a priori error estimation of a four node reissner mindlin plate element for elasto dynamics abstract the explicit finite element method for transient dynamics of linear elasticity by reissner mindlin plate model is introduced for clamped rectangular plate the a priori error estimates are derived for the four node bathe dvorkin element for fixed thickness the convergence rates of deflection rotation and their velocities measured both in h 1 norm and l 2 norm can possibly all be optimal under certain conditions in some cases the numerical examples show that the convergence rate stays optimal for a certain range of thickness in other cases however the deterioration in rate of convergence and even locking may occur to the velocity terms

nonequilibrium phase transition due to isolation of communities we introduce a simple model of a growing system with m competing communities the model corresponds to the phenomenon of defeats suffered by social groups living in isolation a nonequilibrium phase transition is observed when at critical time t c the first isolated cluster occurs in the one dimensional system the volume of the new phase i e the number of the isolated individuals increases with time as z ensuremath sim t 3 for a large number of possible communities the critical density of filled space is equal to ensuremath rho c m n 1 3 where n is the system size a similar transition is observed for erd ifmmode mbox h o else h o fi s r enyi random graphs and barab asi albert scale free networks analytical results are in agreement with numerical simulations

analysis of kinematic linked interpolation methods for reissner mindlin plate problems the approximation to the solution of reissner mindlin plate problem is considered in the framework of finite element techniques a general strategy involving a linking operator between rotations and vertical displacements is analyzed an abstract convergence result is provided examples of elements falling into this framework are presented and shown to be stable and locking free numerical tests detail the performances of the elements email lovadina ing unitn it

a new class of mixed finite element methods for reissner mindlin plates a new class of finite elements for the reissner mindlin plate problem is presented the family is based on a modified mixed formulation recently introduced by arnold and brezzi boundary value problems for partial differential equations and applications j l lions and c baiocchi eds masson paris 1993 a result of stability and convergence uniformly in the thickness is provided

real space renormalization group and totalitarian paradox of majority rule voting abstract the effect of majority rule voting in hierarchical structures is studied using the basic concepts from real space renormalization group it shows in particular that a huge majority can be self eliminated while climbing up the hierarchy levels this majority democratic self elimination articulates around the existence of fixed points in the voting flow an unstable fixed point determines the critical threshold to full and total power it can be varied from 50 up to 77 of initial support our model could shed new light on the last century eastern european communist collapse

an hp error analysis of mitc plate elements we give an hp error analysis of several rectangular families of finite elements for the reissner mindlin plate bending equations we consider both the original mitc families k j bathe f brezzi and m fortin internat j numer methods engrg 28 1989 pp 1787 1801 and some new ones introduced in this paper for the deflection and rotation we give error estimates which are optimal with respect to the mesh size h and optimal up to ordo p varepsilon varepsilon 0 arbitrary with respect to the polynomial degree p we also obtain estimates for the error in the shear force calculated via two different methods our analysis utilizes some recent results of ours for the mixed method for the stokes problem as well as hp interpolation estimates for mixed methods for second order elliptic equations in this regard we derive new hp results in this paper for the brezzi douglas fortin marini spaces and improve upon previous estimates for the brezzi douglas marini spaces

a posteriori error analysis of the linked interpolation technique for plate bending problems we develop a posteriori error estimates for the so called linked interpolation technique to approximate the solution of plate bending problems we show that the proposed residual based estimator is both reliable and efficient

scaling and universality in proportional elections a most debated topic of the last years is whether simple statistical physics models can explain collective features of social dynamics a necessary step in this line of endeavor is to find regularities in data referring to large scale social phenomena such as scaling and universality we show that in proportional elections the distribution of the number of votes received by candidates is a universal scaling function identical in different countries and years this finding reveals the existence in the voting process of a general microscopic dynamics that does not depend on the historical political and or economical context where voters operate a simple dynamical model for the behavior of voters similar to a branching process reproduces the universal distribution

a discontinuous galerkin method for nonlinear shear flexible shells abstract in this paper a discontinuous galerkin method for a nonlinear shear flexible shell theory is proposed that is suitable for both thick and thin shell analysis the proposed method extends recent work on reissner mindlin plates to avoid locking without the use of projection operators such as mixed methods or reduced integration techniques instead the flexibility inherent to discontinuous galerkin methods in the choice of approximation spaces is exploited to satisfy the thin plate compatibility conditions a priori a benefit of this approach is that only generalized displacements appear as unknowns we take advantage of this to craft the method in terms of a discrete energy minimization principle thereby restoring the rayleigh ritz approach in addition to providing a straightforward and elegant derivation of the discrete equilibrium equations the variational character of the method could afford numerous advantages in terms of mesh adaptation and available solution techniques the proposed method is exercised on a set of benchmarks and example problems to assess its performance numerically and to test for shear and membrane locking

mixed interpolated elements for reissner mindlin plates dcpartement de mathtmatiyue l nit ersitt 1 aral quthec canado summary we present in this paper a procedure to establish reissner mindlin plate bending elements the procedure is based on the idea to combine known resuits on the approximation of stokes problems with known results on the approximation of elliptic problems the proposed elements satisfy the mathematical conditions of stability and convergence and some of them promise to provide efficient elements for practical solutions

shell deformation states and the finite element method a benchmark study of cylindrical shells abstract we demonstrate some of the basic mathematical characteristics of shell deformation states and shell models from the point of view of finite element approximation as benchmark cases we analyze in detail three simple cylindrical shell problems these problems are seemingly similar but turn out to be quite different we 1 compute the exact displacement and strain fields in the model problems both numerically and symbolically using two variants of classical shell models 2 for comparison compute numerically the displacements and strains corresponding to certain higher order dimension reduction models derived from the energy principle 3 demonstrate the dissimilarity of the three benchmark problems as to their asymptotic behaviour in the limit of zero thickness and 4 show both theoretically and experimentally how this diversity is reflected in the accuracy of standard finite element approximations of both low and high order

analysis for quadrilateral mitc elements for the reissner mindlin plate problem the present paper is made up of two parts in the first part we study the mathematical stability and convergence of the quadrilateral mitc elements for the reissner mindlin plate problem in an abstract setting we generalize the brezzi bathe fortin conditions to the quadrilateral mitc elements by weakening the second and fourth conditions under these conditions we show the well posedness of the discrete problem and establish an abstract error estimate in the energy norm the conclusion of this part is sparsity in the mathematical research of the quadrilateral mitc elements in the sense that one only needs to check these five conditions in the second part we extend four families of rectangular mitc elements of stenberg and suri to the quadrilateral meshes we prove that these quadrilateral elements satisfy the generalized brezzi bathe fortin conditions from the first part we develop the h p error estimates in both energy and l 2 norm for these quadrilateral elements for the first three families of quadrilateral elements the error estimates indicate that their convergent rates in both energy and l 2 norm depend on the mesh distortion parameter a we can get optimal error estimates for them provided that a 1 in addition we show the optimal convergence rates in energy norm uniformly in a for the fourth family of quadrilateral elements like their rectangular counterparts these quadrilateral elements are locking free

finite element methods for timoshenko beam circular arch and reissner mindlin plate problems in this paper some finite element methods for timoshenko beam circular arch and reissner mindlin plate problems are discussed to avoid locking phenomenon the reduced integration technique is used and a bubble function space is added to increase the solution accuracy the method for timoshenko beam is aligned with the petrov galerkin formulation derived in loula et al 1987 and can be naturally extended to solve the circular arch and the reissner mindlin plate problems optimal order error estimates are proved uniform with respect to the small parameters numerical examples for the circular arch problem shows that the proposed method compares favorably with the conventional reduced integration method

locking free reissner mindlin elements without reduced integration abstract in a recent paper of arnold et al d n arnold f brezzi l d marini a family of discontinuous galerkin finite elements for the reissner mindlin plate j sci comput 22 2005 25 45 the ideas of discontinuous galerkin methods were used to obtain and analyze two new families of locking free finite element methods for the approximation of the reissner mindlin plate problem by following their basic approach but making different choices of finite element spaces we develop and analyze other families of locking free finite elements that eliminate the need for the introduction of a reduction operator which has been a central feature of many locking free methods for k 2 all the methods use piecewise polynomials of degree k to approximate the transverse displacement and possibly subsets of piecewise polynomials of degree k 1 to approximate both the rotation and shear stress vectors the approximation spaces for the rotation and the shear stress are always identical the methods vary in the amount of interelement continuity required in terms of smallest number of degrees of freedom the simplest method approximates the transverse displacement with continuous piecewise quadratics and both the rotation and shear stress with rotated linear brezzi douglas marini elements

majority model on a network with communities we focus on the majority model in a topology consisting of two coupled fully connected networks thereby mimicking the existence of communities in social networks we show that a transition takes place at a value of the interconnectivity parameter above this value only symmetric solutions prevail where both communities agree with each other and reach consensus below this value in contrast the communities can reach opposite opinions and an asymmetric state is attained the importance of the interface between the subnetworks is shown

on mixed finite element methods for the reissner mindlin plate model in this paper we analyze the convergence of mixed finite element approximations to the solution of the reissner mindlin plate problem we show that several known elements fall into our analysis thus providing a unified approach we also introduce a low order triangular element which is optimalorder convergent uniformly in the plate thickness

comparison of voter and glauber ordering dynamics on networks we study numerically the ordering process of two very simple dynamical models for a two state variable on several topologies with increasing levels of heterogeneity in the degree distribution we find that the zero temperature glauber dynamics for the ising model may get trapped in sets of partially ordered metastable states even for finite system size and this becomes more probable as the size increases voter dynamics instead always converges to full order on finite networks even if this does not occur via coherent growth of domains the time needed for order to be reached diverges with the system size in both cases the ordering process is rather insensitive to the variation of the degreee distribution from sharply peaked to scale free

global estimates for mixed methods for second order elliptic equations global error estimates in l2 92 l 9 and h s q 2 in r2 or a re derived for a mixed finite element method for the dirichlet problem for the elliptic operator lp div a grad p bp cp based on the raviart thomas nedelec space vh x wh c h div 92 x l2 g2 optimal order estimates are obtained for the approximation of p and the associated velocity field u a grad p bp in l2 g2 and h s 92 0 6 s k 1 and if q c r2 forp in lv2

spline approximation of thin shell dynamics abstract a spline based method for approximating thin shell dynamics is presented here while the method is developed in the context of the donnell mushtari thin shell equations it can be easily extended to the byrne flugge lur ye equations or other models for shells of revolution as warranted by applications the primary requirements for the method include accuracy flexibility and efficiency in smart material applications to accomplish this the method was designed to be flexible with regard to boundary conditions material nonhomogeneities due to sensors and actuators and inputs from smart material actuators such as piezoceramic patches the accuracy of the method was also of primary concern both to guarantee full resolution of structural dynamics and to facilitate the development of pde based controllers which ultimately require real time implementation several numerical examples provide initial evidence demonstrating the efficacy of the method

two families of mixed finite elements for second order elliptic problems two families of mixed finite elements one based on triangles and the other on rectangles are introduced as alternatives to the usual raviart thomas nedelec spaces error estimates inl 2 andh 5 are derived for these elements a hybrid version of the mixed method is also considered and some superconvergence phenomena are discussed

robust bddc preconditioners for reissner mindlin plate bending problems and mitc elements a balancing domain decomposition method by constraints bddc is constructed and analyzed for the reissner mindlin plate bending problem discretized with mixed interpolation of tensorial components mitc finite elements this bddc algorithm is based on selecting the plate rotations and deflection degrees of freedom at the subdomain vertices as primal continuity constraints after the implicit elimination of the interior degrees of freedom in each subdomain the resulting plate schur complement is solved by the preconditioned conjugate gradient method the preconditioner is based on the solution of local reissner mindlin plate problems on each subdomain with clamping conditions at the primal degrees of freedom and on the solution of a coarse reissner mindlin plate problem for the primal degrees of freedom the main results of the paper are the proof and numerical verification that the proposed bddc plate algorithm is scalable quasi optimal and most important robust with respect to the plate thickness while this result is due to an underlying mixed formulation of the problem both the interface plate problem and the preconditioner are positive definite the numerical results also show that the proposed algorithm is robust with respect to discontinuities of the material properties

opinion formation model with strong leader and external impact a mean field approach abstract we study a model of opinion formation based on the theory of social impact and the concept of cellular automata the case is considered when two strong agents influence the group a strong leader and an external social impact acting uniformly on every individual there are two basic stationary states of the system cluster of the leader s adherents and unification of opinions in the deterministic limit the variation of parameters like the leader s strength or external impact can change the size of the cluster or when they reach some critical values make the system jump to another phase for a certain range of parameters multistability and hysteresis phenomena are observed in the presence of noise social temperature the rapid changes can be regarded as the first order phase transitions when both agents are in a kind of balance a second order transition and critical behaviour can be observed another kind of noise induced transitions are the inverses flips of the unified group opinion due to random flips of the leader s opinion analytical results obtained within a mean field approximation are well reproduced in computer simulations

the hp mitc finite element method for the reissner mindlin plate problem the popular mitc finite elements used for the approximation of the reissner mindlin plate are extended to the case where elements of non uniform degree p distribution are used on locally refined meshes such an extension is of particular interest to the hp version and hp adaptive finite element methods a priori error bounds are provided showing that the method is locking free the analysis is based on new approximation theoretic results for non uniform brezzi douglas fortin marini spaces and extends the results obtained in the case of uniform order approximation on globally quasi uniform meshes presented by stenberg and suri siam j numer anal 34 1997 544 numerical examples illustrating the theoretical results and comparing the performance with alternative standard galerkin approaches are presented for two new benchmark problems with known analytic solution including the case where the shear stress exhibits a boundary layer the new method is observed to be locking free and able to provide exponential rates of convergence even in the presence of boundary layers

a general methodology for deriving shear constrained reissner mindlin plate elements in this paper the necessary requirements for the good behaviour of shear constrained reissner mindlin plate elements for thick and thin plate situations are re interpreted and a simple explicit form of the substitute shear strain matrix is obtained this extends the previous work of the authors presented in references 18 and 31 the general methodology is applied to the re formulation of some well known quadrilateral plate elements and some new triangular and quadrilateral plate elements which show promising features some examples of the good behaviour of these elements are given

new rectangular plate elements based on twist kirchhoff theory abstract we introduce a new framework for the development of thin plate finite elements the twist kirchhoff theory a family of rectangular plate elements is derived that takes advantage of the special structure of this new theory particular attention is focused on the lowest order member of the family an eight degree of freedom four node element with mid side rotations whose stiffness matrix is exactly computed with one point gaussian quadrature we prove a convergence theorem for it and various error estimates these are also generalized to the higher order elements in the family numerical tests corroborate the theoretical results

phase transitions as a persistent feature of groups with leaders in models of opinion formation a class of models of opinion formation based on the concept of cellular automata and the theory of social impact is studied in particular the case when a strong leader and external impact are present the rapid changes of the opinion distribution with a continuous change of a system parameter which was previously observed for the model with geometric structure prove to be present also for much larger class of mutual interaction architectures we study random connections with dierent probability distributions the theoretical results obtained in the framework of mean eld approximation are conrmed by the numerical simulations of the model c 2000 elsevier science b v all rights reserved

superelastic shell structures modelling part i element formulation abstract a c0 three node shell finite element belonging to the assumed shear strain elements family is extended to account for large strains when a rotating frame formulation is adopted to describe the material behaviour within an incremental method associated with the newton iterative scheme a strain measure is defined and interpolated in an intermediate configuration assuming a linear interpolation of the incremental geometric transformation this strain measure allows the definition in a rotated configuration of a constitutive incremental strain obtained from a material cumulated tensorial strain the proposed approach is validated herein considering several elastic finite strains examples

time dependent linear daes with discontinuous inputs existence and uniqueness results are proved for initial value problems associated with linear time varying differential algebraic equations the right hand sides are chosen in a space of distributions allowing for solutions exhibiting discontinuities as well as impulses this approach also provides a satisfactory answer to the problem of inconsistent initial conditions of crucial importance for physical applications furthermore our theoretical results yield an efficient numerical procedure for the calculation of the jump and impulse of a solution at a point of discontinuity numerical examples are given

two lower order nonconforming rectangular elements for the reissner mindlin plate in this paper we propose two lower order nonconforming rectangular elements for the reissner mindlin plate the first one uses the conforming bilinear element to approximate both components of the rotation and the modified nonconforming rotated q 1 element to approximate the displacement whereas the second one uses the modified nonconforming rotated q 1 element to approximate both the rotation and the displacement both elements employ a projection operator to overcome the shear force locking we prove that both methods converge at optimal rates uniformly in the plate thickness t in both the h 1 and l 2 norms and consequently they are locking free

a four node plate bending element based on mindlin reissner plate theory and a mixed interpolation this communication discusses a 4 node plate bending element for linear elastic analysis which is obtained as a special case from a general nonlinear continuum mechanics based 4 node shell element formulation the formulation of the plate element is presented and the results of various example solutions are given that yield insight into the predictive capability of the plate and shell element

numerical approximation of mindlin reissner plates we consider a finite element approximation of the so called mindlin reissner formulation for moderately thick elastic plates we show that stability and optimal error bounds hold independently of the value of the thickness 1 introduction the so called mindlin reissner model for moderately thin plates is often used by engineers in connection with plate and shell problems it is well known that many numerical schemes for this model are satisfactory only when the thickness parameter t is not too small for a very small t some bad behavior such as the locking phenomenon might occur here we present a method which is uniformly good as t goes to zero and we prove optimal error estimates for transversal displacement rotations and shear stresses with constants independent of t

dynamics of majority rule in two state interacting spin systems we introduce a two state opinion dynamics model where agents evolve by majority rule in each update a group of agents is specified whose members then all adopt the local majority state in the mean field limit where a group consists of randomly selected agents consensus is reached in a time that scales ln n where n is the number of agents on finite dimensional lattices where a group is a contiguous cluster the consensus time fluctuates strongly between realizations and grows as a dimension dependent power of n the upper critical dimension appears to be larger than 4 the final opinion always equals that of the initial majority except in one dimension

the problem of membrane locking in finite element analysis of cylindrical shells we analyse the problem of membrane locking in h p finite element models of a thin hemicylindrical shell roof loaded by a smoothly varying normal pressure distribution we show that in the standard finite element method locking occurs especially at low values ofp and when the finite element grid is not aligned with the axis of the cylinder a general strategy of avoiding locking by using modified bilinear forms is introduced and a special implementation of this strategy on aligned rectangular grids is considered

on locking and robustness in the finite element method a numerical scheme for the approximation of a parameter dependent problem is said to exhibit locking if the accuracy of the approximations deteriorates as the parameter tends to a limiting value a robust numerical scheme for the problem is one that is essentially uniformly convergent for all values of the parameter precise mathematical definitions for these terms are developed their quantitative characterization is given and some general theorems involving locking and robustness are proven a model problem involving heat transfer is analyzed in detail using this mathematical framework and various related computational results are described applications to some different problems involving locking are presented

targeted attack on networks coupled by connectivity and dependency links abstract coupled systems used to increase capacity were shown beneficial as long as it does not open pathways to cascades previous studies on the robustness of coupled networks except for interdependent networks are almost the cases of random attack many challenges remain exist in targeted attack problem of coupled networks since nodes within coupled networks show different functions for each network this paper both analytically and numerically analyzed the robustness of coupled networks under three types of targeted attacking strategies including attacking on nodes by considering internal and external degree internal degree only and external degree only for coupled network with both interdependent and interconnected links all degree distributions of intra and inter connectivity links are poissonian we find the system undergoes from second to first order phase transition as coupling strength q increases the fraction of nodes in the giant component p at stable state the critical phase transition threshold p c first order threshold p c i and second order threshold p c i i and the critical point p c q c separating the first and second order phase transitions are analytically obtained for three types of attacking strategies with attacking probability parameter 0 1 we also find the system becomes more vulnerable as the average degree of intra links k or inter links k decreases therefore the minimum average degrees k m i n and k m i n to maintain the system stable are obtained for the case of 0 1 moreover we discussed three typical cases of coupled networks interdependent networks k 0 interacting networks q 0 and bipartite network k 0 q 0 the analytical expressions of p p c and p c q c only for interdependent are given respectively besides we study the equivalence relations between interdependent networks and coupled networks with connectivity and dependency links for the same p c the results imply that we can adjust the parameters q k and k to make the two systems have the same robustness moreover the results imply that one should not only protect nodes with high degree of intra links or inter links but also defend nodes the sum of whose degree of intra links and inter links is big can avoid the system becoming vulnerable

application of the quadrilateral area co ordinate method a new element for mindlin reissner plate the quadrilateral area co ordinate method is used to formulate a new quadrilateral element for mindlin reissner plate bending problem firstly an independent shear field is assumed based on the locking free timoshenko s beam formulae secondly a fourth order deflection field is assumed by introducing some generalized conforming conditions thirdly the rotation field is determined by the strain displacement relations furthermore a hybrid post processing procedure is suggested to improve the stress internal force solutions following this procedure a new 4 node 12 dof quadrilateral element named ac mq4 is successfully constructed since all formulations are expressed by the area co ordinates element ac mq4 presents some different but beneficial characters when compared with other usual models numerical examples show the new element is free of shear locking insensitive to mesh distortion and possesses excellent accuracy in the analysis of both thick and thin plates it has also been demonstrated that the area co ordinate method the generalized conforming condition method and the hybrid post processing procedure are efficient tools for developing simple effective and reliable finite element models copyright 2005 john wiley sons ltd