a stabilized conforming nodal integration for galerkin mesh free methods domain integration by gauss quadrature in the galerkin mesh free methods adds considerable complexity to solution procedures direct nodal integration on the other hand leads to a numerical instability due to under integration and vanishing derivatives of shape functions at the nodes a strain smoothing stabilization for nodal integration is proposed to eliminate spatial instability in nodal integration for convergence an integration constraint ic is introduced as a necessary condition for a linear exactness in the mesh free galerkin approximation the gradient matrix of strain smoothing is shown to satisfy ic using a divergence theorem no numerical control parameter is involved in the proposed strain smoothing stabilization the numerical results show that the accuracy and convergent rates in the mesh free method with a direct nodal integration are improved considerably by the proposed stabilized conforming nodal integration method it is also demonstrated that the gauss integration method fails to meet ic in mesh free discretization for this reason the proposed method provides even better accuracy than gauss integration for galerkin mesh free method as presented in several numerical examples copyright 2001 john wiley sons ltd

mimo system identification state space and subspace approximations versus transfer function and instrumental variables the identification of multi input multi output mimo linear systems has previously received a new impetus with the introduction of the state space ss approach based on subspace approximations this approach has immediately gained popularity owing to the fact that it avoids the use of canonical forms requires the determination of only one structural parameter and has been empirically shown to yield mimo models with good accuracy in many cases however the ss approach suffers from several drawbacks there is no well established rule tied to this approach for determining the structural parameter and perhaps more important the ss parameter estimates depend on the data in a rather complicated way which renders almost futile any attempt to analyze and optimize the performance of the estimator in this paper we consider a transfer function tf approach based on instrumental variables iv as an alternative to the ss approach we use the simplest canonical tf parameterization in which the denominator is equal to a scalar polynomial times the identity matrix the analysis and optimization of the statistical accuracy of the tf approach is straightforward additionally a simple test tailored to this approach is devised for estimating the single structural parameter needed a simulation study in which we compare the performances of the ss and the tf approaches shows that the latter can provide more accurate models than the former at a lower 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

an efficient newton barrier method for minimizing a sum of euclidean norms a new newton barrier method is proposed for minimizing a sum of euclidean norms msn f x sum i 1 k a i t x b i 2 msn is a nonsmooth problem because f is not differentiable at any point x where any of the norms is zero the method used is based on approximating f with a smooth function which in the limit has the same optimal value as f msn is shown to have a dual problem with properties very similar to duality theory in linear programming this is used in the development of the method and to give a proof of when an optimal solution for the smooth approximation is epsilon optimal measured in the duality gap for the original problem an implementation of the algorithm is described for large sparse problems and numerical results are presented for problems with more than 270 000 nonlinear variables these problems arise from plastic collapse analysis

subspace based fault detection robust to changes in the noise covariances the detection of changes in the eigenstructure of a linear time invariant system by means of a subspace based residual function has been proposed previously while enjoying some success in its applicability in particular in the context of vibration monitoring the robustness of this framework against changes in the noise properties has not been properly addressed yet in this paper a new robust residual is proposed and the robustness of its statistics against changes in the noise covariances is shown the complete theory for hypothesis testing for fault detection is derived and a numerical illustration is provided

consistency and asymptotic normality of some subspace algorithms for systems without observed inputs asymptotic normality for a class of subspace algorithms which estimate the state in a first step is derived expressions for the asymptotic variance are given linear systems with unobserved white noise inputs are considered a class of subspace estimates for the system matrices obtained by estimating the state in the first step is analyzed the main result presented here states asymptotic normality of subspace estimates in addition a consistency result for the system matrix estimates is given an algorithm to compute the asymptotic variances of the estimates is presented in a final section the implications of the result are discussed

on implementing a primal dual interior point method for conic quadratic optimization based on the work of the nesterov and todd on self scaled cones an implementation of a primal dual interior point method for solving large scale sparse conic quadratic optimization problems is presented the main features of the implementation are it is based on a homogeneous and self dual model it handles rotated quadratic cones directly it employs a mehrotra type predictor corrector extension and sparse linear algebra to improve the computational efficiency finally the implementation exploits fixed variables which naturally occurs in many conic quadratic optimization problems this is a novel feature for our implementation computational results are also presented to document that the implementation can solve very large problems robustly and efficiently

a dual algorithm for shakedown analysis of plate bending in this paper the duality between the lower and the upper bound shakedown analyses of plate bending is presented based on the duality theory the shakedown load multiplier formulated by static theorem is proved actually to be the dual form of the shakedown load multiplier formulated by kinematic theorem a dual algorithm based upon the von mises yield criterion and a non linear optimization procedure is then developed to compute simultaneously both the upper and lower bounds of the plastic collapse limit and the shakedown limit the dkq plate bending element is used to discrete the problem field numerical examples are presented to show the excellent convergence and accuracy of solutions obtained by the present method copyright 2011 john wiley sons ltd

analysis of the asymptotic properties of the moesp type of subspace algorithms the moesp type of subspace algorithms are used for the identification of linear discrete time finite dimensional state space systems they are based on the geometric structure of covariance matrices and exploit the properties of the state vector extensively in this paper the asymptotic properties of the algorithms are examined the main results include consistency and asymptotic normality for the estimates of the system matrices under suitable assumptions on the noise sequence the input process and the underlying true system

an upper bound limit analysis of mindlin plates using cs dsg3 method and second order cone programming the paper presents a numerical procedure for kinematic limit analysis of mindlin plate governed by von mises criterion the cell based smoothed discrete shear gap method cs dsg3 is combined with a second order cone optimization programming socp for determining the upper bound limit load of the mindlin plates the limit analysis problem of mindlin plates is formulated by minimizing the dissipation power subjected to a set of constraints of boundary conditions and unitary external work this minimization problem is then transformed into an explicit form suitable for the solution using the socp the numerical results of some benchmark problems show that the proposal procedure can provide the reliable upper bound collapse multipliers for the mindlin plates cs dsg3 is combined with socp for determining upper bound limit load of mindlin plates limit analysis problem is transformed into an explicit form suitable for solution using socp and cs dsg3 numerical results show that cs dsg3 is free of shear locking and can provide reliable upper bound collapse multipliers for mindlin plates

the leavitt path algebra of a graph abstract for any row finite graph e and any field k we construct the leavitt path algebra l e having coefficients in k when k is the field of complex numbers then l e is the algebraic analog of the cuntz krieger algebra c e described in i raeburn graph algebras in cbms reg conf ser math vol 103 amer math soc 2005 the matrix rings m n k and the leavitt algebras l 1 n appear as algebras of the form l e for various graphs e in our main result we give necessary and sufficient conditions on e which imply that l e is simple

the asymptotic variance of subspace estimates abstract we give new simple general expressions for the asymptotic covariance of the estimated system parameters a b c d in subspace identification the formulas can be applied to a whole class of subspace methods including n4sid moesp cva etc the asymptotic expressions highlight how the conditioning of the estimation problem influences the accuracy of the estimates

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

subspace identification for non linear systems with measured input non linearities this paper uses subspace methods to identify a class of multi input multi output discrete time non linear time varying systems specifically we identify systems that are non linear in measured data and linear in unmeasured states numerical examples are presented to demonstrate the efficacy of the method

mesh adaptive computation of upper and lower bounds in limit analysis summary an efficient procedure to compute strict upper and lower bounds for the exact collapse multiplier in limit analysis is presented with a formulation that explicitly considers the exact convex yield condition the approach consists of two main steps first the continuous problem under the form of the static principle of limit analysis is discretized twice one per bound using particularly chosen finite element spaces for the stresses and velocities that guarantee the attainment of an upper or a lower bound the second step consists of solving the resulting discrete non linear optimization problems these are reformulated as second order cone programs which allows for the use of primal dual interior point methods that optimally exploit the convexity and duality properties of the limit analysis model to benefit from the fact that collapse mechanisms are typically highly localized a novel method for adaptive meshing is introduced the method first decomposes the total bound gap as the sum of positive contributions from each element in the mesh and then refines those elements with higher contributions the efficiency of the methodology is illustrated with applications in plane stress and plane strain problems copyright q 2008 john wiley sons ltd

subspace model identification part 2 analysis of the elementary output error state space model identification algorithm the elementary moesp algorithm presented in the first part of this series of papers is analysed in this paper this is done in three different ways first we study the asymptotic properties of the estimated state space model when only considering zero mean white noise perturbations on the output sequence it is shown that in this case the moespl implementation yields asymptotically unbiased estimates an important constraint to this result is that the underlying system must have a finite impulse response and subsequently the size of the hankel matrices constructed from the input and output data at the beginning of the computations depends on the number of non zero markov parameters this analysis however leads to a second implementation of the elementary moesp scheme namely moesp2 the latter implementation has the same asymptotic properties without the finite impulse response constraint secondly we compare the moesp2 algorithm with a classical state space model identification scheme the latter

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

a projected newton algorithm for the dual convex program of elastoplasticity summary in this paper we study a dual optimization problem that arises when taking a mathematical programming approach to incremental state update in nonlinear problems the mathematical programming approach stems from energy based descriptions of constitutive models we describe a projected newton algorithm to solve the dual optimization problem this algorithm requires solution of an unconstrained optimization problem at the integration point level rather than a constrained one as carried out by classical return mapping schemes especially implementation of multi surface plasticity models is no more involved than that of single surface models we explore characteristics and performance of the projected newton algorithm through numerical examples insights gained from such a further exploration of mathematical programming algorithms are likely to aid in development of successive convex programming approaches to geometric nonlinear and other non convex problems such as non associated flow models copyright 2014 john wiley sons ltd

flow invariants in the classification of leavitt path algebras abstract we analyze in the context of leavitt path algebras some graph operations introduced in the context of symbolic dynamics by williams parry and sullivan and franks we show that these operations induce morita equivalence of the corresponding leavitt path algebras as a consequence we obtain our two main results the first gives sufficient conditions for which the leavitt path algebras in a certain class are morita equivalent while the second gives sufficient conditions which yield isomorphisms we discuss a possible approach to establishing whether or not these conditions are also in fact necessary in the final section we present many additional operations on graphs which preserve morita equivalence resp isomorphism of the corresponding leavitt path algebras

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

limit analysis of plates and slabs using a meshless equilibrium formulation a meshless element free galerkin efg equilibrium formulation is proposed to compute the limit loads which can be sustained by plates and slabs in the formulation pure moment fields are approximated using a moving least squares technique which means that the resulting fields are smooth over the entire problem domain there is therefore no need to enforce continuity conditions at interfaces within the problem domain which would be a key part of a comparable finite element formulation the collocation method is used to enforce the strong form of the equilibrium equations and a stabilized conforming nodal integration scheme is introduced to eliminate numerical instability problems the combination of the collocation method and the smoothing technique means that equilibrium only needs to be enforced at the nodes and stable and accurate solutions can be obtained with minimal computational effort the von mises and nielsen yield criteria which are used in the analysis of plates and slabs respectively are enforced by introducing second order cone constraints ensuring that the resulting optimization problem can be solved using efficient interior point solvers finally the efficacy of the procedure is demonstrated by applying it to various benchmark plate and slab problems

a non linear programming method approach for upper bound limit analysis this paper presents a finite element model based on mathematical non linear programming in order to determine upper bounds of colapse loads of a mechanical structure the proposed formulation is derived within a kinematical approach framework employing two simultaneous and independent field approximations for the velocity and strain rate fields the augmented lagrangian is used to establish the compatibility between these two fields in this model only continuous velocity fields are used uzawa s minimization algorithm is applied to determine the optimal kinematical field that minimizes the difference between external and dissipated work rate the use of this technique allows to bypass the complexity of the non linear aspects of the problem since non linearity is addressed as a set of small local subproblems of optimization for each finite element the obtained model is quite versatile and suitable for solving a wide range of collapse problems this paper studies 3d strut and tie structures 2d plane strain stress and 3d solid problems copyright 2007 john wiley sons ltd

on consistency of subspace methods for system identification subspace methods for identification of linear time invariant dynamical systems typically consist of two main steps first a so called subspace estimate is constructed this first step usually consists of estimating the range space of the extended observability matrix secondly an estimate of system parametersis obtained based on the subspace estimate in this paper the consistency of a large class of methods for estimating the extended observability matrix is analyzed persistence of excitation conditions on the input signal are given which guarantee consistent estimates for systems with only measurement noise for systems with process noise it is shown that a persistence of excitation condition on the input is not sufficient more precisely an example for which the subspace methods fail to give a consistent estimate of the transfer function is given this failure occurs even if the input is persistently exciting of any order it is also shown that this problem can be eliminated if stronger conditions on the input signal are imposed

subspace based system identification weighting and pre filtering of instruments subspace based system identification is typically based on an estimate of the extended observability matrix it is thus of great interest to investigate and also optimize the estimate of the observability matrix of special interest in this paper is the fact that the influence of certain weighting matrices is an unresolved issue in the literature on subspace identification here an asymptotic analysis of the estimated observability matrix is presented the main result of the analysis is that novel weighting matrices and pre filters of instrumental variables are derived

limit analysis of plates using the efg method and second order cone programming the meshless element free galerkin efg method is extended to allow computation of the limit load of plates a kinematic formulation that involves approximating the displacement field using the moving least squares technique is developed only one displacement variable is required for each efg node ensuring that the total number of variables in the resulting optimization problem is kept to a minimum with far fewer variables being required compared with finite element formulations using compatible elements a stabilized conforming nodal integration scheme is extended to plastic plate bending problems the evaluation of integrals at nodal points using curvature smoothing stabilization both keeps the size of the optimization problem small and also results in stable and accurate solutions difficulties imposing essential boundary conditions are overcome by enforcing displacements at the nodes directly the formulation can be expressed as the problem of minimizing a sum of euclidean norms subject to a set of equality constraints this non smooth minimization problem can be transformed into a form suitable for solution using second order cone programming the procedure is applied to several benchmark beam and plate problems and is found in practice to generate good upper bound solutions for benchmark problems

identification of the deterministic part of mimo state space models given in innovations form from input output data the problem of linear multivariable state space model identification from input output data can under the presence of process and measurement noise be solved in a non iterative way when incorporating instrumental variables constructed from both input and output sequences in the recently developed class of multivariable output error state space model class of subspace model identification schemes abstract in this paper we describe two algorithms to identify a linear time invariant finite dimensional state space model from input output data the system to be identified is assumed to be excited by a measurable input and an unknown process tloise and the measurements are disturbed by unknown measurement noise both noise sequences are discrete zero mean white noise the first algorithm gives consistent estimates only for the case where the input also is zero mean white noise while the same result is obtained with the second algorithm without this constraint for the special case where the input signal is discrete zero mean white noise it is explicitly shown that this second algorithm is a special case of the recently developed multivariable output error state space moesp class of algorithms based on instrumental variables the usefulness of the presented schemes is highlighted in a realistic simulation study

analysis of state space system identification methods based on instrumental variables and subspace fitting subspace based state space system identification 4sid methods have recently been proposed as an alternative to more traditional techniques for multivariable system identification the advantages are that the user has simple and few design variables and that the methods have robust numerical properties and relatively low computational complexities though subspace techniques have been demonstrated to perform well in a number of cases the performance of these methods is neither fully understood nor analyzed our principal objective is to undertake a statistical investigation of subspace based system identification techniques the studied methods consist of two steps the subspace spanned by the extended observability matrix is first estimated the asymptotic properties of this subspace estimate are derived herein in the second step the structure of the extended observability matrix is used to find a system model estimate two possible methods are considered the simplest one only uses a certain shift invariance property while in the other method a parametric representation of the null space of the observability matrix is exploited explicit expressions for the asymptotic estimation error variances of the corresponding pole estimates are given

an efficient primal dual interior point method for minimizing a sum of euclidean norms the problem of minimizing a sum of euclidean norms dates from the 17th century and may be the earliest example of duality in the mathematical programming literature this nonsmooth optimization problem arises in many different kinds of modern scientific applications we derive a primal dual interior point algorithm for the problem by applying newton s method directly to a system of nonlinear equations characterizing primal and dual feasibility and a perturbed complementarity condition the main work at each step consists of solving a system of linear equations the schur complement equations this schur complement matrix is not symmetric unlike in linear programming we incorporate a mehrotra type predictor corrector scheme and present some experimental results comparing several variations of the algorithm including as one option explicit symmetrization of the schur complement with a skew corrector term we also present results obtained from a code implemented to solve large sparse problems using a symmetrized schur complement this has been applied to problems arising in plastic collapse analysis with hundreds of thousands of variables and millions of nonzeros in the constraint matrix the algorithm typically finds accurate solutions in less than 50 iterations and determines physically meaningful solutions previously unobtainable

computation of the collapse state in limit analysis using the lp primal affine scaling algorithm abstract the object of this work is twofold the first goal is to demonstrate that for the duality problem of limit analysis with linearized yield condition the lp primal affine scaling algorithm shows properties which are significantly different from those of the simplex method and that as a consequence of this better results can be obtained the second goal is to compute the collapse state for a classical and hard problem in plane strain tension of a rectangular bar with symmetric thin cuts both the collapse multiplier and collapse fields are computed to a better accuracy and detail than previously

classification of unital simple leavitt path algebras of infinite graphs we prove that if e and f are graphs with a finite number of vertices and an infinite number of edges if k is a field and if lk e and lk f are simple leavitt path algebras then lk e is morita equivalent to lk f if and only if k0alg lk e k0alg lk f and the graphs e and f have the same number of singular vertices and moreover in this case one may transform the graph e into the graph f using basic moves that preserve the morita equivalence class of the associated leavitt path algebra we also show that when k is a field with no free quotients the condition that e and f have the same number of singular vertices may be replaced by k1alg lk e k1alg lk f and we produce examples showing this cannot be done in general we describe how we can combine our results with a classification result of abrams louly pardo and smith to get a nearly complete classification of unital simple leavitt path algebras the only missing part is determining whether the sign of the determinant condition is necessary in the finite graph case we also consider the cuntz splice move on a graph and its effect on the associated leavitt path algebra

applications of second order cone programming in a second order cone program socp a linear function is minimized over the intersection of an affine set and the product of second order quadratic cones socps are nonlinear convex problems that include linear and convex quadratic programs as special cases but are less general than semidefinite programs sdps several efficient primaldual interior point methods for socp have been developed in the last few years after reviewing the basic theory of socps we describe general families of problems that tan be recast as socps these include robust linear programming and robust leastsquares problems problems involving sums or maxima of norms or with convex hyperbolic constraints we discuss a variety of engineering applications such as filter design antenna array weight design truss design and grasping forte optimization in robotics we describe an efficient primaldual interior point method for solving socps which shares many of the features of primaldual interior point methods for linear program

a stabilized discrete shear gap finite element for adaptive limit analysis of mindlin reissner plates summary this paper presents a numerical formulation for computation of collapse load of mindlin reissner plates that uses stabilized discrete shear gap finite elements and second order cone programming displacement fields are approximated using the discrete shear gap in combination with a stabilized strain smoothing technique ensuring that shear locking problem can be avoided and that accurate solutions can be obtained the underlying optimization problem is formulated in the form of a standard second order cone programming so that it can be solved using highly efficient primal dual interior point algorithm an error indicator based on plastic dissipation will be used in the adaptive refinement scheme various plates with arbitrary geometries and boundary conditions are examined to illustrate the performance of the proposed procedure copyright 2013 john wiley sons ltd

computing limit loads by minimizing a sum of norms this paper treats the problem of computing the collapse state in limit analysis for a solid with a quadratic yield condition such as for example the von mises condition after discretization with the finite element method using divergence free elements for the plastic flow the kinematic formulation reduces to the problem of minimizing a sum of euclidean vector norms subject to a single linear constraint this is a nonsmooth minimization problem since many of the norms in the sum may vanish at the optimal point recently an efficient solution algorithm has been developed for this particular convex optimization problem in large sparse form the approach is applied to test problems in limit analysis in two different plane models plane strain and plates in the first case more than 80 of the terms in the objective function are zero in the optimal solution causing extreme ill conditioning in the second case all terms are nonzero in both cases the method works very well and problems are solved which are larger by at least an order of magnitude than previously reported the relative accuracy for the solution of the discrete problems measured by duality gap and feasibility is typically of the order 10 8

automatic mesh refinement in limit analysis a strategy for automatic mesh refinement in limit analysis is combined with a recently developed computational method in the absence of estimates of the local error the strategy can be based on the deformations and on slack in the yield condition the approach is tested on standard problems in plane strain including the classical punch problem very accurate results are obtained with the use of moderate computational power

consistency and relative efficiency of subspace methods we give a consistency proof for two subspace methods we then show the asymptotic equivalence of a special subspace method and the initial estimate proposed by hannan and rissanen finally a simulation study comparing two subspace methods and the maximum likelihood method is performed

k theory for leavitt path algebras computation and classification abstract we show that the long exact sequence for k groups of leavitt path algebras deduced by ara brustenga and cortinas extends to leavitt path algebras of countable graphs with infinite emitters in the obvious way using this long exact sequence we compute explicit formulas for the higher algebraic k groups of leavitt path algebras over certain fields including all finite fields and all algebraically closed fields we also examine classification of leavitt path algebras using k theory it is known that the k 0 group and k 1 group do not suffice to classify purely infinite simple unital leavitt path algebras of infinite graphs up to morita equivalence when the underlying field is the rational numbers we prove for these leavitt path algebras if the underlying field is a number field which includes the case when the field is the rational numbers then the pair consisting of the k 0 group and the k 6 group does suffice to classify these leavitt path algebras up to morita equivalence

locking free stabilized conforming nodal integration for meshfree mindlin reissner plate formulation abstract the cause of shear locking in mindlin reissner plate formulation is due to the inability of the numerical formulation in representing pure bending mode without producing parasitic shear deformation lack of kirchhoff mode to resolve shear locking in meshfree formulation of mindlin reissner plates the following two issues are addressed 1 construction of approximation functions capable of reproducing kirchhoff modes and 2 formulation of domain integration of galerkin weak form capable of producing exact solution under pure bending condition in this study we first identify the kirchhoff mode reproducing conditions kmrc and show that the employment of a second order monomial basis in the reproducing kernel or moving least square approximation of translational and rotational degrees of freedom is an effective means to meet kmrc next the integration constraints that fulfill bending exactness be in the galerkin meshfree discretization of mindlin reissner plate are derived a nodal integration with curvature smoothing stabilization that fulfills be is then formulated for mindlin reissner plate the curvature smoothing stabilization is introduced in the nodally integrated galerkin weak form the resulting meshfree formulation is stable and free of shear locking in the limit of thin plate both computational efficiency and accuracy are achieved in the proposed meshfree mindlin reissner plate formulation

n4sid subspace algorithms for the identification of combined deterministic stochastic systems abstract recently a great deal of attention has been given to numerical algorithms for subspace state space system identification n4sid in this paper we derive two new n4sid algorithms to identify mixed deterministic stochastic systems both algorithms determine state sequences through the projection of input and output data these state sequences are shown to be outputs of non steady state kalman filter banks from these it is easy to determine the state space system matrices the n4sid algorithms are always convergent non iterative and numerically stable since they only make use of qr and singular value decompositions both n4sid algorithms are similar but the second one trades off accuracy for simplicity these new algorithms are compared with existing subspace algorithms in theory and in practice

asymptotic properties of subspace estimators since the proposal of subspace methods in the 1980s and early 1990s substantial efforts have been made in the analysis of the statistical properties of the algorithms this paper surveys the literature on the asymptotic properties of particular subspace methods used for linear dynamic time invariant discrete time systems the goals of this paper are threefold first this survey tries to present the most relevant results on the asymptotic properties of estimators obtained using subspace methods secondly the main methods and tools that have been used in the derivation of these results are presented to make the literature more accessible thirdly main unsolved questions and rewarding research topics are identified some of which can be attacked using the toolbox discussed in the paper

conditions for locking free elasto plastic analyses in the element free galerkin method the use of finite elements with linear displacement fields in volume preserving elasto plastic problems can lead to volumetric locking due to the inability of the shape functions to describe certain displacement modes a response of the structure can be obtained which is much too stiff the element free galerkin efg method can provide shape functions that have an intrinsic richer nature and do not exhibit volumetric locking it is shown that the finite element fe method can be conceived as a specialisation of the efg method and that for a specific choice of the efg parameters the fe shape functions are retrieved then volumetric locking behaviour is found again however for other choices of the efg parameters shape functions are obtained that are able to describe isochoric elasto plasticity without volumetric locking

parameterization and identification of multivariable state space systems a canonical approach in this paper the problem of determining a canonical state space representation for multivariable systems is revisited a method is derived to build a canonical state space representation directly from data generated by a linear time invariant system contrary to the classic construction methods of canonical parameterizations the technique developed in this paper does not assume the availability of any observability or controllability indices however it requires the a matrix of any minimal realization of the system to be non derogatory a subspace based identification algorithm is also introduced to estimate such a canonical state space parameterization directly from input output data

brief subspace identification of closed loop systems by the orthogonal decomposition method in this paper we consider a problem of identifying the deterministic part of a closed loop system by applying the stochastic realization technique of signal process 52 2 1996 145 in the framework of the joint input output approach using a preliminary orthogonal decomposition the problem is reduced to that of identifying the plant and controller based on the deterministic component of the joint input output process we discuss the role of input signals in closed loop identification and the realization method based on a finite data and then sketch a subspace method for identifying state space models of the plant and controller since the obtained models are of higher order a model reduction procedure should be applied for deriving lower order models some numerical results are included to show the applicability of the present technique

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

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

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

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

numerical conditioning and asymptotic variance of subspace estimates new formulas for the asymptotic variance of the parameter estimates in subspace identification show that the accuracy of the parameter estimates depends on certain indices of near collinearity of the state and future input subspaces of the system to be identified this complements the numerical conditioning analysis of subspace methods presented in the companion paper on the ill conditioning of subspace identification with inputs automatica doi 10 1016 j automatica 2003 11 009

subspace model identification part 1 the output error state space model identification class of algorithms in this paper we present two novel algorithms to realize a finite dimensional linear time invariant state space model from input output data the algorithms have a number of common features they are classified as one of the subspace model identification schemes in that a major part of the identification problem consists of calculating specially structured subspaces of spaces defined by the input output data this structure is then exploited in the calculation of a realization another common feature is their algorithmic organization an rq factorization followed by a singular value decomposition and the solution of an overdetermined set or sets of equations the schemes assume that the underlying system has an output error structure and that a measurable input sequence is available the latter characteristic indicates that both schemes are versions of the mimo output error state space model identification moesp approach the first algorithm is denoted in particular as the elementary moesp scheme

subspace based methods for the identification of linear time invariant systems subspace based methods for system identification have attracted much attention during the past few years this interest is due to the ability of providing accurate state space models for multivariable linear systems directly from input output data the methods have their origin in classical state space realization theory as developed in the 1960s the main computational tools are the qr and the singular value decompositions here an overview of existing subspace based techniques for system identification is given the methods are grouped into the classes of realization based and direct techniques similarities between different algorithms are pointed out and their applicability is commented upon we also discuss some recent ideas for improving and extending the methods a simulation example is included for comparing different algorithms the subspace based approach is found to perform competitive with respect to prediction error methods provided the system is properly excited

adaptive element free galerkin method applied to the limit analysis of plates the implementation of an h adaptive element free galerkin efg method in the framework of limit analysis is described the naturally conforming property of meshfree approximations with no nodal connectivity required facilitates the implementation of h adaptivity nodes may be moved discarded or introduced without the need for complex manipulation of the data structures involved with the use of the taylor expansion technique the error in the computed displacement field and its derivatives can be estimated throughout the problem domain with high accuracy a stabilized conforming nodal integration scheme is extended for use in error estimation and results in an efficient and truly meshfree adaptive method to demonstrate its effectiveness the procedure is then applied to plates with various boundary conditions

an iterative algorithm for limit analysis with nonlinear yield functions abstract a mathematical programming algorithm is proposed for the general limit analysis problem plastic behavior is described by a set of linear or nonlinear yield functions abstract formulations of limit analysis are first considered and a quasi newton strategy for solving the optimality conditions is then sketched the structure of the problem arising from a finite element discretization is taken into account in order that the algorithm should be able to solve large scale problems

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

formulation and solution of some plasticity problems as conic programs abstract the application of conic programming to some traditionally difficult plasticity problems is considered convenient standard forms for conic programming of both limit and incremental elastoplastic analysis are given the types of yield criteria that can be treated by conic programming is discussed and it is shown that the three dimensional mohr coulomb criterion can be cast as a set of conic constraints thus facilitating efficient treatment by dedicated algorithms finally the performance of a number of mixed finite elements is evaluated together with a state of the art second order cone programming algorithm

on the performance of non conforming finite elements for the upper bound limit analysis of plates summary in this paper the upper bound limit analysis of thin plates in bending is addressed using various types of triangular finite elements for the generation of velocity fields and second order cone programming for the minimization problem three different c1 discontinuous finite elements are considered the quadratic six node lagrange triangle t6 an enhanced t6 element with a cubic bubble function at centroid t6b and the cubic hermite triangle h3 through numerical examples involving johansen and von mises yield criteria it is shown that cubic elements h3 give far better results in terms of convergence rate and precision than fully conforming elements found in the literature especially for problems involving clamped boundaries copyright 2013 john wiley sons ltd

a novel subspace identification approach with enforced causal models subspace identification methods sims for estimating state space models have been proven to be very useful and numerically efficient they exist in several variants but all have one feature in common as a first step a collection of high order arx models are estimated from vectorized input output data in order not to obtain biased estimates this step must include future outputs however all but one of the submodels include non causal input terms the coefficients of them will be correctly estimated to zero as more data become available they still include extra model parameters which give unnecessarily high variance and also cause bias for closed loop data in this paper a new model formulation is suggested that circumvents the problem within the framework the system matrices a b c d and markov parameters can be estimated separately it is demonstrated through analysis that the new methods generally give smaller variance in the estimate of the observability matrix and it is supported by simulation studies that this gives lower variance also of the system invariants such as the poles

asymptotic variance of subspace methods by data orthogonalization and model decoupling a comparative analysis this is a companion of the paper chiuso and picci 2004d where we do asymptotic error analysis of a weighted pi moesp type method and compare accuracy with respect to estimates obtained by customary joint subspace methods the analysis shows that under certain conditions methods based on orthogonal decomposition of the input output data and block decoupled parametrization perform better than traditional joint model based methods in the circumstance of nearly parallel regressors

a new discontinuous upper bound limit analysis formulation summary a new upper bound formulation of limit analysis of two and three dimensional solids is presented in contrast to most discrete upper bound methods the present one is formulated in terms of stresses rather than velocities and plastic multipliers however by means of duality theory it is shown that the formulation does indeed result in rigorous upper bound solutions also kinematically admissible discontinuities which have previously been shown to be very efficient are given an interpretation in terms of stresses this allows for a much simpler implementation and in contrast to existing formulations extension to arbitrary yield criteria in two and three dimensions is straightforward finally the capabilities of the new method are demonstrated through a number of examples copyright 2005 john wiley sons ltd

application of discontinuity layout optimization to plane plasticity problems a new and potentially widely applicable numerical analysis procedure for continuum mechanics problems is described the procedure is used here to determine the critical layout of discontinuities and associated upper bound limit load for plane plasticity problems potential discontinuities which interlink nodes laid out over the body under consideration are permitted to crossover one another giving a much wider search space than when such discontinuities are located only at the edges of finite elements of fixed topology highly efficient linear programming solvers can be employed when certain popular failure criteria are specified e g tresca or mohr coulomb in plane strain stress velocity singularities are automatically identified and visual interpretation of the output is straightforward the procedure coined discontinuity layout optimization dlo is related to that used to identify the optimum layout of bars in trusses with discontinuities e g slip lines in a translational failure mechanism corresponding to bars in an optimum truss hence a recently developed adaptive nodal connection strategy developed for truss layout optimization problems can advantageously be applied here the procedure is used to identify critical translational failure mechanisms for selected metal forming and soil mechanics problems close agreement with the exact analytical solutions is obtained