synchronization in general complex dynamical networks with coupling delays abstract complex networks have attracted increasing attention from various fields of science and engineering today due to the finite speeds of transmission and spreading as well as traffic congestions a signal or influence travelling through a complex network often is associated with time delays and this is very common in biological and physical networks in this paper we introduce complex dynamical network models with coupling delays for both continuous and discrete time cases and then investigate their synchronization phenomena and criteria based on these new complex network models we derive synchronization conditions for both delay independent and delay dependent asymptotical stabilities in terms of linear matrix inequalities lmi we finally use a network with a fixed delay and a specific coupling scheme as an example to illustrate the theoretical results

a posteriori error estimation for unilateral contact with matching and non matching meshes in this paper we consider the unilateral contact problem between elastic bodies we propose an error estimator based on the concept of error in the constitutive relation in order to evaluate the finite element approximation involving matching and non matching meshes on the contact zone the determination of the a posteriori error estimate is linked to the building of kinematically admissible stress fields and statically admissible stress fields we then propose a finite element method for approximating the unilateral contact problem taking into account matching and non matching meshes on the contact zone then we describe the construction of admissible fields lastly we present optimized computations by using both the error estimates and a convenient mesh adaptivity procedure 2000 elsevier science s a all rights reserved

on nonconvex quadratic programming with box constraints nonconvex quadratic programming with box constraints is a fundamental mathcal np hard global optimization problem recently some authors have studied a certain family of convex sets associated with this problem we prove several fundamental results concerned with these convex sets we determine their dimension characterize their extreme points and vertices show their invariance under certain affine transformations and show that various linear inequalities induce facets we also show that the sets are closely related to the boolean quadric polytope a fundamental polytope in the field of polyhedral combinatorics finally we give a classification of valid inequalities and show that this yields a finite recursive procedure to check the validity of any proposed inequality

convex relaxations of non convex mixed integer quadratically constrained programs extended formulations this paper addresses the problem of generating strong convex relaxations of mixed integer quadratically constrained programming miqcp problems miqcp problems are very difficult because they combine two kinds of non convexities integer variables and non convex quadratic constraints to produce strong relaxations of miqcp problems we use techniques from disjunctive programming and the lift and project methodology in particular we propose new methods for generating valid inequalities from the equation y x x t we use the non convex constraint y x x t preccurlyeq 0 to derive disjunctions of two types the first ones are directly derived from the eigenvectors of the matrix y x x t with positive eigenvalues the second type of disjunctions are obtained by combining several eigenvectors in order to minimize the width of the disjunction we also use the convex sdp constraint y x x t succcurlyeq 0 to derive convex quadratic cuts and we combine both approaches in a cutting plane algorithm we present computational results to illustrate our findings

an exact algorithm for nonconvex quadratic integer minimization using ellipsoidal relaxations we propose a branch and bound algorithm for minimizing a not necessarily convex quadratic function over integer variables the algorithm is based on lower bounds computed as continuous minima of the objective function over appropriate ellipsoids in the nonconvex case we use ellipsoids enclosing the feasible region of the problem in spite of the nonconvexity these minima can be computed quickly the corresponding optimization problems are equivalent to trust region subproblems we present several ideas that allow us to accelerate the solution of the continuous relaxation within a branch and bound scheme and examine the performance of the overall algorithm by computational experiments good computational performance is shown especially for ternary instances

a geometrical based contact algorithm using a barrier method most methods employed in the numerical solution of contact problems in finite element simulations rely on equality based optimization methods typically a gap function which is non differentiable at the point of contact is used in these kind of approaches the gap function can be seen as the macaulay bracket of some distance function where the latter is differentiable at the point of contact in this article we propose to use the distance function directly instead of using the gap function this will give rise to a formulation involving inequality constraints this approach eliminates the artificially introduced non differentiability to this end we propose a barrier algorithm as the method of choice to solve the problem the method originates in optimization literature where convergence proofs for the method are available

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

solving max cut to optimality by intersecting semidefinite and polyhedral relaxations we present a method for finding exact solutions of max cut the problem of finding a cut of maximum weight in a weighted graph we use a branch and bound setting that applies a dynamic version of the bundle method as bounding procedure this approach uses lagrangian duality to obtain a nearly optimal solution of the basic semidefinite max cut relaxation strengthened by triangle inequalities the expensive part of our bounding procedure is solving the basic semidefinite relaxation of the max cut problem which has to be done several times during the bounding process we review other solution approaches and compare the numerical results with our method we also extend our experiments to instances of unconstrained quadratic 0 1 optimization and to instances of the graph equipartition problem the experiments show that our method nearly always outperforms all other approaches in particular for dense graphs where linear programming based methods fail our method performs very well exact solutions are obtained in a reasonable time for any instance of size up to n 100 independent of the density for some problems of special structure we can solve even larger problem classes we could prove optimality for several problems of the literature where to the best of our knowledge no other method is able to do so

contact impact modeling in explicit transient dynamics abstract in this article we discuss the treatment of contact impact modeling in a large deformation explicit dynamic setting such problems are posed mathematically by demanding the usual satisfaction momentum balance equations and boundary conditions for each body separately while imposing an additional set of constraints that govern the interaction of these bodies with each other in applying such methods to contact problems we emphasize two requirements first that the treatment of contact should follow from the development of the local weak and global strong forms of the contact equations in the continuum setting algorithms developed from this framework are seen to readily handle the three dimensional multi body friction case second and equally important especially in large applications is the practical aspect of computing the closest point projection for contact nodes an essential component of defining the contact constraints this calculation is global in nature accounting for the fact that contact impact involves multiple bodies interacting in unforeseeable ways these requirements have guided the development of algorithms capable of treating contact impact in pronto3d m w heinstein s w attaway j w swegle f j mello a general purpose contact detection algorithm for nonlinear structural analysis sodes sand92 2141 sandia national laboratories albuquerque n 87185 1992 are discussed in this paper

hamiltonian structures and stability for rigid bodies with flexible attachments the dynamics of a rigid body with flexible attachments is studied a general framework for problems of this type is established in the context of poisson manifolds and reduction a simple model for a rigid body with an attached linear extensible shear beam is worked out for illustration second the energy casimir method for proving nonlinear stability is recalled and specific stability criteria for our model example are worked out the poisson structure and stability results take into account vibrations of the string rotations of the rigid body their coupling at the point of attachment and centrifugal and coriolis forces

portfolio optimization with an envelope based multi objective evolutionary algorithm the problem of portfolio selection is a standard problem in financial engineering and has received a lot of attention in recent decades classical mean variance portfolio selection aims at simultaneously maximizing the expected return of the portfolio and minimizing portfolio variance in the case of linear constraints the problem can be solved efficiently by parametric quadratic programming i e variants of markowitz critical line algorithm however there are many real world constraints that lead to a non convex search space e g cardinality constraints which limit the number of different assets in a portfolio or minimum buy in thresholds as a consequence the efficient approaches for the convex problem can no longer be applied and new solutions are needed in this paper we propose to integrate an active set algorithm optimized for portfolio selection into a multi objective evolutionary algorithm moea the idea is to let the moea come up with some convex subsets of the set of all feasible portfolios solve a critical line algorithm for each subset and then merge the partial solutions to form the solution of the original non convex problem we show that the resulting envelope based moea significantly outperforms existing moeas

a solution method for general contact impact problems in this paper a solution method is presented for the analysis of contact impact between deformable bodies the method is different from lagrange multipliers and penalty methods having defined a body as contactor and the other as target it is assumed that contact forces are developed between contactor nodes and target surface the method is based on stiffness transformation and eliminating the normal degree of freedom of contactor node the method is absolutely general and can be used in static and dynamic nonlinear problems all the drawbacks of lagrange multipliers and penalty method are vanished in this technique and it can be easily implemented in computer programs the efficiency and applicability of the method is demonstrated by several illustrative examples

robust stability and stabilization for singular systems with state delay and parameter uncertainty considers the problems of robust stability and stabilization for uncertain continuous singular systems with state delay the parametric uncertainty is assumed to be norm bounded the purpose of the robust stability problem is to give conditions such that the uncertain singular system is regular impulse free and stable for all admissible uncertainties while the purpose of the robust stabilization is to design a state feedback control law such that the resulting closed loop system is robustly stable these problems are solved via the notions of generalized quadratic stability and generalized quadratic stabilization respectively necessary and sufficient conditions for generalized quadratic stability and generalized quadratic stabilization are derived a strict linear matrix inequality lmi design approach is developed an explicit expression for the desired robust state feedback control law is also given finally a numerical example is provided to demonstrate the application of the proposed method

exact quadratic convex reformulations of mixed integer quadratically constrained problems we propose a solution approach for the general problem qp of minimizing a quadratic function of bounded integer variables subject to a set of quadratic constraints the resolution is based on the reformulation of the original problem qp into an equivalent quadratic problem whose continuous relaxation is convex so that it can be effectively solved by a branch and bound algorithm based on quadratic convex relaxation we concentrate our efforts on finding a reformulation such that the continuous relaxation bound of the reformulated problem is as tight as possible furthermore we extend our method to the case of mixed integer quadratic problems with the following restriction all quadratic sub functions of purely continuous variables are already convex finally we illustrate the different results of the article by small examples and we present some computational experiments on pure integer and mixed integer instances of qp most of the considered instances with up to 53 variables can be solved by our approach combined with the use of cplex

an intriguing hybrid synchronization phenomenon of two coupled complex networks this paper investigates the hybrid synchronization problem of two coupled complex networks employing the linear feedback and the adaptive feedback control methods which are simple efficient and easy to implement in practical applications we obtain some useful criteria of the hybrid synchronization of two coupled networks based on the lyapunov stability theory and lasalle s invariance principle it shows that under suitable conditions two coupled complex networks can realize an intriguing hybrid synchronization the outer anti synchronization between the driving network and the response network and the inner complete synchronization in the driving network and the response network respectively numerical simulations demonstrate the effectiveness of the proposed hybrid synchronization scheme

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 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

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

synchronization of complex dynamical networks with hybrid coupling delays on time scales by handling multitude kronecker product terms the problem of synchronization is studied for complex dynamical networks with hybrid coupling delays on time scales the hybrid coupling delays consist of both discrete and distributed coupling delays some novel and useful synchronization criteria of complex dynamical networks are derived based on stability theory of error dynamical system by employing the standard lyapunov krasovskii functional matrix expansion method to handle multitude kronecker product terms and the modified jensen s inequalities on time scale new sufficient conditions guaranteeing the global exponential stability of the origin of complex dynamical networks are established interms of linear matrix inequality lmi numerical examples are included to demonstrate the effectiveness of the proposed method

synchronization criteria of fuzzy complex dynamical networks with interval time varying delays this paper presents new delay dependent synchronization criteria for fuzzy complex dynamical networks with interval time varying delays by construction of a suitable lyapunov krasovskii s l k functional and utilization of finsler s lemma new synchronization criteria for the networks are established in terms of linear matrix inequalities lmis which can be easily solved by various effective optimization algorithms one numerical example is given to illustrate the effectiveness of the proposed methods

the hamiltonian structure of nonlinear elasticity the material and convective representations of solids rods and plates it is our belief that a thorough understanding of the mathematical underpinnings of elasticity is crucial to its analytical and numerical implementation for example in the analysis of rotating structures the coupling of the equations for geometrically inexact models obtained by linearization or other approximations with those for rotating rigid bodies can easily lead to misleading artificial softening effects that can significantly alter numerical results see simo and vuquoc 1986c especially equations 3 and 5 in this paper we consider fully nonlinear geometrically exact models for rods plates and shells which take into account shear and torsion as well as the usual bending effects in traditional rod and plate models these models can be obtained either from the three dimensional theory by a systematic use of projection methods see e g antman 1972 and naghdi 1972 or by a direct approach within the context of cosserat continuum remarkably the two approaches lead to essentially the same form of the governing field equations in the present context we have chosen as a model problem a particular rod model which may be regarded as an extension of the classical kirchhoff love model see love 1944 to include shear deformations as in

synchronization of singular complex dynamical networks with time varying delays abstract this paper considers delay dependent synchronizations of singular complex dynamical networks with time varying delays a modified lyapunov krasovskii functional is used to derive a sufficient condition for synchronization in terms of lmis linear matrix inequalities which can be easily solved by various convex optimization algorithms numerical examples show the effectiveness of the proposed method

a contact formulation based on localized lagrange multipliers formulation and application to two dimensional problems the non penetration condition in contact problems is traditionally based on the classical lagrange multiplier method this method makes extensive use of modelling details of the contacting bodies for contact enforcement as the contact surface meshes are in general non matching to deal with this problem we introduce a novel element in the lagrange multiplier approach of contact modelling namely a contact frame placed in between contacting bodies it acts as a medium through which contact forces are transferred without violating equilibrium in the contact domain for discrete contact models only nodal information of the contacting bodies is required which makes the proposed contact enforcement generic the contact frame has its own independent freedoms which allows the formulation to pass contact patch tests by design copyright 2002 john wiley sons ltd

synchronization stability of general complex dynamical networks with time varying delays a piecewise analysis method the synchronization problem of some general complex dynamical networks with time varying delays is investigated both time varying delays in the network couplings and time varying delays in the dynamical nodes are considered the delays considered in this paper are assumed to vary in an interval where the lower and upper bounds are known based on a piecewise analysis method the variation interval of the time delay is firstly divided into several subintervals by checking the variation of the derivative of a lyapunov function in every subinterval then the convexity of matrix function method and the free weighting matrix method are fully used in this paper some new delay dependent synchronization stability criteria are derived in the form of linear matrix inequalities two numerical examples show that our method can lead to much less conservative results than those in the existing references

synchronization criterions and pinning control of general complex networks with time delay the problems of synchronization and pinning control for general time delay complex dynamical networks are investigated in this paper less conservative criterions for both continuous time and discrete time complex dynamical networks with time delay are obtained pinning control strategies are respectively designed to make these complex dynamical networks synchronized moreover the problems of designing controllers are converted into solving optimal problems of a series of linear matrix inequalities which reduces the computation complexity finally numerical simulations verify the effectiveness of our methodology

a branch and cut algorithm for nonconvex quadratic programs with box constraints we present the implementation of a branch and cut algorithm for bound constrained nonconvex quadratic programs we use a class of inequalities developed in 12 as cutting planes we present various branching strategies and compare the algorithm to several other methods to demonstrate its effectiveness

an effective branch and bound algorithm for convex quadratic integer programming we present a branch and bound algorithm for minimizing a convex quadratic objective function over integer variables subject to convex constraints in a given node of the enumeration tree corresponding to the fixing of a subset of the variables a lower bound is given by the continuous minimum of the restricted objective function we improve this bound by exploiting the integrality of the variables using suitably defined lattice free ellipsoids experiments show that our approach is very fast on both unconstrained problems and problems with box constraints the main reason is that all expensive calculations can be done in a preprocessing phase while a single node in the enumeration tree can be processed in linear time in the problem dimension

a time varying complex dynamical network model and its controlled synchronization criteria today complex networks have attracted increasing attention from various fields of science and engineering it has been demonstrated that many complex networks display various synchronization phenomena in this note we introduce a time varying complex dynamical network model we then further investigate its synchronization phenomenon and prove several network synchronization theorems especially we show that synchronization of such a time varying dynamical network is completely determined by the inner coupling matrix and by the eigenvalues and the corresponding eigenvectors of the coupling configuration matrix of the network

generalized quadratic stability for continuous time singular systems with nonlinear perturbation this note considers the generalized quadratic stability problem for continuous time singular system with nonlinear perturbation the perturbation is a function of time and system state and satisfies a lipschitz constraint in this work a sufficient condition for the existence and uniqueness of solution to the singular system is firstly presented then by using s procedure and matrix inequality approach a necessary and sufficient condition is presented in terms of linear matrix inequality under which the maximal perturbation bound is obtained to guarantee the generalized quadratic stability of the system that is the system remains exponential stable and the nominal system is regular and impulse free furthermore robust stability for nonsingular systems with perturbation can be obtained as a special case finally the effectiveness of the developed approach for both singular and nonsingular systems is illustrated by numerical examples

an adaptive finite element approach for frictionless contact problems the derivation of an a posteriori error estimator for frictionless contact problems under the hypotheses of linear elastic behaviour and infinitesimal deformation is presented the approximated solution of this problem is obtained by using the finite element method a penalization or augmented lagrangian technique is used to deal with the unilateral boundary condition over the contact boundary an a posteriori error estimator suitable for adaptive mesh refinement in this problem is proposed together with its mathematical justification up to the present time this mathematical proof is restricted to the penalization approach several numerical results are reported in order to corroborate the applicability of this estimator and to compare it with other a posteriori error estimators copyright 2001 john wiley sons ltd

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

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

a 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

exponential mean square stability of time delay singular systems with markovian switching and nonlinear perturbations abstract this paper considers exponential stability in mean square of singular markovian jump systems the systems under consideration involve nonlinear perturbation and time varying delays by using the lyapunov krasovskii functional delay dependent stability conditions in terms of linear matrix inequality lmi are addressed which guarantee exponential mean square stability and a prescribed h performance index for the considered systems two numerical examples are given to illustrate the effectiveness of the proposed main results

l2 l synchronization for singularly perturbed complex networks with semi markov jump topology abstract this paper is concerned with the problem of l 2 l synchronization for singularly perturbed complex networks spcns with semi markov jump topology in which the phenomenon of the singular perturbation is fully taken into consideration the topology of complex dynamical network is time varying switching regulated by the semi markov jump mechanism the priority of this work is to obtain some conditions which ensure the underlying complex dynamical network cdn is stochastically synchronized with a stated l 2 l performance level based on lyapunov method and convex optimization technique the synchronization conditions can be obtained via solving convex optimization problems finally the correctness and validity of our proposed synchronization method are well demonstrated by a simulation example

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

semidefinite relaxations for non convex quadratic mixed integer programming we present semidefinite relaxations for unconstrained non convex quadratic mixed integer optimization problems these relaxations yield tight bounds and are computationally easy to solve for medium sized instances even if some of the variables are integer and unbounded in this case the problem contains an infinite number of linear constraints these constraints are separated dynamically we use this approach as a bounding routine in an sdp based branch and bound framework in case of a convex objective function the new sdp bound improves the bound given by the continuous relaxation of the problem numerical experiments show that our algorithm performs well on various types of non convex instances

a novel three dimensional contact finite element based on smooth pressure interpolations this article proposes a new three dimensional contact finite element which employs continuous and weakly coupled pressure interpolations on each of the interacting boundaries the resulting formulation circumvents the geometric bias of one pass methods as well as the surface locking of traditional two pass node on surface methods a lagrange multiplier implementation of the proposed element is validated for frictionless quasi static contact by a series of numerical simulations published in 2001 by john wiley sons ltd

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

ellipsoid bounds for convex quadratic integer programming solving convex quadratic integer minimization problems by a branch and bound algorithm requires tight lower bounds on the optimal objective value to obtain such dual bounds we follow the approach of c buchheim a caprara and a lodi math program 135 2012 pp 369 395 and underestimate the objective function by another convex quadratic function that can be minimized over the integers by simply rounding its continuous minimizer in geometric terms we approximate the sublevel sets of the original objective function by auxiliary ellipsoids having the strong rounding property introduced by r hu bner and a scho bel european j oper res 237 2014 pp 404 410 we first consider axisparallel ellipsoids corresponding to separable convex quadratic functions and show how to efficiently compute an axisparallel ellipsoid yielding the tightest lower bound both in the situation where the location of the continuous minimizer is given and in the situation where it varies as it happens in a branch and bound approach in the latter case we compute both worst case and average case optimal ellipsoids moreover we consider the class of quasi round ellipsoids from hu bner and scho bel in this case we do not know whether optimal auxiliary ellipsoids can be computed efficiently however we present a heuristic for computing an appropriate quasi round ellipsoid that still yields valid dual bounds it turns out that using this approach within a branch and bound scheme outperforms the approaches based on axisparallel ellipsoid in terms of running times we finally combine both approaches by introducing the concept of quasi axisparallel ellipsoids and present a corresponding extension of the heuristic bound computation

unconditionally stable algorithms for rigid body dynamics that exactly preserve energy and momentum we show that for rigid body dynamics the mid point rule formulated in body co ordinates exactly conserves energy and the norm of the angular momentum for incremental force free motions but fails to conserve the direction of the angular momentum vector further we show that the mid point rule formulated in the spatial representation is in general physically and geometrically meaningless an alternative algorithm is developed which exactly preserves energy and the total spatial angular momentum in incremental force free motions the implicit version of this algorithm is unconditionally stable and second order accurate the explicit version conserves exactly angular momentum in incremental force free motions numerical simulations are presented which illustrate the excellent performance of the proposed procedure even for incremental rotations over 65 degrees the procedure is directly applicable to transient dynamic calculations of geometrically exact rods and shells

a simple algorithm for localized construction of non matching structural interfaces a simple and effective algorithm for the modular construction of non matched interfaces is presented for the partitioned solution of large scale structural problems the formulation is based on a recently developed four field variational principle which introduces a connection frame between the interfaced partitions a key result of the present study is a frame nodal placement criterion that uniquely determines the frame discretization into piecewise linear elements so that the interface patch test condition is satisfied a priori the method is demonstrated with several 2d and 3d example problems