backward perturbation analysis of certain characteristic subspaces this paper gives optimal backward perturbation bounds and the accuracy of approximate solutions for subspaces associated with certain eigenvalue problems such as the eigenvalue problemax x the generalized eigenvalue problem ax bx and the singular value decomposition of a matrixa this paper also gives residual bounds for certain eigenvalues generalized eigenvalues and singular values

a new dissipative time stepping algorithm for frictional contact problems formulation and analysis this paper presents a new time stepping algorithm for frictional contact problems that exhibits unconditional positive energy dissipation more specifically the proposed scheme preserves a priori stability estimates of the continuum problem for both frictionless and frictional contact leading to improved numerical stability properties in particular for the normal contact component the algorithm exhibits full energy conservation between released states while the energy does not increase over its initial value due to the enforcement of the normal contact constraint during persistent contact a penalty regularization is considered to this purpose a new regularization of the stick conditions is considered for the frictional part the new scheme is shown rigorously to exhibit positive energy dissipation like the continuum physical problem in this frictional case coulomb friction is assumed complete analyses of these considerations as well as a detailed description of their finite element implementation are included in the general finite deformation range representative numerical simulations are presented to assess the performance of the newly proposed methods

exact energy and momentum conserving algorithms for general models in nonlinear elasticity implicit time integration schemes that inherit the conservation laws of total energy linear and angular momentum are considered for initial boundary value problems in finite deformation elastodynamics conserving schemes are constructed for general hyperelastic material models both compressible and incompressible and are formulated in a way that is independent of spatial discretization three numerical examples for ogden type material models implemented using a finite element discretization in space are given to illustrate the performance of the proposed schemes these examples show that relative to the standard implicit mid point rule the conserving schemes exhibit superior numerical stability properties without a compromise in accuracy

on the formulation of high frequency dissipative time stepping algorithms for nonlinear dynamics part ii second order methods we present in this paper the formulation of a new high frequency dissipative time stepping algorithm for nonlinear elastodynamics that is second order accurate in time the new scheme exhibits unconditional energy dissipation and momentum conservation and thus the given name of energy dissipative momentum conserving second order scheme edmc 2 leading also to the conservation of the relative equilibria of the underlying physical system the unconditional character of these properties applies not only with respect to the time step size but equally important with respect to the considered elastic potential moreover the dissipation properties are fully controlled through an algorithmic parameter reducing to existing fully conserving schemes if desired the design of the new algorithm is described in detail including a complete analysis of its dissipation conservation properties in the fully nonlinear range of finite elasticity to motivate the different constructions that lead to the dissipative properties of the final scheme the same arguments are used first in the construction of new linear time stepping algorithms for the system of linear elastodynamics including first and second order schemes the new schemes exhibit a rigorous decay of the physical energy with the second order schemes formulated in a general two stage formula accommodating the aforementioned control parameter in the dissipation of the energy a complete spectral analysis of the new schemes is presented in this linear range to evaluate their different numerical properties in particular the dissipative character of the proposed schemes in the high frequency range is fully demonstrated in fact it is shown that the new second order scheme is l stable most remarkably the extension of these ideas to the nonlinear range is accomplished avoiding the use of multi stage formulae given the freedom gained in using general nonlinear relations while preserving the conservation laws of the momenta and the corresponding relative equilibria several representative numerical simulations are presented in the context of nonlinear elastodynamics to evaluate the performance of the newly proposed schemes

an accurate and robust contact detection algorithm for particle solid interaction in combined finite discrete element analysis when applying the combined finite discrete element method for analysis of dynamic problems contact is often encountered between the finite elements and discrete elements and thus an effective contact treatment is essential in this paper an accurate and robust contact detection algorithm is proposed to resolve contact problems between spherical particles which represent rigid discrete elements and convex quadrilateral mesh facets which represent finite element boundaries of structural components different contact scenarios between particles and mesh facets or edges or vertices have been taken into account for each potential contact pair the contact search is performed in an hierarchical way starting from mesh facets possibly going to edges and even further to vertices the invalid contact pairs can be removed by means of two reasonable priorities defined in terms of geometric primitives and facet identifications this hierarchical contact searching scheme is effective and its implementation is straightforward numerical examples demonstrated the accuracy and robustness of the proposed algorithm copyright 2015 john wiley sons ltd

formulation and analysis of two energy consistent methods for nonlinear elastodynamic frictional contact problems energy conserving algorithms are necessary to solve nonlinear elastodynamic problems in order to recover long term time integration accuracy and stability furthermore some physical phenomena such as friction can generate dissipation then in this work we present and analyse two energy consistent algorithms for hyperelastodynamic frictional contact problems which are characterised by a conserving behaviour for frictionless impacts but also by an admissible frictional dissipation phenomenon the first approach permits one to enforce respectively the kuhn tucker and persistency conditions during each time step by combining an adapted continuation of the newton method and a lagrangean formulation in addition the second method which is based on the work in p hauret p le tallec energy controlling time integration methods for nonlinear elastodynamics and low velocity impact comput methods appl mech eng 195 2006 4890 4916 represents a specific penalisation of the unilateral contact conditions some numerical simulations are presented to underscore the conservative or dissipative behaviour of the proposed methods

mixed fem of higher order for time dependent contact problems abstract in this paper mixed finite element methods of higher order for time dependent contact problems are discussed the mixed methods are based on resolving the contact conditions by the introduction of lagrange multipliers dynamic signorini problems with and without friction are considered involving thermomechanical and rolling contact rothe s method is used to provide a suitable time and space discretization to discretize in time a stabilized newmark method is applied as an adequate time stepping scheme the space discretization relies on finite elements of higher order in each time step the resulting problems are solved by uzawa s method or alternatively by methods of quadratic programming via a suitable formulation in terms of the lagrange multipliers numerical results are presented towards an application in production engineering the results illustrate the performance of the presented techniques for a variety of problem formulations

adaptive timestep control for the contact stabilized newmark method the aim of this paper is to devise an adaptive timestep control in the contact stabilized newmark method contacx for dynamical contact problems between two viscoelastic bodies in the framework of signorini s condition in order to construct a comparative scheme of higher order accuracy we extend extrapolation techniques this approach demands a subtle theoretical investigation of an asymptotic error expansion of the contact stabilized newmark scheme on the basis of theoretical insight and numerical observations we suggest an error estimator and a timestep selection which also cover the presence of contact finally we give a numerical example

time integration schemes for the finite element dynamic signorini problem a large variety of discretizations have been proposed in the literature for the numerical solution of the dynamic signorini problem we classify the different discretizations into four groups the first three groups correspond to different ways of enforcing the contact condition exact enforcement enforcement with penalty and enforcement with contact condition in velocity the fourth approach is based on a modification of the mass matrix numerical simulations on two one dimensional benchmark problems with analytical solutions illustrate the properties of representative methods within each class focusing first on spurious oscillations triggered by contact and then on energy behavior after multiple impacts selected schemes are also tested on a two dimensional benchmark

energy consistent corotational schemes for frictional contact problems in this paper we consider the unilateral frictional contact problem of a hyperelastic body in the case of large displacements and small strains in order to retain the linear elasticity framework we decompose the deformation into a large global rotation and a small elastic displacement this corotational approach is combined with a primal dual active set strategy to tackle the contact problem the resulting algorithm preserves both energy and angular momentum

formulation and analysis of conserving algorithms for frictionless dynamic contact impact problems this paper presents the formulation of conserving time stepping algorithms for frictionless dynamic contact of solids a new class of finite element methods is proposed for the solution of these problems that exhibit the same conservation laws as the underlying continuum dynamical system the proposed methods are based on a penalty regularization of the constrained contact problem and lead to full conservation of the total energy of the system including the regularization penalty potential during persistent contact and restoration of the original energy upon release both linear and angular momenta are conserved by the scheme furthermore the newly developed methods have the ability to enforce the associated constraints in the velocity besides the impenetrability constraint in the displacements while preserving the conservation restoration properties of the final numerical scheme a modification of these schemes is described that assures positive energy dissipation if desired even in the highly nonlinear setting of contact impact problems leading to contact schemes with high frequency energy dissipation representative numerical simulations are presented illustrating the performance of the proposed numerical schemes

time domain boundary elements for dynamic contact problems abstract this article considers a unilateral contact problem for the wave equation the problem is reduced to a variational inequality for the dirichlet to neumann operator for the wave equation on the boundary which is solved in a saddle point formulation using boundary elements in the time domain as a model problem also a variational inequality for the single layer operator is considered a priori estimates are obtained for galerkin approximations both to the variational inequality and the mixed formulation in the case of a flat contact area where the existence of solutions to the continuous problem is known numerical experiments demonstrate the performance of the proposed mixed method they indicate the stability and convergence beyond flat geometries

contact impact by the pinball algorithm with penalty and lagrangian methods contact impact algorithms which are sometimes called slideline algorithms are a computationally time consuming part of many explicit simulations of non linear problems because they involve many branches so they are not amenable to vectorization which is essential for speed on supercomputers the pinball algorithm is a simplified slideline algorithm which is readily vectorized its major idea is to embed pinballs in surface elements and to enforce the impenetrability condition only to pinballs it can be implemented in either a lagrange multiplier or penalty method it is shown that in any lagrange multiplier method no iterations are needed to define the contact surface examples of solutions and running times are given

design and analysis of a dissipative scheme to solve a generalized multi dimensional higgs boson equation in the de sitter space time abstract in this work we design a numerically efficient finite difference technique for the solution of a fractional extension of the higgs boson equation in the de sitter space time the model under investigation is a multidimensional equation with riesz fractional derivatives of orders in 0 1 1 2 which considers a generalized potential and a time dependent diffusion factor an energy integral for the mathematical model is readily available and we propose an explicit and consistent numerical technique based on fractional order centered differences with similar hamiltonian properties as the continuous model a fractional energy approach is used then to prove the properties of stability and convergence of the technique for simulation purposes we consider both the classical and the fractional higgs real valued scalar fields in the 3 1 dimensional de sitter space time and find results qualitatively similar to those available in the literature the present work is the first paper to report on a hamiltonian discretization of the higgs boson equation both fractional and non fractional in the de sitter space time and its numerical analysis more precisely the present manuscript is the first paper of the literature in which a dissipation preserving scheme to solve the multi dimensional fractional higgs boson equation in the de sitter space time is proposed and thoroughly analyzed indeed it is worth pointing out that previous efforts used techniques based on the runge kutta method or discretizations that did not preserve the dissipation nor were rigorously analyzed

design of energy conserving algorithms for frictionless dynamic contact problems this paper proposes a formulation of dynamic contact problems which enables exact algorithmic conservation of linear momentum angular momentum and energy in finite element simulations it is seen that a lagrange multiplier enforcement of an appropriate contact rate constraint produces these conservation properties a related method is presented in which a penalty regularization of the aforementioned rate constraint is utilized this penalty method sacrifices the energy conservation property but is dissipative under all conditions of changing contact so that the global algorithm remains stable notably it is also shown that augmented lagrangian iteration utilizing this penalty kernel reproduces the energy conserving i e lagrange multiplier solution to any desired degree of accuracy the result is a robust stable method even in the context of large deformations as is shown by some representative numerical examples in particular the ability of the formulation to produce accurate results where more traditional integration schemes fail is emphasized by the numerical simulations 1997 by john wiley sons ltd

level sets fields placement and velocity based formulations of contact impact problems by introducing unknown sign like fields of level sets type the signorini moreau dynamic contact conditions are set merely as boundary equations from this setting a continuous hybrid weak strong formulation for dynamic contact between deformable solids is derived and a new lagrangian formulation we call stabilized generalizing both the classical and augmented ones is obtained friction phenomena are treated similarly in the global problem the irregular sign like fields stand for the intrinsic contact unknown ones this problem is discretized by means of time space and collocation schemes some numerical experimentations are carried out showing the potential of our developments copyright 2006 john wiley sons ltd

two variational inequality problems for the wave equation in a half space an important problem in the theory of elasticity is the dynamic planestrain type crack problem the subject of dynamic cracks in solids has received much attention in the past two decades see freund 4 poruchikov 11 and walton and herrmann 17 most of the work done however has not explicitly imposed the physical condition that the two faces of the crack do not interpenetrate this type of condition is known as a unilateral constraint imposing this type of condition amounts to imposing certain inequalities on the displacements or tractions to the problem problems in elasticity involving the contact of two elastic bodies give another example of problems with unilateral constraints imposed on boundaries see kikuchi and oden 7 a particular case of a contact problem is the punch problem which consists of a rigid body the punch indenting an elastic halfspace while static contact problems have been studied extensively see kikuchi and oden 7 the case of dynamic contact problems has not been studied nearly as much there is no work to our knowledge on the dynamic crack problem taking into account the condition of noninterpenetration the mathematical formulation of the dynamic crack and punch problems with unilateral constraints involve the dynamic equations of linear elasticity in this paper we consider two simplified dynamic problems with unilateral constraints obtained when the elasticity equations are replaced by a single wave equation although these simplified problems have no physical meaning we will still call them the crack and punch problems respectively

recursive partitioning for heterogeneous causal effects in this paper we propose methods for estimating heterogeneity in causal effects in experimental and observational studies and for conducting hypothesis tests about the magnitude of differences in treatment effects across subsets of the population we provide a data driven approach to partition the data into subpopulations that differ in the magnitude of their treatment effects the approach enables the construction of valid confidence intervals for treatment effects even with many covariates relative to the sample size and without sparsity assumptions we propose an honest approach to estimation whereby one sample is used to construct the partition and another to estimate treatment effects for each subpopulation our approach builds on regression tree methods modified to optimize for goodness of fit in treatment effects and to account for honest estimation our model selection criterion anticipates that bias will be eliminated by honest estimation and also accounts for the effect of making additional splits on the variance of treatment effect estimates within each subpopulation we address the challenge that the ground truth for a causal effect is not observed for any individual unit so that standard approaches to cross validation must be modified through a simulation study we show that for our preferred method honest estimation results in nominal coverage for 90 confidence intervals whereas coverage ranges between 74 and 84 for nonhonest approaches honest estimation requires estimating the model with a smaller sample size the cost in terms of mean squared error of treatment effects for our preferred method ranges between 7 22

energy consistent algorithms for dynamic finite deformation plasticity abstract this paper addresses the theoretical development and numerical implementation of energy consistent algorithms for dynamic elastoplasticity emphasizing finite strain constitutive formulations so that unconditional stability of the algorithms is assured even in the fully nonlinear regime the key concept behind energy consistency is the requirement that the discretized system obey an a priori stability estimate which may be derived in general using the first and second laws of thermodynamics this approach to computational dynamic plasticity differs from typical application of traditional algorithms such as newmark or hilber hughes taylor methods where local time integration schemes for plasticity laws are developed somewhat independently from the global time integration scheme for the equations of motion without explicit consideration of thermodynamical restrictions two algorithms based on both additive and multiplicative finite deformation plasticity model are formulated within the energy consistent framework both algorithms possess the desirable feature of nonlinear stability of previous energy momentum algorithms for elastodynamics

transient three dimensional domain decomposition problems frame indifferent mortar constraints and conserving integration the present work deals with transient large deformation domain decomposition problems the tying of dissimilar meshed grids is performed by applying the mortar method in this connection a reformulation of the original linear mortar constraints is proposed which retains frame indifference for arbitrary discretizations of the interface furthermore a specific coordinate augmentation technique is proposed to make possible the design of an energy momentum scheme numerical examples demonstrate the robustness and enhanced numerical stability of the newly developed energy momentum scheme for three dimensional problems copyright 2009 john wiley sons ltd

numerical analysis of a dynamic bilateral thermoviscoelastic contact problem with nonmonotone friction law abstract we study a fully dynamic thermoviscoelastic contact problem the contact is assumed to be bilateral and frictional where the friction law is described by a nonmonotone relation between the tangential stress and the tangential velocity weak formulation of the problem leads to a system of two evolutionary possibly nonmonotone subdifferential inclusions of parabolic and hyperbolic type respectively we study both semidiscrete and fully discrete approximation schemes and bound the errors of the approximate solutions under regularity assumptions imposed on the exact solution optimal order error estimates are derived for the linear element solution this theoretical result is illustrated numerically

a frictionless viscoelastodynamic contact problem with energy consistent properties numerical analysis and computational aspects a dynamic frictionless contact problem between a viscoelastic body and a rigid obstacle is numerically studied in this paper the contact is modelled using an adapted unilateral contact law in terms of velocities in order to obtain some energy conservation properties the variational formulation is briefly recalled then a fully discrete scheme is introduced based on the finite element method to approximate the spatial variable and the midpoint scheme to discretize the time derivatives error estimates are derived on the approximative solutions from which the linear convergence of the algorithm is deduced under suitable regularity conditions furthermore we focus our interest on the analysis of the discrete energy evolution and the presentation of an adapted numerical algorithm finally a representative two dimensional example is presented to demonstrate the accuracy and the energy consistent properties of the numerical scheme

on the central difference algorithm in discrete element modelling of impact the paper provides a comprehensive analysis of the accuracy and stability of the central difference scheme when applied to simulate a simple impact problem in the context of the discrete element approach it is revealed that the algorithm exhibits some different behaviour due to the inherent nonlinearity discontinuity of the impact system particularly for an elastic or slightly inelastic impact the stable unstable region governing the selection of a maximum time step size is essentially different from that defined by the conventional linear stability criterion and thus a smaller time step should be employed in order to reduce the possible occurrence of an unexpected numerical instability

estimation and evaluation of linear individualized treatment rules to guarantee performance summary in clinical practice an informative and practically useful treatment rule should be simple and transparent however because simple rules are likely to be far from optimal effective methods to construct such rules must guarantee performance in terms of yielding the best clinical outcome highest reward among the class of simple rules under consideration furthermore it is important to evaluate the benefit of the derived rules on the whole sample and in pre specified subgroups e g vulnerable patients to achieve both goals we propose a robust machine learning method to estimate a linear treatment rule that is guaranteed to achieve optimal reward among the class of all linear rules we then develop a diagnostic measure and inference procedure to evaluate the benefit of the obtained rule and compare it with the rules estimated by other methods we provide theoretical justification for the proposed method and its inference procedure and we demonstrate via simulations its superior performance when compared to existing methods lastly we apply the method to the sequenced treatment alternatives to relieve depression star d trial on major depressive disorder and show that the estimated optimal linear rule provides a large benefit for mildly depressed and severely depressed patients but manifests a lack of fit for moderately depressed patients

a note on the approximation of two sided rayleigh quotient to eigenvalues abstract we consider the two sided rayleigh quotient introduced by ostrowski as convergence acceleration tool for eigenvalue solvers an interesting property of the two sided rayleigh quotient is established its approximation to eigenvalues depends on the eigenvalue condition number this fact is valid not only for matrix but also for matrix polynomial multiparameter system and periodic matrix pairs

projected event capturing time stepping schemes for nonsmooth mechanical systems with unilateral contact and coulomb s friction this work addresses the problem of the numerical time integration of nonsmooth mechanical systems subjected to unilateral contacts impacts and coulomb s friction the considered systems are the space discretized continuous systems obtained by using a finite element method fem approach or the multi body systems or a mix of them as in flexible multibody dynamics up to now two main numerical schemes are available for this purpose the moreau jean scheme which solves the constraints at the velocity level together with a newton impact law and the schatzman paoli scheme which directly considers the constraints at the position level in both schemes the position and velocity constraints are not both satisfied in discrete time a first attempt is made by directly using the gear gupta leimkuhler ggl approach for differential algebraic equations dae that solves in discrete time the constraints on both position and velocity levels the obtained direct projection scheme succeeds in solving in discrete time both position and velocity constraints but introduces some chattering at contact after a finite accumulation of impacts the proposed scheme improves the direct projected scheme by combining several steps of activation and projection to avoid the chattering effect the stability and the local order of the scheme will be discussed the usefulness of the scheme is demonstrated on several academic examples and is illustrated on an industrial application the modeling and simulation of an electrical circuit breaker

a finite element formulation of non smooth contact based on oriented volumes for quadrilateral and hexahedral elements this paper concerns the finite element modeling of contact between solid bodies with a special emphasis on the treatment of non smooth conditions a new approach for the formulation of the contact constraint that allows for a simple and unified treatment of all potential contact scenarios in the presence of large deformations is presented based on the calculation of an oriented volume this approach possesses the ability to resolve complicated contact scenarios efficiently while being simple to implement and more widely applicable than the contact formulations available to date we show that the formulation boils down to a node to surface gap function that works effectively for non smooth contact situations the numerical implementation using the midpoint rule shows the need to guarantee the conservation of the total energy during impact for which a lagrange multiplier method is used the result is a robust contact detection and resolution algorithm

unilateral non linear dynamic contact of thin walled structures using a primal dual active set strategy the efficient modelling of three dimensional contact problems is still a challenge in non linear implicit structural analysis we use a primal dual active set strategy siam j optim 2003 13 865 888 based on dual lagrange multipliers siam j numer anal 2000 38 989 1012 to handle the non linearity of the contact conditions this allows us to enforce the contact constraints in a weak integral sense without any additional parameter due to the biorthogonality condition of the basis functions the lagrange multipliers can be locally eliminated we perform a static condensation to achieve a reduced system for the displacements the lagrange multipliers representing the contact pressure can be easily recovered from the displacements in a variationally consistent way for the application to thin walled structures we adapt a three dimensional non linear shell formulation including the thickness stretch of the shell to contact problems a reparametrization of the geometric description of the shell body gives us a surface oriented shell element which allows the application of contact conditions directly to nodes lying on the contact surface shell typical locking phenomena are treated with the enhanced assumed strain method and the assumed natural strain method the discretization in time is done with the implicit generalized method j appl mech 1993 60 371 375 and the generalized energy momentum method comp methods appl mech eng 1999 178 343 366 to compare the development of energies within a frictionless contact description in order to conserve the total energy within the discretized frictionless contact framework we follow an approach from laursen and love int j numer methods eng 2002 53 245 274 who introduced a discrete contact velocity to update the velocity field in a post processing step various examples show the good performance of the primal dual active set strategy applied to the implicit dynamic analysis of thin walled structures

a new solution procedure for application of energy conserving algorithms to general constitutive models in nonlinear elastodynamics abstract this paper develops a novel solution strategy for temporal discretization of initial value problems in nonlinear elastodynamics enabling exact energy and momentum conservation for a spatially discretized problem this new energy momentum algorithm fits into the general framework established by simo and tarnow z angew math phys 43 1992 757 however in contrast to the presentation given in that reference the current approach extends the critical stress update formula to encompass generic stored energy functions for the hyperelastic continuum in a manner which also allows for quadratically convergent newton raphson solution of the nonlinear algorithmic equations numerical examples using a neo hookean material model are given to illustrate the excellent performance of the proposed scheme not only is the new algorithm guaranteed to be second order accurate and unconditionally stable in the fully nonlinear regime as are other energy momentum strategies but also the approach advocated is demonstrated to be more robust and versatile than its predecessors

dynamic contact impact problems energy conservation and planetary gear trains abstract the paper is a continuation of the work presented in comp meth appl mech eng 190 2001 1903 aimed at modeling of a general class of dynamic contact impact problems for systems of rigid bodies the contact is assumed to be frictionless and the main challenge is to model the exchange between the kinetic and elastic energies in the system this calls for a discretization scheme that conserves linear and angular momentum and first of all the total energy at the discrete level such a scheme has been presented in comp meth appl mech eng 190 2001 1903 and in this work we complement it with a very general treatment of the no penetration condition for two elastic bodies the approach is based on the concept of the sign rvachev function and it provides a natural generalization of the classical point to line condition arch computat meth eng 2 1995 1 the work has been motivated with the modeling of planetary gear trains and has resulted in the first to our best knowledge two dimensional parallel finite element simulator for gear sets parallel finite element simulator of planetary gear trains ph d dissertation the university of texas 2001

isogeometric analysis and domain decomposition methods in the present work we use the mortar finite element method for the coupling of nonconforming discretized sub domains in the framework of nonlinear elasticity the mortar method has been shown to preserve optimal convergence rates see laursen 2002 25 for details and is variationally consistent we show that the method can be applied to isogeometric analysis with little effort once the framework of nurbs based shape functions has been implemented furthermore a specific coordinate augmentation technique allows the design of an energy momentum scheme for the constrained mechanical system under consideration the excellent performance of the redesigned mortar method as well as the energy momentum scheme is illustrated in representative numerical examples

concordance assisted learning for estimating optimal individualized treatment regimes in this article we propose a new concordance assisted learning for estimating optimal individualized treatment regimes we first introduce a type of concordance function for prescribing treatment and propose a robust rank regression method for estimating the concordance function we then find treatment regimes up to a threshold to maximize the concordance function named prescriptive index finally within the class of treatment regimes that maximize the concordance function we find the optimal threshold to maximize the value function we establish the convergence rate and asymptotic normality of the proposed estimator for parameters in the prescriptive index an induced smoothing method is developed to estimate the asymptotic variance of the proposed estimator we also establish the n1 3 consistency of the estimated optimal threshold and its limiting distribution in addition a doubly robust estimator of parameters in the prescriptive index is developed under a class of monotonic index models the practical use and effectiveness of the proposed methodology are demonstrated by simulation studies and an application to an aids data

lagrange constraints for transient finite element surface contact a new approach to enforce surface contact conditions in transient non linear finite element problems is developed in this paper the method is based on the lagrange multiplier concept and is compatible with explicit time integration operators compatibility with explicit operators is established by referencing lagrange multipliers one time increment ahead of associated surface contact displacement constraints however the method is not purely explicit because a coupled system of equations must be solved to obtain the lagrange multipliers an important development herein is the formulation of a highly efficient method to solve the lagrange multiplier equations the equation solving strategy is a modified gauss seidel method in which non linear surface contact force conditions are enforced during iteration the new surface contact method presented has two significant advantages over the widely accepted penalty function method surface contact conditions are satisfied more precisely and the method does not adversely affect the numerical stability of explicit integration transient finite element analysis results are presented for problems involving impact and sliding with friction a brief review of the classical lagrange multiplier method with implicit integration is also included

improved implicit integrators for transient impact problems geometric admissibility within the conserving framework the value of energy and momentum conserving algorithms has been well established for the analysis of highly non linear systems including those characterized by the nonsmooth non linearities of an impact event this work proposes an improved integration scheme for frictionless dynamic contact seeking to preserve the stability properties of exact energy and momentum conservation without the heretofore unavoidable compromise of violating geometric admissibility as established by the contact constraints the physically motivated introduction of a discrete contact velocity provides an algorithmic framework that ensures exact conservation locally while remaining independent of the choice of constraint treatment thus making full conservation equally possible in conjunction with a penalty regularization as with an exact lagrange multiplier enforcement the discrete velocity effects are incorporated as a post convergence update to the system velocities and thus have no direct effect on the non linear solution of the displacement equilibrium equation the result is a robust implicit algorithmic treatment of dynamic frictionless impact appropriate for large deformations and fully conservative for a range of geometric constraints copyright 2001 john wiley sons ltd

a stable energy conserving approach for frictional contact problems based on quadrature formulas a common approach for the numerical simulation of non linear multi body contact problems is the use of lagrange multipliers to model the contact conditions the stability of standard algorithms is improved by introducing a modified mass matrix which assigns no mass to the potential contact nodes by this the spurious algorithmic oscillations in the multiplier do not occur any more which facilitates the application of the primal dual active set strategy to dynamical contact problems the new mass matrix is calculated via a modified quadrature formula that needs no extra computational cost in addition the conservation properties of the underlying algorithm are transferred to the modified mass version different numerical examples for frictional two body contact problems illustrate the improvement in the results for the contact stresses copyright 2007 john wiley sons ltd

a formulation of conserving impact system based on localized lagrange multipliers this paper proposes a new finite element method of frictional impact of elastic bodies the formulation introduces a contact frame that is placed in between contacting bodies and represents the contact surface the nonpenetration condition and the slip stick condition are defined between the contacting body and the contact frame with the aid of the independent localized lagrange multipliers representing the contact forces the position of the contact frame and the local coordinate of the contacting node along the contact frame are also treated as the independent variable which enables the exact satisfaction of the constraint conditions without the deficiency or redundant constraint the energy and momentum conservation algorithm is applied to the proposed impact system for the case of frictional impact the linear momentum is exactly conserved and the angular momentum is approximately conserved with negligible error copyright 2006 john wiley sons ltd

elasto plastic contact problems with heat exchange and fatigue abstract we deal with a one dimensional temperature dependent model for fatigue accumulation in a moving visco elasto plastic material in contact with an elasto plastic obstacle the problem for the unknown displacement and temperature is formulated using hysteresis operators as solution operators of the underlying variational inequalities the existence result for this problem consisting of the momentum and energy balance equations and an evolution equation for the fatigue is obtained using a priori estimates established for the space discretized problem the uniqueness result follows from the lipschitz continuity of the nonlinearities

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

regularity of solutions to a dynamic frictionless contact problem with normal compliance the regularity in time of solutions to a problem of frictionless dynamic contact between a viscoelastic body and a reactive foundation is established contact is modeled with the normal compliance condition it is shown that the differentiability of the normal compliance function its behavior at the onset of contact determines the regularity of the solution and additional differentiability of the data and appropriate compatibility on the initial conditions yield higher solutions differentiability unlike the case when the signorini condition is used in this problem there is no intrinsic regularity ceiling a simple example shows that these results are close to being optimal

a weighted finite element mass redistribution method for dynamic contact problems abstract this paper deals with a one dimensional wave equation being subjected to a unilateral boundary condition an approximation of this problem combining the finite element and mass redistribution methods is proposed the mass redistribution method is based on a redistribution of the body mass such that there is no inertia at the contact node and the mass of the contact node is redistributed on the other nodes the convergence as well as an error estimate in time is proved the analytical solution associated with a benchmark problem is introduced and it is compared to approximate solutions for different choices of mass redistribution however some oscillations for the energy associated with approximate solutions obtained for the second order schemes can be observed after the impact to overcome this difficulty a new unconditionally stable and a very lightly dissipative scheme is proposed

a finite element finite strain formulation for modeling colliding blocks of gent materials the present paper is devoted to the analysis of the contact impact problems with coulomb friction and large deformation between two hyperelastic bodies of gent model the total lagrangian formulation is adopted to describe the geometrically non linear behavior for the finite element implementation the explicit expression of the incremental law of gent model is derived a first order algorithm is applied for the numerical integration of the time discretized equation of motion efficiency and accuracy of the resulting method is illustrated on a two dimensional static contact problem and a three dimensional dynamic contact problem as compared with ansys simulations

an energy momentum conserving algorithm using the variational formulation of visco plastic updates in this paper we use the variational formulation of elasto plastic updates proposed by ortiz and stainier comput methods appl mech eng 1999 171 419 444 in the context of consistent time integration schemes we show that such a formulation is well suited to obtain a general expression of energy momentum conserving algorithms moreover we present numerical examples that illustrate the efficiency of our developments copyright 2005 john wiley sons ltd

hybrid mixed discretization of elasto dynamic contact problems using consistent singular mass matrices summary an alternative spatial semi discretization of dynamic contact based on a modified hamilton s principle is proposed the modified hamilton s principle uses displac ement velocity and momentum as variables which allows their independent spatial discretization al ong with a local static condensation for velocity and momentum it leads to an approach with a hybrid mixed consistent mass matrix hmcmm an attractive feature of such a formulation is the possibility to construc t hybrid singular mass matrices hsmm with zero components at those nodes where contact is collocated this improves numerical stability of the semidiscrete problem the differential index of the underlying differential algebraic system is reduced from 3 to 1 and spurious oscillations in the contact pressure whi ch are commonly reported for formulations with lagrange multipliers are significantly reduced resu lts of numerical experiments for truss and timoshenko beam elements are discussed in addition the properties of the novel discretization scheme for an unconstrained dynamic problem are assessed by a dispersion analysis copyright c 2010 john wiley sons ltd received

a nonsmooth generalized α scheme for flexible multibody systems with unilateral constraints summary mechanical systems are usually subjected not only to bilateral constraints but also to unilateral constraints inspired by the generalized time integration method for smooth flexible multibody dynamics this paper presents a nonsmooth generalized method which allows a consistent treatment of the nonsmooth phenomena induced by unilateral constraints and an accurate description of the structural vibrations during free motions both the algorithm and the implementation are illustrated in detail numerical example tests are given in the scope of both rigid and flexible body models taking account for both linear and nonlinear systems and comprising both unilateral and bilateral constraints the extended nonsmooth generalized method is verified through comparison to the traditional moreau jean method and the fully implicit newmark method results show that the nonsmooth generalized method benefits from the accuracy and stability property of the classical generalized method with controllable numerical damping in particular when it comes to the analysis of flexible systems the nonsmooth generalized method shows much better accuracy property than the other two methods copyright 2013 john wiley sons ltd

riemann solutions and spacetime discontinuous galerkin method for linear elastodynamic contact abstract we derive riemann solutions for stick slip and separation contact modes in a linear elastic material with an isotropic coulomb friction relation and explore their numerical implementation the riemann solutions preserve the characteristic structure of the underlying elastodynamic system and imply dynamic contact conditions that are distinct from the quasi static conditions used in some numerical models nonphysical discontinuities in the standard coulomb model at stick slip transitions can cause contact mode chatter in numerical simulations we restate the coulomb relation to remove these artificial discontinuities and eliminate the need for algorithmic remedies discontinuous response at abrupt separation to contact transitions is physically reasonable and we propose a regularization scheme to address this case we implement the riemann contact solutions within an adaptive spacetime discontinuous galerkin sdg code and report numerical results that demonstrate the model s efficacy

on the solution of a generalized higgs boson equation in the de sitter space time through an efficient and hamiltonian scheme abstract the present work is the first paper in the literature to report on a hamiltonian discretization of the fractional higgs boson equation in the de sitter space time and its theoretical analysis more precisely we design herein a numerically efficient finite difference hamiltonian technique for the solution of a fractional extension of the higgs boson equation in the de sitter space time the model under investigation is a multidimensional equation with generalized potential and riesz space fractional derivatives of orders in 1 2 an energy integral for the model is readily available and we propose a nonlinear implicit and consistent numerical technique based on fractional order centered differences with similar hamiltonian properties in the discrete scenario a fractional energy approach is used then to prove the properties of stability and convergence of the technique for simulation purposes we consider both the classical and the fractional higgs real valued scalar fields in the de sitter space time and find results qualitatively similar to those available in the literature for the sake of convenience we provide the matlab code of an alternative linear discretization of the method presented in this work this linear implicit approach is thoroughly analyzed also

dynamic analysis of rigid and deformable multibody systems with penalty methods and energy momentum schemes abstract a multibody formulation for the nonlinear dynamics of mechanical systems composed of both rigid and deformable bodies is proposed in this work focusing on its conservation properties for basic magnitudes such as total energy and momentum the approach is based on the use of dependent variables cartesian coordinates of selected points and the enforcement of the constraints through the penalty method this choice has the advantage of providing a simple overall structure that allows the inclusion of both rigid bodies discrete model and elastic bodies continuum model discretised with the finite element method under the same framework in order to build a single set of ordinary differential equations the elastic bodies are represented by general hyperelastic models and may undergo large displacements rotations and strains an energy momentum time integration method has been employed achieving remarkable stability and robustness with exact conservation of total energy this approach effectively overcomes drawbacks associated with penalty formulations in other time integration algorithms this important result in fact proves to be the main conclusion of this work some representative numerical simulations are presented for mechanical systems comprised of rigid and deformable bodies

robust estimation of optimal dynamic treatment regimes for sequential treatment decisions a dynamic treatment regime is a list of sequential decision rules for assigning treatment based on a patient s history q and a learning are two main approaches for estimating the optimal regime i e that yielding the most beneficial outcome in the patient population using data from a clinical trial or observational study q learning requires postulated regression models for the outcome while a learning involves models for that part of the outcome regression representing treatment contrasts and for treatment assignment we propose an alternative to q and a learning that maximizes a doubly robust augmented inverse probability weighted estimator for population mean outcome over a restricted class of regimes simulations demonstrate the method s performance and robustness to model misspecification which is a key concern

a robust consistent configuration framework and formulation for 3d finite strain dynamic impact problems as a first step towards the next generation of computational tools for contact impact applications a robust consistent configuration dynamic formulation for frictional contact impact dynamic problems is described based on a newly developed decoupled point to segment gap vector projection and decoupled contact model in conjunction with the so called arbitrary reference configuration arc formulation for finite elastic inelastic deformation and the forward incremental displacement central difference time integration scheme for the equation of motion as a consequence the resulting normal and tangential contact boundary formulations are easy to be solved and the contact constraints are satisfied exactly this formulation is highly robust and efficient for the numerical simulation of finite deformation elastic inelastic frictional contact impact dynamic applications numerical results with comparisons to available experimental data and those obtained from other codes are also presented thereby demonstrating the inherent advantages

regularity and rothe method error estimates for parabolic hemivariational inequality this paper deals with regularity of solutions to the abstract operator version of parabolic partial differential inclusion of the form u t au t j u t f t with the multivalued term given in the form of clarke subdifferential of a locally lipschitz functional j using the rothe method it is shown that under appropriate assumptions on the data the solution has the increased regularity three regularity theorems are given the first one concerns the regularity of solution in the besov space b2 1 2 0 t h the second theorem provides assumption under which the solution lies in the space h1 0 t h l 0 t v c 0 t vweak the last one shows that if the operator a is strongly monotone and the multivalued term satisfies the relaxed monotonicity assumption then the unique solution also belongs to h1 0 t v w1 0 t h in the last case the error estimates on the rothe method are also proved

numerical analysis of a dynamic piezoelectric contact problem arising in viscoelasticity a dynamic frictionless contact problem between a viscoelastic piezoelectric body and a deformable obstacle is numerically studied in this paper the contact is modelled using the normal compliance contact condition and the linear electro viscoelastic constitutive law is employed to simulate the piezoelectric effects the variational formulation is a coupled system composed of a parabolic nonlinear variational equation for the velocity field and a linear variational equation for the electric potential an existence and uniqueness result is recalled then a fully discrete scheme is introduced based on the finite element method to approximate the spatial variable and the backward euler scheme to discretize the time derivatives error estimates are derived on the approximative solutions from which the linear convergence of the algorithm is deduced under suitable regularity conditions finally some two dimensional examples are presented to demonstrate the accuracy and the performance of the algorithm

geometric numerical integration of inequality constrained nonsmooth hamiltonian systems we consider the geometric numerical integration of hamiltonian systems subject to both equality and hard inequality constraints as in the standard geometric integration setting we target long term structure preservation additionally however we also consider invariant preservation over persistent simultaneous and or frequent boundary interactions appropriately formulating geometric methods for these cases has long remained challenging due the inherent nonsmoothness and one sided conditions that they impose to resolve these issues we thus focus both on symplectic momentum preserving behavior and the preservation of additional structures unique to the inequality constrained setting toward these goals we introduce for the first time a fully nonsmooth discrete hamilton s principle and obtain an associated framework for composing geometric numerical integration methods for inequality equality constrained systems applying this framework we formulate a new family of geometric numerical integra

interactive model building for q learning evidence based rules for optimal treatment allocation are key components in the quest for efficient effective health care delivery q learning an approximate dynamic programming algorithm is a popular method for estimating optimal sequential decision rules from data q learning requires the modeling of nonsmooth nonmonotone transformations of the data complicating the search for adequately expressive yet parsimonious statistical models the default q learning working model is multiple linear regression which is not only provably misspecified under most data generating models but also results in nonregular regression estimators complicating inference we propose an alternative strategy for estimating optimal sequential decision rules for which the requisite statistical modeling does not depend on nonsmooth nonmonotone transformed data does not result in nonregular regression estimators is consistent under a broader array of data generation models than q learning results in estimated sequential decision rules that have better sampling properties and is amenable to established statistical approaches for exploratory data analysis model building and validation we derive the new method iq learning via an interchange in the order of certain steps in q learning in simulated experiments iq learning improves on q learning in terms of integrated mean squared error and power the method is illustrated using data from a study of major depressive disorder

finite elements in space and time for dynamic contact problems dynamic obstacle and signorini problems are discretized by continuous and discontinuous finite elements in space and time the resulting discrete problems are attributed to a standard implicit time stepping scheme through relaxation of impact phenomena and suitable numerical integration the method can cope with dynamic contact problems which is shown by an analysis of a model problem moreover numerical examples demonstrate that it is actually able to approximate the solution of dynamic contact problems which are not fully covered by the theory copyright 2008 john wiley sons ltd

adaptive confidence intervals for the test error in classification the estimated test error of a learned classifier is the most commonly reported measure of classifier performance however constructing a high quality point estimator of the test error has proved to be very difficult furthermore common interval estimators e g confidence intervals are based on the point estimator of the test error and thus inherit all the difficulties associated with the point estimation problem as a result these confidence intervals do not reliably deliver nominal coverage in contrast we directly construct the confidence interval by using smooth data dependent upper and lower bounds on the test error we prove that for linear classifiers the proposed confidence interval automatically adapts to the nonsmoothness of the test error is consistent under fixed and local alternatives and does not require that the bayes classifier be linear moreover the method provides nominal coverage on a suite of test problems using a range of classification algorithms and sample sizes this ar

a mortar method for energy momentum conserving schemes in frictionless dynamic contact problems summary in the present work the mortar method is applied to planar large deformation contact problems without friction in particular the proposed form of the mortar contact constraints is invariant under translations and rotations these invariance properties lay the foundation for the design of energy momentum timestepping schemes for contact impact problems the iterative solution procedure is embedded into an active set algorithm lagrange multipliers are used to enforce the mortar contact constraints the solution of generalized saddle point systems is circumvented by applying the discrete null space method numerical examples demonstrate the robustness and enhanced numerical stability of the newly developed energymomentum scheme copyright q 2008 john wiley sons ltd

a time discretization scheme based on rothe s method for dynamical contact problems with friction abstract we present a new dissipative and contact stabilized time discretization scheme for dynamic frictional contact problems which is based on rothe s method especially for the case of coulomb friction the stability of the contact stresses is of crucial importance as they directly influence the frictional behavior in our approach we obtain an accurate description of the frictional stresses by a time discretized friction law allowing for an implicit treatment of the contact forces in the framework of the newmark scheme moreover undesirable oscillations at the contact interface are removed by employing an additional l 2 projection within the predictor step since the implicit treatment of the material behavior and the frictional response requires a quasi variational inequality to be solved in each time step we derive a non smooth multiscale method which allows for the efficient and robust solution of these highly non linear problems the convergence of this multiscale method is proven for the case of tresca friction for the case of coulomb friction an inexact fixed point iteration in the normal stresses is used we furthermore consider the case of two body contact here the information transfer at the contact interface is realized by means of mortar methods which provide a stable discretization of the relative displacements and the stresses at the contact boundary numerical results for the resulting fully discrete scheme in 3d are presented showing the high accuracy of the proposed method

the singular dynamic method for constrained second order hyperbolic equations application to dynamic contact problems the purpose of this paper is to present a new family of numerical methods for the approximation of second order hyperbolic partial differential equations submitted to a convex constraint on the solution the main application is dynamic contact problems the principle consists in the use of a singular mass matrix obtained by the mean of different discretizations of the solution and of its time derivative we prove that the semi discretized problem is well posed and energy conserving numerical experiments show that this is a crucial property to build stable numerical schemes

on practical integration of semi discretized nonlinear equations of motion part 1 reasons for probable instability and improper convergence time integration is the most versatile method for analyzing the general case of nonlinear semi discretized equations of motion however the approximate responses of such analyses generally do not converge properly and might even display numerical instability this is a very significant shortcoming especially in practical time integration herein after illustrating that this phenomenon is viable even for very simple nonlinear dynamic models sources of the shortcoming are discussed in detail the conclusion is that in time integration of nonlinear dynamic mathematical models of physically stable structural systems responses may converge improperly for three major reasons these reasons are 1 inadequate number of iterations before terminating nonlinearity solutions 2 deficiencies in the formulation of some time integration methods and 3 the inherent behaviour of the models of some special dynamic systems in addition limitations on computational facilities and improper consideration of these limitations may impair the numerical stability and convergence of the computed responses the differences between static and dynamic analyses are also discussed from the viewpoint of the numerical errors induced by nonlinearity

an adaptive multi scale approach to the modelling of masonry structures we present an adaptive multi scale approach for predicting the mechanical behaviour of masonry structures modelled as dynamic frictional multi body contact problems in this approach the iterative splitting of the contact problem into normal contact and frictional contact is combined with a semismooth newton primal dual active set procedure to calculate deformations and openings in the model structures this algorithm is then coupled with a novel adaptive multi scale technique involving a macroscopic scale which is the size of the masonry structure and a mesoscopic scale which is the size of the constituents bricks stone blocks to predict appearance of dislocations and stress distribution in large scale masonry structures comparisons of the numerical results with data from experimental tests and from practical observations illustrate the predictive capability of the multi scale algorithm

a family of space time connecting discretization schemes with local impact detection for elastodynamic contact problems abstract we derive formulate and analyze a new family of discretization schemes for elastodynamic contact problems which implicitly resolve the individual impact times for each node on the contact interface within our approach information from the space discrete setting is incorporated into the time discretization by means of pointwise chosen parameters for the time discretization scheme the members of this family can be interpreted as modified newmark schemes thus making them easily understandable and implementable we prove that for certain parameter choices the algorithms are dissipative methods further as our analysis and our numerical experiments show a special solution dependent choice of parameters leads to a new space time connecting discretization with a highly stable behavior of displacements velocities and boundary stresses at the contact interface

an energy approach to space time galerkin bem for wave propagation problems in this paper we consider dirichlet or neumann wave propagation problems reformulated in terms of boundary integral equations with retarded potential starting from a natural energy identity a space time weak formulation for 1d integral problems is briefly introduced and continuity and coerciveness properties of the related bilinear form are proved then a theoretical analysis of an extension of the introduced formulation for 2d problems is proposed pointing out the novelty with respect to existing literature results at last various numerical simulations will be presented and discussed showing unconditional stability of the space time galerkin boundary element method applied to the energetic weak problem copyright 2009 john wiley sons ltd

perturbation analysis for the eigenproblem of periodic matrix pairs this paper is devoted to perturbation analysis for the eigenproblem of periodic matrix pairs a j e j j 1 k we first study perturbation expansions of periodic deflating subspaces and eigenv

a co rotational element time integration strategy for non linear dynamics new procedures are proposed for implicit dynamic analysis using the finite element method the main aim is to give stable solutions with significant rigid body motions in particular rotations in contrast to most conventional approaches the time integration strategy is closely linked to the element technologies with the latter involving a form of co rotational procedure for the undamped situation one of the solution procedures leads to an algorithm that exactly conserves energy when constant external forces are applied i e with gravity loading

conservative discretization of contact impact problems for nearly rigid bodies abstract a discretization scheme for contact impact problems related to modeling of gears is proposed the problem is first discretized in time and then a variational formulation for the resulted one step problem is developed a finite element discretization completes the discretization process the scheme is a reinterpretation of the general simo laursen chavla algorithm in the context of the rigid body motion superimposed with small elastic deformation it conserves precisely the linear momentum and total energy and approximately the angular momentum the discretization method is illustrated with two numerical examples the standard 1d impact problem for an elastic rod and a 2d model problem of an elastic wheel bouncing within a constraining box

a wave problem in a half space with a unilateral constraint at the boundary in this paper we study the following problem let omega be a half space of mathbb r n defined by omega x x x n in mathbb r x n where x x ldots x n 1 is the usual notation and let there be given functions u 0 in h 1 omega and u 1 in l 2 omega we assume that u 0 x n 0 is nonnegative and similarly partial u 0 partial x n x n 0 which is a priori an element of h 1 2 mathbb r n 1 is nonnegative

mixed interpretation and extensions of the equivalent mass matrix approach for elastodynamics with contact the present paper highlights the idea that the mass redistribution technique introduced by khenous and co workers 2006 17 18 for elastodynamics with impact can be reinterpreted as a mixed formulation in displacements and velocities in which a special compatibility condition is enforced such a formulation opens the route to various extensions and to variational integrators for impact problems potentially with variational time adaption those ideas are exemplified in the design of such integrators and various mass redistribution schemes

the contact stabilized newmark method consistency error of a spatiotemporal discretization the paper considers a slightly improved variant of the contact stabilized newmark method by deuflhard et al which provides a spatio temporal numerical integration of dynamical contact problems between viscoelastic bodies in the frame of the signorini condition up to now the question of consistency in the case of contact constraints has been discussed for time integrators in function space under the assumption of bounded total variation of the solution here interest focuses on the consistency error of the newmark scheme in physical energy norm after discretization both in time and in space the resulting estimate for the local discretization error allows to prove global convergence of the newmark scheme under an additional assumption on the active contact boundaries

finite dimensional multiparameter spectral theory the nonderogatory case abstract a completeness theorem for nonderogatory eigenvalues of multiparameter systems is proved in a finite dimensional setting also a basis for the second root subspace of a simple eigenvalue is given weakly elliptic multiparameter systems are introduced it is shown that simple real eigenvalues of such systems are nonderogatory

numerical approximation of a wave equation with unilateral constraints the system u tt u xx ni f x in 0 l times 0 t with initial data u x 0 u 0 x u t x 0 u 1 x almost everywhere on 0 l and boundary conditions u 0 t 0 for all t geq 0 and the unilateral condition u x l t geq 0 u l t geq k 0 u l t k 0 u x l t 0 models the longitudinal vibrations of a rod whose motion is limited by a rigid obstacle at one end a new variational formulation is given existence and uniqueness are proved finite elements and finite difference schemes are given and their convergence is proved numerical experiments are reported the characteristic schemes perform better in terms of accuracy and the subcharacteristic schemes look better

simultaneous enforcement of constraints at position and velocity levels in the nonsmooth generalized α scheme abstract this paper presents a formalism for the transient simulation of nonsmooth dynamic mechanical systems composed of rigid and flexible bodies kinematic joints and frictionless contact conditions the proposed algorithm guarantees the exact satisfaction of the bilateral and unilateral constraints both at position and velocity levels thus it significantly differs from penalty techniques since no penetration is allowed the numerical scheme is obtained in two main steps firstly a splitting method is used to isolate the contributions of impacts which shall be integrated with only first order accuracy from smooth contributions which can be integrated using a higher order scheme secondly following the idea of gear gupta and leimkuhler the equation of motion is reformulated so that the bilateral and unilateral constraints appear both at position and velocity levels after time discretization the equation of motion involves two complementarity conditions and it can be solved at each time step using a monolithic semi smooth newton method the numerical behavior of the proposed method is studied and compared to other approaches for a number of numerical examples it is shown that the formulation offers a unified and valid approach for the description of contact conditions between rigid bodies as well as between flexible bodies

energy controlling time integration methods for nonlinear elastodynamics and low velocity impact it is now well established that discrete energy conservation dissipation plays a key role for the unconditional stability of time integration schemes in nonlinear elastodynamics in this paper from a rigorous conservation analysis of the hilber hughes taylor time integration scheme h hilber t hughes r taylor improved numerical dissipation for time integration algorithms in structural dynamics earthquake engrg struct dynam 5 1977 283 292 we propose an original way of introducing a controllable energy dissipation while conserving momenta in conservative strategies like j simo n tarnow the discrete energy momentum method conserving algorithms for nonlinear elastodynamics z angew math phys 43 1992 757 792 moreover we extend the technique proposed in o gonzalez exact energy and momentum conserving algorithms for general models in nonlinear elasticity comput methods appl mech engrg 190 13 14 2000 1763 1783 to provide energy controlling time integration schemes for frictionless contact problems enforcing the standard kuhn tucker conditions at time discretization points we also extend this technique to viscoelastic models numerical tests involving the impact of incompressible elastic or viscoelastic bodies in large deformation are proposed to confirm the theoretical analysis

optimal dynamic treatment regimes summary a dynamic treatment regime is a list of decision rules one per time interval for how the level of treatment will be tailored through time to an individual s changing status the goal of this paper is to use experimental or observational data to estimate decision regimes that result in a maximal mean response to explicate our objective and to state the assumptions we use the potential outcomes model the method proposed makes smooth parametric assumptions only on quantities that are directly relevant to the goal of estimating the optimal rules we illustrate the methodology proposed via a small simulation

numerical analysis and simulations of a dynamic frictionless contact problem with damage the process of dynamic frictionless contact between a viscoelastic body and a reactive foundation which includes material damage is modelled numerically analyzed and simulated contact is modelled with the normal compliance condition the damage of the material resulting from tension or compression is described by the damage field which measures the pointwise fractional decrease in the load carrying capacity of the material the evolution of the damage is governed by a parabolic differential inclusion a fully discrete scheme for the problem is proposed and error estimates on the numerical solutions derived the scheme has been implemented and numerical simulations of the evolution of the mechanical state of the system and its material damage are presented