distribution estimation consistent in total variation and in two types of information divergence the problem of the nonparametric estimation of a probability distribution is considered from three viewpoints the consistency in total variation the consistency in information divergence and consistency in reversed order information divergence these types of consistencies are relatively strong criteria of convergence and a probability distribution cannot be consistently estimated in either type of convergence without any restrictions on the class of probability distributions allowed histogram based estimators of distribution are presented which under certain conditions converge in total variation in information divergence and in reversed order information divergence to the unknown probability distribution some a priori information about the true probability distribution is assumed in each case as the concept of consistency in information divergence is stronger than that of convergence in total variation additional assumptions are imposed in the cases of informational divergences

a general algorithm for limit solutions of plane stress problems a computational approach to limit solutions is considered most challenging for two major reasons a limit solution is likely to be non smooth such that certain non differentiable functions are perfectly admissible and make physical and mathematical sense moreover the possibility of non unique solutions makes it difficult to analyze the convergence of an iterative algorithm or even to define a criterion of convergence in this paper we use two mathematical tools to resolve these difficulties a duality theorem defines convergence from above and from below the exact solution a combined smoothing and successive approximation applied to the upper bound formulation perturbs the original problem into a smooth one by a small parameter e as e 0 the solution of the original problem is recovered this general computational algorithm is robust such that from any initial trial solution the first iteration falls into a convex hull that contains the exact solution s of the problem unlike an incremental method thut invariably renders the limit problem ill conditioned the algorithm is numerically stable limit analysis itself is a highly efficient concept which bypasses the tedium of the intermediate elastic plastic deformation and seeks the most important information directly with the said algorithm we have produced many limit solutions of plane stress problems certain non smooth characters of the limit solutions are shown in the examples presented two well known as well as one parametric family of yield functions are used to allow comparison with some classical solutions

on the interplay between conditional entropy and error probability fano s inequality relates the error probability of guessing a finitely valued random variable x given another random variable y and the conditional entropy of x given y it is not necessarily tight when the marginal distribution of x is fixed this paper gives a tight upper bound on the conditional entropy of x given y in terms of the error probability and the marginal distribution of x a new lower bound on the conditional entropy for countably infinite alphabets is also found the relationship between the reliability criteria of vanishing error probability and vanishing conditional entropy is also discussed a strengthened form of the schur concavity of entropy which holds for finite or countably infinite random variables is given

a mixed stress model for linear elastodynamics of arbitrarily curved beams this work presents a mixed stress finite element for linear elastodynamics of arbitrarily curved beams based on a modified hellinger reissner functional a rational approach to choose the stress approximation is proposed in particular the self equilibrated stress is augmented by some stress modes obtained from the lower order displacement approximation using the equilibrium equations in such a way that the total number of stress modes is equal to the number of strain modes the rationale is to preserve all the interactions among the stresses proper of a curved structure without compromising the flexibility of the element an arbitrarily curved geometry is described using a parametric hermitian interpolation scheme tuned by minimizing the initial curvature of the arch the effectiveness of the present approach is numerically demonstrated copyright 2007 john wiley sons ltd

an algorithm for plastic limit analysis abstract this paper introduces an algorithm for the limit analysis of perfectly plastic bodies the algorithm is based on the finite element technique and mathematical programming using an ellipsoid yield surface identical upper and lower bounds of the limit load can be determined for a discrete body in the case of using a non ellipsoid yield surface an iteration procedure is suggested to obtain the limit load in each iteration the non ellipsoid yield surface is approached by an ellipsoid at each point of the body the parameters of the approximated ellipsoid are different at different body points and determined based on the previous iteration numerical examples are presented to demonstrate the validity of the present method

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

modeling and computation of shakedown problems for nonlinear hardening materials abstract the paper is concerned with shakedown analysis of perfectly plastic nonlinear kinematic hardening linear unlimited kinematical hardening and cyclic kinematical hardening materials a 3 d overlay model being able to describe nonlinear kinematic hardening material behavior is reviewed and a static shakedown theorem is formulated which is shown to be an extension of the melan s static shakedown theorems for both perfectly plastic and linear unlimited kinematic hardening materials different numerical algorithms are presented which efficiently solve the nonlinear discretized optimization problems using the finite element method the influence of kinematic hardening on shakedown limits is discussed it is shown how the exactness of the numerical shakedown limits can efficiently be improved by using the adaptive mesh refinement a possibility for analytical determination of shakedown limits in case of alternating plasticity is demonstrated by a square plate with a central circular hole under biaxial uniform loading the shakedown behaviour of materials with cyclic kinematical hardening has been investigated by an incremental computation method the theoretical and numerical aspects discussed are illustrated by the examples given in the paper

a spatially curved beam element with warping and wagner effects this paper presents a new spatially curved beam element with warping and wagner effects that can be used for the non linear large displacement analysis of members that are curved in space the non linear behaviour of members curved in space shows that the wagner effects are substantial in the large twist rotation analysis most existing finite beam element models such as abaqus and ansys cannot predict the non linear large displacement response of members curved in space correctly because the wagner effects viz the wagner moment and the corresponding finite strain terms have not been considered in these finite beam elements as a consequence these finite beam elements do not provide correct predictions for the out of plane buckling and postbuckling behaviour of arches as well in this paper the symmetric tangent stiffness matrix has been derived based on the finite rotations parameterized by the conventional displacements the warping and wagner effects both the wagner moment and the corresponding finite strain terms and their constitutive relationship are included in the spatially curved beam element two components of the initial curvature the initial twist and their interactions with the displacements are also considered in the spatially curved beam element this ensures that the large twist rotation analysis for the members curved in space is accurate comparisons with existing experimental analytical and numerical results show that the spatially curved beam element is accurate and efficient for the non linear elastic analysis of curved members buckling and postbuckling analysis of arches and in its ability to predict large deflections and twist rotations in more arbitrarily curved members copyright 2005 john wiley sons ltd

numerical shakedown analysis of damaged structures a numerical method is proposed to predict the failure of mechanical structures it is based on the generalization of the classical static shakedown theorem to damaged inelastic structures ductile plastic damage is taken into account by using the models of lemaitre and shichun hua the obtained results are compared in the special case of limit analysis to those obtained by incremental methods

in plane stability of arches classical buckling theory is mostly used to investigate the in plane stability of arches which assumes that the pre buckling behaviour is linear and that the effects of pre buckling deformations on buckling can be ignored however the behaviour of shallow arches becomes non linear and the deformations are substantial prior to buckling so that their effects on the buckling of shallow arches need to be considered classical buckling theory which does not consider these effects cannot correctly predict the in plane buckling load of shallow arches this paper investigates the in plane buckling of circular arches with an arbitrary cross section and subjected to a radial load uniformly distributed around the arch axis an energy method is used to establish both non linear equilibrium equations and buckling equilibrium equations for shallow arches analytical solutions for the in plane buckling loads of shallow arches subjected to this loading regime are obtained approximations to the symmetric buckling of shallow arches and formulae for the in plane anti symmetric bifurcation buckling load of non shallow arches are proposed and criteria that define shallow and non shallow arches are also stated comparisons with finite element results demonstrate that the solutions and indeed approximations are accurate and that classical buckling theory can correctly predict the in plane anti symmetric bifurcation buckling load of non shallow arches but overestimates the in plane anti symmetric bifurcation buckling load of shallow arches significantly

kinematic limit analysis of frictional materials using nonlinear programming abstract in this paper a nonlinear numerical technique is developed to calculate the plastic limit loads and failure modes of frictional materials by means of mathematical programming limit analysis and the conventional displacement based finite element method the analysis is based on a general yield function which can take the form of the mohr coulomb or drucker prager criterion by using an associated flow rule a general nonlinear yield criterion can be directly introduced into the kinematic theorem of limit analysis without linearization the plastic dissipation power can then be expressed in terms of kinematically admissible velocity fields and a nonlinear optimization formulation is obtained the nonlinear formulation only has one constraint and requires considerably less computational effort than a linear programming formulation the calculation is based entirely on kinematically admissible velocities without calculation of the stress field the finite element formulation of kinematic limit analysis is developed and solved as a nonlinear mathematical programming problem subject to a single equality constraint the objective function corresponds to the plastic dissipation power which is then minimized to give an upper bound to the true limit load an effective direct iterative algorithm for kinematic limit analysis is proposed in this paper to solve the resulting nonlinear mathematical programming problem the effectiveness and efficiency of the proposed method have been illustrated through a number of numerical examples

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

non linear buckling and postbuckling analysis of arches with unequal rotational end restraints under a central concentrated load abstract this paper presents an analytical study of the non linear elastic in plane buckling and postbuckling behaviour of pin ended shallow circular arches having unequal elastic rotational end restraints under a central concentrated radial load the principle of stationary potential energy is used to derive the differential equations of equilibrium based on which the analytical solution for the non linear equilibrium path is derived it is found that the non linear behaviour of an arch having unequal rotational end restraints is much more complicated than that of an arch with equal rotational end restraints the arch may have a non linear equilibrium path that consists of one or two unstable equilibrium paths and two or four limit points and it may even have a non linear looped equilibrium path in some cases the number of limit points on the non linear equilibrium path of an arch depends on its slenderness ratio and included angle and on the stiffnesses of the unequal rotational end restraints the switches in terms of an arch geometry parameter which is introduced in the paper are derived for distinguishing between arches with two limit points and those with four limit points as well as for distinguishing between arches and beams curved in elevation the principle of conservation of energy at neutral equilibrium is used to derive the differential equations of buckling equilibrium which are then used to investigate the buckling behaviour it is found that an arch with unequal rotational end restraints cannot buckle in a bifurcation mode comparisons with finite element results show that the analytical solutions can accurately predict the non linear buckling and postbuckling behaviour

universal weak variable length source coding on countably infinite alphabets motivated from the fact that universal source coding on countably infinite alphabets infty alphabets is not feasible this work introduces the notion of almost lossless source coding analog to the weak variable length source coding problem studied by han ieee trans inf theory vol 46 no 4 pp 1217 1226 jul 2000 almost lossless source coding aims at relaxing the lossless block wise assumption to allow an average per letter distortion that vanishes asymptotically as the block length tends to infinity in this setup we show on one hand that shannon entropy characterizes the minimum achievable rate similarly to the case of finite alphabet sources while on the other that almost lossless universal source coding becomes feasible for the family of finite entropy stationary memoryless sources with infty alphabets furthermore we study a stronger notion of almost lossless universality that demands uniform convergence of the average per letter distortion to zero where we establish a necessary and sufficient condition for the so called family of envelope distributions to achieve it remarkably this condition is the same necessary and sufficient condition needed for the existence of a strongly minimax lossless universal source code for the family of envelope distributions finally we show that an almost lossless coding scheme offers faster rate of convergence for the minimax redundancy compared to the well known information radius developed for the lossless case at the expense of tolerating a non zero distortion that vanishes to zero as the block length grows this shows that even when lossless universality is feasible an almost lossless scheme can offer different regimes on the rates of convergence of the worst case redundancy versus the worst case distortion

lower bound shakedown analysis by using the element free galerkin method and non linear programming abstract shakedown analysis is a powerful tool for assessing the safety of structures under variable repeated loads by using the element free galerkin efg method and non linear programming a novel numerical solution procedure is developed to perform lower bound shakedown analysis of structures made up of elasto perfectly plastic material the numerical implementation is very simple and convenient because it is only necessary to construct an array of nodes in the domain under consideration the reduced basis technique is adopted here to solve the mathematical programming iteratively in a sequence of reduced self equilibrium stress subspaces with very low dimensions the self equilibrium stress field is expressed by linear combination of several self equilibrium stress basis vectors with parameters to be determined these self equilibrium stress basis vectors are generated by performing an equilibrium iteration procedure during elasto plastic incremental analysis the complex method is used to solve the non linear programming and determine the lower bound of shakedown load the proposed numerical method is verified by using several numerical examples and the results show good agreement with other available solutions

limit analysis of ductile composites based on homogenization theory a numerical method is presented in this paper for determining the load bearing capacities of ductile composites such as metal matrix composites based on homogenization theory and the kinematic limit theorem a representative volume element is chosen to reflect the microstructure of a periodic composite by directly introducing the von mises yield criterion into the kinematic limit theorem a nonlinear optimization formulation can be obtained to calculate the ultimate strength of a ductile composite the finite element modelling of the kinematic limit analysis is formulated as a nonlinear mathematical programming problem with equality constraint conditions which can be solved by a direct iterative algorithm an interface failure model based on the microscopic fluctuation displacements is proposed to account for the effects of interfaces on the failure of composites the present method can effectively reveal the effects of the microstructure on the macroscopic properties and micromechanical failure mechanisms of composites finally some numerical examples illustrate the validity of the present method

the interplay between entropy and variational distance the relation between the shannon entropy and variational distance two fundamental and frequently used quantities in information theory is studied in this paper by means of certain bounds on the entropy difference between two probability distributions in terms of the variational distance between them and their alphabet sizes we also show how to find the distribution achieving the minimum or maximum entropy among those distributions within a given variational distance from any given distribution these results are applied to solve a number of problems that are of fundamental interest for entropy estimation we obtain an analytic formula for the confidence interval solving a problem that has been opened for more than 30 years for approximation of probability distributions we find the minimum entropy difference between two distributions in terms of their alphabet sizes and the variational distance between them in particular we show that the entropy difference between two distributions that are close in variational distance can be arbitrarily large if the alphabet sizes of the two distributions are unconstrained for random number generation we characterize the tradeoff between the amount of randomness required and the distortion in terms of variation distance new tools for non convex optimization have been developed to establish the results in this paper

mutual information metric entropy and cumulative relative entropy risk assume p theta theta epsilon theta is a set of probability distributions with a common dominating measure on a complete separable metric space y a state theta epsilon theta is chosen by nature a statistician obtains n independent observations y 1 dots y n from y distributed according to p theta for each time t between 1 and n based on the observations y 1 dots y t 1 the statistician produces an estimated distribution hat p t for p theta and suffers a loss l p theta hat p t the cumulative risk for the statistician is the average total loss up to time n of special interest in information theory data compression mathematical finance computational learning theory and statistical mechanics is the special case when the loss l p theta hat p t is the relative entropy between the true distribution p theta and the estimated distribution hat p t here the cumulative bayes risk from time 1 to n is the mutual information between the random parameter theta and the observations y 1 dots y n new bounds on this mutual information are given in terms of the laplace transform of the hellinger distance between pairs of distributions indexed by parameters in theta from these bounds on the cumulative minimax risk are given in terms of the metric entropy of theta with respect to the hellinger distance the assumptions required for these bounds are very general and do not depend on the choice of the dominating measure they apply to both finite and infinite dimensional theta they apply in some cases where y is infinite dimensional in some cases where y is not compact in some cases where the distributions are not smooth and in some parametric cases where asymptotic normality of the posterior distribution fails

a numerical method for plastic limit analysis of 3 d structures abstract based on the upper bound theorem of plasticity the 3 d limit analysis of rigid perfectly plastic structures is formulated as a discrete nonlinear mathematical programming problem with only equality constraints by means of the finite element technique the penalty function method is used to deal with the plastic incompressibility condition a direct iterative algorithm is employed in solving this formulation at each step of the iteration the rigid and plastic zones are continually distinguished the respective constraint conditions are imposed on them and the goal function is modified appropriately the numerical difficulties caused by the nonlinearity and nonsmoothness of the goal function and the incompressibility of plastic deformation are overcome the limit load multiplier and the associated velocity field computed by the iteration procedure converge monotonically to the upper bounds of real solutions the numerical procedure has been used to carry out the limit analysis for cylindrical shells with part through slot type defects under internal pressure numerical examples are given to demonstrate the applicability of the procedure

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

there is no universal source code for an infinite source alphabet shows that a discrete infinite distribution with finite entropy cannot be estimated consistently in information divergence as a corollary the authors show that there is no universal source code for an infinite source alphabet over the class of all discrete memoryless sources with finite entropy

mixed models and reduced selective integration displacement models for nonlinear analysis of curved beams simple mixed models are developed for the geometrically nonlinear analysis of deep arches a total lagrangian description of the arch deformation is used and the analytical formulation is based on a form of the nonlinear deep arch theory with the effects of transverse shear deformation included the fundamental unknowns consist of the six internal forces and generalized displacements of the arch and the element characteristic arrays are obtained by using hellinger reissner mixed variational principle the polynomial interpolation functions used in approximating the forces are one degree lower than those used for approximating the displacements and the forces are discontinuous at the interelement boundaries the equivalence between the mixed models developed herein and displacement models based on reduced integration of both the transverse shear and extensional energy terms is discussed the advantages of mixed models over equivalent displacement models are outlined numerical results are presented to demonstrate the high accuracy and effectiveness of the mixed models developed and compare their performance with other mixed models reported in the literature

a dual form for discretized kinematic formulation in shakedown analysis shakedown analysis with the discretization in kinematically admissible finite elements and the use of von mises yield criterion is considered in this paper the shakedown load multiplier formulated by kinematic theorem under nonlinear form is proved to be the primal form of the shakedown load multiplier formulated by static theorem based on this duality an efficient dual algorithm for shakedown analysis of structures is established and implemented connecting with finite element discretization technique some numerical examples are presented

numerical shakedown analysis of axisymmetric sandwich shells an upper bound formulation shakedown analysis of axisymmetric elastic perfectly plastic sandwich shells is performed here using a new upper bound formulation based on a special form of koiter s theorem concerning piecewise linearized yield surfaces starting from finite element techniques and the tresca sandwich yield condition shakedown analysis is reduced to a linear programming problem which is solved by a powerful simplex algorithm numerical results are given for a number of examples and a comparison is made with a previously computed lower bound formulation