude direction by the sum of spectral quantities in addition this approach allows for a unified and efficient numerical implementation in which a particular hyperelastic viscoplastic behavior is obtained by a specific choice of the elastic plastic and dissipative pseudo potentials

a nonlinear programming approach to kinematic shakedown analysis of frictional materials abstract this paper develops a novel nonlinear numerical method to perform shakedown analysis of structures subjected to variable loads by means of nonlinear programming techniques and the displacement based finite element method the analysis is based on a general yield function which can take the form of most soil yield criteria e g the mohr coulomb or drucker prager criterion using an associated flow rule a general yield criterion can be directly introduced into the kinematic theorem of shakedown analysis without linearization the plastic dissipation power can then be expressed in terms of the kinematically admissible velocity and a nonlinear formulation is obtained by means of nonlinear mathematical programming techniques and the finite element method a numerical model for kinematic shakedown analysis is developed as a nonlinear mathematical programming problem subject to only a small number of equality constraints the objective function corresponds to the plastic dissipation power which is to be minimized and an upper bound to the shakedown load can be calculated an effective direct iterative algorithm is then proposed to solve the resulting nonlinear programming problem the calculation is based on the kinematically admissible velocity with one step calculation of the elastic stress field only a small number of equality constraints are introduced and the computational effort is very modest the effectiveness and efficiency of the proposed numerical method have been validated by several numerical examples

the b bar method and the limitation principles abstract the generalized elastic material provides a reference model to cast in a unitary framework many structural models which are based on nonlinear monotone multivalued relations such as viscoelasticity plasticity and unilateral models the modified forms of the hu washizu and hellinger reissner principles and the displacement based variational formulation are recovered for the generalized elastic material starting from a functional in the complete set of state variables the related limitation principles are derived and their specialization to elasticity and elastoplasticity with mixed hardening are provided it is shown that the interpolating fields for the pressure and the volumetric strain usually adopted in the b bar method lead to a limitation principle accordingly the same elastic and elastoplastic solutions can be obtained by means of an approximate mixed displacement pressure variational principle a second application is concerned with the conditions ensuring the coincidence of the solutions between an approximate two field mixed formulation and the displacement based method numerical examples are provided to show the coincidence of the solutions obtained from different mixed finite element formulations in elasticity or elastoplasticity under the validity of the limitation principles

capacity bounds via duality with applications to multiple antenna systems on flat fading channels a technique is proposed for the derivation of upper bounds on channel capacity it is based on a dual expression for channel capacity where the maximization of mutual information over distributions on the channel input alphabet is replaced with a minimization of average relative entropy over distributions on the channel output alphabet we also propose a technique for the analysis of the asymptotic capacity of cost constrained channels the technique is based on the observation that under fairly mild conditions capacity achieving input distributions escape to infinity the above techniques are applied to multiple antenna flat fading channels with memory where the realization of the fading process is unknown at the transmitter and unknown or only partially known at the receiver it is demonstrated that for high signal to noise ratio snr the capacity of such channels typically grows only double logarithmically in the snr to better understand this phenomenon and the rates at which it occurs we introduce the fading number as the second order term in the high snr asymptotic expansion of capacity and derive estimates on its value for various systems it is suggested that at rates that are significantly higher than the fading number communication becomes extremely power inefficient thus posing a practical limit on practically achievable rates upper and lower bounds on the fading number are also presented for single input single output siso systems the bounds coincide thus yielding a complete characterization of the fading number for general stationary and ergodic fading processes we also demonstrate that for memoryless multiple input single output miso channels the fading number is achievable using beam forming and we derive an expression for the optimal beam direction this direction depends on the fading law and is in general not the direction that maximizes the snr on the induced siso channel using a new closed form expression for the expectation of the logarithm of a noncentral chi square distributed random variable we provide some closed form expressions for the fading number of some systems with gaussian fading including siso systems with circularly symmetric stationary and ergodic gaussian fading the fading number of the latter is determined by the fading mean fading variance and the mean squared error in predicting the present fading from its past it is not directly related to the doppler spread for the rayleigh ricean and multiple antenna rayleigh fading channels we also present firm nonasymptotic upper and lower bounds on channel capacity these bounds are asymptotically tight in the sense that their difference from capacity approaches zero at high snr and their ratio to capacity approaches one at low snr

product of two envelopes taken from alpha mu kappa mu and eta mu distributions this paper presents exact novel formulations for the probability density function and cumulative distribution function for the product of two independent and non identically distributed alpha mu kappa mu and eta mu variates the expressions are given in terms of both 1 generalized fox h function and 2 easily computable series expansions the formulations derived can be directly used to explore the performance of a number of wireless communication processes including multihop systems cascaded channels radar communications multiple input multiple output links and others due to the high flexibility of the above mentioned distributions the results presented here comprise a substantial number of useful product distributions as application examples performance metrics for the cascaded fading channel are derived the validity of the expressions is confirmed via monte carlo simulation it is noteworthy that because any composite multipath shadowing fading model is obtained as a particular case of the product of two fading variables the results given here provide a plethora of composite multipath shadowing fading scenarios

n ast nakagami a novel stochastic model for cascaded fading channels a generic and novel distribution referred to as nakagami constructed as the product of n statistically independent but not necessarily identically distributed nakagami m random variables rvs is introduced and analyzed the proposed distribution turns out to be a very convenient tool for modelling cascaded nakagami m fading channels and analyzing the performance of digital communications systems operating over such channels the moments generating probability density cumulative distribution and moments functions of the n nakagami distribution are developed in closed form using the meijer s g function using these formulas generic closed form expressions for the outage probability amount of fading and average error probabilities for several binary and multilevel modulation signals of digital communication systems operating over the n nakagami fading and the additive white gaussian noise channel are presented complementary numerical and computer simulation performance evaluation results verify the correctness of the proposed formulation the suitability of the n nakagami fading distribution to approximate the lognormal distribution is also being investigated using kolmogorov smirnov tests the rate of convergence of the central limit theorem as pertaining to the multiplication of nakagami m rvs is quantified

a novel unified expression for the capacity and bit error probability of wireless communication systems over generalized fading channels analysis of the average binary error probabilities abep and average capacity ac of wireless communications systems over generalized fading channels have been considered separately in past years this paper introduces a novel moment generating function mgf based unified expression for the abep and ac of single and multiple link communications with maximal ratio combining in addition this paper proposes the hyper fox s h fading model as a unified fading distribution of a majority of the well known generalized fading environments as such the authors offer a generic unified performance expression that can be easily calculated and that is applicable to a wide variety of fading scenarios the mathematical formulism is illustrated with some selected numerical examples that validate the correctness of the authors newly derived results

an edge based finite element method es fem with adaptive scaled bubble functions for plane strain limit analysis abstract this paper deals with critical roles of cubic bubble functions for the edge based finite element method es fem formulation within the framework of the kinematic theorem for predicting the plastic collapse loads of structures we show that the bubble function can be scaled by a non zero coefficient alpha while the volumetric locking is entirely eliminated based on this finding the present method is designed in a very small value with a bubble function that is maximum at the center of the element this can lead to the loss of the partition of unity for easy reference the present method is termed as bes fem the significant advantage of the present method lies in the rigorous treatment of the volumetric locking free that can occur in the fully plastic range the bes fem works well with high efficiency by using triangular meshes it achieves both simplicity and computational efficiency for implementation into packages of plastic limit analyses in case of bes fem the locking issue can be solved conveniently by two schemes 1 the usual piecewise linear displacements enriched with a cubic bubble function on a primal mesh of triangular elements and 2 a projection operator of strain rates through a dual mesh associated with the edges in the mesh the optimization formulation of finite element limit analysis is written in the form of a second order cone programming socp the well established interior point solvers can be exploited efficiently the bes fem using a small number of integration points enables to solve the large scale optimization problems efficiently in addition an adaptive meshing procedure based on an alternative indicator of dissipation is also derived to further enhance the quality of the solution without increasing significantly the number of degrees of freedom of the model numerical results show the robustness of the proposed method

a unified approach for variationally consistent finite elements in elastoplasticity abstract a general variationally consistent approach for elastoplastic finite element analysis is presented a weak formulation of the finite step i e in terms of finite increments elastoplastic boundary value problem is obtained by enforcing the stationarity of a mixed functional of hu washizu type a peculiarity of the present formulation is that the constitutive equations are expressed in weak form also all fields are then independently discretized in terms of so called generalized variables the result is a set of non linear algebraic equations a subset of which can be interpreted as the backward difference time integrated constitutive law of the finite element an iterative procedure where all calculations are at the element and not at the gauss point level resting on newton raphson scheme is proposed for the solution of the governing equations it is shown how the customary displacement approach and also some other mixed formulations in elastoplasticity can be regarded as special cases of the present formulation

mixed finite element methods reduced and selective integration techniques a unification of concepts the equivalence of certain classes of mixed finite element methods with displacement methods which employ reduced and selective integration techniques is established this enables one to obtain the accuracy of the mixed formulation without incurring the additional computational expense engendered by the auxiliary field of the mixed method applications and numerical examples are presented for problems with constraints which can be difficult to enforce in finite element approximations and have often dictated the use of mixed principles these include thin beams and plates and linear and nonlinear incompressible and nearly incompressible continuum problems in solid and fluid mechanics

convergence rate analysis of the forward douglas rachford splitting scheme operator splitting schemes are a class of powerful algorithms that solve complicated monotone inclusion and convex optimization problems that are built from many simpler pieces they give rise to algorithms in which all simple pieces of the decomposition are processed individually this leads to easily implementable and highly parallelizable or distributed algorithms which often obtain nearly state of the art performance in this paper we analyze the convergence rate of the forward douglas rachford splitting fdrs algorithm which is a generalization of the forward backward splitting fbs and douglas rachford splitting algorithms under general convexity assumptions we derive the ergodic and nonergodic convergence rates of the fdrs algorithm and show that these rates are the best possible under lipschitz differentiability assumptions we show that the best iterate of fdrs converges as quickly as the last iterate of the fbs algorithm under strong convexity assumptions we derive convergence rates

extremum properties of finite step solutions in elastoplasticity with nonlinear mixed hardening abstract the class of elastic plastic constitutive laws assumed herein can be described as follows we envisage y 1 yield criteria or modes which define the current yield surface each yield function consists of two addends an effective stress and a yield limit y 1 y the former is an order one positively homogeneous function of the difference between the stresses ii and reference stresses ii which are generally nonlinear functional of the plastic strain history so that kinematic hardening is accounted for the yield limit y is generally a nonlinear function of y nondecreasing internal variables so that another hardening mechanism which may reduce to isotropic hardening is accommodated in the model the rates of these variables play the role of plastic multipliers in the flow rule a finite step in the geometrically linear evolutive analysis of such solids is defined according to the backward difference or stepwise holonomic strategy for approximate time integration for the finite step boundary value problem thus arising various extremum characterizations of solutions are established and the underlying constitutive restrictions are pointed out and discussed

effects of softening in elastic plastic structural dynamics softening understood as unstable behaviour of material or structural components is considered herein for its possible consequences on the overall behaviour of discrete dynamic models of elastic plastic beam structures in the absence of geometric effects it is shown that multiplicity of incremental solutions response bifurcations and manifestations of overall instability may occur the bifurcated responses may exhibit different scenarios for the same excitation e g shakedown or local damage up to failure an insight into and criteria for such occurrences are achieved by formulating the rate and the finite increment problem as linear complementarity problems period doubling and deterministic chaos under harmonic excitation are observed when reversible holonomic softening behaviour is assumed the strong sensitivity of the phenomena investigated with respect to the choice of the structural model is pointed out the findings are elucidated by illustrative examples

arock an algorithmic framework for asynchronous parallel coordinate updates finding a fixed point to a nonexpansive operator i e x tx abstracts many problems in numerical linear algebra optimization and other areas of data science to solve fixed point problems

accuracy and stability of integration algorithms for elastoplastic constitutive relations an analysis of accuracy and stability of algorithms for the integration of elastoplastic constitutive relations is carried out in this paper reference is made to a very general internal variable formulation of plasticity and to two families of algorithms that generalize the well known trapezoidal and midpoint rules to fit the present context other integration schemes such as the radial return mean normal and closest point procedures are particular cases of this general formulation the meaning of first and second order accuracy in the presence of the plastic consistency condition is examined in detail and the criteria derived are used to identify two second order accurate members of the proposed algorithms a general methodology is also derived whereby the numerical stability properties of integration schemes can be systematically assessed with the aid of this methodology the generalized midpoint rule is seen to have far better stability properties than the generalized trapezoidal rule finally numerical examples are presented that illustrate the performance of the algorithms

a discrete formulation for elastic solids with damaging interfaces abstract an elastic solid with embedded interfaces loci of possible displacement discontinuities is considered here decohesion and quasi brittle fracture processes are simulated by making use of softening interface laws which relate tractions to displacements jumps a discrete formulation in terms of interface variables only is obtained the space discretization is carried out by means of a mixed finite element approach in which all interface variables are modelled study of uniqueness of the rate problem formulated in terms of interface variables and of stability of the equilibrium states is presented some examples are shown in order to clarify the formulation

h transforms for wireless communication the h transforms are integral transforms that involve fox s h functions as kernels a large variety of integral transforms can be put into particular forms of the h transform since h functions subsume most of the known special functions including meijer s g functions in this paper we embody the h transform theory into a unifying framework for modeling and analysis in wireless communication first we systematize the use of elementary identities and properties of the h transform by introducing operations on parameter sequences of h functions we then put forth h fading and degree 2 irregular h fading to model radio propagation under composite specular and or inhomogeneous conditions the h fading describes composite effects of multipath fading and shadowing as a single h variate including most of typical models such as rayleigh nakagami m weibull alpha mu n ast nakagami m generalized k fading and weibull gamma fading as its special cases as a new class of h variates called the degree zeta irregular h variate the degree 2 irregular h fading characterizes specular and or inhomogeneous radio propagation in which the multipath component consists of a strong specularly reflected or line of sight los wave as well as unequal power or correlated in phase and quadrature scattered waves this fading includes a variety of typical models such as rician nakagami q kappa mu eta mu rician los gamma and kappa mu los gamma fading as its special cases finally we develop a unifying h transform analysis for the amount of fading error probability channel capacity and error exponent in wireless communication using the new systematic language of transcendental h functions by virtue of two essential operations called mellin and convolution operations involved in the mellin transform and mellin convolution of two h functions the h transforms for these performance measures culminate in h functions using the algebraic asymptotic expansions of the h transform we further analyze the error probability and capacity at high and low signal to noise ratios in a unified fashion

linear convergence and metric selection for douglas rachford splitting and admm recently several convergence rate results for douglas rachford splitting and the alternating direction method of multipliers admm have been presented in the literature in this paper we show global linear convergence rate bounds for douglas rachford splitting and admm under strong convexity and smoothness assumptions we further show that the rate bounds are tight for the class of problems under consideration for all feasible algorithm parameters for problems that satisfy the assumptions we show how to select step size and metric for the algorithm that optimize the derived convergence rate bounds for problems with a similar structure that do not satisfy the assumptions we present heuristic step size and metric selection methods

quadratic velocity linear stress interpolations in limit analysis summary we compare a family of mixed interpolations on triangles with straight edges as applied to limit analysis the aim of this paper is to prove theoretically that the approximate collapse factors obtained with these finite elements always comply with certain inequalities that exist among them two of these interpolations are used in limit analysis for the first time in this article the inequalities in the proposition are also demonstrated via numerical applications to this end the most frequently used benchmark problems in limit analysis are revisited and discussed with respect to the results computed with these finite elements copyright 2014 john wiley sons ltd

a symmetric galerkin boundary domain element method for finite elastic deformations abstract the symmetric galerkin boundary element method sgbem is reformulated for problems of finite elasticity with hyperelastic material and incompressibility using fundamental solutions related to a fictitious homogeneous isotropic and compressible linear elastic material the proposed formulation contains besides the standard boundary integrals domain integrals which account for the problem s nonlinearities through some fictitious initial strain and stress fields required to satisfy appropriate consistency equations the boundary domain integral equation problem so obtained is shown to admit a stationarity principle a consequence of the hu washizu one which covers a number of particular cases including the compressible case as well as the fully linear case either incompressible and compressible so recovering known results of the literature the continuum rate problem is also addressed and suitably discretized by boundary and domain elements the related algebraic solving equation system is shown to exhibit symmetry and some sign definiteness features it is formally solved in terms of the node values of the displacement gradient the idrostatic pressure the initial strain and stress fields a long with the unknown boundary displacements and tractions details regarding the fundamental solutions and the stationarity principle are reported in three appendices at the end of the paper

an iteration algorithm for kinematic shakedown analysis abstract this paper investigates the computational shakedown analysis of an elastic plastic body subjected to a set of loads varying within a given domain using an ellipsoid yield surface an iteration algorithm based on a kinematic formulation is proposed to approach the shakedown load the convergence of the algorithm is guaranteed this algorithm can be applied to shakedown problems with strainhardening and certain geometric effects numerical examples are presented to illustrate the validity of the present method

finding best approximation pairs relative to a convex and prox regular set in a hilbert space we study the convergence of an iterative projection reflection algorithm originally proposed for solving what are known as phase retrieval problems in optics there are two features that frustrate any analysis of iterative methods for solving the phase retrieval problem nonconvexity and infeasibility the algorithm that we developed called relaxed averaged alternating reflections raar was designed primarily to address infeasibility though our strategy has advantages for nonconvex problems as well in the present work we investigate the asymptotic behavior of the raar algorithm for the general problem of finding points that achieve the minimum distance between two closed convex sets in a hilbert space with empty intersection and for the problem of finding points that achieve a local minimum distance between one closed convex set and a closed prox regular set also possibly nonintersecting the nonconvex theory includes and expands prior results limited to convex sets with nonempty intersection to place the raar algorithm in context we develop parallel statements about the standard alternating projections algorithm and gradient descent all of the various algorithms are unified as instances of iterated averaged alternating proximal reflectors applied to a sum of regularized maximal monotone mappings

three dimensional limit analysis of rigid blocks assemblages part ii load path following solution procedure and validation a novel solution procedure for the non associated limit analysis of rigid blocks assemblages is proposed this proposal produces better solutions than previously proposed procedures and it is also able to provide an insight into the structural behaviour prior to failure the limit analysis model proposed in part i of this paper and the solution procedure are validated through illustrative examples in three dimensional masonry piers and walls the use of limit analysis for three dimensional problems incorporating non associated flow rules and a coupled yield surface is novel in the literature

a two scale finite element relaxation analysis of shear bands in non convex inelastic solids small strain theory for standard dissipative materials abstract we propose a fundamentally new approach to the treatment of shear band localizations in strain softening elastic plastic solids at small strains based on energy minimization principles associated with micro structure developments the point of departure is a general internal variable formulation that determines the inelastic response as a standard dissipative medium consistent with this type of inelasticity we consider an incremental variational formulation of the local constitutive response where a quasihyperelastic stress potential is obtained from a local constitutive minimization problem with respect to the internal variables the existence of this variational formulation allows the definition of the material stability of an inelastic solid based on weak convexity conditions of the incremental stress potential in analogy to treatments in finite elasticity furthermore localization phenomena are interpreted as micro structure developments on multiple scales associated with non convex incremental stress potentials in analogy to elastic phase decomposition problems these micro structures can be resolved by the relaxation of non convex energy functionals based on a convexification of the stress potential the relaxed problem provides a well posed formulation for a mesh objective analysis of localizations as close as possible to the non convex original problem we develop based on an approximated rank one convexification of the incremental stress potential a computational two scale procedure for a mesh objective treatment of localization problems it constitutes a local minimization problem for a relaxed incremental stress potential with just one scalar variable representing the intensity of the micro shearing of a rank one laminate aligned to the shear band this problem is sufficiently robust with regard to applications to large scale inhomogeneous deformation processes of elastic plastic solids the performance of the proposed energy relaxation method is demonstrated for a representative set of numerical simulations of straight and curved shear bands which illustrate the mesh independence of the results

the variational formulation of viscoplastic constitutive updates we present a class of constitutive updates for general viscoplastic solids including such aspects of material behavior as finite elastic and plastic deformations non newtonian viscosity rate sensitivity and arbitrary flow and hardening rules the distinguishing characteristic of the proposed constitutive updates is that by construction the corresponding incremental stress strain relations derive from a pseudo elastic strain energy density this in turn confers the incremental boundary value problem a variational structure in particular the incremental deformation mapping follows from a minimum principle this minimum principle may conveniently be taken as a basis for error estimation and mesh adaption the accuracy and robustness of the variational constitutive updates is demonstrated with the aid of convergence tests involving the finitely deforming mises solid and ductile single crystals the ability of the updates to resolve the complex patterns of slip activity which arise in the latter application is particularly noteworthy

a consistent approach to continuum and discrete rate elastoplastic structural problems abstract the rate elasto plastic structural problem with hardening is presented and is cast within the general theory of structural models with convex constraints a consistent derivation of the constitutive variational principles is performed and the equivalence with the elastic predictor plastic corrector scheme of computational plasticity is proved following general concepts of convex analysis and of potential theory the more general variational formulation is derived the space discretization is achieved by the finite element approach the definition of a global yield function instead of a local one leads to a unique scalar plastic multiplier instead of a field of plastic multipliers and avoids their discretization mixed variational principles can thus be derived from the continuous ones and related computational schemes are also presented

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

mixed finite element formulations and related limitation principles a general treatment abstract the complete set of variational principles for an elastic structural model with non homogeneous boundary conditions and inelastic strains is presented a general methodology for deriving the approximate mixed formulation and the relevant matrix form is also shown and applied the limitation principles for a structural model with a linear elastic behaviour are derived and it is shown that each principle relating two different approximate formulations depends upon the state variable interpolated in one formulation and not in the other

a strain gradient isotropic elastoplastic damage model with j3 dependence abstract a plastic strain gradient version of an isotropic elastoplastic damage model that depends on the third invariant j3 of the stress deviator is developed the model is based on the non local equivalent plastic strain ep defined by peerlings et al 2001 and engelen et al 2003 and introduces a material length l to the constitutive equations it is shown that the non local equivalent plastic strain ep at a material point p can be identified with the average value of the local von mises equivalent plastic strain e p over a sphere centered at p and of radius approximately equal to 3 l a methodology for the numerical integration of the constitutive equations is presented the algorithm is appropriate for rate independent as well as rate dependent viscoplastic models the model is implemented in the abaqus general purpose finite element program and both quasi static and dynamic problems are solved two possible abaqus implementations are discussed first user elements are developed which can be used for the solution of both quasi static and dynamic problems reduced 1 point gauss integration is discussed in 8 node hexahedral elements and the physical stabilization method of puso 2000 is used to remove the resulting numerical singularities hourglass control second the implementation of the model via user material subroutines is discussed quasi static problems can be solved with abaqus standard using a coupled temperature displacement steady state analysis together with user subroutine umat in which temperature is identified with the non local equivalent plastic strain ep the solution of dynamic problems requires use of abaqus explicit together with a dynamic temperature displacement analysis option and user subroutines vumat and dflux several example problems are solved

on the linear convergence of the admm in decentralized consensus optimization in decentralized consensus optimization a connected network of agents collaboratively minimize the sum of their local objective functions over a common decision variable where their information exchange is restricted between the neighbors to this end one can first obtain a problem reformulation and then apply the alternating direction method of multipliers admm the method applies iterative computation at the individual agents and information exchange between the neighbors this approach has been observed to converge quickly and deemed powerful this paper establishes its linear convergence rate for the decentralized consensus optimization problem with strongly convex local objective functions the theoretical convergence rate is explicitly given in terms of the network topology the properties of local objective functions and the algorithm parameter this result is not only a performance guarantee but also a guideline toward accelerating the admm convergence

non smooth multisurface plasticity and viscoplasticity loading unloading conditions and numerical algorithms rate independent plasticity and viscoplasticity in which the boundary of the elastic domain is defined by an arbitrary number of yield surfaces intersecting in a non smooth fashion are considered in detail it is shown that the standard kuhn tucker optimality conditions lead to the only computationally useful characterization of plastic loading on the computational side an unconditionally convergent return mapping algorithm is developed which places no restrictions aside from convexity on the functional forms of the yield condition flow rule and hardening law the proposed general purpose procedure is amenable to exact linearization leading to a closed form expression of the so called consistent algorithmic tangent moduli for viscoplasticity a closed form algorithm is developed based on the rate independent solution the methodology is applied to structural elements in which the elastic domain possesses a non smooth boundary numerical simulations are presented that illustrate the excellent performance of the algorithm

shakedown analysis in poroplasticity by linear programming static lower bound and kinematic upper bound theorems for shakedown analysis and limit analysis as special case are presented for two phase fully saturated poroplastic solids in a context characterized by the following features quasi static non associative non softening perfect or hardening poroplasticity piecewise linearized yield loci and hardening constant permeability linear fluid transport law small deformations non traditional galerkin finite element discretization with reference to cyclic periodic external actions numerical examples centred on linear programming evidence the computational potentialities and limitations of direct non evolutive methods of integrity assessment according to limit state design concepts in poroplasticity copyright 2000 john wiley sons ltd

plane isoparametric hybrid stress elements invariance and optimal sampling formulation and applications of the hybrid stress finite element model to plane elasticity problems are examined conditions for invariance of the element stiffness are established for two dimensional problems the results of which are easily extended to three dimensional cases next the hybrid stress functional for a 3 d continuum is manipulated into a more convenient form in which the location of optimal stress strain sampling points can be identified to illustrate these concepts 4 and 8 node plane isoparametric hybrid stress elements which are invariant and of correct rank are developed and compared with existing hybrid stress elements for a 4 node element lack of invariance is shown to lead to spurious zero energy modes under appropriate element rotation alternative 8 node elements are considered and the best invariant element is shown to be one in which the stress compatibility equations are invoked results are also presented which demonstrate the validity of the optimal sampling points the effects of reduced orders of numerical integration and the behaviour of the elements for nearly incompressible materials

a variational theory for finite step elasto plastic problems abstract an extended version ofgeneralized standard elasto plastic material is considered in the framework of an internal variable theory of associated plasticity according to a backward difference scheme for time integration of the flow rule a finite step structural problem is formulated in a geometrically linear range convex analysis and a brand new potential theory for monotone multivalued operators are shown to provide the natural mathematical setting for the derivation of the related variational formulation a general stationarity principle is obtained and then specialized to obtain a minimum principle in terms of displacements plastic strains and internal variables a critical comparison with an analogous minimum principle recently proposed in literature is performed showing the inadequacy of classical procedures in deriving non smooth variational formulations

finite elements with embedded displacement discontinuity a generalized variable formulation this paper is intended to bring a contribution towards a satisfactory simulation of those fracture phenomena which result in the appearance and development of discrete cracks to this purpose a general mixed finite element formulation is proposed based on the concept of generalized variables in prager s sense the displacement field inside an element is modelled by the sum of two contributions a regular continuous part which is governed by standard shape functions and a possibly discontinuous one which is introduced soon after a suitable criterion is satisfied the formulation is first specialized to a one dimensional case then a triangular element for two dimensional problems is described in detail analytical and numerical examples are presented in order to clarify the formulation and to point out the essential role of inter element conformity copyright 2000 john wiley sons ltd

a unified approach for displacement equilibrium and hybrid finite element models in elasto plasticity abstract finite element models for elasto plastic incremental analysis are derived from a three field variational principle the newton raphson method is applied to solve the nonlinear system of equations which is obtained from the stationarity condition of this principle the iterative schemes are discussed in detail for pure displacement and for pure equilibrium models from which iterative schemes for hybrid models follow directly in the displacement model the compatibility of the strains and the plasticity criterium are satisfied during the whole iterative process while the equilibrium of the stresses is restored only in the mean after convergence in the equilibrium model the plasticity criterium and the compatibility of the strains are verified in the mean during the iterative process when convergence is achieved the stresses are locally in equilibrium with the applied external loads in both cases a tangential stiffness matrix can be constructed even for perfectly plastic materials and it allows one to obtain always very good convergence properties examples are shown for plane stress and axisymmetric cases

the fading number of multiple input multiple output fading channels with memory the fading number of a general not necessarily gaussian regular multiple input multiple output mimo fading channel with arbitrary temporal and spatial memory is derived the channel is assumed to be noncoherent i e neither receiver nor transmitter have knowledge about the channel state but they only know the probability law of the fading process the fading number is the second term in the asymptotic expansion of channel capacity when the signal to noise ratio snr tends to infinity it is related to the border of the high snr region with double logarithmic capacity growth

an adaptive approach to limit analysis abstract the main objective of this paper is to propose an adaptive mesh refinement procedure for finite element models in limit analysis we use an a posteriori indicator based on the local directional interpolation error and a recovering scheme to compute second derivatives of the finite element solution the proposed mesh adaptation process gives improved results in localizing regions of rapid or abrupt variations of the variables whose location is not known a priori limit analysis of bodies in plane strain and plane stress is considered in the applications

computation of limit and shakedown loads using a node based smoothed finite element method summary this paper presents a novel numerical procedure for computing limit and shakedown loads of structures using a node based smoothed fem in combination with a primal dual algorithm an associated primal dual form based on the von mises yield criterion is adopted the primal dual algorithm together with a newton like iteration are then used to solve this associated primal dual form to determine simultaneously both approximate upper and quasi lower bounds of the plastic collapse limit and the shakedown limit the present formulation uses only linear approximations and its implementation into finite element programs is quite simple several numerical examples are given to show the reliability accuracy and generality of the present formulation compared with other available methods copyright 2011 john wiley sons ltd

on the equivalence of the primal dual hybrid gradient method and douglas rachford splitting the primal dual hybrid gradient pdhg algorithm proposed by esser zhang and chan and by pock cremers bischof and chambolle is known to include as a special case the douglas rachford splitting algorithm for minimizing the sum of two convex functions we show that conversely the pdhg algorithm can be viewed as a special case of the douglas rachford splitting algorithm

rational approach for assumed stress finite elements a new method for the formulation of hybrid elements by the hellinger reissner principle is established by expanding the essential terms of the assumed stresses as complete polynomials in the natural coordinates of the element the equilibrium conditions are imposed in a variational sense through the internal displacements which are also expanded in the natural co ordinates the resulting element possesses all the ideal qualities i e it is invariant it is less sensitive to geometric distortion it contains a minimum number of stress parameters and it provides accurate stress calculations for the formulation of a 4 node plane stress element a small perturbation method is used to determine the equilibrium constraint equations the element has been proved to be always rank sufficient

upper and lower bounds in limit analysis adaptive meshing strategies and discontinuous loading summary upper and lower bounds of the collapse load factor are here obtained as the optimum values of two discrete constrained optimisation problems the membership constraints for von mises and mohrcoulomb plasticity criteria are written as a set of quadratic constraints which permits to solve the optimisation problem using specific algorithms for second order conic program socp from the stress field at the lower bound and the velocities at the upper bound we construct a novel error estimate based on elemental and edge contributions to the bound gap these contributions are employed in an adaptive remeshing strategy that is able to reproduce fan type mesh patterns around points with discontinuous surface loading the solution of this type of problems is analysed in detail and from this study some additional meshing strategies are also described we particularise the resulting formulation and strategies to two dimensional problems in plane strain and we demonstrate the effectiveness of the method with a set of numerical examples extracted from the literature copyright c 2007 john wiley sons ltd