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

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

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

corotational nonlinear dynamic analysis of thin shell structures with finite rotations a new formulation for corotational nonlinear dynamic analysis of thin shell structures involving large displacements and finite rotations has been presented in this paper by introducing the kinematic description of the geometrically exact quasi static shell model to describe the motion of an arbitrary material point in a triangular shell element the new expressions for the inertial force vector and tangent inertia matrix were derived systematically the elastic deformation was handled by using the consistent symmetrizable equilibrated corotational formulation which is independent with respect to the local finite element modeling an energy momentum conserving algorithm and an energy decaying momentum conserving algorithm were developed for nonlinear dynamic analysis by applying the generalized energy momentum method in the corotational formulation three classic numerical examples including the dynamic response free motion and dynamic buckling of thin shell structures were computed to verify the ac

energy conserving algorithms for a corotational formulation standard nonlinear schemes for the the simulation of elastodynamic problems have several shortcomings when considering high speed rotations to tackle these problems we use a corotational framework and a corresponding specific linearization to design new energy conserving numerical schemes in the two dimensional case an algorithm preserving also angular momentum is presented the existence of a solution for the fully discrete setting of this algorithm is established numerical results illustrate the flexibility and efficiency of the proposed algorithms

energy dissipative momentum conserving time stepping algorithms for finite strain multiplicative plasticity abstract this paper presents a new energy dissipative momentum conserving algorithm for multiplicative models of finite strain plasticity the proposed scheme preserves exactly the conservation laws of linear and angular momenta and leads to the exact energy dissipation between the two computed solutions in a given time step in particular the energy is exactly conserved if the step is elastic thus recovering existing energy momentum conserving schemes in the purely elastic range extensions accommodating a strictly non negative numerical energy dissipation in the high frequency to handle the numerical stiffness of the problem are also discussed briefly these conservation dissipation properties are proven rigorously in the very nonlinear setting of multiplicative finite strain plasticity in fact the analysis drives the design of the new return mapping algorithm proposed to integrate the plastic evolution equations so the above dissipation conservation properties hold these analyses account for the spatial discretization of the problem in the context of the finite element method several representative numerical simulations are presented to illustrate the performance of the new algorithm

existence theorem to the cauchy problem of fuzzy differential equations under compactness type conditions kaleva fuzzy sets and systems 35 1990 389 396 has concluded that the peano theorem does not hold for fuzzy differential equations on en d this paper deals with the cauchy problem of fuzzy differential equations the existence theorems under compactness type conditions are obtained

variational time integrators for finite dimensional thermo elasto dynamics without heat conduction this paper focuses on the formulation of variational integrators vis for finite dimensional thermo elastic systems without heat conduction the dynamics of these systems happen to have a hamiltonian structure after thermal displacements are introduced it is then possible to formulate integrators by taking advantage of standard methods in vi the class of integrators we construct have some remarkable features a they are symplectic b they exactly conserve the entropy of the system or in other words they exactly satisfy the second law of the thermodynamics for reversible adiabatic processes c they nearly exactly conserve the value of the energy for very long times and d they exactly conserve linear and angular momentum we first describe how to adapt any vi for the classical mechanical systems to integrate adiabatic thermo elastic ones and then formulate three new types of integrators the first class based on a generalized trapezoidal rule gives rise to two first order explicit integrators and a second order implicit one by composing then the two first order integrators we construct a second order explicit one finally we formulate a fourth order implicit integrator which is a symplectic partitioned runge kutta method the performance of these new algorithms is showcased through numerical examples copyright 2011 john wiley sons ltd

impulsive stabilization of a class of singular systems with time delays abstract this paper deals with the impulsive stabilization problem for a class of linear singular systems with time delays the stabilization is achieved by only exerting impulsive action on the slow state variables two novel lyapunov methods are presented to determine exponential stability of the impulsively controlled systems for the case where the time delay is unknown and may be time varying a lyapunov razumikhin method is developed in which the razumikhin condition is constructed by exploiting the relation among the fast state variables the slow state variables and their initial values for the case where the delay derivative is strictly less than 1 a descriptor type of impulse time dependent lyapunov functional is introduced which is discontinuous at impulse times but does not grow along the state trajectories by construction by using a convex technique the stability criteria are expressed in terms of linear matrix inequalities lmis then the impulsive controllers can be designed in the framework of lmis the effectiveness and advantages of the proposed methods are confirmed through simulation results

stability criteria for switched and hybrid systems the study of the stability properties of switched and hybrid systems gives rise to a number of interesting and challenging mathematical problems the objective of this paper is to outline some of these problems to review progress made in solving them in a number of diverse communities and to review some problems that remain open an important contribution of our work is to bring together material from several areas of research and to present results in a unified manner we begin our review by relating the stability problem for switched linear systems and a class of linear differential inclusions closely related to the concept of stability are the notions of exponential growth rates and converse lyapunov theorems both of which are discussed in detail in particular results on common quadratic lyapunov functions and piecewise linear lyapunov functions are presented as they represent constructive methods for proving stability and also represent problems in which significant progress has been made we also comment on the inherent difficulty in determining stability of switched systems in general which is exemplified by np hardness and undecidability results we then proceed by considering the stability of switched systems in which there are constraints on the switching rules through both dwell time requirements and state dependent switching laws also in this case the theory of lyapunov functions and the existence of converse theorems are reviewed we briefly comment on the classical lur e problem and on the theory of stability radii both of which contain many of the features of switched systems and are rich sources of practical results on the topic finally we present a list of questions and open problems which provide motivation for continued research in this area

the cauchy problem for continuous fuzzy differential equations abstract we prove a version of the classical peano s theorem for the initial value problem for a fuzzy differential equation in the metric space of normal fuzzy convex sets with distance given by the maximum of the hausdorff distances between level sets

on the formulation of high frequency dissipative time stepping algorithms for nonlinear dynamics part i low order methods for two model problems and nonlinear elastodynamics abstract we present in this paper the development of a class of time stepping algorithms for nonlinear elastodynamics that exhibits the controllable numerical dissipation in the high frequency range required for the robust solution of the resulting numerically stiff systems to motivate and illustrate better the developments in this general case we present first the formulation and analysis of these methods for two simple model problems namely we consider a nonlinear elastic spring mass system and a simplified model of thin elastic beams as it is discussed in detail in this paper the conservation by the numerical algorithm of the momenta and corresponding relative equilibria of these characteristic hamiltonian systems with symmetry is of the main importance these conservation properties lead for a fixed and finite time step to a correct qualitative picture of the phase space where the discrete dynamics takes place even in the presence of the desired and controlled numerical dissipation of the energy this situation is contrasted with traditional dissipative numerical schemes which are shown through rigorous analyses to not only lose their dissipative character in the general nonlinear range but also the aforementioned conservation properties thus leading to a qualitatively distorted approximation of the phase dynamics the key for a successful algorithm in this context is the incorporation of the numerical dissipation in the internal modes of the motion while not affecting the group motions of the systems the algorithms presented in this work accomplish these goals the focus in this first part is given to first order methods representative numerical simulations ranging from applications in nonlinear structural dynamics to nonlinear continuum three dimensional elastodynamics are presented in the context of the finite element method to illustrate these ideas and results

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

fuzzy differential equations abstract in this paper we show the existence and uniqueness of fuzzy solutions of the equation d u t d t f t u t u 0 u 0 e n using the properties of hasegawa s functionals and successive approximation

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

approximate solutions existence and uniqueness of the cauchy problem of fuzzy differential equations abstract the cauchy problem of fuzzy differential equations is investigated by the use of the concept of h differentiability due to m l puri and d a ralescu j math anal appl 91 1983 552 558 the existence and uniqueness theorem is obtained for the solution of the cauchy problem x t f t x t x t 0 x 0 for the fuzzy valued mappings of a real variable whose values are normal convex upper semicontinuous and compactly supported fuzzy sets in r n where the function f satisfies the generalized lipschitz condition

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

a hyperelastic based large strain elasto plastic constitutive formulation with combined isotropic kinematic hardening using the logarithmic stress and strain measures summary this paper addresses the formulation of a set of constitutive equations for finite deformation metal plasticity the combined isotropic kinematic hardening model of the infinitesimal theory of plasticity is extended to the large strain range on the basis of three main assumptions i the formulation is hyperelastic based ii the stress strain law preserves the elastic constants of the infinitesimal theory but is written in terms of the hencky strain tensor and its elastic work conjugate stress tensor and iii the multiplicative decomposition of the deformation gradient is adopted since no stress rates are present the formulation is of course numerically objective in the time integration it is shown that the model gives adequate physical behaviour and comparison is made with an equivalent constitutive model based on the additive decomposition of the strain tensor

variational integrators and the newmark algorithm for conservative and dissipative mechanical systems the purpose of this work is twofold first we demonstrate analytically that the classical newmark family as well as related integration algorithms are variational in the sense of the veselov formulation of discrete mechanics such variational algorithms are well known to be symplectic and momentum preserving and to often have excellent global energy behavior this analytical result is veried through numerical examples and is believed to be one of the primary reasons that this class of algorithms performs so well second we develop algorithms for mechanical systems with forcing and in particular for dissipative systems in this case we develop integrators that are based on a discretization of the lagrange d alembert principle as well as on a variational formulation of dissipation it is demonstrated that these types of structured integrators have good numerical behavior in terms of obtaining the correct amounts by which the energy changes over the integration run

stability analysis of positive descriptor systems abstract in this paper we discuss stability properties of positive descriptor systems in the continuous time as well as in the discrete time case we present characterisations of positivity and establish generalised stability criteria for the case of positive descriptor systems we show that if the spectral projector onto the finite deflating subspace of the matrix pair e a is nonnegative then all stability criteria for standard positive systems take a comparably simple form in the positive descriptor case furthermore we provide sufficient conditions that guarantee entry wise nonnegativity along with positive semidefiniteness of solutions of generalised projected lyapunov equations as an application of the framework established throughout this paper we exemplarily generalise two criteria for the stability of two switched standard positive systems under arbitrary switching to the descriptor case

a consistent co rotational formulation for shells using the constant stress constant moment triangle the facet shell formulation involves the combination of the constant strain membrane triangle with a constant curvature bending triangle the paper describes a technique whereby this facet formulation is extended to handle geometric non linearity by means of a co rotational procedure emphasis is placed on the derivation of a technique that is increment independent with both the internal force vector and tangent stiffness matrix being derived from the total strain measures in a consistent manner

the quasi weierstras form for regular matrix pencils regular linear matrix pencils a e k n n where k q r or c and the associated differential algebraic equation dae e u x ax are studied the wong sequences of subspaces are investigate and invoked to decompose the k n into v w where any bases of the linear spaces v and wtransform the matrix pencil into the quasi weierstras form the quasi weierstras form of the matrix pencil decouples the original dae into the underlying ode and the pure dae or in other words decouples the set of initial values into the set of consistent initial values vand pure inconsistent initial values w 0 furthermore vand ware spanned by the general ized eigenvectors at the finite and infinite eigenvalues resp the quasi weierstras form is used to show how chains of generalized eigenvectors at finite and infinite eigenvalues of a e lead to the well known weierstras form so the latter can be viewed as a generalized jordan form finally it is shown how eigenvector chains constitute a basis for the solution space of e u x ax

on the validity of the peano theorem for fuzzy differential equations abstract kaleva 6 attempted to derive the validity of the classical peano theorem over a locally compact subset of en d based on this attempt kloeden 8 concluded that the peano theorem is also valid over en dp this paper challenges both attempts by counterexamples

on the implementation of rate independent standard dissipative solids at finite strain variational constitutive updates this paper is concerned with an efficient variationally consistent implementation for rate independent dissipative solids at finite strain more precisely focus is on finite strain plasticity theory based on a multiplicative decomposition of the deformation gradient adopting the formalism of standard dissipative solids which allows to describe constitutive models by means of only two potentials being the helmholtz energy and the yield function or equivalently a dissipation functional finite strain plasticity is recast into an equivalent minimization problem in contrast to previous models the presented framework covers isotropic and kinematic hardening as well as isotropic and anisotropic elasticity and yield functions based on this approach a novel numerical implementation representing the main contribution of the paper is given in sharp contrast to by now classical approaches such as the return mapping algorithm and analogously to the theoretical part the numerical formulation is variationally consistent i e all unknown variables follow naturally from minimizing the energy of the considered system consequently several different numerically efficient and robust optimization schemes can be directly employed for solving the resulting minimization problem extending previously published works on variational constitutive updates the advocated model does not rely on any material symmetry and therefore it can be applied to a broad range of different plasticity theories as two examples an anisotropic hill type and a barlat type model are implemented numerical examples demonstrate the applicability and the performance of the proposed implementation

on peano theorem for fuzzy differential equations nieto s theorem states that every fuzzy differential equation with bounded and continuous right hand side admits a solution in this paper we show that the provided proof of this result is not correct

the cauchy problem for complex fuzzy differential equations abstract we discuss the existence of a solution to the cauchy problem for fuzzy differential equations that accommodates the notion of fuzzy sets defined by complex valued membership functions we first propose definitions of complex fuzzy sets and discuss entailed results which parallel those of regular fuzzy numbers we then give two existence results relevant to the cauchy problem for fuzzy differential equations in the case of bounded integral operators these results require either holder continuous or lipschitz continuous response functions

geometrically exact 3d beam theory implementation of a strain invariant finite element for statics and dynamics geometrically exact 3d beam theory has been used as a basis for development of a variety of finite element formulations it has recently become apparent that the important requirement of objectivity of adopted strain measures although provided by the theory itself does not automatically extend to a finite element formulation in this paper we present a new finite element formulation of the geometrically exact 3d beam theory specifically designed to preserve the objectivity of the adopted strain measures in order to do so the current local rotations are interpolated in a manner similar to that adopted in co rotational approaches however no approximations typical for co rotational approaches are introduced into the procedure so in contrast to co rotational formulations the present formulation fully preserves the geometric exactness of the theory a range of numerical examples serves to illustrate the problem and to assess the formulation

a new bernoulli wavelet method for accurate solutions of nonlinear fuzzy hammerstein volterra delay integral equations in this article bernoulli wavelet method has been developed to solve nonlinear fuzzy hammerstein volterra integral equations with constant delay this type of integral equation has a particular case the fuzzy variant of a mathematical model from epidemiology bernoulli wavelets have been generated by dilation and translation of bernoulli polynomials the properties of bernoulli wavelets and bernoulli polynomials are first presented the present wavelet method reduces these integral equations to a system of nonlinear algebraic equations and again these algebraic systems have been solved numerically by newton s method convergence analysis of the present method has been discussed in this article also the results obtained by present wavelet method have been compared with that of by b spline wavelet method some illustrative examples have been demonstrated to show the applicability and accuracy of the present method

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

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

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

ancfis a neurofuzzy architecture employing complex fuzzy sets complex fuzzy sets cfss are an extension of type 1 fuzzy sets in which the membership of an object to the set is a value from the unit disc of the complex plane although there has been considerable progress made in determining the properties of cfss and complex fuzzy logic there has yet to be any practical application of this concept we present the adaptive neurocomplex fuzzy inferential system ancfis which is the first neurofuzzy system architecture to implement complex fuzzy rules and in particular the signature property of rule interference we have applied this neurofuzzy system to the domain of time series forecasting which is an important machine learning problem we find that ancfis performs well in one synthetic and five real world forecasting problems and is also very parsimonious experimental comparisons show that ancfis is comparable with existing approaches on our five datasets this work demonstrates the utility of complex fuzzy logic on real world problems

stabilization of switched linear differential algebraic equations and periodic switching we investigate the stabilizability of switched linear systems of differential algebraic equations daes for such systems we introduce a parameterized family of switched ordinary differential equations that approximate the dynamic behavior of the switched dae a necessary and sufficient criterion for the stabilizability of a switched dae system using time dependent switching is obtained in terms of these parameterized approximations furthermore we provide conditions for the stabilizability of switched daes via fast switching as well as using solely the consistency projectors of the constituent systems the stabilization of switched daes with commuting vector fields is also analyzed

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

fuzzy complex numbers abstract this paper first defines fuzzy complex numbers and shows closure under the basic arithmetic operations it is shown that arithmetic of fuzzy complex numbers may be performed in terms of cuts next two special types of fuzzy complex numbers based on the forms z x iy and z re i for regular complex numbers are investigated introducing a metric on the space of fuzzy complex numbers then allows us to discuss continuity and differentiability of fuzzy complex functions

assumed strain finite element methods for conserving temporal integrations in non linear solid dynamics this paper presents a new class of assumed strain finite elements to use in combination with general energy momentum conserving time stepping algorithms so that these conservation properties in time are preserved by the fully discretized system in space and time the case of interest corresponds to nearly incompressible material responses in the fully non linear finite strain elastic and elastoplastic ranges the new elements consider the classical scaling of the deformation gradient with an assumed jacobian its determinant defined locally through a weighted averaging procedure at the element level the key aspect of the newly proposed formulation is the definition of the associated linearized strain operator or b bar operator the developments presented here start by identifying the conditions that this discrete operator must satisfy for the fully discrete system in time and space to inherit exactly the conservation laws of linear and angular momenta and the conservation dissipation law of energy for elastic and inelastic problems respectively care is also taken of the preservation of the relative equilibria and the corresponding group motions associated with the momentum conservation laws and characterized by purely rotational and translational motions superimposed to the equilibrium deformed configuration with these developments at hand a new general b bar operator is introduced that satisfies these conditions the new operator not only accounts for the spatial interpolations e g bilinear displacements with piece wise constant volume but also depends on the discrete structure of the equations in time the aforementioned conservation dissipation properties of energy and momenta are then proven to hold rigorously for the final numerical schemes unconditionally of the time step size and the material model elastic or elastoplastic different finite elements are considered in this framework including quadrilateral and triangular elements for plane problems and brick elements for three dimensional problems several representative numerical simulations are presented involving in particular the use of energy dissipating momentum conserving time stepping schemes recently developed by the author and co workers for general finite strain elastoplasticity in order to illustrate the properties of the new finite elements including these conservation dissipation properties in time and their locking free response in the quasi incompressible case copyright 2007 john wiley sons ltd

stabilisability of nonlinear systems by means of time dependent switching rules given a family of linear systems which admit an asymptotically stable convex combination the existence of stabilising time dependent switching rules can be proved by using the baker campbell hausd

a general framework for the numerical solution of problems in finite elasto plasticity this article discusses a general framework for the analysis of initial boundary value problems of rate independent finite elasto plasticity based on the theory of green and naghdi a constitutive model is developed within the context of the above theory employing generalized measures of lagrangian strain and work conjugate measures of stress computational implications of the proposed formulation are discussed in conjunction with an implicit time integrator for the differential algebraic equations of plastic flow representative numerical simulations demonstrate the applicability and predictive capacity of the model in the presence of large plastic deformations

complex fuzzy logic a novel framework for logical reasoning termed complex fuzzy logic is presented in this paper complex fuzzy logic is a generalization of traditional fuzzy logic based on complex fuzzy sets in complex fuzzy logic inference rules are constructed and fired in a manner that closely parallels traditional fuzzy logic the novelty of complex fuzzy logic is that the sets used in the reasoning process are complex fuzzy sets characterized by complex valued membership functions the range of these membership functions is extended from the traditional fuzzy range of 0 1 to the unit circle in the complex plane thus providing a method for describing membership in a set in terms of a complex number several mathematical properties of complex fuzzy sets which serve as a basis for the derivation of complex fuzzy logic are reviewed in this paper these properties include basic set theoretic operations on complex fuzzy sets namely complex fuzzy union and intersection complex fuzzy relations and their composition and a novel form of set aggregation vector aggregation complex fuzzy logic is designed to maintain the advantages of traditional fuzzy logic while benefiting from the properties of complex numbers and complex fuzzy sets the introduction of complex valued grades of membership to the realm of fuzzy logic generates a framework with unique mathematical properties and considerable potential for further research and application

numerical stabilization of bilinear control systems extremal lyapunov exponents for bilinear control systems with constrained control values are computed numerically by solving discounted optimal control problems based on this computation a numerical algorithm to calculate stabilizing control functions is developed

volume preserving energy momentum schemes for isochoric multiplicative plasticity abstract this paper presents a new energy dissipative momentum conserving algorithm for multiplicative finite strain plasticity f f e f p that also preserves exactly the plastic volume for isochoric plastic models the new algorithm exhibits exactly the conservation laws of linear and angular momentum of the underlying physical problem as well as its energy evolution a strictly positive energy dissipation in fact the exact energy dissipation is obtained by design during plastic steps while enforcing the plastic consistency i e the yield condition on the final stress appearing in the equations of motion exact energy conservation is attained in particular during elastic steps the aforementioned preservation of the plastic volume is obtained by a new treatment of the geometric structure behind the considered multiplicative models of finite strain plasticity namely we present a new approximation of the reference and elastic metrics whose contractions with the incremental total and elastic strains lead exactly to the increment of the total and elastic natural volumetric strains respectively the elastic metric is defined in the intermediate configuration defined itself by the proper discrete approximation in time of the plastic deformation gradient f p the new algorithm extends to the plastic range existing energy momentum conserving schemes for nonlinear elastic problems but incorporating a new modified elastic stress formula consistent with this new geometric setting the inherited conservation laws of momenta and especially the non negative character of the energy dissipation leads to an improved performance over existing more classical schemes showing numerical instabilities in the considered highly nonlinear geometric setting of large deformations and strains several numerical simulations are presented illustrating these properties

energy conserving time integration scheme for geometrically exact beam an energy conserving finite element formulation for the dynamic analysis of geometrically non linear beam like structures undergoing large overall motions has been developed the formulation uses classical displacement based planar beam finite elements described in an inertial frame it takes into account finite axial bending and shear strains a theoretically consistent approach is used to derive a novel and simple energy conserving scheme using the unconventional incremental strain update rather than the standard strong form numerical examples demonstrate perfect energy and momenta conservation stability and robustness of the scheme and good convergence properties in terms of both the newton raphson method and time step size c 2006 elsevier b v all rights reserved

fuzzy complex numbers representations operations and its analysis abstract as a key theoretical basis of fuzzy complex analysis a new representation of fuzzy complex numbers is proposed in this paper which unifies the exponential form trigonometric form and algebraic form of fuzzy complex numbers and some arithmetic operations are investigated the concepts of strong sum and strong difference are defined in order to simplify the addition and subtraction operations of complex fuzzy numbers and establish the calculus theory of fuzzy complex valued functions the metric between two fuzzy complex numbers the derivative differentiability and analyticity of fuzzy complex valued functions are defined and characterized the necessary and sufficient conditions of the analyticity of fuzzy complex valued functions are investigated furthermore the integral of fuzzy complex valued functions and cauchy integral theorem are given and discussed

asynchronous multi domain variational integrators for nonlinear hyperelastic solids we present the asynchronous multi domain variational time integrators with a dual domain decomposition method for the initial hyperbolic boundary value problem in hyperelasticity variational time integration schemes based on the principle of minimal action within the lagrangian framework are constructed for the equation of motion and implemented into a variational finite element framework which is systematically derived from the three field de veubeke hu washizu variational principle to accommodate the incompressibility constraint present in an analysis of nearly incompressible materials for efficient parallel computing we use the dual domain decomposition method with local lagrange multipliers to ensure the continuity of the displacement field at the interface between subdomains the method for time discretization and the multi domain spatial decomposition enable us to use different types of integrators explicit vs implicit and different time steps on different parts of a computational domain and thus efficiently capture the underlying physics with less computational effort the energy conservation of our nonlinear midpoint asynchronous integration scheme is investigated using the energy method and both local and the global energy error estimates are derived we illustrate the performance of proposed variational multi domain time integrators by means of three examples first the method of manufactured solutions is used to examine the consistency of the formulation in the second example we investigate energy conservation and stability finally we apply the method to the motion of a heterogeneous plane domain where different integrators and time discretization steps are used accordingly with disparate material data of individual parts

initial value problem for fuzzy differential equations under dissipative conditions a new concept of inner product on the fuzzy space e n d is introduced studied and used to prove several theorems stating the existence uniqueness and boundedness of solutions of fuzzy differential equations a stability result is also proved in the same context

energy conserving and decaying algorithms in non linear structural dynamics a generalized formulation of the energy momentum methodwill be developed within the framework of the generalizedmethodwhich allows at the same time guaranteed conservation or decay of total energy and controllable numerical dissipation of unwanted high frequency response furthermore the latter algorithm will be extended by the consistently integrated constraints of energy and momentum conservation originally derived for the constraint energy momentum algorithm the goal of this general approach of implicit energyconserving and decaying time integration schemes is to compare these algorithms on the basis of an equivalent notation by the means of an overall algorithmic design and hence to investigate their numerical properties numerical stability and controllable numerical dissipation of high frequencies will be studied in application to non linear structural dynamics among the methods considered will be the newmark method the classical methods the energy momentum methodwith and without numerical dissipation the constraint energymomentum algorithm and the constraint energy method copyright 1999 john wiley sons ltd

a first order energy dissipative momentum conserving scheme for elasto plasticity using the variational updates formulation abstract in a previous paper l noels l stainier j p ponthot an energy momentum conserving algorithm using the variational formulation of visco plastic updates int j numer methods engrg 65 2006 904 942 the authors demonstrated the efficiency of the variational formulation of elasto plastic updates to develop energy momentum conserving time integration algorithms indeed within such a framework the stress tensor always derives from an incremental potential even when plastic behavior is considered therefore the verification of the conservation of energy in the non linear range can easily be demonstrated the sum of the reversible stored energy and irreversible dissipated energy exactly corresponds to the work of the external forces applied to the structure although this formulation was shown to be accurate and robust the introduction of numerical dissipation for high frequency numerical modes can be necessary to simulate complex phenomena in this work we propose a modification of the variational updates framework to introduce this numerical property leading to a new energy dissipative momentum conserving time integration algorithm for elasto plasticity

constraint energy momentum algorithm and its application to non linear dynamics of shells abstract a modified time integration method is developed for non linear structural dynamics combining controllable algorithmic dissipation of higher modes and at the same time conservation of energy as well as linear and angular momentum although these features seem to be actually inconsistent numerical stability with large time steps for dynamic buckling and snap through problems as well as for dynamical systems with smooth solutions is guaranteed arbitrary implicit one step time integration schemes with newmark approximations are suitable for use as basic algorithms for the proposed method the desired conservation attributes are obtained if the basic algorithm is augmented by energy and momentum constraints the potential of the suggested algorithm is demonstrated by selected applications to non linear dynamics of shell structures

fuzzy differential equations abstract this paper deals with fuzzy set valued mappings of a real variable whose values are normal convex upper semicontinuous and compactly supported fuzzy sets in rn we study differentiability and integrability properties of such functions and give an existence and uniqueness theorem for a solution to a fuzzy differential equation

conservation properties of a time fe method part ii time stepping schemes for non linear elastodynamics in the present paper one step implicit integration algorithms for non linear elastodynamics are developed the discretization process rests on galerkin methods in space and time in particular the continuous galerkin method applied to the hamiltonian formulation of semidiscrete non linear elastodynamics lies at the heart of the time stepping schemes algorithmic conservation of energy and angular momentum are shown to be closely related to quadrature formulas that are required for the calculation of time integrals we newly introduce the assumed strain method in time which enables the design of energy momentum conserving schemes and which can be interpreted as temporal counterpart of the well established assumed strain method for finite elements in space the numerical examples deal with quasi rigid motion as well as large strain motion copyright 2001 john wiley sons ltd

energy momentum consistent finite element discretization of dynamic finite viscoelasticity this paper is concerned with energy momentum consistent time discretizations of dynamic finite viscoelasticity energy consistency means that the total energy is conserved or dissipated by the fully discretized system in agreement with the laws of thermodynamics the discretization is energy momentum consistent if also momentum maps are conserved when group motions are superimposed to deformations the performed approximation is based on a three field formulation in which the deformation field the velocity field and a strain like viscous internal variable field are treated as independent quantities the new non linear viscous evolution equation satisfies a non negative viscous dissipation not only in the continuous case but also in the fully discretized system the initial boundary value problem is discretized by using finite elements in space and time thereby the temporal approximation is performed prior to the spatial approximation in order to preserve the stress objectivity for finite rotation increments incremental objectivity although the present approach makes possible to design schemes of arbitrary order the focus is on finite elements relying on linear lagrange polynomials for the sake of clearness the discrete energy momentum consistency is based on the collocation property and an enhanced second piola kirchhoff stress tensor the obtained coupled non linear algebraic equations are consistently linearized the corresponding iterative solution procedure is associated with newly proposed convergence criteria which take the discrete energy consistency into account the iterative solution procedure is therefore not complicated by different scalings in the independent variables since the motion of the element is taken into account for solving the viscous evolution equation representative numerical simulations with various boundary conditions show the superior stability of the new time integration algorithm in comparison with the ordinary midpoint rule both the quasi rigid deformations during a free flight and large deformations arising in a dynamic tensile test are considered copyright 2009 john wiley sons ltd

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

on a stress resultant geometrically exact shell model part vi conserving algorithms for non linear dynamics in parts i to v of the present work the formulation and finite element implementation of a non linear stress resultant shell model are considered in detail this paper is concerned with the extension of these results to incorporate completely general non linear dynamic response of special interest here is the dynamics of very flexible shells undergoing large overall motion which conserves the total linear and angular momentum and for the hamiltonian case the total energy a main goal of this paper is the design of non linear time stepping algorithms and the construction of finite element interpolations which preserve exactly these fundamental constants of motion it is shown that only a very special class of algorithms namely a formulation of the mid point rule in conservation form exactly preserves the total linear and angular momentum for the hamiltonian case a somewhat surprising result is proved regardless of the degree of non linearity in the stored energy function a generalized mid point rule algorithm always exists which exactly conserves energy the conservation properties of a time stepping algorithm need not and in general will not be preserved by the spatial discretization precise conditions which ensure preservation of these conservation properties are derived a number of numerical simulations are presented which illustrate the exact conservation properties of the proposed methodology

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

stability and stabilizability of switched linear systems a survey of recent results during the past several years there have been increasing research activities in the field of stability analysis and switching stabilization for switched systems this paper aims to briefly survey recent results in this field first the stability analysis for switched systems is reviewed we focus on the stability analysis for switched linear systems under arbitrary switching and we highlight necessary and sufficient conditions for asymptotic stability after a brief review of the stability analysis under restricted switching and the multiple lyapunov function theory the switching stabilization problem is studied and a variety of switching stabilization methods found in the literature are outlined then the switching stabilizability problem is investigated that is under what condition it is possible to stabilize a switched system by properly designing switching control laws note that the switching stabilizability problem has been one of the most elusive problems in the switched systems literature a necessary and sufficient condition for asymptotic stabilizability of switched linear systems is described here

averaging for switched daes convergence partial averaging and stability abstract averaging is a useful technique to simplify the analysis of switched systems in this paper we present averaging results for the class of systems described by switched differential algebraic equations daes conditions on the consistency projectors are given which guarantee convergence towards a non switched averaged system a consequence of this result is the possibility to stabilize switched daes via fast switching we also study partial averaging in case the consistency projectors do not satisfy the conditions for convergence the averaged system is then still a switched system but is simpler than the original the practical interest of the theoretical averaging results is demonstrated through the analysis of the dynamics of a switched electrical circuit

a consistent time fe method for large strain elasto plasto dynamics in the present paper energy consistent momentum conserving time stepping schemes for geometrically nonlinear multiplicative elasto plasto dynamics referred to as ecmc cg methods are developed in this context the entire discretisation procedure of the global equations of motion is based on galerkin methods in space and time whereby special emphasis is placed on the desired conservation properties related to the approximation of time integrals to guarantee energy consistency also for higher order finite elements in time a thermodynamically motivated enhanced stress tensor which defines a non standard quadrature rule is derived for elasto plastic material behaviour concerning the integration of the local evolution equations in time exemplarily a well established first order accurate exponential update is applied and adapted according to the global time stepping scheme based on linear finite elements in time the performance of the resulting scheme is demonstrated by means of several representative numerical examples whereby it is shown that global energy consistency is guaranteed exactly within the calculation accuracy by applying the proposed concepts

hybrid stress triangular finite element with enhanced performance for statics and dynamics abstract in this paper we develop the mixed variational formulation with independent displacement rotation and stress fields based on the work of hughes and brezzi 1989 however we further suppress rotation field to obtain element superior performance for classical continuum case with hybrid stress interpolation the lowest order whitney s interpolation or raviart thomas vector space is employed to discretize stress field which delivers superior performance by enforcing the continuity of traction field across element boundary we further extend this optimal choice of hybrid stress discrete approximation to dynamic analysis by choosing the appropriate time integration scheme that enforces stability for long term computation several numerical simulations are given to illustrate an enhanced performance of the proposed element and algorithm

embedding of level continuous fuzzy sets on banach spaces abstract in this paper we present an extension of the minkowski embedding theorem showing the existence of an isometric embedding between the class f c x of compact convex and level continuous fuzzy sets on a real separable banach space x and c 0 1 b x the banach space of real continuous functions defined on the cartesian product between 0 1 and the unit ball b x in the dual space x also by using this embedding we give some applications to the characterization of relatively compact subsets of f c x in particular an ascoli arzela type theorem is proved and applied to solving the cauchy problem x t f t x t x t0 x0 on f c x

on dimensionality reduction and the stability of a class of switched descriptor systems in this paper we present a dimensionality reduction result for linear descriptor systems this result is then used to derive stability conditions for special classes of switched descriptor systems examples are given to illustrate the efficacy of our stability conditions

stability of fuzzy differential equations with the second type of hukuhara derivative in this paper we consider fuzzy differential equations with the second type of hukuhara derivative with the help of lyapunov like functions we establish stability uniform stability and uniformly asymptotical stability theorems respectively for a class of fuzzy differential equations with the second type of hukuhara derivative besides a very useful comparison principle is derived which connects the stability relationships between fuzzy differential equations with the second type of hukuhara derivative and scalar differential equations in addition some examples are shown to illustrate the effectiveness of the results

the strain based beam finite elements in multibody dynamics we present a strain based finite element formulation for the dynamic analysis of flexible elastic planar multibody systems composed of planar beams we consider finite displacements rotations and strains the discrete dynamic equations of motion are obtained by the collocation method the strains are the basic interpolated variables which makes the formulation different from other formulations the further speciality of the formulation is the strong satisfaction of the cross sectional constitutive conditions at collocation points in order to avoid the nested integrations a special algorithm for the numerical integration over the length of the finite element is proposed the midpoint scheme is used for the time integration the performance of the formulation is illustrated via numerical examples including a stiff multibody system

a framework for finite strain elastoplasticity based on maximum plastic dissipation and the multiplicative decomposition part ii computational aspects computational aspects of the formulation of elastoplasticity proposed in part i of this work employing a multiplicative decomposition and based on the principle of maximum plastic dissipation are examined in detail in particular the implementation of the proposed hyperelastic j2 flow theory is shown to reduce to a trivial modification of the classical radial return algorithm which is amenable to exact linearization this results in a closed form expression for the consistent elastoplastic tangent moduli the algorithmic treatment of the general case is considered subsequently it is emphasized that objective rates and incrementally objective algorithms play no role in the present approach a number of numerical experiments are presented that illustrate the excellent performance of the proposed formulation

existence and uniqueness of solutions to cauchy problem of fuzzy differential equations we studied the cauchy problem of fuzzy dierential equations on the basis of introducing the concept of dierentiation which is a generalization of the denition of h dierentiability due to puri and ralescu 1983 for fuzzy set valued mappings of real variables whose values are in the fuzzy number space e n d the existence and uniqueness theorem is obtained for the cauchy problem x 0 f t x x t 0 x0 when f satises the generalized lipschitz condition c 2000