equivalent spatial and material descriptions of finite deformation elastoplasticity in principal axes abstract a spatial description of the theory of rate independent finite deformation elastoplasticity in which the stress tensor is defined through the strain energy function is discussed the main assumption of isotropic elastic response and invariance requirements under superposed rigid body motion restrict the acceptable forms of the strain energy function to those given in terms of principal values of the strain measure of elastic distortion the formulation is developed on a manifold and the corresponding material description is obtained simply by pull back of the derived spatial form by appealing to the notion of covariance the method of principal axes is systematically exploited to derive the explicit expression for the stress tensor computation for an arbitrary form of the strain energy function and the explicit form of the evolution equation for an arbitrary form of the yield function a model problem of volume preserving plastic flow is discussed in the closure

a constitutive frame of elastoplasticity at large strains based on the notion of a plastic metric abstract the article presents a constitutive framework of large strain elastoplasticity in both the lagrangian and the eulerian geometric setting which takes into account anisotropic material response in summary the key ingredients of this framework are i the introduction of a plastic metric which is assumed to describe locally the history dependent inelastic material response in the sense of an internal variable formulation ii the definition of a convex elastic domain in the space of the local stress like variable conjugate to the plastic metric denoted as the plastic force iii an equivalent lagrangian and eulerian representation of all constitutive functions as isotropic tensor functions in terms of an extended set of arguments denoted as anisotropy variables iv the set up of normality rules for the evolution of the plastic metric and the anisotropy variables yielding a canonical symmetric form of the elastoplastic tangent moduli v a geometrically exact decomposition of the set of constitutive equations into possibly decoupled volumetric and isochoric contributions applications of the constitutive framework are demonstrated by means of several conceptual model problems which cover isotropic initial anisotropic and induced anisotropic elastoplastic response

stress rate and the lagrangian formulation of the finite strain plasticity for a von mises kinematic hardening model abstract the use of the jaumann stress rate in kinematic hardening finite strain plasticity in the case of simple shear generates oscillations in the stress field alternate theories have been introduced to define other stress rates by making use of the polar decomposition and consequently producing increasing shear stress in this work a lagrangian formulation is introduced which for the case of simple shear produces monotonically increasing stress strain relationships the yield criterion is originally expressed in terms of the cauchy stress and subsequently transformed to the lagrangian reference frame the associated flow rule used here preserves the normality rule in the second piola kirchhoff stress space and is equivalent to that of the cauchy stress space this approach preserves the accuracy of the interpretation of the material behavior in the eulcrian reference frame and it also bypasses the use of the jaumann stress rate in the formulation of kinematic hardening finite strain plasticity

on constitutive relations at finite strain hypo elasticity and elasto plasticity with isotropic or kinematic hardening abstract the question of generalization to finite strains of the constitutive relations of infinitesimal strain theory of elasticity and classical elasto plasticity with isotropic and kinematic hardening is critically examined simple generalizations which lead to physically plausible material behaviour are presented the current controversies surrounding i the choice of stress rate in the above generalization and ii the anomaly of oscillatory stresses in kinematic hardening plasticity as discussed by e h lee and others are analyzed it is found that these controversies are easily resolvable

a discussion of stress rates in finite deformation problems abstract it has recently been shown that the finite elastic plastic solution of the simple shear problem exhibits an oscillatory stress response when kinematic hardening is employed while the solution for isotropic hardening gives a monotonically increasing stress this paper analyzes this response on the basis of continuum mechanical descriptions of the problem three objective stress rates are recalled and spatial descriptions of plasticity at finite deformation are reviewed for the usual generalization of the infinitesimal theory as well as a theory based on an invariant measure of true stress in light of the equations for the evolution of the yield surface the hypoelastic solution to the simple shear problem for each of the three stress rates is presented it is shown that the use of the jaumann rate in the generalization of the infinitesimal theory leads to an oscillation in the evolution of the yield surface in simple shear which is explained on the basis of the hypoelastic solution an alternative theory which makes use of the polar decomposition predicts a monotonically increasing shear stress

decentralized state feedback stabilization and robust control of uncertain large scale systems with integrally constrained interconnections abstract this paper is concerned with a problem of stabilization and robust control design for interconnected uncertain systems a new class of uncertain large scale systems is considered in which interconnections between subsystems as well as uncertainties in each subsystem are described by integral quadratic constraints the problem is to design a set of local decentralized controllers which stabilize the overall system and guarantee robust disturbance attenuation in the presence of the uncertainty in interconnections between subsystems as well as in each subsystem the paper presents necessary and sufficient conditions for the existence of such a controller the proposed design is based on recent absolute stabilization and minimax optimal control results and employs solutions of a set of game type riccati algebraic equations arising in h control

an algebraic approach to h output feedback control problems abstract we derive an output feedback controller which stabilizes a system and satisfies a prescribed h norm bound of the closed loop transfer function the proposed design method is available for any system i e there are no restrictions on d12 and d21 this approach utilizes only algebraic operations thus proofs are simple and clear

geometrically non linear and elastoplastic three dimensional shear flexible beam element of von mises type hardening material a three dimensional elastoplastic beam element being capable of incorporating large displacement and large rotation is developed and examined elastoplastic constitutive equations are applied to the beam element based upon the assumption of small deformational strain leading to a material formulation which is completely objective for the application of stress update procedures the continuum type equations of plastic model of j2 mixed hardening are transformed into the beam equations by satisfying beam hypotheses an effective stress update algorithm is proposed to integrate elastoplastic rate equations by means of the so called multistep method which is a method of successive control of residuals on yield surfaces it avoids severe divergence when the displacement increments become large which is usual for the continuation methods material tangent stiffness matrix is derived by using consistent elastoplastic modulus resulting from the integration algorithm and is combined with geometric tangent stiffness matrix different from other elements the present element is shear flexible and can satisfy the plasticity condition in a pointwise fashion a great number of numerical examples are analysed and compared with the literature the proposed beam element is verified to be not only quite accurate but also very effective for the analyses of pre buckling and large deflection collapse of spatial framed structures

a method for robust stabilization related to the popov stability criterion it is well known that the popov stability criterion is equivalent to the existence of a lyapunov function of the lur e postnikov form in this paper this idea is extended to the problem of output feedback robust stabilization the paper defines a notion of absolute stabilization with a lyapunov function of the lur e postnikov form the main result is a necessary and sufficient condition for this property this condition is given in terms of the existence of suitable solutions to a pair of algebraic riccati equations

vorticity and symplecticity in multi symplectic lagrangian gas dynamics the lagrangian multi dimensional ideal compressible gas dynamic equations are written in a multi symplectic form in which the lagrangian fluid labels m i the lagrangian mass coordinates and time t are the independent variables and in which the eulerian position of the fluid element and the entropy are the dependent variables constraints in the variational principle are incorporated by means of lagrange multipliers the constraints are the entropy advection equation s t 0 the lagrangian map equation where is the fluid velocity and the mass continuity equation which has the form where is the jacobian of the lagrangian map in which and is the specific volume of the gas the internal energy per unit volume of the gas corresponds to a non barotropic gas the lagrangian is used to define multi momenta and to develop de donder weyl hamiltonian equations the de donder weyl equations are cast in a multi symplectic form the pullback conservation laws and the symplecticity conservation laws are obtained one class of symplecticity conservation laws give rise to vorticity and potential vorticity type conservation laws and another class of symplecticity laws are related to derivatives of the lagrangian energy conservation law with respect to the lagrangian mass coordinates m i we show that the vorticity symplecticity laws can be derived by a lie dragging method and also by using noether s second theorem and a fluid relabelling symmetry which is a divergence symmetry of the action we obtain the cartan poincare form describing the equations and we discuss a set of differential forms representing the equation system

predictive likelihood inference with applications summary conditional and marginal predictive likelihood are defined and used in predicting un observed or missing data a distinction is made between predictive and estimative goals of a data analysis such methodology and distinctions are illustrated in the context of outlier theory and mixed model ano va the prediction of unobserved or missing data is considered from a likelihood perspective a general predictive likelihood is proposed for such purposes and contrasted with parametric likelihood the resulting maximum likelihood predictor is also compared with the limiting imputation from the em algorithm the new methodology is illustrated and contrasted with estimative likelihood analysis in the context of outlier theory and mixed model ano va predictions are proposed that are based on conditional and marginal predictive likelihoods for the unobserved data which are predictive adaptations of the methods developed by kalbfleisch and sprott 1970 1973 these authors were concerned with the elimination of nuisance parameters in order to make inference about another set of structural parameters prediction in the frame work of parametric distributions involves the elimination of all parameters in such a way that inference about the unobserved data is possible therefore in the predictive setting all para meters are nuisance parameters and the unobserved data now play a role similar to that of the structural parameters various predictive approaches to statistical inference have been advocated principally by geisser 1971 1975 stone 1974 aitchison and dunsmore 1975 and guttman 1970 a survey is provided by geisser 1980 and a brief overview in a parametric setting is presented in the next section following this a conditional likelihood approach is developed and shown to be closely related to the lauritzen 1974 hinkley 1979 likelihood method but specified in a manner allowing for a wider range of applicability a marginal predictive likelihood procedure is also specified which when applicable essentially agrees with the conditional likelihood procedure for the examples considered for a general account of likelihood based inference see fraser

multisymplectic conservation laws for differential and differential difference equations many well known partial differential equations can be written as multisymplectic systems such systems have a structural conservation law from which scalar conservation laws can be derived these c

vorticity and symplecticity in lagrangian fluid dynamics the relationship between potential vorticity pv and the symplectic form is explored for the shallow water equations governing lagrangian particle paths starting with the symplectic form the pv is found by the pull back operation to the reference space at first sight the encoding of pv in the symplectic form appears to be independent of the particle relabelling symmetry the analysis is carried a step further in two ways using the conservation of symplecticity as a starting point the fluxes of symplecticity arise as differential forms and a complete pull back of the flux forms leads to a geometric description of pv conservation secondly symmetry methods are used to give a rigorous connection between particle relabelling symplecticity and pv conservation generalizations of these issues to semi geostrophic flow and three dimensional lagrangian fluid flows and the connection with ertel s theorem are also discussed

a geometric formulation of the conservation of wave action and its implications for signature and the classification of instabilities action symplecticity signature and complex instability are fundamental concepts in hamiltonian dynamics which can be characterized in terms of the symplectic structure in this paper hamiltonian pdes on unbounded domains are characterized in terms of a multisymplectic structure where a distinct differential two form is assigned to each space direction and time this leads to a new geometric formulation of the conservation of wave action for linear and nonlinear hamiltonian pdes and via stokes s theorem a conservation law for symplecticity each symplectic structure is used to define a signature invariant on the eigenspace of a normal mode the first invariant in this family is classical krein signature or energy sign when the energy is time independent and the other spatial signatures are energy flux signs leading to a classification of instabilities that includes information about directional spatial spreading of an instability the theory is applied to several examples the boussinesq equation the water wave equations linearized about an arbitrary stokes s wave rotating shallow water flow and flow past a compliant surface some implications for non conservative systems are also discussed

asymptotic likelihood based prediction functions this paper develops asymptotic prediction functions that approximate the shape of the density of future observations and correct for parameter uncertainty the functions are based on extensions to a definition of predictive likelihood originally suggested by lauritzen and hinkley the prediction function is shown to possess efficiency properties based on the kullback leibler measure of information loss examples of the application of the prediction function and the derivation of relative efficiency are shown for linearnormal models nonnormal models and arch models

absolute stabilization and minimax optimal control of uncertain systems with stochastic uncertainty this paper is concerned with existence and optimality properties of so called guaranteed cost controllers for an uncertain system subject to structured uncertainty the uncertainty in the system is assumed to have a stochastic character and to satisfy certain stochastic integral constraints it is shown that a minimax optimal guaranteed cost state feedback controller for a stochastic system can be synthesized as a state feedback controller absolutely stabilizing this system for each initial state of the system this controller can be found by parametric optimization of solutions of a parameter dependent generalized matrix riccati equation arising in stochastic h infty theory

nonlinear versus linear control in the absolute stabilizability of uncertain systems with structured uncertainty this note considers a stabilization problem for a class of uncertain linear systems containing structured uncertainty described by a certain integral quadratic constraint the notion of stabilizability considered is that of absolute stabilizability the main result gives a necessary and sufficient condition for the absolute stabilizability of this class of uncertain systems in terms of the existence of a solution to a corresponding diagonally scaled h sup spl infin control problem it follows from this result that absolute stabilizability via nonlinear control implies absolute stabilizability via linear control

on the relationship between the eulerian and lagrangian descriptions of finite rigid plasticity the motivation for the present paper is to clarify certain unresolved issues pertaining to the relation between the lagrangian or referential and eulerian or spatial strain space formulations of finite plasticity for conceptual simplicity attention is confined to rigid plastic materials it is shown first that for constitutive equations in which the hardening parameter is a scalar the lagrangian and eulerian descriptions are equivalent and that additionally the choice of objective stress rate is immaterial in the light of these developments the role of objective rates is further explored in connection with more general anisotropic hardening laws which contain a shift tensor a form of the constitutive equation for the rate of the shift tensor is motivated in which the choice of objective rate is arbitrary it is then demonstrated that the structure of the constitutive equations of the theory in both the eulerian and lagrangian descriptions is form invariant under arbitrary transformations of objective rate the approach taken here contrasts with that adopted in a number of recent papers in which preference is given to one particular objective rate or another

robust stabilization of uncertain linear systems quadratic stabilizability and h sup infinity control theory the problem of robustly stabilizing a linear uncertain system is considered with emphasis on the interplay between the time domain results on the quadratic stabilization of uncertain systems and the frequency domain results on h sup infinity optimization a complete solution to a certain quadratic stabilization problem in which uncertainty enters both the state and the input matrices of the system is given relations between these robust stabilization problems and h sup infinity control theory are explored it is also shown that in a number of cases if a robust stabilization problem can be solved via lyapunov methods then it can be also be solved via h sup infinity control theory based methods

robust h infty control of an uncertain system via a stable output feedback controller this technical note presents a new approach to the robust control of an uncertain system via a stable output feedback controller the uncertain systems under consideration contain structured uncertainty described by integral quadratic constraints the controller is designed to achieve absolute stabilization with a specified level of disturbance attenuation the main result involves solving a state feedback version of the problem by solving an algebraic riccati equation dependent on a set of scaling parameters then two further algebraic riccati equations are solved which depend on a further set of scaling parameters

likelihood and other approaches to prediction in dynamic models abstract in this paper we consider the problem of generating multi period predictions from two simple dynamic models an autoregressive model and a geometric random walk the autoregressive model constitutes a useful paradigm for many of the practical problems of prediction because it possesses a number of features that differentiate it sharply from the standard linear regression model the geometric random walk model is widely used in macroeconomics and finance and is fundamentally non normal the ideal situation for the prediction problem would be to know the true density of the future observations unfortunately that density depends on parameters that are unknown and must be estimated we analyze six prediction functions approximations of the true density that attempt to circumvent this problem we contrast the theoretical properties of the likelihood prediction function proposed by cooley and parke 1986 with certainty equivalence prediction functions and mean squared error prediction functions the results of a monte carlo study illustrate the relative performance of the alternative prediction functions for conditional predictions and for the analysis of policy interventions the results confirm the importance of accounting for parameter uncertainty and approximating the true shape of the future density

predictive efficiency for simple non linear models this paper demonstrates the use of exact predictive likelihood functions for simple non linear models a measure of predictive efficiency based on the concept of expected information loss is introduced as a way of comparing alternative prediction functions it is shown that the predictive likelihood function minimizes expected information loss over a wide class of potential prediction functions some monte carlo experiments illustrate the performance of alternative prediction functions in settings where prediction is difficult

on the lagrangian description of vorticity this paper exploits a lagrangian form of the vorticity field that is based on a formula of beltrami the merits of which do not seem to have been fully appreciated a number of new results are readily derived by using the lagrangian description and the classical vorticity theorems are also included the results being purely kinematical apply to all deformable media including viscous fluids and may also be of value in computations

disturbance attenuation and h optimization a design method based on the algebraic riccati equation this note presents a method for designing a state feedback control law to reduce the effect of disturbances on the output of a given linear system the problem under consideration involves attenuating the disturbances to a prespecified level the construction of the state feedback control law requires the solution of a certain algebraic riccati equation by applying the procedure with successively smaller values of the prespecifled disturbance level the result also provides an approach to the h infty optimization problem for the state feedback case

perfect fluid theory and its extensions we review the canonical theory for perfect fluids in euler s and lagrange s formulations the theory is related to a description of extended structures in higher dimensions internal symmetry and supersymmetry degrees of freedom are incorporated additional miscellaneous subjects that are covered include physical topics concerning quantization as well as mathematical issues of volume preserving diffeomorphisms and representations of chern simons terms vortex or magnetic helicity