on a special type of solutions of arbitrary higher spin dirac operators in this paper an explicit expression is determined for the elliptic higher spin dirac operator acting on functions f x taking values in an arbitrary irreducible finite dimensional module for the group spin m characterized by a half integer highest weight also a special class of solutions of these operators is constructed and the connection between these solutions and transvector algebras is explained

a contact domain method for large deformation frictional contact problems part 2 numerical aspects this second part of the work describes the numerical aspects of the developed contact domain method for large deformation frictional contact problems the theoretical basis of this contact method is detailed in the first part of this work starting from this the present contribution focuses on describing important algorithmic details that go along with the finite element implementation for two dimensional problems important aspects are the construction of the contact domain mesh via a constraint delaunay triangulation the linearization of the discretized contact contributions and some important technical aspects about the extrapolation procedure used for the predictive active set strategy finally a set of numerical examples is presented to demonstrate the performance of the developed contact strategy demanding static and dynamic contact problems in the context of large deformations including frictional effects as well as self contact show the wide applicability and the robustness of the proposed method

new results on stability analysis for systems with discrete distributed delay the integral inequality technique is widely used to derive delay dependent conditions and various integral inequalities have been developed to reduce the conservatism of the conditions derived in this study a new integral inequality was devised that is tighter than existing ones it was used to investigate the stability of linear systems with a discrete distributed delay and a new stability condition was established the results can be applied to systems with a delay belonging to an interval which may be unstable when the delay is small or nonexistent three numerical examples demonstrate the effectiveness and the smaller conservatism of the method

thermo mechanical contact problems on non matching meshes non matching meshes and domain decomposition techniques based on lagrange multipliers provide a flexible and efficient discretization technique for variational inequalities with interface constraints although mortar methods are well analyzed for variational inequalities its application to dynamic thermo mechanical contact problems with friction is still a field of active research in this work we extend the mortar approach for dynamic contact problems with coulomb friction to the thermo mechanical case we focus on the discretization and on algorithmic aspects of dynamic effects such as frictional heating and thermal softening at the contact interface more precisely we generalize the mortar concept of dual lagrange multipliers to non linear robin type interface conditions and apply local static condensation to eliminate the heat flux numerical examples in the two dimensional and the three dimensional setting illustrate the flexibility of the discretization on non matching meshes

further improvement of jensen inequality and application to stability of time delayed systems this paper is concerned with the delay dependent stability for the linear systems with a time varying delay to get a result in the form of lmi from a lyapunov krasovskii functional an integral inequality is necessary and jensen inequality has been a most powerful inequality in the last few years recently based on wirtinger inequality an improved integral inequality encompassing jensen inequality was proposed and its application to the stability showed a quite improvement in this paper without using wirtinger inequality a further improved integral inequality in the form of infinite series is derived and based on this a delay dependent stability condition in the form of lmi is derived finally its contribution on the stability criterion is shown by well known two examples

a mortar segment to segment contact method for large deformation solid mechanics abstract contact modeling is still one of the most difficult aspects of non linear implicit structural analysis most 3d contact algorithms employed today use node on segment approaches for contacting dissimilar meshes two pass node on segment contact approaches have the well known deficiency of locking due to over constraint in this work we develop and demonstrate a segment to segment contact approach based on the mortar method by eliminating the over constraint this method appears to be much more robust than the node on segment approach furthermore node on segment approaches suffer when individual nodes slide out of contact at contact surface boundaries or when contacting nodes slide from facet to facet this causes jumps in the contact forces due to the discrete nature of the constraint enforcement and difficulties in convergence for implicit solution techniques these jumps in forces are avoided in the segment to segment approach since penetration is measured by the occluded weighted volume which varies smoothly with perturbations until now all mortar schemes have been developed for small deformation sliding and have mainly been applied on flat surfaces here we will present the integration scheme and the linearization approach used for handling the contact surface integrals in the event of large sliding the schemes are designed to conserve linear momentum and can be applied to arbitrarily curved 3d surfaces although expensive our numerical examples demonstrate that the approach is far more robust than even smoothed node on segment contact techniques that is problems previously not solvable with node on segment can now be solved with our segment to segment contact

a primal dual active set algorithm for three dimensional contact problems with coulomb friction in this paper efficient algorithms for contact problems with tresca and coulomb friction in three dimensions are presented and analyzed the numerical approximation is based on mortar methods for nonconforming meshes with dual lagrange multipliers using a nonsmooth complementarity function for the three dimensional friction conditions a primal dual active set algorithm is derived the method determines active contact and friction nodes and at the same time resolves the additional nonlinearity originating from sliding nodes no regularization and no penalization are applied and superlinear convergence can be observed locally in combination with a multigrid method it defines a robust and fast strategy for contact problems with tresca or coulomb friction the efficiency and flexibility of the method is illustrated by several numerical examples

construction of conformally invariant higher spin operators using transvector algebras this paper deals with a systematic construction of higher spin operators defined as conformally invariant differential operators acting on functions on flat space rm with values in an arbitrary half integer irreducible representation for the spin group to be more precise the higher spin version of the dirac operator and associated twistor operators will be constructed as generators of a transvector algebra hereby generalising the well known fact that the classical dirac operator on rm and its symbol generate the orthosymplectic lie superalgebra osp 1 2 to do so we will use the extremal projection operator and its relation to transvector algebras in the second part of the article the conformal invariance of the constructed higher spin operators will be proven explicitly

finite deformation frictional mortar contact using a semi smooth newton method with consistent linearization a two dimensional finite deformation frictional contact formulation with coulomb s law is presented the approach considers multibody contact and is based on a mortar formulation the enforcement of contact constraints is realized with dual lagrange multipliers these alternative multiplier spaces are constructed in a way that the multipliers can easily be eliminated from the global system of equations by static condensation such that the system size does not increase friction kinematic variables are formulated in an objective way and enter non smooth complementarity functions for expressing the contact constraints an active set strategy is derived by applying a semismooth newton method which treats contact nonlinearities material and geometrical nonlinearities in one single iterative scheme by further carrying out a consistent linearization for both normal and frictional contact forces and constraints a robust and highly efficient algorithm for linear and higher order quadratic interpolation is achieved efficiency of the proposed method and quality of results are demonstrated in serveral exemples

consistent treatment of boundaries with mortar contact formulations using dual lagrange multipliers abstract computational modelling of contact problems raises two basic questions which method should be used to enforce the contact conditions and how should this method be discretised the most popular enforcement methods are the lagrange multiplier method the penalty method and combinations of these two a frequently used discretisation method is the so called node to segment approach however this approach might lead to problems like jumps in contact forces loss of convergence or failure to pass the patch test thus in the last few years several segment to segment contact algorithms based on the mortar method were proposed combination of a mortar discretisation with a penalty based enforcement of the contact conditions leads to unphysical penetrations on the other hand a lagrange multiplier mortar method requires additional unknowns hence condensation of the lagrange multipliers is desirable to preserve the initial size of the system of equations this can be achieved by interpolating the lagrange multipliers with so called dual shape functions discretising two contacting bodies leads to opposed contact surface representations of finite element edges called slave and master elements respectively in current versions of dual lagrange multiplier mortar formulations an inconsistency at the boundary appears when only a part of a slave element instead of the entire element belongs to the contact area we present a modified definition of the dual shape functions in such slave elements the basic idea is to construct dual shape functions that fulfill the so called biorthogonality condition within the contact area this leads to consistent mortar matrices also in the boundary region to avoid ill conditioning of the stiffness matrix the modified mortar matrices are weighted with appropriate weighting factors in doing so the corresponding modified lagrange multiplier nodal values are of the same order as the unmodified ones various examples demonstrate the performance of the modified mortar contact algorithm

an unbiased computational contact formulation for 3d friction to high accuracy as is shown a new 3d friction formulation is also proposed that is a direct extension of the 1d setup expressing the friction variables in the parameter space used for the curvilinear surface description the new formulation resorts to classical expressions in the continuum limit the current approach uses c 1 smooth contact surface representations based on either hermite or nurbs interpolation a penalty regularization is considered for the impenetrability and tangential sticking constraints the new unbiased friction formulation is illustrated by several 2d and 3d examples which include an extensive analysis of the model parameters a convergence study and the comparison with a classical biased master slave contact algorithm

a contact domain method for large deformation frictional contact problems part 1 theoretical basis in the first part of this work the theoretical basis of a frictional contact domain method for two dimensional large deformation problems is presented most of the existing contact formulations impose the contact constraints on the boundary of one of the contacting bodies which necessitates the projection of certain quantities from one contacting surface onto the other in this work the contact constraints are formulated on a so called contact domain which has the same dimension as the contacting bodies this contact domain can be interpreted as a fictive intermediate region connecting the potential contact surfaces of the deformable bodies the introduced contact domain is subdivided into a non overlapping set of patches and is endowed with a displacement field interpolated from the displacements at the contact surfaces this leads to a contact formulation that is based on dimensionless strain like measures for the normal and tangential gaps and that exactly passes the contact patch test in addition the contact constraints are enforced using a stabilized lagrange multiplier formulation based on an interior penalty method nitsche method this allows the condensation of the introduced lagrange multipliers and leads to a purely displacement driven problem an active set strategy based on the concept of effective gaps as entities suitable for smooth extrapolation is used for determining the active normal stick and slip patches of the contact domain

2d contact smooth formulation based on the mortar method abstract in this paper we apply a smoothing technique to solve contact problems using a segment to segment formulation based on the mortar method in contact smoothing the c 0 finite element description of the geometry is replaced by an improved smoothed one usually with c 1 continuity so far these techniques have been applied to solve contact problems based on node to segment interaction some numerical examples are solved to compare the performance of the smoothing and non smoothing formulations the examples show that the non smoothed mortar formulation is improved mainly for problems with matching curved surfaces discretized with non conforming meshes

a weighted point based formulation for isogeometric contact abstract in the context of isogeometric contact analysis surfaces of objects can be described smoothly due to the high continuity of the involved shape functions this facilitates construction of a continuous normal field which may be beneficial for modeling of contact problems this property allows for stable collocation of the virtual contact work using considerable less evaluation points than numerical integration while the approximation quality of the computational results is almost the same in this context a weighted point based method pts is introduced as an extension of the point to segment method pts proposed previously by matzen et al 2013 the weights enable transmission of contact stresses instead of contact forces along the contact surfaces in normal direction the non penetration condition is enforced by the lagrange multiplier method combined with the penalty method in tangential direction corresponding to the collocation weights a constant or nurbs lagrange multiplier field is introduced a comparison between the collocation based contact formulations pts pts and a mortar method is drawn showing that weighted collocation is able to achieve almost the same accuracy as the integration based mortar formulation

stability analysis for neural networks with time varying delay based on quadratic convex combination in this paper a novel method is developed for the stability problem of a class of neural networks with time varying delay new delay dependent stability criteria in terms of linear matrix inequalities for recurrent neural networks with time varying delay are derived by the newly proposed augmented simple lyapunov krasovski functional different from previous results by using the first order convex combination property our derivation applies the idea of second order convex combination and the property of quadratic convex function which is given in the form of a lemma without resorting to jensen s inequality a numerical example is provided to verify the effectiveness and superiority of the presented results

delay dependent stability criteria for generalized neural networks with two delay components this paper investigates the delay dependent stability for generalized continuous neural networks with time varying delays a novel lyapunov krasovskii functional lkf that considers more information on activation functions of delayed neural networks and delay upper bounds is developed simultaneously most commonly used techniques for treating the derivative of the lkf are reviewed and compared with each other with the way of introducing slack matrices those techniques are classified into two categories including free weighting matrix fwm based techniques and reciprocally convex combination based techniques it is found that the introduced slack matrices play an important role in conservatism reducing and those four types of fwm based methods lead to same results and are equivalent moreover the obtained criteria are extended to the system with a single time varying delay two numerical examples are given to verify the effectiveness of the proposed method

stability for neural networks with time varying delays via some new approaches this paper considers the problem of delay dependent stability criteria for neural networks with time varying delays first by constructing a newly augmented lyapunov krasovskii functional a less conservative stability criterion is established in terms of linear matrix inequalities second by proposing novel activation function conditions which have not been proposed so far further improved stability criteria are proposed finally three numerical examples used in the literature are given to show the improvements over the existing criteria and the effectiveness of the proposed idea

an approximate numerical method for solving cauchy singular integral equations composed of multiple implicit parameter functions with unknown integral limits in contact mechanics abstract cauchy singular integral equations are widely used in physics and mathematics especially in solid contact mechanics the solution of cauchy singular integral equations composed of explicit functions has already been achieved in existing research however when dealing with the contact problem between two solid bodies with irregular surfaces described by implicit parametric functions difficulties arise when trying to solve the cauchy singular integral because it is composed of multiple implicit parameter functions moreover the integral limits are unknown and constrained by physical characteristics to solve this kind of problem an approximate calculation method with high accuracy will be provided in this paper specifically based on the quadrature method and taking the constraint function of the boundary as the convergence criterion both the integral limits satisfying the physical characteristics condition and the solution of the cauchy singular integral equations composed of multiple parameter functions can be derived by an iterative method finally five different examples are calculated using the new method and the absolute errors between the approximate values provided by the new method and the true values are analysed

mortar based frictional contact formulation for higher order interpolations using the moving friction cone abstract finite element discretizations including contact usually apply the standard nts node to segment element thus a coupling with higher order solid elements leads to inconsistencies in the transmission of contact stresses one can circumvent this using the mortar method which includes a weak projection of the contact constraints in this paper we present a penalty formulation based on the mortar concept for two dimensional large deformation frictional contact the discretization of the contact surfaces contains quadratic approximations which can be used within a quadratic approximation of the solid elements to obtain a simple and efficient matrix formulation the moving friction cone algorithm is applied

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

on the contact domain method a comparison of penalty and lagrange multiplier implementations this work focuses on the assessment of the relative performance of the so called contact domain method using either the lagrange multiplier or the penalty strategies the mathematical formulation of the contact domain method and the imposition of the contact constraints using a stabilized lagrange multiplier method are taken from the seminal work as cited later whereas the penalty based implementation is firstly described here although both methods result into equivalent formulations except for the difference in the constraint imposition strategy in the lagrange multiplier method the constraints are enforced using a stabilized formulation based on an interior penalty method which results into a different estimation of the contact forces compared to the penalty method several numerical examples are solved to assess certain numerical intricacies of the two implementations the results show that both methods perform similarly as one increases the value of the penalty parameter or decreases the value of the stabilization factor in case of the lagrange multiplier method however there seems to exist a clear advantage in using the lagrange multiplier based strategy in a few critical situations where the penalty method fails to produce convincing results due to excessive penetration

isogeometric dual mortar methods for computational contact mechanics in recent years isogeometric analysis iga has received great attention in many fields of computational mechanics research especially for computational contact mechanics an exact and smooth surface representation is highly desirable as a consequence many well known finite element methods and algorithms for contact mechanics have been transferred to iga in the present contribution the so called dual mortar method is investigated for both contact mechanics and classical domain decomposition using nurbs basis functions in contrast to standard mortar methods the use of dual basis functions for the lagrange multiplier based on the mathematical concept of biorthogonality enables an easy elimination of the additional lagrange multiplier degrees of freedom from the global system this condensed system is smaller in size and no longer of saddle point type but positive definite a very simple and commonly used element wise construction of the dual basis functions is directly transferred to the iga case the resulting lagrange multiplier interpolation satisfies discrete inf sup stability and biorthogonality however the reproduction order is limited to one in the domain decomposition case this results in a limitation of the spatial convergence order to o h3 2 in the energy norm whereas for unilateral contact due to the lower regularity of the solution optimal convergence rates are still met numerical examples are presented that illustrate these theoretical considerations on convergence rates and compare the newly developed isogeometric dual mortar contact formulation with its standard mortar counterpart as well as classical finite elements based on first and second order lagrange polynomials

wirtinger based integral inequality application to time delay systems in the last decade the jensen inequality has been intensively used in the context of time delay or sampled data systems since it is an appropriate tool to derive tractable stability conditions expressed in terms of linear matrix inequalities lmis however it is also well known that this inequality introduces an undesirable conservatism in the stability conditions and looking at the literature reducing this gap is a relevant issue and always an open problem in this paper we propose an alternative inequality based on the fourier theory more precisely on the wirtinger inequalities it is shown that this resulting inequality encompasses the jensen one and also leads to tractable lmi conditions in order to illustrate the potential gain of employing this new inequality with respect to the jensen one two applications on time delay and sampled data stability analysis are provided

free matrix based integral inequality for stability analysis of systems with time varying delay the free weighting matrix and integral inequality methods are widely used to derive delay dependent criteria for the stability analysis of time varying delay systems because they avoid both the use of a model transformation and the technique of bounding cross terms this technical note presents a new integral inequality called a free matrix based integral inequality that further reduces the conservativeness in those methods it includes well known integral inequalities as special cases using it to investigate the stability of systems with time varying delays yields less conservative delay dependent stability criteria which are given in terms of linear matrix inequalities two numerical examples demonstrate the effectiveness and superiority of the method

complete delay decomposing approach to asymptotic stability for neural networks with time varying delays this paper is concerned with the problem of stability of neural networks with time varying delays a novel lyapunov krasovskii functional decomposing the delays in all integral terms is proposed by exploiting all possible information and considering independent upper bounds of the delay derivative in various delay intervals some new generalized delay dependent stability criteria are established which are different from the existing ones and improve upon previous results numerical examples are finally given to demonstrate the effectiveness and the merits of the proposed method

an interior point method for isogeometric contact abstract the interior point method is applied to frictionless contact mechanics problems and is shown to be a viable alternative to the augmented lagrangian approach the method is derived from a mixed formulation which induces a contact discretization scheme in the spirit of the mortar method and naturally delivers slack variables that help constrain the solution to the feasible region the derivation of the algorithm as well as its robustness benefits from the contact interface description that is induced by nurbs based isogeometric volume discretizations various interior point algorithms are discussed including a primal dual approach that satisfies the unilateral contact constraints exactly in addition to two primal approaches that retain an arbitrary barrier parameter the developed algorithms can easily be pursued starting from an augmented lagrangian implementation numerical investigations on benchmark problems demonstrate the efficiency and the robustness of the framework but also highlight current limitations that suggest paths for future research overall the results indicate that the interior point method can challenge the augmented lagrangian method in contact mechanics even displaying potential for higher efficiency and robustness

delay derivative dependent stability for delayed neural networks with unbound distributed delay in this brief based on lyapunov krasovskii functional approach and appropriate integral inequality a new sufficient condition is derived to guarantee the global stability for delayed neural networks with unbounded distributed delay in which the improved delay partitioning technique and general convex combination are employed the lmi based criterion heavily depends on both the upper and lower bounds on time delay and its derivative which is different from the existent ones and has wider application fields than some present results finally three numerical examples can illustrate the efficiency of the new method based on the reduced conservatism which can be achieved by thinning the delay interval

a mixed formulation of mortar based contact with friction abstract a classical three field mixed variational formulation of frictionless contact is extended to the frictional regime the construction of the variational framework with respect to a curvilinear coordinate system naturally induces projected mortar counterparts of tangential kinetic and kinematic quantities while automatically satisfying incremental objectivity of the associated discrete penalty regularized mortar constraints mixed contact variables that contribute to the boundary value problem are then obtained through unconstrained lumped or constrained recovery approaches complemented by uzawa augmentations patch tests and surface locking studies are presented together with local and global quality monitors of the contact interactions in two and three dimensional settings at the infinitesimal and finite deformation regimes

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

a cut cell finite volume finite element coupling approach for fluid structure interaction in compressible flow we present a loosely coupled approach for the solution of fluid structure interaction problems between a compressible flow and a deformable structure the method is based on staggered dirichlet neumann partitioning the interface motion in the eulerian frame is accounted for by a conservative cut cell immersed boundary method the present approach enables sub cell resolution by considering individual cut elements within a single fluid cell which guarantees an accurate representation of the time varying solid interface the cut cell procedure inevitably leads to non matching interfaces demanding for a special treatment a mortar method is chosen in order to obtain a conservative and consistent load transfer we validate our method by investigating two dimensional test cases comprising a shock loaded rigid cylinder and a deformable panel moreover the aeroelastic instability of a thin plate structure is studied with a focus on the prediction of flutter onset finally we propose a three dimensional fluid structure interaction test case of a flexible inflated thin shell interacting with a shock wave involving large and complex structural deformations

rarita schwinger type operators in clifford analysis abstract in this paper we investigate a generalization of the classical rarita schwinger equations for spin 3 2 fields to the case of functions taking values in irreducible representation spaces with weight k 1 2 these fields may be realised as functions taking values in spaces of spherical monogenics earlier considered in f sommen and n van acker 1993 in clifford algebras and their applications in mathematical physics kluwer academic dordrecht norwell ma in this paper we develop the main function theoretic results

new delay dependent stability results for neural networks with time varying delay this paper studies the problem of stability analysis for neural networks nns with a time varying delay unlike the previous works the activation functions are assumed to be neither monotonic nor differentiable nor bounded by defining a more general type of lyapunov functionals some new less conservative delay dependent stability criteria are established in terms of linear matrix inequalities lmis meanwhile the computational complexity of the newly obtained stability conditions is reduced because less variables are involved numerical examples are given to illustrate the effectiveness and the benefits of the proposed method

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

normal contact with high order finite elements and a fictitious contact material contact problems in solid mechanics are traditionally solved using the h version of the finite element method the constraints are enforced along the surfaces of e g elastic bodies under consideration standard constraint algorithms include penalty methods lagrange multiplier methods and combinations thereof for complex scenarios a major part of the solution time is taken up by operations to identify points that come into contact this paper presents a novel approach to model frictionless contact using high order finite elements here we employ an especially designed material model that is inserted into two respectively three dimensional regions surrounding contacting bodies contact constraints are thus enforced on the same manifold as the accompanying structural problem the application of the current material formulation leads to a regularization of the karush kuhn tucker conditions our formulation can be classified as a barrier type method results are obtained for two and three dimensional problems including a hertzian contact problem comparisons to a commercial fea package are provided the proposed formulation works well for non matching discretizations on adjacent contact interfaces and handles self contact naturally since the non penetrating conditions are solved in a physically consistent manner there is no need for an explicit contact search

a mortar based frictional contact formulation for large deformations using lagrange multipliers abstract in this work a lagrange multiplier method is proposed to solve 2d coulomb frictional contact problems in the context of large deformations as the proposed formulation is based on the mortar method the constraints are imposed in a weak integral sense along the contact surface in order to compute the contact integrals we use a numerical integration based on the definition of the kinematical variables gap slip and their variations at the quadrature points the linearization of non linear equations virtual work and contact constraints is developed in order to apply a newton s method the examples show that the numerical integration still preserves the optimal rate of convergence of the finite element solution

a large deformation frictional contact formulation using nurbs based isogeometric analysis this paper focuses on the application of nurbs based isogeometric analysis to coulomb frictional contact problems between deformable bodies in the context of large deformations a mortar based approach is presented to treat the contact constraints whereby the discretization of the continuum is performed with arbitrary order nurbs as well as c0 continuous lagrange polynomial elements for comparison purposes the numerical examples show that the proposed contact formulation in conjunction with the nurbs discretization delivers accurate and robust predictions results of lower quality are obtained from the lagrange discretization as well as from a different contact formulation based on the enforcement of the contact constraints at every integration point on the contact surface copyright 2011 john wiley sons ltd

isogeometric contact analysis geometric basis and formulation for frictionless contact this paper introduces an isogeometric framework for the numerical analysis of contact problems in this approach nurbs is utilized as basis for geometric representation and analysis the contact surfaces and the underlying solids are parameterized in an identical paradigm the use of nurbs geometry eliminates at the onset the geometric discontinuities induced by the traditional faceted approximation contact detection is carried out patch wise instead of element wise leading to an efficient and robust numerical algorithm a strategy for smoothing sharp corners is also described the algorithm does not rely on fillets but entails only a minor perturbation to the nurbs parameters a variationally consistent surface to surface formulation is developed in the context of frictionless contact numerical examples are presented to demonstrate the performance and utility of the method

further results on delay dependent stability criteria of neural networks with time varying delays in this brief paper an augmented lyapunov functional which takes an integral term of state vector into account is introduced owing to the functional an improved delay dependent asymptotic stability criterion for delayed neural networks nns is derived in term of linear matrix inequalities lmis it is shown that the obtained criterion can provide less conservative result than some existing ones when linear fractional uncertainties appear in nns a new robust delay dependent stability condition is also given numerical examples are given to demonstrate the applicability of the proposed approach

the mortar finite element method with lagrange multipliers the present paper deals with a variant of a non conforming domain decomposition technique the mortar finite element method in the opposition to the original method this variant is never conforming because of the relaxation of the matching constraints at the vertices and the edges in 3d of subdomains it is shown that written under primal hybrid formulation the approximation problem issued from a discretization of a second order elliptic equation in 2d is nonetheless well posed and provides a discrete solution that satisfies optimal error estimates with respect to natural norms finally the parallelization advantages consequence of this variant are also addressed

new results on stability analysis for delayed markovian generalized neural networks with partly unknown transition rates the stability of delayed markovian generalized neural networks is studied where the transition rates of the modes are partly unknown the partly unknown transition rates generalize the traditional works that are with all known transition rates then a lyapunov krasovskii functional lkf with a delay product type dpt term is constructed the dpt term is not only simple but also fully utilizes the information of time delay based on the new dpt lkf stability criteria are presented which are with lower computational complexity and less conservative in the end the validity and superiorities of the analytical results are verified by several examples

incorporation of contact for high order finite elements in covariant form the covariant contact description is applied to incorporate the treatment of contact problems into a high order finite element technique a hierarchical enrichment of the shape functions space allows to construct a contact layer finite element combining both exact geometry representation for contact surfaces and a mesh with linear shape functions for the interior of the contacting bodies the developed contact approach can be viewed as a smoothing technique for linear meshes as well as a general application of high order fem the good approximation property for the developed contact layer elements is shown for the classical hertz problem even within a few contact elements discretizing the contact zone

stability analysis of systems with time varying delays via the second order bessel legendre inequality this paper is concerned with the delay dependent stability of systems with time varying delays the novelty relies on the use of the second order bessel legendre integral inequality which is less conservative than the jensen and wirtinger based inequalities unlike similar contributions the features of this inequality are fully integrated into the construction of augmented lyapunov krasovskii functionals leading to novel stability criteria expressed in terms of linear matrix inequalities the stability condition is tested on some classical numerical examples illustrating the efficiency of the proposed method

on some aspects for contact with rigid surfaces surface to rigid surface and curves to rigid surface algorithms abstract special algorithms allowing a simplified description of contact between deformable body and rigid surfaces are developed based on the geometrically exact covariant description of contact a special attention is given to various geometric combinations where the contact can be represented as a contact between surfaces and b contact between a curve and a surface for contact between surfaces leading to the segment to analytical surface stas approach two algorithms can be distinguished based on the selection of a coordinate system for the closest point projection cpp procedure a rigid surface is a slave surface and b rigid surface is a master surface a special combination of both contact kinematics for the surface to surface and for the curve to curve approaches is employed for the contact between a curve and a surface leading to the curve to rigid surface ctrs approach the last algorithm is verified with the well known euler formula for the rope cylinder interaction as well as with a new derived generalization into a 3d spiral rope on a cylinder the developed algorithms can be straightforwardly implemented within an iso geometric approach as well as within the conventional finite elements where rigid surfaces are given by cad patches any type of elements can be employed for the contacting deformable surface curve because the algorithms are formulated in a covariant form

a segment to segment mortar contact method for quadratic elements and large deformations abstract this paper describes a new extension of mortar based segment to segment algorithms for large deformation contact analysis permitting their use when quadratic interpolations are used in the underlying finite element method the work builds upon results previously described by puso and laursen m a puso t a laursen a mortar segment to segment contact method for large deformation solid mechanics comput methods appl mech engrg 193 2004 601 629 m a puso t a laursen a mortar segment to segment frictional contact method for large deformations comput methods appl mech engrg 193 2004 601 629 where methods were developed for quasistatic and implicit dynamic analysis in the context of linear element interpolations here we see that many algorithmic ideas from the linear case can be adopted for use with quadratic elements along with different alternative interpolations of the mortar contact multipliers the result is a class of methods appropriate for use for either mesh tying true large sliding simulation frictionless or frictional and readily admits mixing of element types several numerical examples are given to demonstrate the effectiveness of the approach

decomposition of the polynomial kernel of arbitrary higher spin dirac operators in a series of recent papers we have introduced higher spin dirac operators which are generalisations of the classical dirac operator whereas the latter acts on spinor valued functions the former acts on functions taking values in arbitrary irreducible half integer highest weight representations for the spin group in this paper we describe how the polynomial kernel spaces of such operators decompose in irreducible representations of the spin group we will hereby make use of results from representation theory

new delay dependent stability criteria for neural networks with time varying delay using delay decomposition approach this brief is concerned with the problem of asymptotic stability of neural networks with time varying delays the activation functions are monotone nondecreasing with known lower and upper bounds novel stability criteria are derived by employing new lyapunov krasovskii functional and the integral inequality the developed stability criteria have delay dependencies and the results are characterized by linear matrix inequalities new and less conservative solutions to the global stability problem are provided in terms of feasibility testing numerical examples are finally given to demonstrate the effectiveness of the proposed method

a finite deformation mortar contact formulation using a primal dual active set strategy in recent years nonconforming domain decomposition techniques and in particular the mortar method have become popular in developing new contact algorithms here we present an approach for two dimensional frictionless multibody contact based on a mortar formulation and using a primal dual active set strategy for contact constraint enforcement we consider linear and higher order quadratic interpolations throughout this work so called dual lagrange multipliers are introduced for the contact pressure but can be eliminated from the global system of equations by static condensation thus avoiding an increase in system size for this type of contact formulation we provide a full linearization of both contact forces and normal non penetration and tangential frictionless sliding contact constraints in the finite deformation frame the necessity of such a linearization in order to obtain a consistent newton scheme is demonstrated by further interpreting the active set search as a semi smooth newton method contact nonlinearity and geometrical and material nonlinearity can be resolved within one single iterative scheme this yields a robust and highly efficient algorithm for frictionless finite deformation contact problems numerical examples illustrate the efficiency of our method and the high quality of results

new lyapunov krasovskii functionals for global asymptotic stability of delayed neural networks this brief deals with the problem of global asymptotic stability for a class of delayed neural networks some new lyapunov krasovskii functionals are constructed by nonuniformly dividing the delay interval into multiple segments and choosing proper functionals with different weighting matrices corresponding to different segments in the lyapunov krasovskii functionals then using these new lyapunov krasovskii functionals some new delay dependent criteria for global asymptotic stability are derived for delayed neural networks where both constant time delays and time varying delays are treated these criteria are much less conservative than some existing results which is shown through a numerical example

three dimensional mortar based frictional contact treatment in isogeometric analysis with nurbs a three dimensional mortar based frictional contact treatment in isogeometric analysis with nurbs is presented in the finite deformation regime within a setting where the nurbs discretization of the contact surface is inherited directly from the nurbs discretization of the volume the contact integrals are evaluated through a mortar approach where the geometrical and frictional contact constraints are treated through a projection to control point quantities the formulation delivers a non negative pressure distribution and minimally oscillatory local contact interactions with respect to alternative lagrange discretizations independent of the discretization order these enable the achievement of improved smoothness in global contact forces and moments through higher order geometrical descriptions it is concluded that the presented mortar based approach serves as a common basis for treating isogeometric contact problems with varying orders of discretization throughout the contact surface and the volume

kronecker products for compact semisimple lie groups a review is given of the application of s function techniques to the evaluation of kronecker products of irreducible representations of compact semisimple lie groups explicit formulae are derived for all irreducible representations of all such groups recent developments involving composite young diagrams are brought to fruition and the vexed problem of so2k is dealt with completely new branching rules for the classical groups are given in an appendix these are exploited in the evaluation of kronecker products by means of a technique which is applied to both classical and exceptional groups a discussion is made of various modification rules which are needed to express the final results in standard form

stability analysis for delayed neural networks considering both conservativeness and complexity this paper investigates delay dependent stability for continuous neural networks with a time varying delay this paper aims at deriving a new stability criterion considering tradeoff between conservativeness and calculation complexity a new lyapunov krasovskii functional with simple augmented terms and delay dependent terms is constructed and its derivative is estimated by several techniques including free weighting matrix and inequality estimation methods then the influence of the techniques used on the conservativeness and the complexity is analyzed one by one moreover useful guidelines for improving criterion and future work are briefly discussed finally the advantages of the proposed criterion compared with the existing ones are verified based on three numerical examples

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 computational contact formulation based on surface potentials this work presents the theory and numerical implementation of a contact formulation based on surface potentials the new theory formulates contact based on distance dependent surface interaction potentials and distinguishes between three interaction classes point interaction short range surface interaction and long range surface interaction here the focus is placed on frictionless contact although the first class readily admits frictional sticking contact as is also shown the proposed contact theory provides a unified framework for various contact formulations ranging from numerical constraint formulations like penalty barrier cross constrained and augmented lagrange multiplier methods to physical interaction formulations like cohesive zone models as well as electrostatic gravitational and van der waals interaction apart from recovering classical penalty and barrier formulations the new theory also naturally leads to a modified penalty and barrier method the formulation also recovers classical one pass contact algorithms however the real advantages lie in a novel two pass contact algorithm denoted the two half pass contact algorithm since each pass only accounts for the contact forces acting on the slave body this implies that traction continuity is only satisfied in theory but not imposed a priori in the algorithm instead it is obtained naturally to high accuracy as is demonstrated by several 2d and 3d numerical examples these include sliding contact peeling contact and electrostatic attraction between deformable solids among the examples is a detailed comparison between the new formulation and classical one pass approaches it is further shown that the new contact formulation passes the contact patch test

delay dependent stability for recurrent neural networks with time varying delays this brief is concerned with the stability for static neural networks with time varying delays delay independent conditions are proposed to ensure the asymptotic stability of the neural network the delay independent conditions are less conservative than existing ones to further reduce the conservatism delay dependent conditions are also derived which can be applied to fast time varying delays expressed in linear matrix inequalities both delay independent and delay dependent stability conditions can be checked using the recently developed algorithms examples are provided to illustrate the effectiveness and the reduced conservatism of the proposed result

geometrically exact theory for contact interactions of 1d manifolds algorithmic implementation with various finite element models abstract the intuitive understanding of contact between bodies is based on the geometry of adjoining bodies a more sophisticated approach of an advanced analysis including the application of various numerical methods is to take advantage of the geometry of an analyzed object and describe the problem in the best coordinate system the best coordinate system to describe contact interaction in all its geometrical details is a coordinate system attached to the geometrical features of contacting bodies this leads to a systematical analysis of geometrical situations leading to contact pairs surface to surface line to surface point to surface line to line point to line each contact pair is inherited with a special coordinate system based on its geometrical properties the current contribution is concentrating on contact between 1d manifolds in 3d space this is the majority of edge to edge beam to beam cable to edge etc contact cases the geometrically exact curve to curve contact approach is then systematically combined together with various finite element approaches classical finite elements isogeometric beam finite elements and also with a new developed solid beam approach examples illustrating the diversity of various finite element combinations e g within knot mechanics are shown

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

contact treatment in isogeometric analysis with nurbs abstract we study nurbs based isogeometric analysis of contact problems and compare with standard c 0 continuous lagrange finite elements a knot to surface kts algorithm is developed to treat the contact constraints with nurbs contact surface discretizations qualitative studies deliver satisfactory results for various finite deformation frictionless thermoelastic contact problems quantitative studies based on the hertz problem suggest the need for a relaxation of the mechanical contact constraints that appear in the standard kts approach the improved mortar based kts algorithm delivers robust and accurate results for nurbs discretizations based on numerical examples we conclude that nurbs based isogeometric analysis is a viable technology for contact problems and offers potential accuracy as well as convergence improvements over c 0 continuous finite elements

combined convex technique on delay dependent stability for delayed neural networks in this brief by employing an improved lyapunov krasovskii functional lkf and combining the reciprocal convex technique with the convex one a new sufficient condition is derived to guarantee a class of delayed neural networks dnns to be globally asymptotically stable since some previously ignored terms can be considered during the estimation of the derivative of lkf a less conservative stability criterion is derived in the forms of linear matrix inequalities whose solvability heavily depends on the information of addressed dnns finally we demonstrate by two numerical examples that our results reduce the conservatism more efficiently than some currently used methods

a comprehensive review of stability analysis of continuous time recurrent neural networks stability problems of continuous time recurrent neural networks have been extensively studied and many papers have been published in the literature the purpose of this paper is to provide a comprehensive review of the research on stability of continuous time recurrent neural networks including hopfield neural networks cohen grossberg neural networks and related models since time delay is inevitable in practice stability results of recurrent neural networks with different classes of time delays are reviewed in detail for the case of delay dependent stability the results on how to deal with the constant variable delay in recurrent neural networks are summarized the relationship among stability results in different forms such as algebraic inequality forms m matrix forms linear matrix inequality forms and lyapunov diagonal stability forms is discussed and compared some necessary and sufficient stability conditions for recurrent neural networks without time delays are also discussed concluding remarks and future directions of stability analysis of recurrent neural networks are given

new approaches on stability criteria for neural networks with interval time varying delays abstract this paper concerns the problem of delay dependent stability criteria for neural networks with interval time varying delays first by constructing a newly augmented lyapunov krasovskii functional and combining with a reciprocally convex combination technique less conservative stability criterion is established in terms of linear matrix inequalities lmis which will be introduced in theorem 1 second by taking different interval of integral terms of lyapunov krasovskii functional utilized in theorem 1 further improved stability criterion is proposed in theorem 2 third a novel approach which divides the bounding of activation function into two subinterval are proposed in theorem 3 to reduce the conservatism of stability criterion finally through two well known numerical examples used in other literature it will be shown the proposed stability criteria achieves the improvements over the existing ones and the effectiveness of the proposed idea

an unbiased nitsche s formulation of large deformation frictional contact and self contact in this paper we propose an extension of nitsche s method for frictional contact in large elastic deformations in fact we develop an unbiased strategy in which no asymmetry is considered between contact surfaces conversely to the master slave strategy this enables to take into account within the same formalism contact of two elastic bodies as well as self contact we provide a numerical study of the performance and robustness of the method

volumetric coupling approaches for multiphysics simulations on non matching meshes summary in finite element analysis of volume coupled multiphysics different meshes for the involved physical fields are often highly desirable in terms of solution accuracy and computational costs we present a general methodology for volumetric coupling of different meshes within a monolithic solution scheme a straightforward collocation approach is compared to a mortar based method for nodal information transfer for the latter dual shape functions based on the biorthogonality concept are used to build the projection matrices thus further reducing the evaluation costs we give a detailed explanation of the integration scheme and the construction of dual shape functions for general first order and second order langrangian finite elements within the mortar method as well as an analysis of the conservation properties of the projection operators moreover possible incompatibilities due to different geometric approximations of curved boundaries are discussed numerical examples demonstrate the flexibility of the presented mortar approach for arbitrary finite element combinations in two and three dimensions and its applicability to different multiphysics coupling scenarios copyright 2016 john wiley sons ltd

node to node scheme for three dimensional contact mechanics using polyhedral type variable node elements abstract a node to node contact scheme which is applicable for three dimensional contact analyses involving large deformations is developed with the aid of polyhedral elements the key issue is to transform nonmatching meshes into matching meshes in a seamless manner because polyhedral elements are allowed to have arbitrary numbers of polygonal faces and nodes they can be used as transition elements for coupling nonmatching meshes in this paper the polyhedral elements make it possible to always maintain node to node contact during the contact deformation the present approach guarantees that the patch test is passed and the nonpenetration condition is satisfied and hence it yields smoother contact pressure with faster convergence than the conventional node to surface or surface to surface contact scheme

global asymptotic stability for a class of generalized neural networks with interval time varying delays this paper is concerned with global asymptotic stability for a class of generalized neural networks nns with interval time varying delays which include two classes of fundamental nns i e static neural networks snns and local field neural networks lfnns as their special cases some novel delay independent and delay dependent stability criteria are derived these stability criteria are applicable not only to snns but also to lfnns it is theoretically proven that these stability criteria are more effective than some existing ones either for snns or for lfnns which is confirmed by some numerical examples

improved delay dependent stability criteria for generalized neural networks with time varying delays abstract this paper is concerned with the problem of stability analysis for generalized neural networks with time varying delays a novel integral inequality which includes several existing inequalities as special cases is presented by employing a suitable lyapunov krasovskii functional lkf and using the proposed integral inequality to estimate the derivative of the lkf improved delay dependent stability criteria expressed in terms of linear matrix inequalities are derived finally four numerical examples are provided to demonstrate the effectiveness and the improvement of the proposed method

a note on wirtinger type integral inequalities for time delay systems different integral inequalities play important role when problems of stability analysis and controller synthesis for time delay systems are considered the connection of jensen s inequality and extended jensen s inequality is well understood now to reduce the conservativeness introduced by the application of jensen s inequality several versions of the wirtinger integral inequality have been published recently this note presents a comparison between some of these inequalities