analysis of a modified first order system least squares method for linear elasticity with improved momentum balance a modified first order system least squares formulation for linear elasticity obtained by adding the antisymmetric displacement gradient in the test space is analyzed this approach leads to surprisingly small momentum balance error compared to standard least squares approaches it is shown that the modified least squares formulation is well posed and its performance is illustrated by adaptive finite element computation based on using a closely related least squares functional as a posteriori error estimator the results of our numerical computations show that for the modified least squares approach the momentum balance error converges at a much faster rate than the overall error we prove that this is due to a strong connection of the stress approximation to that obtained from a mixed formulation based on the hellinger reissner principle with exact local momentum balance the practical significance is that our proposed approach is almost momentum conservative at a smaller number of degrees of freedom than mixed approximations with exact local momentum balance

asymptotic formulas for the eigenvalues of the timoshenko beam abstract asymptotic formulas are derived for the eigenvalues of a free ended timoshenko beam which has variable mass density and constant beam parameters otherwise these asymptotic formulas show how the eigenvalues and hence how the natural frequencies of such a beam depend on the material and geometric parameters which appear as coefficients in the timoshenko differential equations

reconstruction techniques for classical inverse sturm liouville problems this paper gives constructive algorithms for the classical inverse sturm liouville problem it is shown that many of the formulations of this problem are equivalent to solving an overdetermined boundary value problem for a certain hyperbolic operator two methods of solving this latter problem are then provided and numerical examples are presented

a framework for the adaptive finite element solution of large scale inverse problems since problems involving the estimation of distributed coefficients in partial differential equations are numerically very challenging efficient methods are indispensable in this paper we will introduce a framework for the efficient solution of such problems this comprises the use of adaptive finite element schemes solvers for the large linear systems arising from discretization and methods to treat additional information in the form of inequality constraints on the parameter to be recovered the methods to be developed will be based on an all at once approach in which the inverse problem is solved through a lagrangian formulation the main feature of the paper is the use of a continuous function space setting to formulate algorithms in order to allow for discretizations that are adaptively refined as nonlinear iterations proceed this entails that steps such as the description of a newton step or a line search are first formulated on continuous functions and only then evaluated for discrete functions on the other hand this approach avoids the dependence of finite dimensional norms on the mesh size making individual steps of the algorithm comparable even if they used differently refined meshes numerical examples will demonstrate the applicability and efficiency of the method for problems with several million unknowns and more than 10 000 parameters

a perturbation method for the accurate estimation of the vibration spectrum for the timoshenko beam in the stabilization and control of the vibration of flexible structures a knowledge of the system s vibration spectrum is crucial in the past we developed a perturbation approach that when coupled with the asymptotic wave propagation method of keller and rubinow yields highly accurate estimates for the vibration spectra of certain beam problems here we extend this method to a stand alone method applied to the timoshenko beam problem it is seen that the wave propagation method is a special case of this method as are all other asymptotic results that we have found in the literature

analysis of vibration eigenfrequencies of a thin plate by the keller rubnow wave method i clamped boundary conditions with rectangular or circular geometry the wave method of kelley and rubinow ann physics 9 1960 p 24 75 is extended to the biharmonic eigenvalue problem with rectangular or circular geometry and clamped boundary conditions first it is noted from the clues of computer graphics that mode shapes of a clamped circular plate and those of a circular membrane look very similar to each other this suggests that plate and membrane should have very similar vibration behavior and leads to the assumption that the covering space of a rectangular plate is still a torus by adding several waves on the boundary approximate eigenfrequency equations are derived their solutions are shown to agree remarkably with numerical solutions obtained by the legendre tau spectral method here and by the finite element method elsewhere at all frequency ranges the same idea is also applied to the circular plate and yields excellent agreement between the exact values of eigenfrequencies and the asymptotic solutions

patch recovery based on superconvergent derivatives and equilibrium in this paper a postprocessing technique is developed for determining first order derivatives fluxes stresses at nodal points based on derivatives in superconvergent points it is an extension of the superconvergent patch recovery technique presented by zienkiewicz and zhu in contrast to that technique all flux or stress components are interpolated at the same time coupled by equilibrium equations at the superconvergent points the equilibrium equations and use of one order higher degree of interpolation polynomials of stress give a dramatic decrease in error of recovered derivatives even at boundaries

another second order beam vibration theory explicit bending warping flexibility and restraint abstract a new symmetric beam bending vibration theory which explicitly includes bending warping is presented the governing differential equations are of sixth order and the boundary conditions allow enforcement of total fixity of the end of a beam the motivation for the study was the desire to determine if consideration of bending warping restraint in bending theory is as important as is torsion warping restraint in torsion theory natural frequency predictions are given and compared with other theories for constant cross section cantilevered beams of two types short deep rectangular beams and short thin shallow circular cylindrical shells the accuracy of the new theory is comparable with murty s levinson s bickford s and rehfield s theories for beams with rectangular cross sections it is also comparable with cowper s theory for general symmetric cross sections

vertex similarity in networks we consider methods for quantifying the similarity of vertices in networks we propose a measure of similarity based on the concept that two vertices are similar if their immediate neighbors in the network are themselves similar this leads to a self consistent matrix formulation of similarity that can be evaluated iteratively using only a knowledge of the adjacency matrix of the network we test our similarity measure on computer generated networks for which the expected results are known and on a number of real world networks

strategies for computing goal oriented a posteriori error measures in non linear elasticity we investigate the characteristics and performance of goal oriented a posteriori error measures for a class of non linear elasticity models while restriction is made to small strain theory the chosen error measure of the displacement field can be global or local probing the chosen quantity in a specific spatial point the error is computable with the aid of the solution of a dual problem whose data depend on the error measure the main thrust of the paper is to evaluate the performance of a few different approximation strategies for computing the dual solution the chosen strategies are compared in terms of accuracy ease of implementation reliability and cost efficiency a well known numerical example the cook s membrane is used for the numerical evaluations

a posteriori error estimation for finite element discretization of parameter identification problems in this paper we develop an a posteriori error estimator for parameter identification problems the state equation is given by a partial differential equation involving a finite number of unknown parameters the presented error estimator aims to control the error in the parameters due to discretization by finite elements for this we consider the general setting of a partial differential equation written in weak form with abstract parameter dependence exploiting the special structure of the parameter identification problem allows us to derive an error estimator which is cheap in comparison to the overall optimization algorithm several examples illustrating the behavior of an adaptive mesh refinement algorithm based on our error estimator are discussed in the numerical section for the problems considered here both the efficiency of the estimator and the quality of the generated meshes are satisfactory

potential links by neighbor communities abstract the probability of two nodes to be linked is related to their similarities in the network based on statistical inference a network structure similarity index therefore is proposed to find the potential links this index quantifies the effects of the node communities on these links and an algorithm for the index is also successfully designed the experiments on several networks with ground truth groups and temporal attributes reveal that two nodes are likely to be connected if some of their neighbor nodes are in common communities the results from these experiments with tested networks several of which cover more than a million nodes show the reliability of the index and the advantage of its algorithm

accuracy test for link prediction in terms of similarity index the case of ws and ba models abstract link prediction is a technique that uses the topological information in a given network to infer the missing links in it since past research on link prediction has primarily focused on enhancing performance for given empirical systems negligible attention has been devoted to link prediction with regard to network models in this paper we thus apply link prediction to two network models the watts strogatz ws model and barabasi albert ba model we attempt to gain a better understanding of the relation between accuracy and each network parameter mean degree the number of nodes and the rewiring probability in the ws model through network models six similarity indices are used with precision and area under the roc curve auc value as the accuracy metrics we observe a positive correlation between mean degree and accuracy and size independence of the auc value

an efficient algorithm for link prediction in temporal uncertain social networks present a link prediction algorithm in temporal uncertain social networks we transform the link prediction in uncertain network to a random walk in a deterministic one we compute the similarity scores between a node and its neighbors within a subgraph instead of computations in the whole network present an o v 3 method to compute the similarity matrix instead of enumerating the 2 e possible worlds in the network we propose a method for integrating temporal and global topological information in temporal uncertain networks due to the inaccuracy incompleteness and noise in data from real applications uncertainty is a natural feature of real world networks in such networks each edge is associated with a probability value indicating its existence in the network predicting links in uncertain networks is computationally more challenging and differs semantically from predicting connections in deterministic networks this paper presents a method for link prediction in temporal uncertain networks in our method the predicting problem is formalized by designing a random walk in temporal uncertain networks the algorithm first transforms the link prediction problem in uncertain networks to a random walk in a deterministic network then the similarity scores between a node and its neighbors are computed within a sub graph around this node to reduce the computational time the proposed method integrates temporal and global topological information in temporal uncertain networks and can obtain more accurate results experimental results on real social networks show that our method can predict future links efficiently in temporal uncertain social networks and achieves higher quality results than other similar methods

mixed stabilized finite element methods in nonlinear solid mechanics part i formulation abstract this paper exploits the concept of stabilized finite element methods to formulate stable mixed stress displacement and strain displacement finite elements for the solution of nonlinear solid mechanics problems the different assumptions and approximations used to derive the methods are exposed the proposed procedure is very general applicable to 2d and 3d problems implementation and computational aspects are also discussed showing that a robust application of the proposed formulation is feasible numerical examples show that the results obtained compare favorably with those obtained with the corresponding irreducible formulation

free vibration analysis of a flat plate using the hierarchical finite element method abstract the hierarchical finite element method is used to determined the natural frequencies and modes of a flat rectangular plate ten different boundary conditions including free edges and point supports are considered in this paper extensive results are presented for each case including the variation of frequency with the aspect ratio and the poisson ratio and these are shown to be in very good agreement with the work of other investigators this confirms both the applicability and accuracy of solution of the hfem to problem of this type

eigenvalue and eigenfunction asymptotics for regular sturm liouville problems abstract in this paper we obtain asymptotic formulas for eigenvalues eigenfunctions and the reciprocals of the eigenfunction norms for eigenvalue problems associated with the general sturm liouville equation pu r q u 0 having regular endpoints the method is based on a conversion to liouville normal form and an iterative procedure of solving the associated volterra integral equation producing an asymptotic expansion of the solution in higher powers of 1 1 2 as

predicting link directions via a recursive subgraph based ranking abstract link directions are essential to the functionality of networks and their prediction is helpful toward a better knowledge of directed networks from incomplete real world data we study the problem of predicting the directions of some links by using the existence and directions of the rest of links we propose a solution by first ranking nodes in a specific order and then predicting each link as stemming from a lower ranked node and pointing toward a higher ranked one the proposed ranking method works recursively by utilizing local indicators on multiple scales each corresponding to a subgraph extracted from the original network experiments on real networks show that the directions of a substantial fraction of links can be correctly recovered by our method which outperforms either purely local or global methods

link sign prediction by variational bayesian probabilistic matrix factorization with student t prior abstract in signed social networks link sign prediction refers to using the observed link signs to infer the signs of the remaining links which is important for mining and analyzing the evolution of social networks the widely used matrix factorization based approach bayesian probabilistic matrix factorization bmf assumes that the noise between the real and predicted entry is gaussian noise and the prior of latent features is multivariate gaussian distribution however gaussian noise model is sensitive to outliers and is not robust gaussian prior model neglects the differences between latent features that is it does not distinguish between important and non important features thus gaussian assumption based models perform poorly on real world sparse datasets to address these issues a novel variational bayesian probabilistic matrix factorization with student t prior model tbmf is proposed in this paper a univariate student t distribution is used to fit the prediction noise and a multivariate student t distribution is adopted for the prior of latent features due to the high kurtosis of student t distribution tbmf can select informative latent features automatically characterize long tail cases and obtain reasonable representations on many real world datasets experimental results show that tbmf improves the prediction performance significantly compared with the state of the art algorithms especially when the observed links are few

complex dynamic behavior of a rumor propagation model with spatial temporal diffusion terms a spatial temporal rumor propagation model with discrete and non local delays is regarded stability and hopf bifurcation are proved in a strict mathematical way sensitivity analysis is applied to search active parameters hopf bifurcation causes an oscillation phenomenon in this model numerical simulations provide a new insight into rumor spreading in online social networks rumor propagation as a typical form of social communication in online social networks has had a significant negative impact on a harmonious and stable society with the rapid development of mobile communication equipments traditional rumor propagation models which depend on ordinary differential equations ode may not be suitable for describing rumor propagation in an online social network in this paper based on reaction diffusion equations we propose a novel epidemic like model with both discrete and nonlocal delays for investigating the spatial temporal dynamics of rumor propagation by analyzing the corresponding characteristic equations of this model the local stability conditions of a boundary equilibrium point and a positive equilibrium point are established by applying the linear approximation method of nonlinear systems sufficient conditions are derived for the existence of hopf bifurcation at the above two kinds of equilibrium points moreover a sensitivity analysis method based on the density of spreading users is proposed and then in theoretical and experimental aspect we identify some sensitive parameters in the process of rumor propagation finally numerical simulations are performed to illustrate the theoretical results

link prediction in multi relational networks based on relational similarity presented a belief propagation method to calculate the belief of each node in a network proposed a measurement of influence between different types of relations using belief vectors presented a nonnegative matrix factorization based algorithm for link prediction in multi relational networks theoretically proved the convergence and correctness of the proposed algorithm empirically demonstrated the proposed algorithm can achieve higher quality prediction results many real world networks contain multiple types of interactions and relations link prediction in such multi relational networks has become an important area in network analysis for link prediction in multi relational networks we should consider the similarity and influence between different types of relations in this paper we propose a link prediction algorithm in multi relational networks based on relational similarity in the algorithm a belief propagation method is presented to calculate the belief of each node and to construct the belief vector for each type of link we use the similarity between belief vectors to measure the influence between different types of relations based on the influence between different relations we present a nonnegative matrix factorization based method for link prediction in multi relational networks the convergence and correctness of the presented method are proved our experimental results show that our method can achieve higher quality prediction results than other similar algorithms

a stabilized mixed finite element method for finite elasticity formulation for linear displacement and pressure interpolation abstract a stabilized mixed finite element method for finite elasticity is presented the method circumvents the fulfillment of the ladyzenskaya babuska brezzi condition by adding mesh dependent terms which are functions of the residuals of the euler lagrange equations to the usual galerkin method the weak form and the linearized weak form are presented in terms of the reference and current configuration numerical experiments using a tetrahedral element with linear shape functions for the displacements and for the pressure show that the method successfully yields a stabilized element

inversion formulas for the linearized problem for an inverse boundary value problem in elastic prospection the problem of determining an unknown pair gamma lambda mu of lame parameters inside a body by its dirichlet to neumann data map lambda gamma is considered using explicit exact solutions for the case of constant gamma it is seen that the deflection h between gamma h and gamma is uniquely determined by the first order approximation of lambda gamma h at gamma

a closed form solution of a bernoulli euler beam on a viscoelastic foundation under harmonic line loads fourier transform is used in this paper to solve the problem of steady state response of a beam on a viscoelastic foundation subjected to a harmonic line load the solution is constructed in the form of the convolution of the green function of the beam the theorem of residue is employed to evaluate the generalized integral such that a closed form solution can be achieved all the different combinations of damping and vibration frequency are discussed and analytical solutions are presented as a special case the solution of the beam on a winkler foundation is also discussed the validation of the solution is verified by considering the static solution of the beam and comparing the degraded solution to a well known result the closed form expression of the result can be used to construct algorithms for the inverse problems of non destructive testing of pavement structures using vibration devices

generalized parameter identification for finite viscoelasticity elastomeric and other rubber like materials are often simultaneously exposed to short and long time loads within engineering applications when aiming at establishing a general simulation tool for viscoelastic media over these different time scales a suitable material model and its corresponding material parameters can only be determined if an appropriate number of experimental data is taken into account in this work we present an algorithm for the identification of material parameters for large strain viscoelasticity in which data of multiple experiments are considered based on this method the experimental loading intervals for long time experiments can be shortened in time and the parameter identification procedure is now referred to experimental data of tests under short and long time loads without separating the parameters due to these different time scales the employed viscoelastic material law is based on a nonlinear evolution law and valid far from thermodynamic equilibrium the identification is carried out by minimizing a least squares functional comparing inhomogeneous displacement fields from experiments and fem simulations at given measured force loads within this optimization procedure all material parameters are identified simultaneously by means of a gradient based method for which a semi analytical sensitivity analysis is calculated a representative numerical example is referred to measured data based on short time and long time tests of a non cellular polyurethane as an advantage the developed identification scheme renders solely one single set of material parameters

frequency analysis of finite beams on nonlinear kelvin voight foundation under moving loads abstract the vibration of an euler bernoulli beam resting on a nonlinear kelvin voight viscoelastic foundation traversed by a moving load is studied in the frequency domain the objective is to obtain the frequency responses of the beam and the effects of different parameters on the system response the parameters include the magnitude and speed of the moving load and the foundation nonlinearity and its damping coefficient the solution is obtained by using the galerkin method in conjunction with the multiple scales method msm the governing nonlinear partial differential equations of motion are discretized into sets of nonlinear ordinary differential equations subsequently the solution is calculated for different harmonics by using the msm as one of the powerful perturbation techniques the steady state responses of the main harmonic as well as its two super harmonics are then obtained as a case study a conventional railway track is dynamically simulated and the jump phenomenon in the response is observed for three harmonics moreover a thorough stability analysis of the system is carried out

the inverse sturm liouville problem ii soit q q 0 2 l r 2 0 1 le probleme de sturm liouville y q x y y 0 x 1 y 0 cos y 0 sin 0 y 1 cos y 1 sin 0 a un spectre discret de valeurs propres simples 0 q 1 q avec des fonctions propres h 0 x q h 1 x q on fixe p dans 0 2 l r 2 0 1 et soit m p q 0 2 l r 2 0 1 n q n p n 0 l espace de tous les points q de meme spectre que p on etudie m p comme une sous variete de 0 2 l r 2 0 1

aspects of the formulation and finite element implementation of large strain isotropic elasticity the paper presents a formulation of isotropic large strain elasticity and addresses some computational aspects of its finite element implementation on the theoretical side an eulerian setting of isotropic elasticity is discussed exclusively in terms of the finger tensor as a strain measure noval aspects are a direct representation of the eulerian elastic moduli in terms of the finger tensor and their rigorous decomposition into decoupled volumetric and isochoric contributions based on a multiplicative split of the finger tensor into spherical and unimodular parts the isochoric stress response is formulated in terms of the eigenvalues of the unimodular part of the finger tensor a constitutive algorithm for the computation of the stresses and tangent moduli for plane problems is developed and applied to a model problem of rubber elasticity on the computational side the implementation of the constitutive model in three possible finite element formulations is discussed after pointing out algorithmic techniques for the treatment of incompressible elasticity several numerical simulations are presented which show the performance of the proposed constitutive algorithm and the convergence behaviour of the different finite element fomulations for compressible and incompressible elasticity

the well posedness and stability of a beam equation with conjugate variables assigned at the same boundary point a euler bernoulli beam equation subject to a special boundary feedback is considered the well posedness problem of the system proposed by g chen is studied this problem is in sharp contrast to the general principle in applied mathematics that the conjugate variables cannot be assigned simultaneously at the same boundary point we use the riesz basis approach in our investigation it is shown that the system is well posed in the usual energy state space and that the state trajectories approach the zero eigenspace of the system as time goes to infinity the relaxation of the applied mathematics principle gives more freedom in the design of boundary control for suppression of vibrations of flexible structures

solution of the inverse spectral problem for an impedance with integrable derivative part ii the inverse eigenvalue problem for a sturm liouville equation in impedance form with dirichlet boundary conditions on a unit interval is solved the solution of this nonlinear problem requires the investigation of a combined map from the logarithmic derivative of the impedance assumed to be square integrable to two sequences of spectral data the first is the sequence of dirichlet eigenvalues shown to be locally bounded with square roots differing from the sequence of integral multiples of by a square summable sequence the second sequence has as first term the mean of the logarithmic derivative of the impedance each term in the remainder of the sequence is the logarithm of the product of the impedance and the derivative of an eigenfunction evaluated at an endpoint it is shown that this second sequence is a locally bounded square summable sequence the combined map is a real analytic isomorphism a uniqueness result follows from the asymptotics and analyticity shown in the first paper and properties of riesz bases the existence is shown by giving a closed form of the solution it is also shown that the same map solves the inverse sturm liouville problem in impedance form with neumann boundary conditions 1993 john wiley sons inc

on the shear coefficient in timoshenko s beam theory abstract some existing formulations for the shear coefficient in timoshenko s beam theory are discussed especially through evaluation of the accuracy to which natural frequencies of simply supported prismatic thin walled beams can be obtained the main conclusion drawn is that if a consistent expression for the shear coefficient such as those given by cowper 1 or stephen 2 is used in timoshenko s beam theory then very high accuracies can be expected for the natural frequencies even for wavelengths of the same magnitude as the transverse dimension of the beam it is noted that no reduction of the moment of inertia due to shear lag effects should be made as these effects are included in the consistent formulas for the shear coefficient finally some apparently paradoxical results indicating that a reduction in shear stiffness occurs in rare cases if more material is added to a section are discussed and explained as resulting from the use of integrated rather than pointwise deflection measures in the derivation of consistent shear coefficient expressions the results are discussed in the light of the importance of the shear stiffness of the hull girder in ship hull vibration analysis

adaptivity for parameter identification of incompressible hyperelastic materials using stabilized tetrahedral elements abstract this work is concerned with the identification of material parameters for isotropic incompressible hyperelastic material models besides the principal stretch based strain energy function by ogden an invariant based strain energy function by rivlin saunders is considered for which parameter sensitivities are derived the identification is formulated as a least squares minimization problem based on the finite element method to account for inhomogeneous states of stresses and strains in the experimental data which is obtained by optical measurements for the finite element method low order tetrahedral elements in a mixed displacement pressure formulation with stabilization are considered special attention is payed to an adaptive mesh refinement based on a goal oriented a posteriori error indicator to gain reliable material parameters to approximate error terms an element wise recovery technique based on enhanced gradients is introduced

from the hu washizu formulation to the average nodal strain formulation abstract we present a stabilized finite element method for the hu washizu formulation of linear elasticity based on simplicial meshes leading to the stabilized nodal strain formulation or node based uniform strain elements we show that the finite element approximation converges uniformly to the exact solution for the nearly incompressible case

sampling based algorithm for link prediction in temporal networks present a fast sampling based method to predict the links in temporal network the method computes the similarity scores of potential links with a given node in a sub graph instead of in the whole network present a sampling based approach to construct the sub graph for a given node so that the error of the similarity estimated is lower than a given threshold present a quasi local index based method to compute the similarities in o n2 time while other similar methods require o n3 time experimental results show that the methods presented can obtain higher precision results in less time than other methods the problem of link prediction in temporal networks has attracted considerable recent attention from various domains such as sociology anthropology information science and computer science in this paper we propose a fast similarity based method to predict the potential links in temporal networks in this method we first combine the snapshots of the temporal network into a weighted graph a proper damping factor is used to assign greater importance to more recent snapshots then we construct a sub graph centered at each node in the weighted graph by a random walk from the node the sub graph constructed consists of a set of paths starting from the given node because the similarity score is computed within such small sub graphs centered at each node the algorithm can greatly reduce the computation time by choosing a proper number of sampled paths we can restrict the error of the estimated similarities within a given threshold while other random walk based algorithms require o n3 time for a network with n nodes the computation time of our algorithm is o n2 which is the lowest time complexity of a similarity based link prediction algorithm moreover because the proposed method integrates temporal and global topological information in the network it can yield more accurate results the experimental results on real networks show that our algorithm demonstrates the best or comparable quality results in less time than other methods

variational derivation of governing differential equations for truncated version of bresse timoshenko beams abstract in this paper we provide a variational derivation of modified bresse timoshenko equations this process leads to the additional term to so called truncated set of bresse timoshenko equations this new term is associated with the modified slope inertia the two sets of truncated versions of the bresse timoshenko equations are contrasted with each other as well as with the original bresse timoshenko equations on the example of the a beam that is simply supported at its both ends and b the cantilever beam with end mass it is concluded that application of either truncated sets of equations is advantageous over the original bresse timoshenko equations as far as two truncated sets of equations are concerned the variationally derived set appears to be preferable

considerations on second order beam theories abstract by comparing the phase velocity predictions of various higher order beam theories with the second order approximations to the exact frequency equations for circular and thin rectangular section beams it is concluded that equivalence requires the inclusion of rotatory inertia shear deflection lateral contraction inertia and transverse direct stress corrections to the euler bernoulli beam theory in addition it is shown that cowper s expression for the shear coefficient in the constitutive equation for shear is in fact identical to the original timoshenko definition the apparent difference arising through employing averaged rather than centre line displacement quantities

a comparison of infinite timoshenko and euler bernoulli beam models on winkler foundation in the frequency and time domain abstract this paper deals with the dynamic analysis of infinite beam models the translational and the rotational dynamic stiffness of both timoshenko and euler bernoulli beams on winkler foundation are derived and compared in the frequency domain the situation of vanishing elastic foundation is included as a special case here special emphasis is placed on the asymptotic behaviour of the derived stiffness expressions for high frequencies since this is of importance in case of transient excitations it is shown that the dynamic stiffness of the infinite timoshenko beam follows a linear function of i whereas rational powers of i are involved in case of euler bernoulli s model the stiffness formulations can be transformed into the time domain using the mixed variables technique this is based on a rational approximation of the low frequency force displacement relationship and a subsequent algebraic splitting process at the same time the high frequency asymptotic dynamic stiffness is transformed into the time domain in closed form it is shown that the timoshenko beam is equivalent to a simple dashpot in the high frequency limit whereas euler bernoulli s beam model leads to fractional derivatives of the unknown state variables in an equivalent time domain description this finding confirms the superiority of timoshenko s model especially for high frequencies and transient excitations numerical examples illustrate the differences with respect to the two beam models and demonstrate the applicability of the proposed method for the time domain transformation of force displacement relationships

optimal control of the convection diffusion equation using stabilized finite element methods in this paper we analyze the discretization of optimal control problems governed by convection diffusion equations which are subject to pointwise control constraints we present a stabilization scheme which leads to improved approximate solutions even on corse meshes in the convection dominated case moreover the in general different approaches optimize then discretize and discretize then optimize coincide for the proposed discretization scheme this allows for a symmetric optimality system at the discrete level and optimal order of convergence

the superconvergent patch recovery and a posteriori error estimates part 1 the recovery technique this is the first of two papers concerning superconvergent recovery techniques and a posteriori error estimation in this paper a general recovery technique is developed for determining the derivatives stresses of the finite element solutions at nodes the implementation of the recovery technique is simple and cost effective the technique has been tested for a group of widely used linear quadratic and cubic elements for both one and two dimensional problems numerical experiments demonstrate that the recovered nodal values of the derivatives with linear and cubic elements are superconvergent one order higher accuracy is achieved by the procedure with linear and cubic elements but two order higher accuracy is achieved for the derivatives with quadratic elements in particular an o h4 convergence of the nodal values of the derivatives for a quadratic triangular element is reported for the first time the performance of the proposed technique is compared with the widely used smoothing procedure of global l2 projection and other methods it is found that the derivatives recovered at interelement nodes by using l2 projection are also superconvergent for linear elements but not for quadratic elements numerical experiments on the convergence of the recovered solutions in the energy norm are also presented higher rates of convergence are again observed the results presented in this part of the paper indicate clearly that a new powerful and economical process is now available which should supersede the currently used post processing procedures applied in most codes

stabilization of bi linear mixed finite elements for tetrahedra with enhanced interpolation using volume and area bubble functions in order to overcome the oscillatory effects of the mixed bi linear galerkin formulation for tetrahedral elements a stabilization approach is presented to this end the mixed method of incompatible modes and the mixed method of enhanced strains are reformulated thus giving both the interpretation of a mixed finite element method with stabilization terms for non linear problems these are non linearly dependent on the current deformation state and therefore are replaced by linearly dependent stabilization terms the approach becomes most attractive for the numerical implementation since the use of quantities related to the previous newton iteration step typically arising for mixed enhanced elements is completely avoided the stabilization matrices for the mixed method of incompatible modes and the mixed method of enhanced strains are obtained with volume and area bubble functions various numerical examples are presented which illustrate successfully the stabilization effect for bi linear tetrahedral elements copyright 2007 john wiley sons ltd

a root finding technique to compute eigenfrequencies for elastic beams in this manuscript a method to compute eigenfrequencies for elastic beams is presented for beam modeling three fundamental effects are considered bending rotary inertia and shear deformation the method consists on enclosing each eigenfrequency in an interval where the characteristic function is monotonic then a root finding technique is used to compute the eigenfrequency to any desired accuracy the method is applied successfully to equations involving bending and either rotary inertia or shear deformation

a fast algorithm for predicting links to nodes of interest present a fast method to predict the links to nodes of interest the method computes the similarity scores of potential links connecting to a given node in a sub graph instead of in the whole network present an approach to construct the sub graph for the given node so that the errors of the similarities estimated are lower than a given threshold present a quasi global index based method to compute the similarities in the network in o n time while other similar methods require o n3 time experimental results show that the methods presented can obtain high precision results in less time than other methods the problem of link prediction has recently attracted considerable attention in various domains such as sociology anthropology information science and computer science in many real world applications we must predict similarity scores only between pairs of vertices in which users are interested rather than predicting the scores of all pairs of vertices in the network in this paper we propose a fast similarity based method to predict links related to nodes of interest in the method we first construct a sub graph centered at the node of interest by choosing the proper size for such a sub graph we can restrict the error of the estimated similarities within a given threshold because the similarity score is computed within a small sub graph the algorithm can greatly reduce computation time the method is also extended to predict potential links in the whole network to achieve high process speed and accuracy experimental results on real networks demonstrate that our algorithm can obtain high accuracy results in less time than other methods can

an efficient solution methodology to study the response of a beam on viscoelastic and nonlinear unilateral foundation static response abstract many engineering materials and foundations such as soils demonstrate nonlinear and viscoelastic behaviour yet it is challenging to develop static and dynamic models of systems that include these materials and are able to predict the behaviour over a wide range of loading conditions this research is focused on a specific example a pinned pinned beam interacting with polyurethane foam foundation two cases when the foundation can react in tension and compression as well as only in compression are considered the model developed here is capable of predicting the response to static as well as dynamic forces whether concentrated or distributed galerkin s method is used to derive modal amplitude equations in the tensionless foundation case the contact region changes with beam motion and the estimation of the co ordinates of the lift off points is embedded into the solution procedure an efficient solution technique is proposed that is capable of handling cases where there are multiple contact and non contact regions depending on the loading profiles a high number of modes may need to be included in the solution and to speed up computation time a convolution method is used to evaluate the integral terms in the model the adaptability of the solution scheme to complicated loading patterns is demonstrated via examples the solution approach proposed is applicable to dynamic loadings as well and in these cases the automated treatment of complicated response patterns makes the convolution approach particularly attractive the influence of various parameters on the static response is discussed

a new mixed finite element based on different approximations of the minors of deformation tensors finite element formulations for arbitrary hyperelastic strain energy functions that are characterized by a locking free behavior for incompressible materials a good bending performance and accurate solutions for coarse meshes need still attention therefore the main goal of this contribution is to provide an improved mixed finite element for quasi incompressible finite elasticity based on the knowledge that the minors of the deformation gradient play a major role for the transformation of infinitesimal line area and volume elements as well as in the formulation of polyconvex strain energy functions a mixed finite element with different interpolation orders of the terms related to the minors is developed due to the formulation it is possible to condensate the mixed element formulation at element level to a pure displacement form examples show the performance and robustness of the element

calibration of a class of non linear viscoelasticity models with sensitivity assessment based on duality the calibration of constitutive models is based on the solution of an optimization problem whereby the sought parameter values minimize an objective function that measures the discrepancy between experimental observations and the corresponding simulated response by the introduction of an appropriate adjoint problem the resulting formulation becomes well suited for a gradient based optimization scheme a class of viscoelastic models is studied where a discontinuous galerkin method is used to integrate the governing evolution equation in time a practical solution algorithm which utilizes the time flow structure of the underlying evolution equation is presented based on the proposed formulation it is convenient to estimate the sensitivity of the calibrated parameters with respect to measurement noise the sensitivity is computed using a dual method which compares favourably with the conventional primal method the strategy is applied to a viscoelasticity model using experimental data from a uniaxial compression test copyright 2006 john wiley sons ltd

vibration eigenfrequency analysis of a single link flexible manipulator abstract we analyse the vibration eigenfrequencies of a flexible slewing beam with a payload attached at one end a wave propagation method wpm is used there are four types of waves which propagate along a beam two dispersive waves travelling in opposite directions and two evanescent waves near the endpoints we add a fifth time harmonic function corresponding to oscillation of the beam at the payload end we show that the large frequencies are asymptotically identical to those for the clamped free beam independent of the payload for small eigenfrequencies we incorporate wpm with a perturbation iteration procedure the results of which agree well with exact values which result from solving a transcendental equation cited elsewhere in the literature

parameter identification for finite deformation elasto plasticity in principal directions this work is concerned with identification of material parameters based on experimental data which represent nonuniform distributions of stresses and deformations within the volume of the specimen both elastic and inelastic material non linearities in the frame of a finite deformation theory are taken into account gradient based descent methods e g gauss newton method quasi newton method are used for minimization of a least squares function to this end a sensitivity analysis is performed and the resulting expressions are presented in a spatial and a material setting in particular the cases of an isotropic hyperelastic model and a multiplicative plasticity model with an exponential type integration scheme both formulated in principal directions are considered two numerical examples based on simulated data and experimental data obtained by a grating method demonstrate the versatility of our approach

parameter estimation of hyperelasticity relations of generalized polynomial type with constraint conditions abstract in this article the identification of the material parameters occurring in isotropic and incompressible hyperelasticity relations of generalized polynomial type is discussed the underlying strain energy function depends on the first and second invariant of the left cauchy green tensor in the form of a polynomial the material parameters are the polynomial coefficients this leads in several identification processes to linear least square problems however in most applications the parameters are not restricted to a range of validity this article points out that the assumption of merely positive material parameters leads to a non negative strain energy function in any process which is underpinned by requirements with respect to gradient and convexity behaviour in certain deformations furthermore it is shown that for positive material parameters no non monotonic behaviour occurs in simple deformation processes under consideration outside the identification region the second topic of the article deals with some identification applications of tension torsion tests which are carried out by haupt and sedlan archive of applied mechanics 2000 taking into account the inequality constraints emphasized under certain assumptions this naturally leads to new specific models furthermore it is shown that the parameter estimation becomes much less sensitive than in the unconstrained case

dynamic analyses of plane frames by integral equations for bars and timoshenko beams abstract since especially for higher frequencies timoshenko s theory gives more reliable results than euler bernoulli s theory systems of beams like frames under arbitrary dynamic excitations should be analyzed on the basis of this refined theory in this paper after deriving the basic fundamental solutions of a lateral unit point force and of a unit single moment the deflection and the rotation of the beam cross section are given as integral equation forms of the governing second order differential equation system in the laplace and the frequency domain since in frameworks axial displacements also occur the well known integral equations for bars under tension or compression are added to complete the modelling of plane frame structures from these the unknown boundary values may be exactly determined via point collocation at the beam ends and solution of the resulting algebraic system with these boundary values the exact deflection and rotation can also be found at arbitrary interior points finally the convolution quadrature method is applied to the laplace domain integral equation formulation in order to analyze the time dependent wave propagation process two examples are presented to demonstrate the method s exactness compared with conventional finite element results a single beam where the shift of the resonance frequencies when using the timoshenko theory instead of euler bernoulli s theory is shown and a two storey framework where in addition to the frequence response the causality of the propagating wave is studied

information filtering based on transferring similarity in this brief report we propose an index of user similarity namely the transferring similarity which involves all high order similarities between users accordingly we design a modified collaborative filtering algorithm which provides remarkably higher accurate predictions than the standard collaborative filtering more interestingly we find that the algorithmic performance will approach its optimal value when the parameter contained in the definition of transferring similarity gets close to its critical value before which the series expansion of transferring similarity is convergent and after which it is divergent our study is complementary to the one reported in e a leicht p holme and m e j newman phys rev e 73 026120 2006 and is relevant to the missing link prediction problem

parameter identification in constitutive models via optimization with a posteriori error control in this paper we outline a computational technique for the calibration of macroscopic constitutive laws with automatic error control in the most general situation the state variables of the constitutive law as well as the material parameters are spatially non homogeneous the experimental observations are given in space time based on an appropriate dual problem we compute a posteriori the discretization error contributions from approximations of the parameter state and costate elds in space time for an arbitrarily chosen goal oriented error measure of engineering signi cance such a measure can be used in an adaptive strategy not discussed in this paper to meet a prede ned error tolerance an important observation is that the jacobian matrix associated with the resulting newton method is used in principle in solving the dual problem rather than treating the jacobian in a monolithic fashion we utilize a sequential solution strategy whereby the fe topology of the discretized state problem is used repeatedly moreover the proposed solution strategy lends itself naturally to the computation of rst and second order sensitivities which are obtained with little extra computational effort numerical results are given for the prototype model of con ned aquifer ow with spatially non homogeneous permeability the ef ciency of the optimization strategy and the effectivity of the error computation are assessed

updating of finite element models using vibration tests today the adjustment of structural models is an essential step in the modeling of complex structures in this paper we are interested in the improvement of finite element models our approach is a parametric updating using modal test results which supply eigenvalues and associated eigenvectors it is based on the computation of the error measure on the constitutive relation and allows us to correct both the stiffness and the mass matrices in particular this paper shows how this tuning strategy can improve a given finite element model when the measures are noisy several simulation examples illustrate the behavior of this method a e e

predicting link directions using local directed path abstract link prediction in directed network is attracting growing interest among many network scientists compared with predicting the existence of a link determining its direction is more complicated in this paper we propose an efficient solution named local directed path to predict link direction by adding an extra ground node to the network we solve the information loss problem in sparse network which makes our method effective and robust as a quasi local method our method can deal with large scale networks in a reasonable time empirical analysis on real networks shows that our method can correctly predict link directions which outperforms some local and global methods

two mixed finite element formulations with area bubble functions for tetrahedral elements abstract we address the solution of geometrically linear elastic problems for three dimensional solid mechanics using tetrahedral finite elements starting from a five field weak formulation involving fields for compatible displacements incompatible displacements pressure enhanced strains and stresses both the mixed method of incompatible modes and the mixed method of enhanced strains are considered as special cases as a key idea area bubble functions are used for both mixed finite element formulations in order to enrich the displacement field and the enhanced strain field respectively appropriate conditions for satisfaction of the patch test and unique solution of the discrete equation are verified we also observe that contrary to a the standard enhanced assumed strain method applied to triangles and tetrahedra our mixed formulations with pressure as an independent variable are not degenerate in the representative examples firstly a numerical verification of the patch test is obtained two additional examples cook s membrane problem and a plate with a ring hole illustrate the good performance of the presented approaches in comparison to existing finite element formulations

a perturbation approach for the eigenfrequency analysis of separable kirchhoff thin plate problems on a rectangle we introduce a method for the estimation of the eigenfrequencies for separable kirchhoff thin plate problems on a rectangle particularly those involving the free boundary condition we believe that this paper is the first to give such a treatment for the low end of the spectrum the method is an adaptation of an asymptotic perturbation method used for the treatment of various beam problems and in the setting of the plate is shown to be a generalization and refinement of the asymptotic methods of bolotin and keller and rubinow the wave propagation method we compare our results with those of our own legendre tau approximation and where available with numerical results extant in the literature excellent agreement is found in each case

super mediator a new centrality measure of node importance for information diffusion over social network we propose an efficient method to discover a new type of influential nodes in a social network which we name super mediators i e those nodes which if removed decrease information spread it is formulated mathematically as a problem of difference maximization of the average influence degree with respect to removal of a node i e a node that contributes to making the difference large is influential this definition requires use of information diffusion model for their identification and thus is model driven the other definition which is more empirical is that super mediators are those nodes that appear frequently in long diffusion sequences but much less frequently in short diffusion sequences this definition does not require any model but does require abundant information diffusion data and thus is data driven we attempt to characterize the property of super mediators from various angles how the resulting super mediators are different between these two definitions and which is more reasonable how super mediators are compared with nodes identified by other centralities e g betweenness degree closeness etc how super mediators are different from the solution of well studied influence maximization problem i e nodes capable of widely spreading information to other recipient nodes and the solution of reverse influence maximization problem i e nodes capable of widely receiving information from other information source nodes we conducted extensive experiments using three real world social networks the major findings are 1 model driven super mediator degree has the best discrimination capability while influence degree reverse influence degree and data driven super mediator degree are much less discriminative all flat for high ranked nodes 2 model driven super mediators have high scores for either influence degree or reverse influence degree while data driven super mediators have high scores for both and 3 model driven super mediators are closely correlated with betweenness centrality but the strength of the correlation depends on the value of diffusion probability

boundary feedback exponential stabilization of a timoshenko beam with both ends free in the present paper we consider the boundary feedback stabilization of a timoshenko beam with both ends free we propose boundary feedback control law that makes the closed loop system dissipative using asymptotic analysis techniques we give explicit asymptotic formula of eigenvalues of the closed loop system and prove the riesz basis property of eigenvectors and generalized eigenvectors by a detailed analysis of spectrum of the closed loop system we show that the closed system is exponentially stable

model adaptivity on effective elastic properties coupled with adaptive fem abstract the research field of model adaptivity is well established aiming at adaptive selection of mathematical models from a well defined class of models model hierarchy to achieve a preset level of accuracy the present work addresses its application to a class of linear elastic composite problems we will show that the classical bounding theories can provide a model hierarchy in a natural and theoretically consistent manner without combination of different methods using a priori knowledge to arrive at computable higher order bounds the classical singular approximation is made as a new finding this may under certain circumstances give rise to an overlap effect to overcome this a correction is proposed additionally the model adaptivity is coupled to the well established adaptive finite element method fem such that both macro model and macro discretization errors are controlled the proposed adaptive procedure is driven by a goal oriented a posteriori error estimator based on duality techniques for efficient computation of the dual solution a patch based recovery technique is proposed and compared to existing methods for illustration numerical examples are presented

influence maximization in social networks based on discrete particle swarm optimization influence maximization in social networks aims to find a small group of individuals which have maximal influence cascades in this study an optimization model based on a local influence criterion is established for the influence maximization problem the local influence criterion can provide a reliable estimation for the influence propagations in independent and weighted cascade models a discrete particle swarm optimization algorithm is then proposed to optimize the local influence criterion the representations and update rules for the particles are redefined in the proposed algorithm moreover a degree based heuristic initialization strategy and a network specific local search strategy are introduced to speed up the convergence experimental results on four real world social networks demonstrate the effectiveness and efficiency of the proposed algorithm for influence maximization

a class of mixed assumed strain methods and the method of incompatible modes a three field mixed formulation in terms of displacements stresses and an enhanced strain field is presented which encompasses as a particular case the classical method of incompatible modes within this frame work incompatible elements arise as particular compatible mixed approximations of the enhanced strain field the conditions that the stress interpolation contain piece wise constant functions and be l2 ortho gonal to the enhanced strain interpolation ensure satisfaction of the patch test and allow the elimination of the stress field from the formulation the preceding conditions are formulated in a form particularly convenient for element design as an illustration of the methodology three new elements are developed and shown to exhibit good performance a plane 3d elastic plastic quad an axisymmetric element and a thick plate bending quad the formulation described herein is suitable for non linear analysis

improving low order eigenfrequency estimates derived from the wave propagation method for an euler bernoulli beam we state the wpm when combined with the perturbation procedure as developed in this work enables us to capture the entire low medium and high range of the spectrum of vibration of an euler bernoulli beam both asymptotically and numerically

a boundary condition in pade series for frequency domain solution of wave propagation in unbounded domains a boundary condition satisfying the radiation condition at infinity is frequently required in the numerical simulation of wave propagation in an unbounded domain in a frequency domain analysis using finite elements this boundary condition can be represented by the dynamic stiffness matrix of the unbounded domain defined on its boundary a method for determining a pade series of the dynamic stiffness matrix is proposed in this paper this method starts from the scaled boundary finite element equation which is a system of ordinary differential equations obtained by discretizing the boundary only the coefficients of the pade series are obtained directly from the ordinary differential equations which are not actually solved for the dynamic stiffness matrix the high rate of convergence of the pade series with increasing order is demonstrated numerically this technique is applicable to scalar waves and elastic vector waves propagating in anisotropic unbounded domains of irregular geometry it can be combined seamlessly with standard finite elements copyright 2006 john wiley sons ltd

mean field theory for scale free random networks random networks with complex topology are common in nature describing systems as diverse as the world wide web or social and business networks recently it has been demonstrated that most large networks for which topological information is available display scale free features here we study the scaling properties of the recently introduced scale free model that can account for the observed power law distribution of the connectivities we develop a mean eld method to predict the growth dynamics of the individual vertices and use this to calculate analytically the connectivity distribution and the scaling exponents the mean eld method can be used to address the properties of two variants of the scale free model that do not display power law scaling c 1999 elsevier science b v all rights reserved

finite element modelling of infinite euler beams on kelvin foundations exposed to moving loads in convected co ordinates the paper deals with the finite element method fem solution of the problem with loads moving uniformly along an infinite euler beam supported by a linear elastic kelvin foundation with linear viscous damping initially the problem is formulated in a moving co ordinate system following the load using a galilean co ordinate transformation and subsequently the analytical solution to the homogeneous beam problem is shown to be used in more complicated cases where no analytical solutions can be found a numerical approach of the same problem is then suggested based on the fem absorbing boundary conditions to be applied at the ends of the modelled part of the infinite beam are derived the quality of the numerical results for single frequency harmonic excitation is tested by comparison with the indicated analytical solution finally the robustness of the boundary condition is tested for a ricker pulse excitation in the time domain