a mixed finite element model for the elastic contact problem the static elastic contact problem is approached using lagrange multipliers leading to a mixed finite element problem a non linear friction law is introduced explicitly and the non local character of the friction phenomena is implicitly assumed in order to avoid stress oscillations near singular points a perturbed lagrangian functional is considered the algorithms herein proposed do not impose nodal dependencies over the contact surfaces allowing for the independent discretization of both bodies the method is able to model simultaneous contact over different regions of any geometrical shape computer code examples and results presented here are restricted to axisymmetrical and bidimensional cases

algebraic elimination of slide surface constraints in implicit structural analysis slide surface and contact boundary conditions can be implemented via lagrange multipliers in the algebraic equations in implicit structural analysis this indefinite set of equations is difficult to solve by iterative methods and is often too large to be solved by direct methods when there are m constraints and there exists a set of m variables where each variable is only involved in a single constraint we advocate a direct elimination technique which leaves a sparse positive definite system to solve by iterative methods we prove that the amount of fill in created by this process is independent of the size of the slide surfaces in addition the eigenvalues of the reduced matrix do not differ significantly from the eigenvalues of the unconstrained matrix this method can be extended to the case where constrained surfaces intersect and leads to a graph theoretic approach for determining which variables can be eliminated efficiently for constraints with more general structure published in 2003 by john wiley sons ltd

an algorithm for the matrix free solution of quasistatic frictional contact problems a contact enforcement algorithm has been developed for matrix free quasistatic finite element techniques matrix free iterative solution algorithms such as non linear conjugate gradients cg and dynamic relaxation dr are desirable for large solid mechanics applications where direct linear equation solving is prohibitively expensive but in contrast to more traditional newton raphson and quasi newton iteration strategies the number of iterations required for convergence is typically of the same order as the number of degrees of freedom of the model it is therefore crucial that each of these iterations be inexpensive to per form which is of course the essence of a matrix free method in applying such methods to contact problems we emphasize here two requirements first that the treatment of the contact should not make an average equilibrium iteration considerably more expensive and second that the contact constraints should be imposed in such a way that they do not introduce spurious energy that acts against the iterative solver these practical concerns are utilized to develop an iterative technique for accurate constraint enforcement that is suitable for non linear conjugate gradient and dynamic relaxation iterative schemes copyright 1999 john wiley sons ltd

multiplier methods for engineering optimization multiplier methods used to solve the constrained engineering optimization problem are described these methods solve the problem by minimizing a sequence of unconstrained problems defined using the cost and constraint functions the methods proposed in 1969 have been determined to be quite robust although not as efficient as other algorithms they can be more effective for some engineering applications such as optimum design and control oflarge scale dynamic systems since 1969 several modifications and extensions of the methods have been developed therefore it is important to review the theory and computational procedures of these methods so that more efficient and effective ones can be developed for engineering applications recent methods that are similar to the multiplier methods are also discussed these are continuous multiplier update exact penalty and exponential penalty methods

extension of hydrodynamic balance equations for simple fluids a systematic approach to derivation of hydrodynamic like balance equations for systems with a smooth continuous potential as well as hard sphere repulsion is represented cases of many particle local and two particle nonlocal hydrodynamic densities are considered the results are applied for construction of balance equations for fluxes of momentum and energy which form the first extension of conventional hydrodynamics explicit balance equations for the stress tensor and the heat flux in the local frame of reference are obtained

differentiation in star invariant subspaces i boundedness and compactness abstract given a discrete set c r let r p denote the subspace of lp r generated by rational functions with poles in we determine for which s the differentiation operator d dx r p lp r is bounded or compact

generalized boltzmann equation for lattice gas automata in this paper a theory is formulated that predicts velocity and spatial correlations between occupation numbers that occur in lattice gas automata violating semi detailed balance starting from a coupled bbgky hierarchy for then particle distribution functions cluster expansion techniques are used to derive approximate kinetic equations in zeroth approximation the standard nonlnear boltzmann equation is obtained the next approximation yields the ring kinetic equation similar to that for hard sphere systems describing the time evolution of pair correlations the ring equation is solved to determine the nonvanishing pair correlation functions in equilibrium for two models that violate semidetailed balance one is a model of interacting random walkers on a line the other one is a two dimensional fluid type model on a triangular lattice the numerical predictions agree very well with computer simulations

numerical integration of the fluctuating hydrodynamic equations an approach to numerically integrate the landau lifshitz fluctuating hydrodynamic equations is outlined the method is applied to one dimensional systems obeying the nonlinear fourier equation and the full hydrodynamic equations for a dilute gas static spatial correlation functions are obtained from computer generated sample trajectories time series they are found to show the emergence of long range behavior whenever a temperature gradient is applied the results are in very good agreement with those obtained from solving the correlation equations directly

issues in convergence improvement for non linear finite element programs systems of non linear equations as they arise when analysing various physical phenomena and technological processes by the implicit finite element method fem are commonly solved by the newton raphson method the modelling of sheet metal forming processes is one example of highly non linear problems where the iterative solution procedure can become very slow or diverge this paper focuses on techniques to overcome these numerical difficulties several methods to generate initial guesses within the radius of convergence are proposed appropriate stopping criteria for the iterative procedure are discussed a combination of various line search methods with the continuation method is proposed the efficiency and robustness of these numerical procedures are compared based on a set of test examples a particular form of line search was identified which allows the stable and efficient solution of highly non linear sheet metal forming problems even though the present investigations were motivated by the application of the implicit fem to the simulation of sheet metal forming processes the findings are general enough to be applicable to a wide spectrum of non linear fem applications 1997 john wiley sons ltd

generalized linear transport theory in dilute neutral gases and dispersion relation of sound waves the transport processes in dilute neutral gases are studied by using the kinetic equation with a collision relaxation model that meets all conservation requirements the kinetic equation is solved keeping the whole anisotropic part of the distribution function with the use of the continued fractions the conservative laws of the collision operator are taken into account with the projection operator techniques the generalized heat flux and stress tensor are calculated in the linear approximation as functions of the lower moments i e the density the flow velocity and the temperature the results obtained are valid for arbitrary collision frequency ensuremath nu with the respect to k v t and the characteristic frequency ensuremath omega where k ensuremath 1 is the characteristic length scale of the system and v t is the thermal velocity the transport coefficients constitute accurate closure relations for the generalized hydrodynamic equations an application to the dispersion and the attenuation of sound waves in the whole collisionality regime is presented the results obtained are in very good agreement with the experimental data

algorithmic symmetrization of coulomb frictional problems using augmented lagrangians abstract a major drawback of most implicit algorithmic treatments of coulomb frictional contact problems is the nonsymmetry of the algorithmic tangent operator which emanates from the nonassociativity of the slip flow rule reliable algorithms leading to symmetric equation systems are highly desirable especially in three dimensional problems where the computational cost is dominated by equation solving in this paper such an algorithm symmetrization is proposed the method is derived from the augmented lagrangian treatment of friction given by simo and laursen comput structures 42 1992 97 116 and exploits the iterative nature of the classical method of multipliers more specifically symmetrization is achieved by a modified multiplier update scheme in which all nonassociativity is removed from the solution phase and placed in the multiplier update phase the result is an algorithm involving only the solution of symmetric equations which maintains the attributes of an augmented lagrangian method

a contact smoothing method for arbitrary surface meshes using nagata patches abstract this paper presents a contact surface smoothing method combined with the node to segment discretization technique to solve large deformation frictional contact problems between deformable bodies the nagata patch interpolation is used to smooth the surface mesh providing a master surface with quasi g 1 continuity between patches moreover the local support of the interpolation method allows to deal with surface meshes of arbitrary topology regular and irregular finite element discretizations as well as hybrid meshes the non physical oscillations in the contact force evolution induced by the faceted contact surface representation are reduced using the proposed smoothing method furthermore the smooth representation of the master surface allows a more accurately evaluation of the resulting stresses and forces while providing an important improvement in convergence behaviour four representative numerical examples are used to demonstrate the advantages of the proposed contact smoothing method the results show a significant improvement in the accuracy robustness and performance of the numerical simulations using the smoothing approach when compared with the piecewise faceted contact surface description

the solution of large displacement frictionless contact problems using a sequence of linear complementarity problems a newton method for solution of frictionless contact problems is presented a finite element discretization is performed and the contact constraints are given as complementarity conditions the resulting equations which represent the equilibrium of the system are formulated as a generalized equation generalized equations from the discipline of mathematical programming are a way of writing multi valued relations such as complementarity conditions in a way that is similar to ordinary equations newton s method is then used in a straightforward way to solve the present non linear generalized equation resulting in a sequence of linear complementarity problems lcp s

on certain riesz families in vector valued de branges rovnyak spaces abstract we obtain criteria for the riesz basis property for families of reproducing kernels in vector valued de branges rovnyak spaces h b in particular it is shown that in several situations the property implies a special form for the function b we also study the completeness of a related family

a family of simple two pass dual formulations for the finite element solution of contact problems simple stable unbiased algorithms for two pass two body contact have until now eluded researchers in computational mechanics this work examines the subject starting from an interpolation scheme proposed in an earlier work this method though stable and unbiased results in an exceedingly complex algorithm in three dimensions motivated by the need for simplicity a new formulation of the contact problem is introduced which results in a family of simple stable geometrically unbiased elements the starting point of these elements is any algorithm which is stable for the signorini problem a number of example problems are presented to compare the performance of the elements

an augmented lagrangian method for discrete large slip contact problems reference lmaf article 1993 001view record in web of science record created on 2005 09 14 modified on 2017 05 10

bernstein type inequalities for shift coinvariant subspaces and their applications to carleson embeddings abstract we study weighted norm inequalities for the derivatives bernstein type inequalities in the shift coinvariant subspaces k p of the hardy class h p in the upper half plane it is shown that the differentiation operator acts from k p to certain spaces of the form l p w where the weight w x depends on the density of the spectrum of near the point x of the real line we discuss an application of the bernstein type inequalities to the problems of the description of measures for which k p l p and of compactness of such embeddings new versions of carleson type embedding theorems are obtained generalizing the theorems due to w s cohn and a l volberg s r treil

fluctuations in coagulating systems ii in this paper we consider coagulation processes in large but finite systems and study the time dependent behavior of the nonequilibrium fluctuations in the cluster size distribution for this purpose we apply van kampen s expansion to a master equation describing coagulation processes and derive an approximate fokker planck equation for the probability distribution of the fluctuations first we consider two exactly soluble models corresponding to the choicesk i j i jandk i j 1 for the rate constants in the fokker planck equation for these models and monodisperse initial conditions we calculate the probability distribution of the fluctuations and the equal time and two time correlation functions for general initial conditions we study the behavior of the fluctuations at large cluster sizes and in the scaling limit next we consider in general homogeneous rate constants with the propertyk i j a k ai aj for alla 0 and we give asymptotic expressions for the equal time correlation functions at large cluster sizes and in the scaling limit in the scaling limit we find that the fluctuations show relatively simple scaling behavior for all homogeneous rate constantsk i j

united elements method for general contact impact problems abstract this work presents the details of a finite element based numerical method to analyse general contact impact problems called united elements method uem in contrast to usual methods that is lagrange multipliers and penalty function this method is conceptual suitable for computer programming and free from inherent deficiencies of those methods the key points of this procedure are elimination of the normal degree of freedom of the contactor node from the system energy potential functional in terms of target surface motion and proper calculation of target element unbalanced forces to incorporate the contact constraints after a review on classic formulations the mathematical and matrix presentation of the united element stiffness matrix are discussed solution of some examples adopting a newton raphson based solution together with a normal return scheme support the capability and accuracy of the procedure in static and dynamic problems

bases of reproducing kernels in de branges spaces this paper deals with geometric properties of sequences of reproducing kernels related to de branges spaces if b is a nonconstant function in the unit ball of h and tb is the toeplitz operator with symbol b then the de branges space h b associated to b is defined by h b id tbtb 1 2h2 where h2 is the hardy space of the unit disk it is equipped with the inner product such that id tbtb 1 2 is a partial isometry from h2 onto h b first following a work of ahern clark we study the problem of orthogonal basis of reproducing kernels in h b then we give a criterion for sequences of reproducing kernels which form an unconditional basis in their closed linear span as far as concerns the problem of complete unconditional basis in h b we show that there is a dichotomy between the case where b is an extreme point of the unit ball of h and the opposite case

weighted norm inequalities for de branges rovnyak spaces and their applications let h b denote the de branges rovnyak space associated with a function b in the unit ball of h 1 c we study the boundary behavior of the derivatives of functions in h b and obtain weighted norm estimates of the form k f n k l2 ck f k h b where f h b and is a carleson type measure on c r we provide several applications of these inequalities we apply them to obtain embedding theorems for h b spaces these results extend cohn and volberg treil embedding theorems for the model star invariant subspaces which are special classes of de branges rovnyak spaces we also exploit the inequalities for the derivatives to study stability of riesz bases of reproducing kernels k bn in h b under small perturbations of the pointsn

a continuum based finite element formulation for the implicit solution of multibody large deformation frictional contact problems in this paper a formulation is presented for the finite element treatment of multibody large deformation frictional contact problems the term multibody is used to mean that when two bodies mechanically contact both may be deformable a novel aspect of the approach advocated is that the equations governing contact are developed in the continuum setting first before deriving the corresponding finite element equations this feature distinguishes the current work from many earlier treatments of contact problems and renders it considerably more general in particular the approach yields a characterization of the frictional constraint assuming a coulomb law suitable for arbitrary discretizations in either two or three dimensions a geometric framework is constructed within which both frictionless and frictional response are naturally described making subsequent finite element discretization a straightforward substitution of finite dimensional solution spaces for their continuum counterparts to our knowledge this general formulation and implementation of the frictional contact problem in a finite element setting has not been reported previously in the literature the development includes exact linearization of the statement of virtual work which enables optimal convergence properties for newton raphson solution strategies and which appears to be highly desirable if not essential for the general robustness of implicit finite element techniques since the theory and subsequent linearization require no limitations on the amount of deformation or relative sliding that can occur the resulting treatment of frictional contact is suitable for a wide range of examples displaying significant non linear behaviour this assertion is substantiated through presentation of a variety of examples in both two and three dimensions

the harmonic balance method for bifurcation analysis of large scale nonlinear mechanical systems abstract the harmonic balance hb method is widely used in the literature for analyzing the periodic solutions of nonlinear mechanical systems the objective of this paper is to exploit the method for bifurcation analysis i e for the detection and tracking of bifurcations of nonlinear systems to this end an algorithm that combines the computation of the floquet exponents with bordering techniques is developed a new procedure for the tracking of neimark sacker bifurcations that exploits the properties of eigenvalue derivatives is also proposed the hb method is demonstrated using numerical experiments of a spacecraft structure that possesses a nonlinear vibration isolation device

a high order purely frequency based harmonic balance formulation for continuation of periodic solutions combining the harmonic balance method hbm and a continuation method is a well known technique to follow the periodic solutions of dynamical systems when a control parameter is varied however since deriving the algebraic system containing the fourier coefficients can be a highly cumbersome procedure the classical hbm is often limited to polynomial quadratic and cubic nonlinearities and or a few harmonics several variations on the classical hbm such as the incremental hbm or the alternating frequency time domain hbm have been presented in the literature to overcome this shortcoming here we present an alternative approach that can be applied to a very large class of dynamical systems autonomous or forced with smooth equations the main idea is to systematically recast the dynamical system in quadratic polynomial form before applying the hbm once the equations have been rendered quadratic it becomes obvious to derive the algebraic system and solve it by the so called asymptotic numerical method anm continuation technique several classical examples are presented to illustrate the use of this numerical approach

a finite element method for elasto plastic structures and contact problems by parametric quadratic programming in this paper the stiffness matrix of a contact element is introduced by means of a penalty function expression of the contact pressure and frictional force the contact condition and the flow rule are expressed by the same form as in a non associated plastic flow problem a unified pqp parametric quadratic programming model related to contact problems as well as to elasto plastic structures is constructed a series of pqp formulae for contact problems and elastic plastic structures is derived in the text and some numerical examples are illustrated as well

generalized hydrodynamics in enskog gases abstract the generalized hydrodynamic behavior of an enskog moderately dense gas has been studied mainly through the correlation functions approach however the kinetic model based on the grad s method to solve the enskog equation seems to be a good alternative to such studies in this work we explore the behavior of the generalized transport coefficients and obtain several relationships between grad s method and the usual chapman enskog scheme the calculation is developed up to a second order in the density expansion so we can obtain the complete hydrodynamic limit also involving the volumetric thermal effects

nonequilibrium fluctuations in μ space the properties of fluctuations in space in or outside thermal equilibrium are obtained by solving hierarchies of equations derived either from the liouville or the master equation in particular we study the one two etc time correlation functions that describe the spatial and temporal behavior of the fluctuations in space explicit solutions are obtained for a dilute gas the langevin approach is briefly discussed our results are compared with those obtained in the extensive literature which is reviewed in some detail

steady state representation of the homogeneous cooling state of a granular gas the properties of a dilute granular gas in the homogeneous cooling state are mapped to those of a stationary state by means of a change in the time scale that does not involve any internal property of the system the new representation is closely related with a general property of the granular temperature in the long time limit the physical and practical implications of the mapping are discussed in particular simulation results obtained by the direct simulation monte carlo method applied to the scaled dynamics are reported this includes ensemble averages and also the velocity autocorrelation function as well as the self diffusion coefficient obtained from the latter by means of the green kubo representation in all cases the obtained results are compared with theoretical predictions

a method for nonlinear modal analysis and synthesis application to harmonically forced and self excited mechanical systems abstract the recently developed generalized fourier galerkin method is complemented by a numerical continuation with respect to the kinetic energy which extends the framework to the investigation of modal interactions resulting in folds of the nonlinear modes in order to enhance the practicability regarding the investigation of complex large scale systems it is proposed to provide analytical gradients and exploit sparsity of the nonlinear part of the governing algebraic equations a novel reduced order model rom is developed for those regimes where internal resonances are absent the approach allows for an accurate approximation of the multi harmonic content of the resonant mode and accounts for the contributions of the off resonant modes in their linearized forms the rom facilitates the efficient analysis of self excited limit cycle oscillations frequency response functions and the direct tracing of forced resonances the rom is equipped with a large parameter space including parameters associated with linear damping and near resonant harmonic forcing terms an important objective of this paper is to demonstrate the broad applicability of the proposed overall methodology this is achieved by selected numerical examples including finite element models of structures with strongly nonlinear non conservative contact constraints

a dynamic lagrangian frequency time method for the vibration of dry friction damped systems abstract a new frequency time domain procedure the dynamic lagrangian mixed frequency time method dlft is proposed to calculate the non linear steady state response to periodic excitation of structural systems subject to dry friction damping in this formulation the dynamic lagrangians are defined as the non linear contact forces obtained from the equations of motion in the frequency domain with the adjunction of a penalization on the difference between the interface displacements calculate by the non linear solver in the frequency domain and those calculated in the time domain from the non linear contact forces thus accounting for coulomb friction and non penetration conditions the dynamic lagrangians allow one to solve for the non linear forces between two points in contact without using artifacts such as springs the new dlft method is thus particularly well suited to handling finite element models of structures in frictional contact as it does not require a special model for the contact interface dynamic lagrangians are also better suited to frequency domain friction problems than the traditional time domain method of augmented lagrangians furthermore a reduction of the non linear system to relative interface displacements is introduced to decrease the computation time the dlft method is validated for a beam in contact with a flexible dry friction element connected to ground for frictional constraints that feature two dimensional relative motion results are also obtained for a large scale structural system with a large number of one dimensional dry friction dampers the dlft method is shown to be accurate and fast and it does not suffer from convergence problems at least in the examples studied

smooth c1 interpolations for two dimensional frictional contact problems finite deformation contact problems are associated with large sliding in the contact area thus in the discrete problem a slave node can slide over several master segments standard contact formulations of surfaces discretized by low order finite elements leads to sudden changes in the surface normal field this can cause loss of convergence properties in the solution procedure and furthermore may initiate jumps in the velocity field in dynamic solutions furthermore non smooth contact discretizations can lead to incorrect results in special cases where a good approximation of the contacting surfaces is needed in this paper a smooth contact discretization is developed which circumvents most of the aformentioned problems a smooth deformed surface with no slope discontinuities between segments is obtained by a c1 continuous interpolation of the master surface different forms of discretizations are possible among these are bezier hermitian or other types of spline interpolations in this paper we compare two formulations which can be used to obtain smooth normal and tangent fields for frictional contact of deformable bodies the formulation is developed for two dimensional applications and includes finite deformation behaviour examples show the performance of the new discretization technique for contact copyright 2001 john wiley sons ltd

a perturbed lagrangian formulation for the finite element solution of contact problems making use of a perturbed lagrangian formulation a finite element procedure for contact problems is developed for the general case in which node to node contact no longer holds the proposed procedure leads naturally to a discretization of the contact interface into contact segments within the context of a bilinear interpolation for the displacement field a mixed finite element approximation is introduced by assuming discont naous contact pressure constant on the contact segment because of this piece wise constant approximation the gap function enters into the formulation in an average sense instead of through a point wise definition numerical examples are presented that illustrate the performance of the proposed procedure current finite element formulations for contact problems based on either the classical lagrange parameter procedure l 3 12 203 or the penalty function method 4 6 11 are characterized by a point wise enforcement of the contact constraint condition in the sense that penetration of the bodies is established on a nodal basis moreover in this methods the recovery of the contact pressure over the element from the contact nodal forces generally requires an additional procedure within the framework of classical lagrange multiplier methods the contact condition is exactly satisfied by transforming the constrained problem into an unconstrained one with the introduction of additional variables lagrange multipliers these extra variables add computational effort to the solution process which often requires special procedures to handle the presence of zero diagonal terms penalty methods on the other hand enable one to transform the constrained problem into an unconstrained one without introducing additional variables the constraint condition is now satisfied only approximately for finite values of the penalty parameter the main difhculty associated with these methods however lies in the poor conditioning of the problem as the penalty is increased to more accurately enforce the constraint condition this is a well understood phenomenon particularly in the context of the incompressible and nearly incompressible problem in solid and fluid mechanics e g see l 22 25 for a review recently augmented lagrangian procedures have been proposed as a promising way to partially overcome these difficulties and regularize the penalty formulation e g see the survey in 7 8 within the framework of zinearited e u c it is possible to restrict the finite element formulation of contact problems by assuming that node to node contact occurs this is in fact the case often considered in the literature l 2 4 6 12 20 211 in the general context of fully

a consistent tangent stiffness matrix for three dimensional non linear contact analysis a consistent tangent stiffness matrix for the analysis of non linear contact problems is presented the associated element has three or four nodes and establishes contact between three dimensional structures like solids and shells it accounts for the non linear kinematics of large deformation analysis and guarantees a quadratic convergence rate two formulations the penalty method and the lagrange multiplier method are investigated