elastoplastic and contact analysis based on consistent dynamic formulation of co rotational planar elements abstract co rotational formulation is one of the approaches applicable to geometrically nonlinear problems in structural analysis based on the assumptions of small degree of strain and large displacement the cr formulation allows an accurate geometrically nonlinear structural analysis in this paper an improved cr formulation for dynamic nonlinear analysis is developed for the planar element also extension of the local formulation is conducted for an elastoplastic problem a simplified approach for planar elastoplastic analyses is proposed by maintaining the original feature of the cr formulation moreover a modified approach in the local formulation is suggested in order to improve the level of accuracy in the plastic state contact analysis using the lagrange multiplier is then implemented during the present validation procedure of the proposed approaches four different planar elements are employed those elements are investigated with regard to efficiency and accuracy in a general geometrically nonlinear and a geometrically nonlinear elastoplastic problem respectively it is found that the present dynamic formulations gives both accuracy and consistency for all types of the plane element also comparison regarding the choice of the local formulation for the elastoplastic problem is systematically conducted and demonstrated

co rotational beam elements with warping effects in instability problems the present paper investigates the formulation of 3d co rotational beam elements for the buckling and post buckling analysis of frame structures following pacoste and eriksson comput methods app

finite elements with increased freedom in choosing shape functions starting with a mathematical statement of the convergence requirements for an element stiffness matrix the paper discusses displacement shape functions that may be used in connection with the potential energy principle in short these functions must be force orthogonal and energy orthogonal but they need not be conforming satisfy interelement compatibility it is shown that the requirements to the displacement functions may be greatly relaxed through slight modifications of the coupling stiffness between fundamental and higher order displacement modes several alternative formulations are examined in particular a new free formulation is suggested using this form which is very simple the only requirement to the displacement patterns used is that they should contain the fundamental deformation modes and be linearly independent applications of the theory to triangular and rectangular plate bending elements are shown the simple stiffness matrix for the latter is given explicitly the numerical results compare favourably with other types of finite elements

finite element analysis of smooth folded and multi shell structures the paper is concerned with the nonlinear theory and finite element analysis of shell structures with an arbitrary geometry loading and boundary conditions a complete set of shell field equations and side conditions boundary and jump conditions is derived from the basic laws of continuum mechanics the developed shell theory includes the so called drilling couples as well as the drilling rotation it is shown that this property is crucial in the analysis of irregular shell structures such as those containing folds branches column supports stiffeners etc the relevant variational principles with relaxed regularity requirements are also presented these principles provide the mathematical basis for the formulation of various classes of shell finite elements the developed finite elements include a displacement rotation based lagrange family a stress resultant based mixed and a semi mixed family as well as so called assumed strain elements all elements have six degrees of freedom at each node three translational and three rotational ones including the drilling rotation formulated on the foundation of an exact in defined sense shell theory as such they are equally applicable to smooth as well as to irregular shell structures the general applicability of the developed elements is illustrated through an extensive numerical analysis of the representative test examples in order to obtain a still deeper insight into the problem a lagrange family of standard degenerated shell elements with five degrees of freedom per node and an element with six degrees of freedom per node based on the von karman plate theory are considered as well the presented numerical results include complex plate and doubly curved shell structures linear and non linear solutions with a pre and post buckling analysis are discussed

element formulation and numerical techniques for stability problems in shells in the context of instability problems in shells or shell like structures the objective of the present paper is twofold primarily the paper describes how quasi static conservative instability problems can be considered in a multi parametric context where generalized path following procedures for augmented equilibrium problems are used as computational tools these allow systematic treatment of the higher dimensional solution sets generated under the variations of certain parameters deemed relevant for the given problem the efficient implementation of the above mentioned procedures requires however as an essential ingredient a non linear finite element which is not only accurate but also inexpensive to this end a systematic view on a corotational total lagrangian formulation is described the tric element of argyris and coworkers is slightly modified and introduced as core element formulation special emphasis is given to the alternative methods for treatment of finite three dimensional rotations with reference to both the element definition and solution algorithms numerical examples verify the element capabilities and the possibility to completely describe instability phenomena of large discretized models

from taubes currents to almost kahler forms the taubes current is introduced by taubes in j symplectic geom 9 161 250 2011 as an intermediate step to construct almost kahler forms in this paper we prove that an almost complex structures being almost kahler structure in dimension four is the equivalent of the existence of taubes currents precisely we show that taubes currents could be regularized to almost kahler forms up to small perturbations of cohomology classes on any 4 dimensional almost complex manifold m j a similar result is established for higher dimensions under the assumption of almost kahler an application to donaldson s tamed to compatible question is provided

a novel alpha finite element method αfem for exact solution to mechanics problems using triangular and tetrahedral elements abstract the paper presents an alpha finite element method fem for computing nearly exact solution in energy norm for mechanics problems using meshes that can be generated automatically for arbitrarily complicated domains three node triangular fem t3 and four node tetrahedral fem t4 elements with a scale factor are formulated for two dimensional 2d and three dimensional 3d problems respectively the essential idea of the method is the use of a scale factor 0 1 to obtain a combined model of the standard fully compatible model of the fem and a quasi equilibrium model of the node based smoothed fem n sfem this novel combination of the fem and n sfem makes the best use of the upper bound property of the n sfem and the lower bound property of the standard fem using meshes with the same aspect ratio a unified approach has been proposed to obtain a nearly exact solution in strain energy for linear problems the proposed elements are also applied to improve the accuracy of the solution of nonlinear problems of large deformation numerical results for 2d using fem t3 and 3d using fem t4 problems confirm that the present method gives the much more accurate solution comparing to both the standard fem and the n sfem with the same number of degrees of freedom and similar computational efforts for both linear and nonlinear problems

the size of random fragmentation trees we consider the random fragmentation process introduced by kolmogorov where a particle having some mass is broken into pieces and the mass is distributed among the pieces at random in such a way that the proportions of the mass shared among different daughters are specified by some given probability distribution the dislocation law this is repeated recursively for all pieces more precisely we consider a version where the fragmentation stops when the mass of a fragment is below some given threshold and we study the associated random tree dean and majumdar found a phase transition for this process the number of fragmentations is asymptotically normal for some dislocation laws but not for others depending on the position of roots of a certain characteristic equation this parallels the behavior of discrete analogues with various random trees that have been studied in computer science we give rigorous proofs of this phase transition and add further details the proof uses the contraction method we extend some previous results for recursive sequences of random variables to families of random variables with a continuous parameter we believe that this extension has independent interest

corotational nonlinear dynamic analysis of thin shell structures with finite rotations a new formulation for corotational nonlinear dynamic analysis of thin shell structures involving large displacements and finite rotations has been presented in this paper by introducing the kinematic description of the geometrically exact quasi static shell model to describe the motion of an arbitrary material point in a triangular shell element the new expressions for the inertial force vector and tangent inertia matrix were derived systematically the elastic deformation was handled by using the consistent symmetrizable equilibrated corotational formulation which is independent with respect to the local finite element modeling an energy momentum conserving algorithm and an energy decaying momentum conserving algorithm were developed for nonlinear dynamic analysis by applying the generalized energy momentum method in the corotational formulation three classic numerical examples including the dynamic response free motion and dynamic buckling of thin shell structures were computed to verify the ac

numerical analysis of complex instability behaviour using incremental iterative strategies the paper describes how quasi static conservative instability problems can be analysed in a multi parametric space using generalised path following procedures for augmented equilibrium problems

compatible complex structures on symplectic rational ruled surfaces in this article we study the topology of the spacei of complex structures compatible with a fixed symplectic form using the framework of donaldson by comparing our analysis of the spacei with results of mcduff on the spacej of compatible almost complex structures on rational ruled surfaces we find that i is contractible in this case we then apply this result to study the topology of the symplectomorphism group of a rational ruled surface extending results of abreu and mcduff

energy conserving algorithms for a corotational formulation standard nonlinear schemes for the the simulation of elastodynamic problems have several shortcomings when considering high speed rotations to tackle these problems we use a corotational framework and a corresponding specific linearization to design new energy conserving numerical schemes in the two dimensional case an algorithm preserving also angular momentum is presented the existence of a solution for the fully discrete setting of this algorithm is established numerical results illustrate the flexibility and efficiency of the proposed algorithms

fixed points of the smoothing transform two sided solutions given a sequence c t c t1 t2 of real valued random variables with tj 0 for all j 1 and almost surely finite n sup j 1 tj g 0 the smoothing transform associated wi

a formulation for the 4 node quadrilateral element a formulation for the plane 4 node quadrilateral finite element is developed based on the principle of virtual displacements for a deformable body incompatible modes are added to the standard displacement field then expressions for gradient operators are obtained from an expansion of the basis functions into a second order taylor series in the physical co ordinates the internal degrees of freedom of the incompatible modes are eliminated on the element level a modified change of variables is used to integrate the element matrices for a linear elastic material the element stiffness matrix can be separated into two parts these are equivalent to a stiffness matrix obtained from underintegration and a stabilization matrix the formulation includes the cases of plane stress and plane strain as well as the analysis of incompressible materials further the approach is suitable for non linear analysis there an application is given for the calculation of inelastic problems in physically non linear elasticity the element is efficient to implement and it is frame invariant locking effects and zero energy modes are avoided as well as singularities of the stiffness matrix due to geometric distortion a high accuracy is obtained for numerical solutions in displacements and stresses

uniform convergence of martingales in the branching random walk in a discrete time supercritical branching random walk let z n be the point process formed by the n th generation let m lambda be the laplace transform of the intensity measure of z 1 then w n lambda int e lambda x z n dx m lambda n which is the laplace transform of z n normalized by its expected value forms a martingale for any lambda with m lambda finite but nonzero the convergence of these martingales uniformly in lambda for lambda lying in a suitable set is the first main result of this paper this will imply that on that set the martingale limit w lambda is actually an analytic function of lambda the uniform convergence results are used to obtain extensions of known results on the growth of z n nc d with n for bounded intervals d and fixed c this forms the second part of the paper where local large deviation results for z n which are uniform in c are considered finally similar results both on martingale convergence and uniform local large deviations are also obtained for continuous time models including branching brownian motion

solutions to complex smoothing equations we consider smoothing equations of the form begin aligned x mathop limits text law sum j ge 1 t j x j c end aligned where c t 1 t 2 ldots is a given sequence of random variables and x 1 x 2 ldots are independent copies of x and independent of the sequence c t 1 t 2 ldots the focus is on complex smoothing equations i e the case where the random variables x c t 1 t 2 ldots are complex valued but also more general multivariate smoothing equations are considered in which the t j are similarity matrices under mild assumptions on c t 1 t 2 ldots we describe the laws of all random variables x solving the above smoothing equation these are the distributions of randomly shifted and stopped levy processes satisfying a certain invariance property called u alpha stability which is related to operator semi stability the results are applied to various examples from applied probability and statistical physics

supernatural quad4 a template formulation abstract a universal template for a 4 node quadrilateral in plane stress is constructed using a combination of old and new techniques the use of natural quantities strongly advocated by j h argyris since his continua and discontinua 1965 exposition is further expanded the qualifier supernatural means that all governing equations kinematic constitutive and equilibrium are expressed in both cartesian and natural forms these two sets are used to build different components of the template with timely help from a computer algebra system a template that include all possible quadrilateral elements that pass the individual element test of bergan and hanssen emerges it yields an infinite number of hitherto undiscovered instances that may be customized to fit special needs a striking example is the construction of a two trapezoid macroelement that is bending exact about one direction for any amount of distortion this concludes a five decade search that begins with the formulation of the wing cover rectangular panel in argyris 1954 seminal serial on energy methods and structural analysis

a modified corotational framework for triangular shell elements the corotational framework for triangular shell elements has been presented by different authors see the introduction the purpose of this paper is to introduce three modifications in this approach the first one is a simplified definition of the local rotations the second one is a reduction of the number of local degrees of freedom from 18 to 15 the third and principal one concerns the parameterisation of the global finite rotations a new approach based on euler parameters quaternion is proposed in particular it is shown that only three parameters are required the purpose of these three modifications is to obtain a formulation which gives the same numerical results but which is computationally more efficient than the original one this aspect is illustrated in several numerical examples

proof of a mckean conjecture on the rate of convergence of boltzmann equation solutions the present work provides a definitive answer to the problem of quantifying relaxation to equilibrium of the solution to the spatially homogeneous boltzmann equation for maxwellian molecules under really mild conditions on the initial datum and a weak physically consistent angular cutoff hypothesis our main result theorem 1 contains the first precise statement that the total variation distance between the solution and the limiting maxwellian distribution admits an upper bound of the form c e varlambda b t varlambda b being the least negative eigenvalue of the linearized collision operator and c a constant depending only on the initial datum the validity of this quantification was conjectured about fifty years ago by henry p mckean as to the proof of our results we have taken as point of reference an analogy between the problem of convergence to equilibrium and the central limit theorem of probability theory highlighted by mckean

the tric shell element theoretical and numerical investigation the tric facet triangular shell element which is based on the natural mode method is seen under the light of the non consistent formulation proposed by bergan and co workers under this formulation the convergence requirements are fulfilled even with relaxed conditions on the conformity demands of the displacement shape functions the intrinsic connection between the non consistent formulation and the natural mode method is demonstrated establishing thus a rigorous theoretical foundation for the tric element under the perspective of the non consistent formulation tric s convergence characteristics are established by satisfying apriori the patch test due to its inherent properties and thus guaranteeing convergence to the exact solution furthermore the element s accuracy robustness and efficiency are tested in a number of judiciously selected numerical examples on benchmark plate and shell problems while a cpu time comparison with a pure displacement based isoparametric shell element demonstrates its computational merits

a survey of parametrized variational principles and applications to computational mechanics abstract this survey paper describes recent developments in the area of parametrized variational principles pvps and selected applications to finite element computational mechanics a pvp is a variational principle containing free parameters that have no effect on the euler lagrange equations the theory of single field pvps based on gauge functions also known as null lagrangians is a subset of the inverse problem of variational calculus that has limited value on the other hand multifield pvps are more interesting from theoretical and practical standpoints following a tutorial introduction the paper describes the recent construction of multifield pvps in several areas of elasticity and electromagnetics it then discusses three applications to finite element computational mechanics the derivation of high performance finite elements the development of element level error indicators and the construction of finite element templates the paper concludes with an overview of open research areas

generalized nodes and high performance elements the paper concerns the development of robust and high accuracy finite elements with only corner nodes using a partition of unity based finite element approximation construction of the partition of unity based approximation is accomplished by a physically defined local function of displacements a 4 node quadratic tetrahedral element and a 3 node quadratic triangular element are developed eigenvalue analysis shows that linear dependencies in the partition of unity based finite element approximation constructed for the new elements are eliminable numerical calculations demonstrate that the new elements are robust insensitive to mesh distortion and offer quadratic accuracy while also keeping mesh generation extremely simple copyright 2005 john wiley sons ltd

on the diffeomorphism types of certain algebraic surfaces i l invariant de donaldson la geometrie de certaines surfaces rationnelles surfaces dolgachev generalites sur des formes de type 1 n la classe canonique d une chambre et un coin le cone de kahler d une bonne surface generique une etude de p cellules les super p cellules

tric a simple but sophisticated 3 node triangular element based on 6 rigid body and 12 straining modes for fast computational simulations of arbitrary isotropic and laminated composite shells tric is a simple but sophisticated 3 node shear deformable isotropic and composite flat shell element suitable for large scale linear and nonlinear engineering computations of thin and thick anisotropic plate and complex shell structures its stiffness matrix is based on 12 straining modes but essentially requires the computation of a sparse 9 by 9 matrix the element formulation departs from conventional cartesian mechanics as well as previously adopted physical lumping procedures and contains a completely new implementation of the transverse shear deformation it naturally circumvents all previously imposed constraints the methodology is based on physical inspirations of the natural mode finite element method nm fem formalized through appropriate geometrical trigonometrical and engineering mathematical relations and it involves only exact integrations its stiffness mass and geometrical matrices are all explicitly derived the kinematics of the element are hierarchically decomposed into 6 rigid body and 12 straining modes of deformation a simple congruent matrix operation transforms the elemental natural stiffness matrix to the local and global cartesian coordinates the modes show explicitly how the element deforms in axial straining symmetrical and antisymmetrical bending as well as in transverse shearing the latter has only become clear in the formulation presented here and has brought about a completion of the understanding of natural modes as they apply to the triangular shell element a wide range of numerical examples substantiate the conception and purpose of the element tric fast convergence is observed in many examples

improvements in 3 node triangular shell elements low order triangular finite shell elements are computationally economical and easy to implement but often exhibit very slow convergence two new membrane formulations for triangular shell elements are examined which rectify these drawbacks the first element is based on the marguerre shallow shell theory and a strain projection method that eliminates spurious membrane strain energy resulting expressions are provided in an explicit form for easy implementation of the element the second element is based on a linear membrane field governed by normal rotations and reduced quadrature the difficulties with shell normal rotations are analysed and a method for omitting these rotations while preserving rigid body motion is presented and tested finally a set of test problems are examined which show the importance of mesh patterns and degrees of freedom per node on triangular element performance

the curve cone of almost complex 4 manifolds in this paper we study the curve cone of an almost complex 4 manifold which is tamed by a symplectic form in particular we prove the cone theorem as in mori theory for all such manifolds using the seiberg witten theory for small rational surfaces and minimal ruled surfaces we study the configuration of negative curves we define abstract configuration of negative curves which records the homological and intersection information of curves combinatorial blowdown is the main tool to study these configurations as an application of our investigation of the curve cone we prove the nakai moishezon type duality for all almost kahler structures on cp2 kcp2 with k 9 and minimal ruled surfaces with a negative curve this is proved using a version of gram schmidt orthogonalization process for the j tamed symplectic inflation

a unified formulation of small strain corotational finite elements i theory this paper presents a unified theoretical framework for the corotational cr formulation of finite elements in geometrically nonlinear structural analysis the key assumptions behind cr are i strains from a corotated configuration are small while ii the magnitude of rotations from a base configuration is not restricted following a historical outline the basic steps of the element independent cr formulation are presented the element internal force and consistent tangent stiffness matrix are derived by taking variations of the internal energy with respect to nodal freedoms it is shown that this framework permits the derivation of a set of cr variants through selective simplifications this set includes some previously used by other investigators the different variants are compared with respect to a set of desirable qualities including self equilibrium in the deformed configuration tangent stiffness consistency invariance symmetrizability and element independence we discuss the main benefits of the cr formulation as well as its modeling limitations

large elasto plastic finite element analysis of solids and shells with the enhanced assumed strain concept abstract a finite element simulation of arbitrarily large elasto plastic deformations of three dimensional and shell structures is described two numerical aspects originally developed by j c simo have been combined i e the multiplicative large strain plasticity and the enhanced assumed strain finite element concept the constitutive model is worked out in its algorithmic version applying projection methods and consistent linearization the enhanced strain field is added to the conventional hexahedral displacement elements avoiding volumetric locking in the plastic range in addition to solid structures the three dimensional material model without any modifications is also applied to thin walled shell structures here an extended shell formulation a so called seven parameter model is used in which the thickness strain is augmented by a linear term the applicability of the entire formulation is demonstrated by several numerical examples

seneta heyde norming in the branching random walk malization of the general crump mode jagers branching process is obtained in this case the convergence holds almost surely the results rely heavily on a detailed study of the functional equation that the laplace transform of the limit must satisfy 1 introduction this paper considers the usual supercritical branching random walk thus ignoring the spatial element the population grows like a supercritical galton watson process the initial ancestor is at the origin of the real line and the positions of her children are given by a point process z each of these children has children in the same way in that the positions of each family relative to the parent are given by an independent copy of z and so on individuals are labelled by their line of descent so if u i i 1 n then u is the i th child of the i th child of the i th child of the initial nn 11 ancestor now let u be the generation in which u is born and write v u if v is a strict ancestor of u let t be the set of all people ever born which can be viewed as a tree with the population members as the nodes sums products sets and so on defined with an index ranging over individual s labels will be restricted to those actually born without this being made 4

almost kahler forms on rational 4 manifolds we study nakai moishezon type question and donaldson s tamed to compatible question for almost complex structures on rational four manifolds by extending taubes subvarieties current form technique to j nef genus 0 classes we give affirmative answers of these two questions for all tamed almost complex structures on s 2 bundles over s 2 as well as for many geometrically interesting tamed almost complex structures on other rational four manifolds including the del pezzo ones

on a kinetic model for a simple market economy in this paper we consider a simple kinetic model of economy involving both exchanges between agents and speculative trading we show that the kinetic model admits non trivial quasi stationary states with power law tails of pareto type in order to do this we consider a suitable asymptotic limit of the model yielding a fokker planck equation for the distribution of wealth among individuals for this equation the stationary state can be easily derived and shows a pareto power law tail numerical results confirm the previous analysis

generalized potlatch and smoothing processes we consider simple generalizations of the potlatch and smoothing processes which were introduced in 8 and studied in 5 these generalizations provide relatively simple examples of infinite interacting systems which exhibit phase transition the original potlatch and smoothing processes do not exhibit phase transition our results show that for the generalized processes phase transition does not usually occur in one or two dimensions but usually does occur in higher dimensions upper and lower bounds for the relevant critical values are obtained as one application of our results we obtain the limiting behavior of the critical values for the linear contact process in d dimensions as d thus answering a question we raised in 3 this is done by comparing the contact process with an appropriate generalized smoothing process

numerical characterization of the kahler cone of a compact kahler manifold the goal of this work is to give a precise numerical description of the kahler cone of a compact kahler manifold our main result states that the kahler cone depends only on the intersection form of the cohomology ring the hodge structure and the homology classes of analytic cycles if x is a compact kahler manifold the kahler cone k of x is one of the connected components of the set p of real 1 1 cohomology classes which are numerically positive on analytic cycles i e y p 0 for every irreducible analytic set y in x p dim y this result is new even in the case of projective manifolds where it can be seen as a generalization of the well known nakai moishezon criterion and it also extends previous results by campana peternell and eyssidieux the principal technical step is to show that every nef class which has positive highest self intersection numberx n 0 contains a kahler current this is done by using the calabi yau theorem and a mass concentration technique for monge ampere equations the main result admits a number of variants and corollaries including a description of the cone of numerically effective 1 1 classes and their dual cone another important consequence is the fact that for an arbitrary deformation x s of compact kahler manifolds the kahler cone of a very general fibre xt is independent of t i e invariant by parallel transport under the 1 1 component of the gauss manin connection

a novel galerkin like weakform and a superconvergent alpha finite element method sαfem for mechanics problems using triangular meshes a carefully designed procedure is presented to modify the piecewise constant strain field of linear triangular fem models and to reconstruct a strain field with an adjustable parameter a a novel galerkin like weakform derived from the hellinger reissner variational principle is proposed for establishing the discretized system equations the new weak form is very simple possesses the same good properties of the standard galerkin weakform and works particularly well for strain construction methods a superconvergent alpha finite element method email protected is then formulated by using the constructed strain field and the galerkin like weakform for solid mechanics problems the implementation of the email protected is straightforward and no additional parameters are used we prove theoretically and show numerically that the email protected always achieves more accurate and higher convergence rate than the standard fem of triangular elements t3 and even more accurate than the four node quadrilateral elements q4 when the same sets of nodes are used the email protected can always produce both lower and upper bounds to the exact solution in the energy norm for all elasticity problems by properly choosing an a in addition a email protected approach has also been devised to produce very accurate solutions for both displacement and energy norms and a superconvergent rate in the energy error norm furthermore a model based selective scheme is proposed to formulate a combined email protected ns fem model that handily overcomes the volumetric locking problems intensive numerical studies including singularity problems have been conducted to confirm the theory and properties of the email protected

on the convergence of supercritical general c m j branching processes convergence in probability of malthus normed supercritical general branching processes i e crump mode jagers branching processes counted with a general characteristic are established provided the latter satisfies mild regularity conditions if the laplace transform of the reproduction point process evaluated in the malthusian parameter has a finite x log x moment convergence in probability of the empirical age distribution and more generally of the ratio of two differently counted versions of the process also follow

sw gr from the seiberg witten equations to pseudo holomorphic curves the purpose of this article is to explain how pseudo holomorphic curves in a symplectic 4 manifold can be constructed from solutions to the seiberg witten equations as such the main theorem proved here theorem 1 3 is an existence theorem for pseudo holomorphic curves this article thus provides a proof of roughly half of the main theorem in the announcement t1 that theorem theorem 4 1 asserts an equivalence between the seiberg witten invariants for a symplectic manifold and a certain gromov invariant which counts with signs the number of pseudoholomorphic curves in a given homology class the seiberg witten invariants were introduced to mathematicians by witten w based on his joint work with nat seiberg sw1 sw2 a description of these invariants is given in section 1 see also km1 t1 suffice it to say here that when x is a compact oriented 4 dimensional manifold with

the fixed points of the multivariate smoothing transform let mathbf t 1 mathbf t 2 ldots be a sequence of random d times d matrices with nonnegative entries and let q be a random vector with nonnegative entries consider random vectors x with nonnegative entries satisfying begin aligned x mathop limits mathcal l sum i ge 1 mathbf t i x i q end aligned where mathop limits mathcal l denotes equality of the corresponding laws x i i ge 1 are i i d copies of x and independent of q mathbf t 1 mathbf t 2 ldots for d 1 this equation known as fixed point equation of the smoothing transform has been intensively studied under assumptions similar to the one dimensional case we obtain a complete characterization of all solutions x to in the non critical case and existence results in the critical case

central limit theorem for a class of one dimensional kinetic equations we introduce a class of kinetic type equations on the real line which constitute extensions of the classical kac caricature the collisional gain operators are defined by smoothing transformations with rather general properties by establishing a connection to the central limit problem we are able to prove long time convergence of the equation s solutions toward a limit distribution for example we prove that if the initial condition belongs to the domain of normal attraction of a certain stable law then the limit is a scale mixture of under some additional assumptions explicit exponential rates for the convergence to equilibrium in wasserstein metrics are calculated and strong convergence of the probability densities is shown

a framework for creating low order shell elements free of membrane locking summary this paper proposes a first step towards a framework to develop shell elements applicable to any deformation regime here we apply it to the large and moderate deformations of respectively plates and shells showing with standard benchmarks that the resulting low order discretization is competitive against the best elements for either membrane dominated or bending dominated scenarios additionally we propose a new test for measuring membrane locking which highlights the mesh independence properties of our element our strategy is based on building a discrete model that mimics the smooth behavior by construction rather than discretizing a smooth energy the proposed framework consists of two steps i defining a discrete kinematics by means of constraints and ii formulating an energy that vanishes on such a constraint manifold we achieve i by considering each triangle as a tensegrity structure constructed to be unstretchable but bendable isometrically in a discrete sense we then present a choice for ii based on assuming a linear strain field on each triangle using tools from differential geometry for coupling the discrete membrane energy with our locking free kinematic description we argue that such a locking free element is only a member of a new family that can be created using our framework i and ii copyright 2016 john wiley sons ltd

trunc for shells an element possibly to the taste of bruce irons in his delightful and original textbook 18 bruce irons introduces the chapter of plate bending with the remark history of disasters but the pioneering days are past this is certainly true on the other hand we learn in the same context from irons we believe that the world has not yet exhausted the older formulations in this paper we present a review of theoretical aspects of the plate bending triangle trunc reference 4 together with extensive tests in linear statics dynamics buckling and nonlinear large deformations both for plates and shells the unconventional trunc model is based on the patch test which was originated by irons 1 in spite of its limited theoretical foundation the performance of this element on a fairly broad field of applications appears at least from the practical point of view very satisfactory

martingale convergence and the stopped branching random walk we discuss the construction of stopping lines in the branching random walk and thus the existence of a class of supermartingales indexed by sequences of stopping lines applying a method of lyons 1997 and lyons pemantle and peres 1995 concerning size biased branching trees we establish a relationship between stopping lines and certain stopping times consequently we develop conditions under which these supermartingales are also martingales further we prove a generalization of biggins martingale convergence theorem biggins 1977a within this context

the functional equation of the smoothing transform given a sequence t ti i 1 of non negative random variables a function f on the positive halfline can be transformed to e q i 1 f tti we study the fixed points of this transform within the class of decreasing functions by exploiting the intimate relationship with general branching processes a full description of the set of solutions is established without the moment conditions that figure in earlier studies since the class of functions under consideration contains all laplace transforms of probability distributions on 0 1 the results provide the full description of the set of solutions to the fixed point equation of the smoothing transform x d

on steady distributions of kinetic models of conservative economies we analyze the large time behavior of various kinetic models for the redistribution of wealth in simple market economies introduced in the pertinent literature in recent years as specific examples we study models with fixed saving propensity introduced by chakraborti and chakrabarti eur phys j b 17 167 170 2000 as well as models involving both exchange between agents and speculative trading as considered by cordier et al j stat phys 120 253 277 2005 we derive a sufficient criterion under which a unique non trivial stationary state exists and provide criteria under which these steady states do or do not possess a pareto tail in particular we prove the absence of pareto tails in pointwise conservative models like the one in eur phys j b 17 167 170 2000 while models with speculative trades introduced in j stat phys 120 253 277 2005 develop fat tails if the market is risky enough the results are derived by a fourier based technique first developed for the maxwell boltzmann equation gabetta et al in j stat phys 81 901 934 1995 bisi et al in j stat phys 118 1 2 301 331 2005 pareschi and toscani in j stat phys 124 2 4 747 779 2006 and from a recursive relation which allows to calculate arbitrary moments of the stationary state

convergence to stable laws for a class of multidimensional stochastic recursions we consider a markov chain x n n 0 infty on mathbb r d defined by the stochastic recursion xn mn xn 1 qn where qn mn are i i d random variables taking values in the affine group a mathbb r d mathbb r d rtimes rm gl mathbb r d assume that mn takes values in the group of similarities of mathbb r d and the markov chain has a unique stationary measure which has unbounded support we denote by mn the expansion coefficient of mn and we assume mathbb e m alpha 1 for some positive we show that the partial sums s n sum k 0 n x k properly normalized converge to a normal law 2 or to an infinitely divisible law which is stable in a natural sense 2 or of the tails of and of stationary measure for an associated markov operator 2 we extend the results to the situation where mn is a random generalized similarity

elasto plastic analysis of shells with the triangular element tric tric is a simple but sophisticated three node shear deformable isotropic and composite facet shell element suitable for large scale linear and nonlinear engineering computations of thin and moderately thick anisotropic plate and complex shell structures in the present work an elasto plastic constitutive model based on the von mises yield criterion with isotropic hardening is incorporated into the element the characteristic feature of this formulation is that the nonlinear material behaviour is taken into account entirely in the natural system of the element this is achieved by transforming quantities such as equivalent plastic strain equivalent stress the expression of the yield surface and the components of flow vector from the material coordinate system to the natural coordinate system these transformations lead to simple and elegant expressions for the respective quantities in the natural system which eventually result to an efficient and cost effective treatment of the nonlinear analysis of arbitrary shells including material and geometrical nonlinearities

mixed formulation in koiter analysis of thin walled beams abstract the paper extends the asymptotic mixed formulation proposed in g garcea g salerno sanitizing of locking in koiter perturbation analysis through mixed formulation fourth world congress on computational mechanics buenos aires argentina 1988 g garcea g salerno r casciaro comput methods appl mech engrg 180 1 2 1999 137 167 to structures composed of an assemblage of flat slender elastic panels the same type of structure has already been investigated in a d lanzo g garcea r casciaro int j numer methods engrg 38 1995 2325 2345 a d lanzo g garcea int j numer methods engrg 39 1996 3007 3031 with a compatible formulation and using the usual hypothesis of negligible precritical rotations in order to avoid the extrapolation locking see also g garcea g a trunfio r casciaro comput methods appl mech engrg 165 1 4 1998 137 167 produced by the high axial to flexural stiffness ratio of the panels the use of a mixed formulation provides a consistent way of eliminating the extrapolation locking without introducing ad hoc approximations it is thus both reliable and accurate when combined with a quadratic strain displacement relationship as presented here it gives zero fourth order energy variations further computational simplifications and a natural linearization of the eigenvalue problem required by the buckling analysis an extensive numerical testing shows the effectiveness and robustness of the proposed approach

a triangular finite element with local remeshing for the large strain analysis of axisymmetric solids in this work a three node triangular finite element with two degrees of freedom per node for the large strain elasto plastic analysis of axisymmetric solids is presented the formulation resorts to the adjacent elements to obtain a quadratic interpolation of the geometry over a patch of four elements from which an average deformation gradient is defined thus the element formulation falls within the framework of assumed strain elements or more precisely of f bar type formulations the in plane behavior of the element is similar to the linear strain triangle but without the drawbacks of the quadratic triangle e g contact or distortion sensitivity the element does not suffer of volumetric locking in problems with isochoric plastic flow and the implementation is simple it has been implemented in a finite element code with explicit time integration of the momentum equations and tools that allow the simulation of industrial processes the widely accepted multiplicative decomposition of the deformation gradient in elastic and plastic components is adopted here an isotropic material with non linear isotropic hardening has been considered two versions of the element have been implemented based on a total and an updated lagrangian formulation respectively some approximations have been considered in the latter formulation aimed to reduce the number of operations in order to increase numerical efficiency to consider bulk forming with large geometric changes an automatic local remeshing strategy has been developed several examples are considered to assess the element performance with and without remeshing

partition of unity and drilling rotations in the boundary element method bem abstract this paper presents a novel approach to include drilling rotations in the classical two dimensional boundary element method the approach is based on a simple partition of unity strategy that gives rise to a fictitious rotational degree of freedom using the well known allman s triangle strategy a functional based on the rotational residual ties the average fictitious drilling rotation field to the true rotation field induced from the two dimensional elasticity problem and additionally provides the required extra equation for the enriched bem formulation the approach maintains the boundary only character of bem and the partition of unity enrichment makes it general totally kernel independent and efficient just certain areas of the boundary could be enriched the accuracy of the proposed method is assessed with well known benchmark problems e g cook s membrane

a basic flat facet finite element for the analysis of general shells a triangular flat facet finite element for the analysis of general thin shells is presented it is constructed from simple cubic polynomial displacement fields using a complete set of six degrees of freedom at the element vertices thereby easily meeting the requirements of standard commercial computer programs the theoretical development is based on a variational principle which allows a direct formulation of the element stiffness matrix without inversion and which permits considerable simplification of the mathematical formulation the new flat facet element generally produces more accurate numerical results than those obtained in earlier related work it also offers a possible basis for constructing an improved curved approximation to a shell surface and for further developments in connection with applications involving geometric non linearity

a unified co rotational framework for solids shells and beams abstract the paper describes a unified framework for applying the co rotational method to the analysis of solids shells and beams the general method stems from an unusual application of the technique which involves solid elements the proposed framework allows a formulation that is simpler than many of the earlier procedures and in addition gives a direct indication of the terms in the tangent stiffness which may be ignored

the joint distribution of elastic buckets in multiway search trees random search trees are studied when they grow under a general computer memory management scheme in a general scheme the space is released in buckets of certain predesignated sizes for a search tree with branch factor m the nodes may hold up to m 1 keys suppose the buckets of the memory management scheme that can hold less than m keys have key capacities c 1 ldots c p the search tree must then be implemented with multitype nodes of these capacities after n insertions let x n i be the number of buckets of type i i e of capacity c i 1 leq i leq p the multivariate structure of the tree is investigated for the vector bf x n x n 1 ldots x n p t the asymptotic mean and covariance matrix are determined under practical memory management schemes all variances and covariances experience a phase transition for 3 leq m leq 26 all variances and covariances are asymptotically linear in n for higher branch factors the variances and covariances become a superlinear but subquadratic function of n the joint distribution of bf x n is shown to be multivariate normal in a range of m while the tree is growing conversions between types are necessary a multivariate problem concerning these conversions with an asymptotic multivariate normal distribution is also studied the fixed bucket exact fit and buddy system allocation schemes will serve as illustrating examples

optimization of geometrically nonlinear thin shells subject to displacement and stability constraints a methodology is developed for shape optimization of thin plate and shell structures undergoing large deflections subject to displacement and system stability constraints the optimization method considers shape parameters and overall thickness of the structure as the design variables and aims to minimize the total mass of the structure subject to stability or displacement constraint two optimality criteria based on karush kuhn tucker conditions are developed for mass minimization problems optimality criteria are combined with nonlinear corotational analysis to optimize structures with geometric nonlinearity the method is applied to plate and shallow shell structures the efficiency of the developed design optimization methodology is compared with that of the gradient based method of optimization sequential quadratic programming

tail homogeneity of stationary measures for some multidimensional stochastic recursions we consider a stochastic recursion x n 1 m n 1 x n q n 1 n in mathbb n where q n m n are i i d random variables such that q n are translations m n are similarities of the euclidean space mathbb r d and x n in mathbb r d in the present paper we show that if the recursion has a unique stationary measure with unbounded support then the weak limit of properly dilated exists and defines a homogeneous tail measure the structure of is studied and the supports of and are compared in particular we obtain a product formula for

evaluation of the constant strain triangle with drilling rotations the performance of the constant strain triangle with added drilling rotations is evaluated by solving a variety of plane test problems numerical results confirm that the new element is always superior to the standard constant strain triangle and that it is of similar accuracy to the best available alternative triangular elements of other authors it is however less accurate than some rectangular elements which include drilling rotations

allman s triangle rotational dof and partition of unity a simplification of the 1984 allman triangle one of historically most important elements with rotational dofs is presented it is found that this old element takes a typical form of the partition of unity approximation the allman s rotation presented in the partition of unity form offers merits and convenience in formulation and practical applications the stiffness matrix of the 1984 allman triangle which is originally computed from the linear strain triangular element the 6 nodes quadratic triangle can be obtained instead in a cheaper way from that of the constant strain triangular element the constraint of the rotational terms during essential boundary treatment which remains equivocal and ambiguous is understood to be mandatory the partition of unity notion enables a straightforward extension of the allman s rotational dof to meshfree approximations in numerical examples we discuss suppression of spurious zero energy modes and patch tests standard benchmarks are carried out to assess performance of the newly formulated triangle and a meshfree approximation with the rotational dofs copyright 2006 john wiley sons ltd

finite rotation analysis and consistent linearization using projectors abstract a systematic procedure is presented that may be used to extend the capabilities of an existing linear finite element to accomodate finite rotation analysis this procedure is a generalization of the work presented in computers and structures volume 30 pp 257 267 the basis of our approach is the element independent co rotational algorithm where the element rigid body motion translations and rotations is separated from the deformational part of its total motion the variation of this co rotational relation results in a projector matrix with the property that a consistent internal force vector is invariant under its action the consistent tangent stiffness matrix is shown to depend on this invariance condition through the derivative of the projector this results in an unsymmetric tangent matrix whose anti symmetric part depends on the out of balance force vector in this paper we prove that using the symmetric part of the tangent matrix the newton iteration retains its quadratic rate of convergence this approach has been used to solve a number of large rotation test example problems the results demonstrate that it is possible to analyze structures undergoing large rotations within a general co rotational framework using simple and economical finite elements the resulting improvements in the performance of these simple elements are brought about through the use of convenient software utilities as pre and post processors to the element routines

on the choice of the linear element for corotational triangular shells the corotational formulation for triangular thin shell elements presented in a eriksson c pacoste element formulation and numerical techniques for stability problems in shells comput methods

displacement and equilibrium models in the finite element method by b fraeijs de veubeke chapter 9 pages 145 197 of stress analysis edited by o c zienkiewicz and g s holister published by john wiley sons 1965

a study of optimal membrane triangles with drilling freedoms abstract this article compares derivation methods for constructing optimal membrane triangles with corner drilling freedoms the term optimal is used in the sense of exact inplane pure bending response of rectangular mesh units of arbitrary aspect ratio following a comparative summary of element formulation approaches the construction of an optimal three node triangle using the andes formulation is presented the construction is based upon techniques developed by 1991 in student term projects but taking advantage of the more general framework of templates developed since the optimal element that fits the andes template is shown to be unique if energy orthogonality constraints are enforced two other formulations are examined and compared with the optimal model retrofitting the conventional linear strain triangle element by midpoint migrating and congruential transformations is shown unable to produce an optimal element while rank deficiency is inevitable use of the quadratic strain field of the 1988 allman triangle or linear filtered versions thereof is also unable to reproduce the optimal element moreover these elements exhibit serious aspect ratio lock these predictions are verified on benchmark examples

mixed finite element methods reduced and selective integration techniques a unification of concepts the equivalence of certain classes of mixed finite element methods with displacement methods which employ reduced and selective integration techniques is established this enables one to obtain the accuracy of the mixed formulation without incurring the additional computational expense engendered by the auxiliary field of the mixed method applications and numerical examples are presented for problems with constraints which can be difficult to enforce in finite element approximations and have often dictated the use of mixed principles these include thin beams and plates and linear and nonlinear incompressible and nearly incompressible continuum problems in solid and fluid mechanics

on the self similar asymptotics for generalized nonlinear kinetic maxwell models maxwell models for nonlinear kinetic equations have many applications in physics dynamics of granular gases economics etc in the present manuscript we consider such models from a very general point of view including those with arbitrary polynomial non linearities and in any dimension space it is shown that the whole class of generalized maxwell models satisfies properties one of which can be interpreted as an operator generalization of usual lipschitz conditions this property allows to describe in detail a behavior of solutions to the corresponding initial value problem in particular we prove in the most general case an existence of self similar solutions and study the convergence in the sense of probability measures of dynamically scaled solutions to the cauchy problem to those self similar solutions as time goes to infinity a new application of multi linear models to economics and social dynamics is discussed

a simplified co rotational method for quadrilateral shell elements in geometrically nonlinear analysis summary this paper presents a simplified co rotational formulation for quadrilateral shell elements inheriting the merit of element independence from the traditional co rotational approach in literature with the objective of application to nonlinear analysis of civil engineering structures the authors further simply the formulation of the geometrical stiffness using the small strain assumption which is valid in the co rotational approach with the warping effects considered as eccentricities compared with the traditional element independent co rotational method the projector is neglected both in the tangent stiffness matrix and the internal force vector for simplicity in formulation meanwhile a quadrilateral flat shell element allowing for drilling rotations is adopted and incorporated into this simplified co rotational algorithm for geometrically nonlinear analysis involved with large displacements and large rotations several benchmark problems are presented to confirm the efficiency and accuracy of the proposed method for practical applications

plastic instability of beam structures using co rotational elements in a previous paper comput methods appl mech engrg 191 2002 1755 the authors have presented a 3d co rotational elastic beam element including warping effects this formulation is now further developed in order to incorporate elasto plastic deformations the element possesses seven degrees of freedom at each node and can be used to model beams with arbitrary cross sections thus within the present approach the centroid and shear center of the cross section are not necessarily coincident the main purpose of this element is to model elasto plastic instability problems in this context two methods of branch switching are tested and discussed in the first one the bifurcation point is isolated by successive bisections and the branch switching is operated by using the eigenvector associated to the negative eigenvalue in the second one introduced by petryk an energy approach is used to select automatically the stable post bifurcation path six examples including large displacement and stability problems are used in order to assess the performances of the element

improved minimal augmentation procedure for the direct computation of critical points this paper presents a new numerical procedure for the direct computation of critical points for elastic beam structures undergoing large displacements and rotations compared to the approach described by wriggers et al comput methods appl mech engrg 70 1988 329 int j numer methods engrg 30 1990 155 two main modifications are introduced first following eriksson comput methods appl mech engrg 114 1994 77 comput methods appl mech engrg 156 1998 45 comput methods appl mech engrg 179 1999 265 int j struct stability dynam 1 1 2001 the condition of criticality is expressed by a scalar equation instead of a vectorial one next the present procedure does not use exclusively the extended system obtained from the equilibrium equations and the criticality condition but also introduces intermediate iterations based purely on equilibrium equations under load or displacement control eight numerical examples presenting bifurcation and limit points are used in order to compare the performances of this new method and the one presented in comput methods appl mech engrg 70 1988 329 int j numer methods engrg 30 1990 155

co rotational flat facet triangular elements for shell instability analyses abstract this paper investigates the formulation of co rotational flat facet triangular elements for the numerical analysis of instability phenomena in shell structures the elements have three nodes with six degrees of freedom at each node the term co rotational relates here to the provision of a local system that continuously rotates and translates with the element following mainly nour omid and rankin b nour omid and c c rankin finite rotation analysis and consistent linearization using projectors comput methods appl mech engrg 93 1991 353 384 the definition of an element resorts to a change of variables from the local frame to the global one this is done through the use of a projector matrix which relates the variations of the local displacements to the variations of the global ones by extracting the rigid body modes from the latter the main difference from the original formulation lies in the parameterization of 3d finite rotations in contrast to the paper by nour omid and rankin a parameterization based on the rotational vector is here adopted and thus an additional change of variables has to be performed as a result the rotational variables become additive and the necessity of a special updating procedure is avoided the main feature of the adopted formulation is its independence of the local assumptions used to derive the internal forces and tangent stiffness in local coordinates for a certain class of elements i e elements with the same number of nodes and degrees of freedom the main co rotational framework is the same using this property three types of local formulations are considered a set of carefully chosen test problems is used in order to assess the performances of the three element types

shell elements with drilling degree of freedoms based on micropolar elasticity theory based on the theory of micropolar elasticity new degenerated shell elements with drilling degree of freedoms are presented the proper stiffness on the drilling degree of freedom is derived and no spurious modes are encountered in these elements the implementation of these new shell elements on general structural finite element programs has many advantages especially for the analysis of a folded shell or the treatment of the twist moment normal to the shell several numerical examples are carried out to demonstrate the accuracy and applicability of the present elements the effects of the coupling factor and the body moment induced in magneto solid mechanics are also studied

non rigid contour based registration of cell nuclei in 2 d live cell microscopy images using a dynamic elasticity model the analysis of the pure motion of subnuclear structures without influence of the cell nucleus motion and deformation is essential in live cell imaging in this paper we propose a 2 d contour based image registration approach for compensation of nucleus motion and deformation in fluorescence microscopy time lapse sequences the proposed approach extends our previous approach which uses a static elasticity model to register cell images compared with that scheme the new approach employs a dynamic elasticity model for the forward simulation of nucleus motion and deformation based on the motion of its contours the contour matching process is embedded as a constraint into the system of equations describing the elastic behavior of the nucleus this results in better performance in terms of the registration accuracy our approach was successfully applied to real live cell microscopy image sequences of different types of cells including image data that was specifically designed and acquired for evaluation of cell image registration methods an experimental comparison with the existing contour based registration methods and an intensity based registration method has been performed we also studied the dependence of the results on the choice of method parameters