the regularization method for an obstacle problem we give a relatively complete analysis for the regularization method which is usually used in solving non differentiable minimization problems the model problem considered in the paper is an obstacle problem in addition to the usual convergence result and a priori error estimates we provide a posteriori error estimates which are highly desired for practical implementation of the regularization method

qualitative and numerical analysis of quasi static problems in elastoplasticity the quasi static problem of elastoplasticity with combined kinematic isotropic hardening is formulated as a time dependent variational inequality vi of the mixed kind that is it is an inequality involving a nondifferentiable functional and is imposed on a subset of a space this vi differs from the standard parabolic vi in that time derivatives of the unknown variable occur in all of its terms the problem is shown to possess a unique solution we consider two types of approximations to the vi corresponding to the quasi static problem of elastoplasticity semidiscrete approximations in which only the spatial domain is discretized by finite elements and fully discrete approximations in which the spatial domain is again discretized by finite elements and the temporal domain is discretized and the time derivative appearing in the vi is approximated in an appropriate way estimates of the errors inherent in the above two types of approximations in suitable sobolev norms are obtained for the quasi static problem of elastoplasticity in particular these estimates express rates of convergence of successive finite element approximations to the solution of the variational inequality in terms of element size h and where appropriate of the time step size k a major difficulty in solving the problems is caused by the presence of the nondifferentiable terms we consider some regularization techniques for overcoming the difficulty besides the usual convergence estimates we also provide a posteriori error estimates which enable us to estimate the error by using only the solution of a regularized problem

rate dependent projection operators for frictional contact constraints we develop rate dependent regularization approaches for three dimensional frictional contact constraints based on the kelvin and maxwell viscoelastic constitutive models with the present regularization schemes we aim to provide a basis to better model friction and to stabilize the contact analysis while keeping the contact model as simple as possible the key feature of the regularization approaches implemented using an implicit time integrator is that one can recover in the limit the widely used rate independent elastoplastic regularization framework without encountering numerical difficulties intermediate contact tractions are defined in terms of the relative displacement the relative velocity and the regularization parameters the projection operators operate on the intermediate tractions and yield contact tractions that satisfy all the discretized contact constraints the use of projection operators allows a systematic implementation of the present regularization schemes through numerical simulations we observed that the maxwell type regularization effectively avoids convergence problems even for relatively large time step sizes while the kelvin type regularization does not copyright 2003 john wiley sons ltd

on an elastic plastic problem etude d un probleme elastoplastique de valeur limite quasi statique pour des corps pouvant etre discretement heterogenes et elastiquement anisotropes dont le comportement plastique est regi par des fonctions de deformation lineaires par morceaux dependantes de l histoire du materiau et par des lois de durcissement couplees existence unicite et regularite d une solution faible convergence des solutions d elements finis

variational principles and convergence of finite element approximations of a holonomic elastic plastic problem it is shown that a boundary value problem based on a holonomic elastic plastic constitutive law may be formulated equivalently as a variational inequality of the second kind a regularised form of the problem is analysed and finite element approximations are considered it is shown that solutions based on finite element approximation of the regularised problem converge

factorization theorems and the structure of operators on hilbert space soit 7b h un espace de hilbert complexe et soit 7b l 7b h l algebre des operateurs lineaires bornes agissant sur 7b h on demontre des theoremes de factorisation on etudie la structure des operateurs sur 7b h

extremum properties of finite step solutions in elastoplasticity with nonlinear mixed hardening abstract the class of elastic plastic constitutive laws assumed herein can be described as follows we envisage y 1 yield criteria or modes which define the current yield surface each yield function consists of two addends an effective stress and a yield limit y 1 y the former is an order one positively homogeneous function of the difference between the stresses ii and reference stresses ii which are generally nonlinear functional of the plastic strain history so that kinematic hardening is accounted for the yield limit y is generally a nonlinear function of y nondecreasing internal variables so that another hardening mechanism which may reduce to isotropic hardening is accommodated in the model the rates of these variables play the role of plastic multipliers in the flow rule a finite step in the geometrically linear evolutive analysis of such solids is defined according to the backward difference or stepwise holonomic strategy for approximate time integration for the finite step boundary value problem thus arising various extremum characterizations of solutions are established and the underlying constitutive restrictions are pointed out and discussed

a numerical study of holonomic approximations to problems in plasticity the incremental holonomic boundary value problem in elastoplasticity has been shown to be characterized by a variational inequality the problem may be approximated however by a perturbed minimization problem characterized by a variational equality this formulation is used as the basis for constructing finite element approximations of the original boundary value problem leading to a system of non linear algebraic equations procedures for solving these equations are described and numerical results are presented and compared with those obtained using a conventional approach

sharpl error estimates for semilinear elliptic problems with free boundaries a numerical scheme to approximate a semilinear pde involving a singular maximal monotone graph is analyzed inl a preliminary regularization is combined with piecewise linear finite elements defined on a triangulation which is not assumed to be acute the discrete maximum principle is thus avoided sharp pointwise error estimates are derived for both the smoothing and the discretization procedures an optimal choice of the regularization parameter as a function of the mesh size leads to a sharp global rate of convergence these error estimates for solutions in conjunction with nondegeneracy properties of continuous problems provide sharp interface error estimates two model examples are discussed the obstacle problem and a combustion equation

cyclicity of bicyclic operators and completeness of translates we study cyclicity of operators on a separable banach space which admit a bicyclic vector such that the norms of its images under the iterates of the operator satisfy certain growth conditions a simple consequence of our main result is that a bicyclic unitary operator on a banach space with separable dual is cyclic our results also imply that if s a n n in mathbb z longmapsto a n 1 n in mathbb z is the shift operator acting on the weighted space of sequences ell omega 2 mathbb z if the weight satisfies some regularity conditions and n 1 for nonnegative n then s is cyclic if rm lim n rightarrow infty rm log omega n sqrt n 0 on the other hand one can see that s is not cyclic if the series sum n geq 1 rm log omega n n 2 diverges we show that the question of herrero whether either s or s is cyclic on ell omega 2 mathbb z admits a positive answer when the series sum n in mathbb z rm log s n n 2 1 is convergent we also prove completeness results for translates in certain banach spaces of functions on mathbb r

a variational theory for finite step elasto plastic problems abstract an extended version ofgeneralized standard elasto plastic material is considered in the framework of an internal variable theory of associated plasticity according to a backward difference scheme for time integration of the flow rule a finite step structural problem is formulated in a geometrically linear range convex analysis and a brand new potential theory for monotone multivalued operators are shown to provide the natural mathematical setting for the derivation of the related variational formulation a general stationarity principle is obtained and then specialized to obtain a minimum principle in terms of displacements plastic strains and internal variables a critical comparison with an analogous minimum principle recently proposed in literature is performed showing the inadequacy of classical procedures in deriving non smooth variational formulations

on characterizations and regularity of the solution of bilateral obstacle problems in this paper we introduce a new reformulation of bilateral obstacle problems which allows us to characterize the domain of noncontact with the obstacles and give a new proof for h2 regularity of the solution

path following and augmented lagrangian methods for contact problems in linear elasticity a certain regularization technique for contact problems leads to a family of problems that can be solved efficiently using infinite dimensional semismooth newton methods or in this case equivalently primal dual active set strategies we present two procedures that use a sequence of regularized problems to obtain the solution of the original contact problem first order augmented lagrangian and path following methods the first strategy is based on a multiplier update while path following with respect to the regularization parameter uses theoretical results about the path value function to increase the regularization parameter appropriately comprehensive numerical tests investigate the performance of the proposed strategies for both a 2d as well as a 3d contact problem

on the structure of contraction operators ii soit 7b h un espace de hilbert complexe separable de dimension infinie et 7b l 7b h l algebre de tous les operateurs lineaires bornes sur 7b h soit d le disque unite ouvert dans c d et n est l ensemble des entiers positifs il existe r 6 tel que chaque contraction t dans 7b l 7b h avec c t soit a un sous espace hyperinvariant non trivial soit appartient a la classe a 1 r

on the finite element method for mixed variational inequalities arising in elastoplasticity we analyze the finite element method for a class of mixed variational inequalities of the second kind which arises in elastoplastic problems an abstract variational inequality of which the elast

finite element analysis of a holonomic elastic plastic problem a thorough analysis of the finite element method is given for a holonomic elastic plastic problem an inequality of the cea s lemma type is proved which is the basis of error estimates for various finite element solutions difficulty caused by a non differentiable term in the problem can be overcome by using two convergent procedures an iterative procedure and a regularization procedure an a posteriori quantitative error estimate is derived for the regularized solution

analysis of a mixed formulation of a bilateral obstacle problem abstract in this paper we present a reformulation of a bilateral obstacle problem as a mixed formulation problem based on subdifferential of a continuous function of which the subdifferential can characterize the non contact domain then we present the analysis of the discrete problem we prove the convergence of the approximate solution to the exact one and we provide an error estimate this formulation was established in an abstract way then the theoretical results was applied to a bilateral obstacle problem

a theory of friction a rather general theory of friction inspired from the classical theory of plasticity is proposed it includes the contact impenetrability condition as a by product

a free boundary problem for semilinear elliptic equations etude de la nature de la frontiere libre u 0 pour un probleme de dirichlet semilineaire

finite element methods for constrained problems in elasticity several different variational formulations of boundary value problems with constraints are discussed with particular reference to constrained problems in elasticity special attention is given to exterior penalty methods a discussion of the conditions necessary for penalty methods to provide a basis for stable and convergent finite element methods is given in particular the use of reduced integration is discussed and criteria on the order of reduced integration rules sufficient to produce stable and convergent schemes are described applications of reduced integration penalty methods to incompressible elasticity problems and contact problems are described

solution of contact problem using the hp version of the finite element method abstract this paper is concerned with the numerical treatment of mechanical contact problems in two dimensions using the p version of the finite element method coupled with minor iterative modification of the mesh the method of solution is based on the augmented lagrangian technique examples are presented 1999 elsevier science ltd all rights reserved

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

singular inner functions and biinvariant subspaces for dissymetric weighted shifts abstract we consider dissymetric weights on z i e nonincreasing unbounded weights z 1 such that n 1 for n 0 and such that lim n n 1 n 1 where n sup p z n p p a dissymetric weight is said to be quasianalytic if n log n n 2 denote by the unit circle and by d the open unit disc set l 2 f l 2 f n z f n 2 2 n 1 2 we identify the usual hardy space h 2 d to the set f l 2 f n 0 n s f e it e it f e it the usual shift on l 2 if u is a singular inner function denote by e u the closure of span s n u n z in l 2 we show that if is a dissymetric weight such that log n n n then e u is a proper subspace of l 2 for every singular inner function u also if is any dissymetric weight then there exists some singular inner function u such that e u is a proper subspace of l 2 so that s always has nontrivial biinvariant subspaces no nontrivial biinvariant subspaces of s were known so far in the quasianalytic case

a smoothing technique for reduced integration penalty methods in contact problems the paper presents a smoothing technique to the oscillated contact pressure obtained by penalty methods for a class of unilateral contact problems in linear elasticity the main result is to show that the smoothed contact pressure satisfies the so called babuska brezzi condition which dominates the convergence of the penalty method one numerical example is described

stiffness matrix integration rules for contact friction finite elements abstract penalty contact finite elements are effective for modeling discontinuities in finite element analyses a key ingredient in the evaluation of contact element matrices is numerical integration computational experience has shown that use of full integration sometimes gives rise to spurious annoying oscillations in contact stresses while some reduced integration rules do not in this paper we thoroughly investigate the effects of numerical integration on element behavior by comparison to an equivalent mixed method conclusions are drawn regarding desirable characteristics that an integration rule should have and an effective local stress averaging scheme for use at contact interelement boundaries is developed

semismooth newton and augmented lagrangian methods for a simplified friction problem in this paper a simplified friction problem and iterative second order algorithms for its solution are analyzed in infinite dimensional function spaces motivated from the dual formulation a primal dual active set strategy and a semismooth newton method for a regularized problem as well as an augmented lagrangian method for the original problem are presented and their close relation is analyzed local as well as global convergence results are given by means of numerical tests we discuss among others convergence properties the dependence on the mesh and the role of the regularization and illustrate the efficiency of the proposed methodologies