the painleve property for partial differential equations in this paper we define the painleve property for partial differential equations and show how it determines in a remarkably simple manner the integrability the backlund transforms the linearizing transforms and the lax pairs of three well known partial differential equations burgers equation kdv equation and the modified kdv equation this indicates that the painleve property may provide a unified description of integrable behavior in dynamical systems ordinary and partial differential equations while at the same time providing an efficient method for determining the integrability of particular systems

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

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

shape optimization using reproducing kernel particle method and an enriched genetic algorithm combining reproducing kernel particle method rkpm with the proposed multi family genetic algorithm mfga a novel approach to continuum based shape optimization problems is brought forward in this paper taking full advantage of the features of meshfree method and the merits of mfga the new method solves shape optimization problems in such a unique way that remeshing is avoided and particularly the computation burden and errors caused by sensitivity analysis are eliminated completely the effectiveness versatility and performance of the proposed approach are demonstrated via three 2 d numerical examples

painleve expansions for nonintegrable evolution equations abstract the wtc method is applied to a variety of nonintegrable nonlinear evolution equations and shown to provide a systematic procedure for obtaining special solutions some of the special techniques developed for integrable systems are also shown to be applicable to nonintegrable equations

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

stable time step estimation for multi material eulerian hydrocodes the time step estimates used in explicit multi material eulerian hydrocodes are based on a series of upper bound approximations that can lead to unnecessarily small time steps since the cost of the calculation is proportional to the number of time steps the underestimation of the time step size has a direct adverse effect on the cost an accurate method for calculating the stable time step size is presented with example calculations

lie symmetry analysis and some new exact solutions of the wu zhang equation the lie symmetry analysis and the basic similarity reductions are performed for the wu zhang equation a 2 1 dimensional nonlinear dispersive wave equation some new exact solutions generated from the similarity transformation are provided they demonstrate some new three dimensional features of a single solitary wave and two interacting solitary waves

convergence of finite elements enriched with mesh less methods a combined hierarchical approximation based on finite elements and mesh less methods is proposed and studied finite elements are enriched adding hierarchical shape functions based on a particle distribution convergence results are presented and proved

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 simple error estimator and adaptive procedure for practical engineerng analysis a new error estimator is presented which is not only reasonably accurate but whose evaluation is computationally so simple that it can be readily implemented in existing finite element codes the estimator allows the global energy norm error to be well estmated and alos gives a good evaluation of local errors it can thus be combined with a full adaptive process of refinement or more simply provide guidance for mesh redesign which allows the user to obtain a desired accuracy with one or two trials when combined with an automatic mesh generator a very efficient guidance process to analysis is avaiable estimates other than the energy norm have successfully been applied giving for instance a predetermined accuracy of stresses

mixed formulation and locking in path following nonlinear analysis abstract the arc length riks strategy has rapidly become a standard tool for path following analysis of nonlinear structures due to its theoretical ability to surpass limit points the aim of this paper is to show that the failures in convergence that are occasionally experienced are not related to proper defects of the algorithm but come from a subtle locking effect intrinsic to the nonlinear nature of the problem as a consequence its sanitization has to be pursued within a reformulation of the structural model the use of a mixed stress displacement variant of the algorithm in particular appears very promising in this respect the topic is discussed with reference to the analysis of nonlinear frames using a mixed version of the nonlinear beam model discussed in 39 it is shown that with no extra computational cost and only a minor modification in coding with respect to a purely compatible formulation it is possible to achieve a noticeable improvement in convergence and a real gain in both computational time and overall robustness of the algorithm

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

new boundary condition treatments in meshfree computation of contact problems due to the loss of kronecker delta properties in the meshfree shape functions the imposition of essential boundary conditions consumes significant cpu time in meshfree computation in this work two boundary condition treatments are proposed to enhance the computational efficiency of meshfree methods for contact problems the mixed transformation method is modified from the previous full transformation method by introducing a node partitioning and a mixed coordinate so that the matrix inversion and multiplication of coordinate transformation involves operations only on the sub degrees of freedom associated with the boundary group the boundary singular kernel method introduces singularities to the kernel functions of the essential and contact boundary nodes so that the corresponding coefficients of the singular kernel shape functions recover nodal values and consequently kinematic constraints can be imposed directly the effectiveness of the proposed methods is demonstrated in several numerical examples

an iterative method for shakedown analysis abstract shakedown analysis for elastic perfect plastic structures is discussed and a fast incremental iterative solution method is proposed suitable for the fem analyses of large structures the theoretical motivations of the proposed method are discussed in detail and an example of its implementation is described with reference to plane frame analysis some numerical results are presented showing the numerical performances of the method

the singular manifold method revisited for many completely integrable partial differential equations pdes the singular manifold method of weiss allows the recovery of the lax pair and darboux transformation dt and so also the backlund transformation from a truncated painleve expansion recently the so called two singular manifold method has been proposed in order to handle pdes such as the modified korteweg de vries mkdv equation here we present a more natural extension of the weiss singular manifold method which makes use of only one singular manifold but is capable of dealing with such pdes in this approach we allow the possibility that the dt might in fact correspond to an infinite painleve expansion for a certain choice of the arbitrary coefficients this then leads us to a new and more consistent definition of singular manifold equation sme this can give smes different from those usually presented the summation of infinite painleve expansions is effected by seeking a truncation in a new riccati variable z the use o

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

a mixed formulation and mixed finite elements for limit analysis a mixed variational principle for the limit analysis of rigid perfectly plastic continua is discussed in which the nonlinear yield condition and the associated flow rule appear through a suitably defined penalty function a mixed finite element discrete formulation is derived and a sequential unconstrained minimization technique is devised affording a complete static and kinematic solution several results are presented in both structural and soil mechanics compared with previously available exact and numerical solutions

element free galerkin method for wave propagation and dynamic fracture abstract element free galerkin method efg is extended to dynamic problems efg method which is based on moving least square interpolants mls requires only nodal data no element connectivity is needed this makes the method particularly attractive for moving dynamic crack problems since remeshing can be avoided in contrast to the earlier formulation for static problems by authors the weak form of kinematic boundary conditions for dynamic problems is introduced in the implementation to enforce the kinematic boundary conditions with this formulation the stiffness matrix is symmetric and positive semi definite and hence the consistency conergence and stability analyses of time integration remain the same as those in finite element method numerical examples are presented to illustrate the performance of this method the relationship between the element free galerkin method and the smooth particle hydrodynamics sph method is also discussed in this paper results are presented for some one dimensional problems and two dimensional problems with static and moving cracks

solutions of a 2 1 dimensional dispersive long wave equation a special type of multisoliton solution with a particular dispersion relation is obtained for wu zhang equation which describes 2 1 dimensional dispersive long waves by the standard weiss tabor carnvale painleve truncation expansion using a nonstandard truncation of a modified conte s invariant painleve expansion two different types of soliton solutions without any dispersive relation is found two types of periodic wave solutions expressed by jacobi elliptic functions are found by the truncations of a special extended painleve expansion the soliton solutions are special cases of the corresponding periodic solutions

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

the two singular manifold method i modified korteweg de vries and sine gordon equations we address the problem of finding by painleve analysis only the backlund transformation of partial differential equations pdes having two families of movable singularities with opposite principal parts such as the modified korteweg de vries mkdv sine gordon or nonlinear schrodinger equations this first paper gives an almost algorithmic method which extends the singular manifold method of weiss 1986 that is unable to handle these equations first with only one singular manifold at a time we obtain the darboux transformation second we assume that the ratio of two functions defining the singular manifolds satisfies the most general projective riccati system with undetermined coefficients the darboux transformation then generates a very small number of determining equations admitting a unique solution equivalent to the lax pair of the zakharov shabat ablowitz kaup newell segur scheme by the canonical linearization of the riccati system the method is here applied to the mkdv and sine gordon equations

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

lower bound limit analysis by using the efg method and non linear programming intended to avoid the complicated computations of elasto plastic incremental analysis limit analysis is an appealing direct method for determining the load carrying capacity of structures on the basis of the static limit analysis theorem a solution procedure for lower bound limit analysis is presented firstly making use of the element free galerkin efg method rather than traditional numerical methods such as the finite element method and boundary element method 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 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 a 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 these non linear programming sub problems and determine the maximal load amplifier numerical examples show that it is feasible and effective to solve the problems of limit analysis by using the efg method and non linear programming copyright 2007 john wiley sons ltd

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

automated design of linear tree classifiers abstract an automated method is presented for the design of linear tree classifiers i e tree classifiers in which a decision based on a linear sum of features is carried out at each node the method exploits the discriminability of tomek links joining opposed pairs of data points in multidimensional feature space to produce a hierarchically structured piecewise linear decision function the corresponding decision surface is optimized by a gradient descent that maximizes the number of tomek links cut by each linear segment of the decision surface followed by training each node s linear decision segment on the data associated with that node experiments on real data obtained from ship images and character images suggest that the accuracy of the tree classifier designed by this scheme is comparable to that of the k nn classifier while providing much greater decision speeds and that the trade off between the speed and the accuracy in pattern classification can be controlled by bounding the number of features to be used at each node of the tree further experiments comparing the classification errors of our tree classifier with the tree classifier produced by the mui fu technique indicate that our tree classifier is no less accurate and often much faster than the mui fu classifier

shakedown state simulation techniques based on linear elastic solutions abstract the paper extends an iterative method previously applied to the determination of the limit state of a perfectly plastic body 5 to the determination of the shakedown limit state of a body subjected to a cyclic history of mechanical load and temperature a convergence proof is presented for a particular class of problems where the magnitude of a mechanical load at the shakedown limit is found as the limit of a sequence of monotonically reducing upper bounds an implementation of the method in a finite element scheme is discussed and examples of the application of the method to sample problems are presented

a new truncation in painleve analysis the author observes that when the expansion variable in painleve analysis satisfies a system of riccati equations truncation at a level higher than constant level is allowed this extends the range of exact solutions to nonlinear partial differential equations that one is able to obtain using truncated painleve expansions

a natural neighbour based moving least squares approach for the element free galerkin method the element free galerkin method efg and the natural element method nem are two well known and widely used meshless methods whereas the efg method can represent moving boundaries like cracks only by modifying the weighting functions the nem requires an adaptation of the nodal set up but on the other hand the nem is computationally more efficient than efg in this paper a new concept for the automatic adjustment of nodal influence domains in the efg method is presented in order to obtain an efficiency similar to the nem this concept is based on the definition of natural neighbours for each meshless node which can be determined from a voronoi diagram of the nodal set up in this approach adapted nodal influence domains are obtained by interpolating the distances to the natural neighbours depending on the direction in the paper we show that this concept leads especially for problems with grading node density to a reduced number of influencing nodes at the interpolation points and consequently a significant reduction of the numerical effort copyright 2006 john wiley sons ltd

a new approach for numerical modal analysis using the element free method a novel approach in analysing the vibration of elastic body systems is presented and discussed in this paper this method uses a meshless spatial approximation based only on nodes which constitutes an advantage over the finite element method as it is applicable to an elastic body with arbitrary shape it also has advantages over the classical rayleigh ritz method and its extensions the paper is organized as follows in section 2 hamilton s principle is used for obtaining the equations of motion for a three dimensonal simply connected elastic body in section 3 the development of weighted base functions for the moving least squares interpolant is described in section 4 the mass and stiffness matrices are derived using the previous results in section 5 a system synthesis description is given in which we also develop the approach used for integrating the boundary conditions finally in section 6 the theoretical results are validated by case studies chosen to highlight various features of the approach including optimization of the shape function parameters the particle method has already been used for structural dynamics liu et al international journal for numerical methods in engineering 1995 38 1655 1679 but for free vibration of beams and plates to the authors knowledge this paper is the first application of the element free method to modal analysis copyright c 1999 john wiley sons ltd

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

painleve analysis and backlund transformation in the kuramoto sivashinsky equation the authors apply the painleve test to the kuramoto sivashinsky nonlinear partial differential equation which describes many interesting fluid motions the equation passes the test in a weak sense although the painleve analysis does not yield the general solution they perform the backlund transformation in order to obtain new particular solutions the authors find explicitly all the solutions of the set of equations which define the painleve backlund transformation they reduce to only one type namely the already known kink shaped solitary wave

globally optimal fuzzy decision trees for classification and regression a fuzzy decision tree is constructed by allowing the possibility of partial membership of a point in the nodes that make up the tree structure this extension of its expressive capabilities transforms the decision tree into a powerful functional approximant that incorporates features of connectionist methods while remaining easily interpretable fuzzification is achieved by superimposing a fuzzy structure over the skeleton of a cart decision tree a training rule for fuzzy trees similar to backpropagation in neural networks is designed this rule corresponds to a global optimization algorithm that fixes the parameters of the fuzzy splits the method developed for the automatic generation of fuzzy decision trees is applied to both classification and regression problems in regression problems it is seen that the continuity constraint imposed by the function representation of the fuzzy tree leads to substantial improvements in the quality of the regression and limits the tendency to overfitting in classification fuzzification provides a means of uncovering the structure of the probability distribution for the classification errors in attribute space this allows the identification of regions for which the error rate of the tree is significantly lower than the average error rate sometimes even below the bayes misclassification rate

algorithmic method for deriving lax pairs from the invariant painleve analysis of nonlinear partial differential equations given a partial differential equation its painleve analysis will first be performed with a built in invariance under the homographic group acting on the singular manifold function then assuming an order for the underlying lax pair a multicomponent pseudopotential of projective riccati type the components of which are homographically invariant is introduced if the equation admits a classical darboux transformation a very small set of determining equations whose solution yields the lax pair will be generated in the basis of the pseudopotential this new method will be applied to find the yet unpublished lax pair of the scalar hirota satsuma equation

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

dynamic fracture using element free galerkin methods the element free galerkin method for dynamic crack propagation is described and applied to several problems this method is a gridless method which facilitates the modelling of growing crack problems because it does not require remeshing the growth of the crack is modelled by extending its surfaces the essential feature of the method is the use of moving least squares interpolants for the trial and test functions in these interpolants the dependent variable is obtained at any point by minimizing a weighted quadratic form involving the nodal variables within a small domain surrounding the point the discrete equations are obtained by a galerkin method the procedures for modelling dynamic crack propagation based on dynamic stress intensity factors are also described

coupled kdv equations derived from two layer fluids some types of coupled korteweg de vries kdv equations are derived from a two layer fluid system in the derivation procedure an unreasonable y average trick usually adopted in the literature is removed the derived models are classified by means of the painleve test three types of function and multiple soliton solutions of the models are explicitly given via the exact solutions of the usual kdv equation it is also discovered that a non painleve integrable coupled kdv system can have multiple soliton solutions

a total lagrangian framework for simulation of powder compaction process based on a smooth three surface cap model and a mesh free method this paper presents a detailed framework for simulation of cold powder compaction process this framework consists of the following main assumptions the total lagrangian description is employed the powder is assumed to be isotropic and it is modeled by a complete smooth three surface cap model the constitutive formulation is based on the multiplicative decomposition of the deformation gradient and on stress strain pair formed by the hencky logarithmic strain and the rotated kirchhoff stress tensor the elastic constitutive relationship considers that some parameters are dependent upon the relative density of the powder the contact formulation is based on the signorini condition and the friction is modeled by using a regularized coulomb model and the spatial discretization is made by the element free galerkin method where the essential boundary conditions are enforced via an augmented lagrangian method details concerning the discretization and the linearization of the weak form are presented and a master algorithm is proposed some key examples already investigated by other authors but with somewhat different approaches are revisited in this paper in order to investigate the adequacy of the proposed model and attest the performance of the proposed numerical scheme copyright 2008 john wiley sons ltd

a modified element free galerkin method with essential boundary conditions enforced by an extended partition of unity finite element weight function in this work we propose a method which combines the element free galerkin efg with an extended partition of unity finite element method pufem that is able to enforce in some limiting sense the essential boundary conditions as done in the finite element method fem the proposed extended pufem is based on the moving least square approximation mlsa and is capable of overcoming singularity problems in the global shape functions resulting from the consideration of linear and higher order base functions with the objective of avoiding the presence of singular points the extended pufem considers an extension of the support of the classical pufe weight function since the extended pufem is closely related to the efg method there is no need for special approximation functions with complex implementation procedures and no use of the penalty and or multiplier method is required in order to approximately impose the essential boundary condition thus a relatively simple procedure is needed to combine both methods in order to attest the performance of the method we consider the solution of an analytical elastic problem and also some coupled elastoplastic damage problems copyright 2003 john wiley sons ltd

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 nonlinear programming method of wilson han and powell with an augmented lagrangian type line search function the paper represents an outcome of an extensive comparative study of nonlinear optimization algorithms this study indicates that quadratic approximation methods which are characterized by solving a sequence of quadratic subproblems recursively belong to the most efficient and reliable nonlinear programming algorithms available at present the purpose of this paper is to analyse the theoretical convergence properties and to investigate the numerical performance in more detail in part 1 the exactl 1 penalty function of han and powell is replaced by a differentiable augmented lagrange function for the line search computation to the able to prove the global convergence and to show that the steplength one is chosen in the neighbourhood of a solution in part 2 the quadratic subproblem is exchanged by a linear least squares problem to improve the efficiency and to test the dependence of the performance from different solution methods for the quadratic or least squares subproblems

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

an enriched meshless method for non linear fracture mechanics this paper presents an enriched meshless method for fracture analysis of cracks in homogeneous isotropic non linear elastic two dimensional solids subject to mode i loading conditions the method involves an element free galerkin formulation and two new enriched basis functions types i and ii to capture the hutchinson rice rosengren singularity field in non linear fracture mechanics the type i enriched basis function can be viewed as a generalized enriched basis function which degenerates to the linear elastic basis function when the material hardening exponent is unity the type ii enriched basis function entails further improvements of the type i basis function by adding trigonometric functions four numerical examples are presented to illustrate the proposed method the boundary layer analysis indicates that the crack tip field predicted by using the proposed basis functions matches with the theoretical solution very well in the whole region considered whether for the near tip asymptotic field or for the far tip elastic field numerical analyses of standard fracture specimens by the proposed meshless method also yield accurate estimates of the j integral for the applied load intensities and material properties considered also the crack mouth opening displacement evaluated by the proposed meshless method is in good agreement with finite element results furthermore the meshless results show excellent agreement with the experimental measurements indicating that the new basis functions are also capable of capturing elastic plastic deformations at a stress concentration effectively copyright 2003 john wiley sons ltd

the generalized finite difference method for long time dynamic modeling of three dimensional coupled thermoelasticity problems abstract in this study a new framework for the efficient and accurate solutions of three dimensional 3d dynamic coupled thermoelasticity problems is presented in our computations the krylov deferred correction kdc method a pseudo spectral type collocation technique is introduced to perform the large scale and long time temporal simulations the generalized finite difference method gfdm a relatively new meshless method is then adopted to solve the resulting boundary value problems the gfdm uses the taylor series expansions and the moving least squares approximation to derive explicit formulae for the required partial derivatives of unknown variables the method thus is truly meshless that can be applied for solving problems merely defined over irregular clouds of points for problem with complicated geometries this paper also examines a new distance criterion for adaptive selection of nodes in the gfdm simulations preliminary numerical experiments show that the kdc accelerated gfdm methods are very promising for accurate and efficient long time and large scale dynamic simulations

a new implementation of the element free galerkin method abstract element free galerkin methods efg are methods for solving partial differential equations with moving least squares interpolants efg methods require only nodal data no element connectivity is needed in a previous implementation of the efg method lagrange multipliers were used to enforce the essential boundary condition however the use of lagrange multipliers increases the cost of solving the linear algebraic equations a new implementation is developed based on a modified variational principle in which the lagrange multipliers are replaced at the outset by their physical meaning so that the discrete equations are banded in addition weighted orthogonal basis functions are constructed so the need for solving equations at each quadrature point is eliminated numerical examples show that the present implementation effectively computes stress concentrations and stress intensity factors at cracks with very irregular arrangements of nodes the latter makes it very advantageous for modelling progressive cracking

the boundary node method for potential problems the element free galerkin efg method allows one to use a nodal data structure usually with an underlying cell structure within the domain of a body of arbitrary shape the usual efg combines moving least squares mls interpolants with a variational principle weak form and has been used to solve two dimensional 2 d boundary value problems in mechanics such as in potential theory elasticity and fracture this paper proposes a combination of mls interpolants with boundary integral equations bie in order to retain both the meshless attribute of the former and the dimensionality advantage of the latter this new method called the boundary node method bnm only requires a nodal data structure on the bounding surface of a body whose dimension is one less than that of the domain itself an underlying cell structure is again used for numerical integration in principle the bnm for 3 d problems should be extremely powerful since one would only need to put nodes points on the surface of a solid model for an object numerical results are presented in this paper for the solution of laplace s equation in 2 d dirichlet neumann and mixed problems have been solved some on bodies with piecewise straight and others with curved boundaries results from these numerical examples are extremely encouraging 1997 by john wiley sons ltd

higher dimensional painleve integrable models from the kadomtsev petviashvili equation after embedding the kadomtsev petviashvili equation in higher dimensions and extending the painleve analysis approach to a new form such that the coefficients of the expansion around the singular manifold possess conformal invariance and contain explicit new space variables we can get infinitely many painleve integrable models in 3 1 dimensions and higher dimensions some concrete higher dimensional modified korteweg de vries type of extensions are given whether the models are lax integrable or integrable under other meanings remain still open

a point assembly method for stress analysis for two dimensional solids abstract a novel point assembly method pam is presented for stress analysis for two dimensional solids in the present method the boundaries of the problem domain are represented by a set of discrete points and the domain itself is represented by properly scattered points the displacement in the influence triangular areas of a point is interpolated by the displacements at the point and pairs of surrounding points using shape functions the shape functions used in this work are obtained in the same way as those of a triangular element in the conventional finite element method fem a variational weak form of the equilibrium equation is used to produce a set of system equations these equations are assembled for all the points in the domain and solved for the displacement field stresses and strains at a point are then computed using the displacements obtained for the point and pairs of the surrounding points a pam program with an automatic point searching algorithm has been developed in fortran patch tests and convergence studies have been carried out to verify the convergence of the present method and program examples are also presented to demonstrate the efficiency and accuracy of the present method compared with analytical solutions as well as the conventional fem solutions

a comparison of neural net classifiers and linear tree classifiers their similarities and differences abstract both neural net classifiers utilizing multilayer perceptron and linear tree classifiers composed of hierarchically structured linear discriminant functions can form arbitrarily complex decision boundaries in the feature space and have similar decision making processes the structure of the linear tree classifier can be easily mapped to that of the neural nets having two hidden layers by using the hyperplanes produced by the linear tree classifier a new method for mapping the linear tree classifier to the neural nets having one hidden layer is presented with theoretical basis of mapping the convex decision regions produced by the linear tree classifier to the neurons in the neural nets this mapping may be useful for choosing appropriately sized neural nets having one or two hidden layers as well as for initializing the connection weights to speed up the learning rate and avoid the local trapping of the backpropagation algorithm also the internal operations of the hidden layer neurons in the three layer feedforward nets could be well described by this mapping experimental results on both synthetic and real data suggest that this mapping is effective and that there exists no significant difference in the classification accuracy of the neural net classifiers having one and two hidden layers substantial advantages of the neural net classifiers over the linear tree classifier were not found in the experiment while the latter is much faster in both training and classifying stages

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

recognition of handwritten digits based on contour information abstract in this paper a new character recognition method based on topological properties positions of starting point statistical analysis and shape recognition is proposed for recognition of unconstrained handwritten digits based on various contour information first input digits are classified into three groups according to their topological properties in group 1 the features of normalized length of the digit contour the normalized area of the digit and fourier descriptors of the outer contour of a digit are used for recognition of digits in group 2 the relative position of outer and interior contour centroids the position of interior contour centroid the mean and the variance of the outer contour distance function and fourier descriptors of the outer contour of a digit are used for the recognition of digits in group 3 usually there is only one digit 8 but because of the complexity of writing styles some other digits are still classified into this group the final recognition is based on shape comparison of the input digit with models in the recognition process some special models are established and used for recognition of broken digits and digits whose topological properties are destroyed in our experiment 1000 digits from the nist database are used for training and 5278 unseen digits are used for testing the recognition rate has reached 98 5 with a reliability rate of 99 09 a substitution rate of 0 91 and a rejection rate of 0 59

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

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

a simple and robust three dimensional cracking particle method without enrichment abstract a new robust and efficient approach for modeling discrete cracks in meshfree methods is described the method is motivated by the cracking particle method rabczuk t belytschko t international journal for numerical methods in engineering 2004 where the crack is modeled by a set of cracked segments however in contrast to the above mentioned paper we do not introduce additional unknowns in the variational formulation to capture the displacement discontinuity instead the crack is modeled by splitting particles located on opposite sides of the associated crack segments and we make use of the visibility method in order to describe the crack kinematics we apply this method to several two and three dimensional problems in statics and dynamics and show through several numerical examples that the method does not show any mesh orientation bias

lax pairs galore a formula that yields an apparently but only apparently nontrivial lax pair for any nonlinear evolution pde in 1 1 dimensions possessing a local conservation law is presented several examples are exhibited

the relations among a special type of solutions in some d 1 dimensional nonlinear equations among a special type of solutions of some kinds of nonlinear equations in d 1 dimensions such as the cubic nonlinear klein gordon sine gordon double sine gordon ginzburg landau equations etc some mapping relations exist that allow one to find a solution of one system from a solution of another furthermore one can find some new solutions from a known one within the same system some new n kinklike solutions are also presented

an isogeometric meshfree coupling approach for analysis of cracks summary this paper presents a new concurrent simulation approach to couple isogeometric analysis iga with the meshfree method for studying of crack problems in the present method the overall physical domain is divided into two sub domains which are formulated with the iga and meshfree method respectively in the meshfree sub domain the moving least squares mls shape function is adopted for the discretization of the area around crack tips and the iga sub domain is adopted in the remaining area meanwhile the interface region between the two sub domains is represented by coupled shape functions the resulting shape function which comprises both iga and meshfree shape functions satisfies the consistency condition thus ensuring convergence of the method moreover the meshfree shape functions augmented with the enriched basis functions to predict the singular stress fields near a crack tip are presented the proposed approach is also applied to simulate the crack propagation under a mixed mode condition several numerical examples are studied to demonstrate the utility and robustness of the proposed method this article is protected by copyright all rights reserved

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

searching for higher dimensional integrable models from lower ones via painleve analysis extending the painleve approach to a more general form one can get in nitely many new integrablemodels under the meanings that they possess conformal invariance and the painleve property in anyspace dimensions from a given lower dimensional integrable model using the kadomtsev petviashvili nonlinear schrodinger and schwarz korteweg de vries equations as simple examples some explicits3 1 1d dimensional integrable models are given s0031 9007 98 06288 7

the p version of the finite element method in incremental elasto plastic analysis summary whereas the higher order versions of the finite element method p and hp versions are fairly well established as highly efficient methods for monitoring and controlling the discretization error in linear problems little has been done to exploit their benefits in elasto plastic structural analysis in this paper we discuss which aspects of incremental elasto plastic finite element analysis are particularly amenable to improvements by the p version these theoretical considerations are supported by several numerical experiments first we study an example for which an analytical solution is available it is demonstrated that the p version performs very well even in cycles of elasto plastic loading and unloading not only as compared with the traditional h version but also with respect to the exact solution finally an example of considerable practical importancethe analysis of a cold working lug is presented which demonstrates how the modelling tools offered by higher order finite element techniques can contribute to an improved approximation of practical problems

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

a non linear programming approach to kinematic shakedown analysis of composite materials using a representative volume element rve to represent the microstructure of periodic composite materials this paper develops a non linear numerical technique to calculate the macroscopic shakedown domains of composites subjected to cyclic loads the shakedown analysis is performed using homogenization theory and the displacement based finite element method with the aid of homogenization theory the classical kinematic shakedown theorem is generalized to incorporate the microstructure of composites using an associated flow rule the plastic dissipation power for an ellipsoid yield criterion is expressed in terms of the kinematically admissible velocity by means of non linear mathematical programming techniques a finite element formulation of kinematic shakedown analysis is then developed leading to a non linear 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 of a composite is then obtained an effective direct iterative algorithm is proposed to solve the non linear programming problem the effectiveness and efficiency of the proposed numerical method have been validated by several numerical examples this can serve as a useful numerical tool for developing engineering design methods involving composite materials copyright 2005 john wiley sons ltd