survey paper transfer functions of distributed parameter systems a tutorial in this tutorial article the rich variety of transfer functions for systems described by partial differential equations is illustrated by means of several examples under various boundary conditions an important feature is the strong influence of the choice of boundary conditions on the dynamics and on system theoretic properties such as pole and zero locations properness relative degree and minimum phase it is sometimes possible to design a controller using the irrational transfer function and several such techniques are outlined more often the irrational transfer function is approximated by a rational one for the purpose of controller design various approximation techniques and their underlying theory are briefly discussed

approximation of linear distributed parameter systems by delay systems the present work addresses continuous time approximation of distributed parameter systems governed by linear one dimensional partial differential equations while approximation is usually realized by lumped systems that is finite dimensional systems we propose to approximate the plant by a time delay system within the graph topology we prove that if the plant admits a coprime factorization in the algebra of bibo stable systems any linear distributed parameter plant can be approximated by a time delay system governed by coupled differential difference equations considerations on stabilization and state space realization are carried out a numerical method for constructive approximation is also proposed and illustrated

transfer functions of regular linear systems part ii the system operator and the lax phillips semigroup this paper is a sequel to a paper by the second author on regular linear systems 1994 referred to here as part i we introduce the system operator of a well posed linear system which for a finite dimensional system described by x ax bu y cx du would be the s dependent matrix s s a si c b d in the general case s s is an unbounded operator and we show that it can be split into four blocks as in the finite dimensional case but the splitting is not unique the upper row consists of the uniquely determined blocks a si and b as in the finite dimensional case but the lower row is more problematic for weakly regular systems which are introduced and studied here there exists a special splitting of s s where the right lower block is the feedthrough operator of the system using s 0 we give representation theorems which generalize those from part i to well posed linear systems and also to the situation when the initial time is we also introduce the lax phillips semigroup t induced by a well posed linear system which is in fact an alternative representation of a system used in scattering theory our concept of a lax phillips semigroup differs in several respects from the classical one for example by allowing an index r which determines an exponential weight in the input and output spaces this index allows us to characterize the spectrum of a and also the points where s s is not invertible in terms of the spectrum of the generator of for various values of the system is dissipative if and only if with index zero is a contraction semigroup

extrapolation vs projection methods for linear systems of equations it is shown that the four vector extrapolation methods minimal polynomial extrapolation reduced rank extrapolation modified minimal polynomial extrapolation and topological epsilon algorithm when applied to linearly generated vector sequences are krylov subspace methods and are equivalent to some well known conjugate gradient type methods a unified recursive method that includes the conjugate gradient conjugate residual and generalized conjugate gradient methods is developed finally the error analyses for these methods are unified and some known and some new error bounds for them are given

implicit algorithm for finite deformation hypoelastic viscoplasticity in fcc metals an implicit objective stress update algorithm is proposed for a hypoelastic viscoplastic model a thermal dynamic yield function which is derived based on the thermal activation analysis and dislocation interaction mechanisms is used along with the consistency approach and the framework of additive viscoplasticity in deriving the proposed model for fcc metals the corotational formulation approach is utilized in developing the proposed model in the finite deformation field for the case of the newton raphson iteration method a new expression for the consistent algorithmic tangent stiffness matrix of rate dependent metals is derived by direct linearization of the stress update algorithm finite element simulations are performed by implementing the proposed viscoplasticity constitutive models in the commercial finite element program abaqus numerical implementation for a simple tensile problem is used for validating the material parameters of the ofhc copper under low and high strain rates and temperatures the numerical results of the adiabatic true stress true strain curves compare very well with the experimental data the effectiveness of the present approach is tested by studying strain localization in a simple plane strain problem results indicate excellent performance of the present framework in describing the strain localization problem and in obtaining mesh independent results copyright 2006 john wiley sons ltd

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

admissibility of unbounded control operators for linear systems described by dot x t ax t bu t where a generates a semigroup on the state space x and b is an unbounded operator some necessary as well as some sufficient conditions are given for b to be admissible i e for any t the state x t should be in x and should depend continuously on the input u in l p this approach begins with an axiomatic description of such a system in terms of a functional equation the results are applied to the wave equation on a bounded interval

a method of finite element tearing and interconnecting and its parallel solution algorithm a novel domain decomposition approach for the parallel finite element solution of equilibrium equations is presented the spatial domain is partitioned into a set of totally disconnected subdomains each assigned to an individual processor lagrange multipliers are introduced to enforce compatibility at the interface nodes in the static case each floating subdomain induces a local singularity that is resolved in two phases first the rigid body modes are eliminated in parallel from each local problem and a direct scheme is applied concurrently to all subdomains in order to recover each partial local solution next the contributions of these modes are related to the lagrange multipliers through an orthogonality condition a parallel conjugate projected gradient algorithm is developed for the solution of the coupled system of local rigid modes components and lagrange multipliers which completes the solution of the problem when implemented on local memory multiprocessors this proposed method of tearing and interconnecting requires less interprocessor communications than the classical method of substructuring it is also suitable for parallel vector computers with shared memory moreover unlike parallel direct solvers it exhibits a degree of parallelism that is not limited by the bandwidth of the finite element system of equations

an efficient stress algorithm with applications in viscoplasticity and plasticity this paper deals with two main topics the first one concerns the equivalence of stress algorithms based on a backward euler step applied on viscoplastic models of chaboche type and their elastoplastic counterpart generally the stress algorithm yields a system of non linear algebraic equations and the corresponding consistent tangent operator occurring in the principle of virtual displacements leads to a system of linear equations this procedure can be obtained utilizing only numerical methods the second topic concerns a special constitutive relation based on a kinematic hardening model using a sum of armstrong frederick terms which is equivalent to a multi surface plasticity model applying this model a so called problem adapted stress algorithm is derived where only one non linear equation must be solved this result is independent of the number of terms in the hardening model furthermore only the viscoplastic algorithm must be implemented since it includes the elastoplastic constitutive model as a special case 1997 by john wiley sons ltd

directed structure at infinity for infinite dimensional systems in this article the structure at infinity of infinite dimensional linear time invariant systems with finite dimensional input and output spaces is discussed it is shown that a diagonal form describing behaviour near infinity can be found this diagonal form is a generalisation of the smith mcmillan form at infinity for rational matrices it is then used to simplify certain solvability conditions of a regulation problem examples on time delay and distributed parameter systems are given

variational inequality in classical plasticity applications to armstrong frederick elasto plastic model abstract in this paper the quasi static initial and boundary value problem for an elasto plastic mixed hardening material is reformulated within the constitutive framework of small strains the plastic factor plays the basic role in describing the rate independent evolution equations for the plastic strain and hardening variables the plastic factor is equivalently represented as the solution of an appropriate local inequality involving the yield function the main idea was to introduce the variational inequality at any time t to be solved for the velocity field and the complementary plastic factor there is the plastic factor in a strain driven process the solution procedure proposed here to solve the initial and boundary value problem is based on the solutions of the variational inequality at time t coupled with an update algorithm in order to evaluate the current state of the material for an incremental deformation process this time the return mapping algorithm is avoided as the values of the plastic factor and the velocity are known at time t as we developed a procedure to simultaneously solve the equilibrium equation coupled with the rate independent evolution equations no necessity to compute the algorithmic elasto plastic tangent moduli occurs the numerical simulations are done for the mixed hardening elasto plastic model involving armstrong frederick kinematic hardening to validate the proposed numerical algorithms we compare the solutions based on the variational inequality and those based on return mapping algorithm computed for the same prager kinematic hardening law

integral control of infinite dimensional linear systems subject to input saturation closing the loop around an exponentially stable single input single output regular linear system subject to a globally lipschitz and nondecreasing actuator nonlinearity and compensated by an integral controller is shown to ensure asymptotic tracking of constant reference signals provided that a the steady state gain of the linear part of the plant is positive b the positive integrator gain is sufficiently small and c the reference value is feasible in a very natural sense the class of actuator nonlinearities under consideration contains standard nonlinearities important in control engineering such as saturation and deadzone

new riccati equations for well posed linear systems we consider the classic problem of minimizing a quadratic cost functional for well posed linear systems over the class of inputs that are square integrable and that produce a square integrable output as is well known the minimum cost can be expressed in terms of a bounded nonnegative self adjoint operator x that in the finite dimensional case satisfies a riccati equation unfortunately the infinite dimensional generalization of this riccati equation is not always well defined we show that x always satisfies alternative riccati equations which are more suitable for algebraic and numerical computations

geometrical numerical algorithms for a plasticity model with armstrong frederick kinematic hardening rule under strain and stress controls in this paper we approach the numerical integration problem of a plasticity model with the armstrong frederick kinematic hardening rule on back stress through a combination of the techniques of integral representation and geometrical integrator first the internal symmetry group of the constitutive model is investigated then we develop two geometrical integrators for strain control and stress control respectively these integrators are obtained by a discretization of the integral representation of the constitutive equations and an exponential approximation of the quasi linear differential equations system for the relative stress which guarantee to retain the consistency condition exactly without the need for any iterations some numerical examples are used to assess the performance of the new algorithms the measures in terms of stress relative errors and also isoerror maps confirm that our schemes are superior to the classical radial return methods

on the implementation of inelastic constitutive equations with special reference to large deformation problems abstract methods for finite element analysis of inelastic problems are reviewed problems with currently popular methods based on rate principles of virtual work are pointed out a formulation is presented based on the exact incremental virtual work equation the procedure for integration of the constitutive rate equations to obtain incremental constitutive equations is based on the assumption of a constant strain rate or straight strain path during the increment full newton raphson iteration is used to solve the resulting set of nonlinear equations the treatment of the constitutive equations in this newton raphson scheme leads to a linearized form which is substantially different from the classical rate equations the procedure is implemented in a finite element program and its effectiveness is shown in a number of examples

an analysis of a new class of integration algorithms for elastoplastic constitutive relations an accuracy analysis of a new class of integration algorithms for finite deformation elastoplastic constitutive relations recently proposed by the authors is carried out in this paper for simplicity attention is confined to infinitesimal deformations the integration rules under consideration fall within the category of return mapping algorithms and follow in a straightforward manner from the theory of operator splitting applied to elastoplastic constitutive relations general rate independent and rate dependent behaviour with plastic hardening or softening associated or non associated flow rules and nonlinear elastic response can be efficiently treated within the present framework isoerror maps are presented which demonstrate the good accuracy properties of the algorithm even for strain increments much larger than the characteristic strains at yielding

non canonical minkowski and pseudo riemann frames of plasticity models with anisotropic quadratic yield criteria abstract including the von mises the drucker prager and the hill there are many material plastic models with the yield criteria based on the quadratic yield functions in this paper we study the associated plastic flow model with an anisotropic yield criterion tc 1 2vt 2sy where is a suitable stress vector and v reflects the asymmetric yield strength in tension and compression and with an anisotropic elastic law k e in the elastic phase we first consider the term tc 1 to be a strain energy which means that the anisotropic tensor c is positive definite and coincides with the elastic tensor k under this additional assumption we can prove that the governing equations of plasticity can be linearized in a non canonical minkowski space the internal symmetry of the plastic equation is a special orthochronous pseudo linear group sl n 1 r a further variable transformation reveals a canonical minkowski structure of which the plastic equation exhibits the proper orthochronous lorentz group symmetry soo n 1 then we release the constraint by allowing the above c 1 to be free which may be positive non positive or even singular for this case the plastic equation becomes highly non linear we approach this problem by converting the non linear constitutive equations to a lie system x a x t x on a pseudo riemann manifold where a sl n 1 r is a real lie algebra of the special orthochronous pseudo linear group sl n 1 r the underlying space in the plastic phase is a cone with the metric tensor indefinite having a signature n 1 and also dependent on the temporal component based on these symmetry groups the exact solutions or the cayley transform are developed which can update the stress point exactly on the yield surface at every time increment without any iteration as numerical examples we calculate the stress responses for the drucker prager and hill models

a backstepping approach to the output regulation of boundary controlled parabolic pdes in this article the output regulation problem for boundary controlled parabolic systems with spatially varying coefficients is solved by applying the backstepping approach thereby the outputs to be controlled are not required to be measurable and can be pointwise distributed or boundary quantities whereas the measurement is located at the boundary by solving the state feedback regulator problem in the backstepping coordinates regulator equations with a simple structure result so that their analysis and solution is facilitated the output feedback regulator design is completed by determining a finite dimensional reference observer and an infinite dimensional disturbance observer for the latter a backstepping approach is presented that consists of a triangular decoupling in the backstepping coordinates this allows a systematic design and the explicit derivation of directly verifiable existence conditions for the disturbance observer it is shown that for the resulting compensator the separation principle holds implying output regulation for the exponentially stable closed loop system with a prescribed stability margin the output regulation results of the article are illustrated by means of a parabolic system with an in domain pointwise controlled output

analysis of the anisotropic viscoplastic damage response of composite laminates continuum basis and computational algorithms the mathematical structure underlying the rate equations of a recently developed constitutive model for the coupled viscoplastic damage response of anisotropic composites is critically examined in this regard a number of tensor projection operators have been identified and their properties were exploited to enable the development of a general computational framework for their numerical implementation using the euler fully implicit integration method in particular this facilitated i the derivation of explicit expressions of the consistent material tangent stiffnesses that are valid for both three dimensional as well as subspace e g plane stress formulations ii the implications of the symmetry or unsymmetry properties of these tangent operators from a thermodynamic standpoint and iii the development of an effective time step control strategy to ensure accuracy and convergence of the solution in addition the special limiting case of inviscid elastoplasticity is treated the results of several numerical simulations are given to demonstrate the effectiveness of the schemes developed

an implicit integration algorithm with a projection method for viscoplastic constitutive equations robinson s viscoplastic model a representative of the so called overstress models is integrated by use of the generalized midpoint rule the solution of the non linear system of algebraic equations arising from time discretization of the constitutive equations is determined using a projection method in combination with newton s method consistent tangent moduli are calculated and the quadratic convergence of the global newton equilibrium iteration is shown the time increment size is controlled by the convergence behaviour of the equilibrium iteration and the accuracy of the numerical integration various numerical examples are considered to demonstrate the efficiency of the methods

prandtl reuss elastoplasticity on off switch and superposition formulae abstract constitutive postulates for prandtl reuss elastoplasticity are selected based on them sufficient and necessary conditions for plastic irreversibility are found to be the yield condition and the straining condition this is then analyzed and it is pointed out that prandtl reuss elastoplasticity is nothing but a two phase linear system with an on off switch which is operated in the pace of an intrinsic measure of plastic irreversibility then the temporally global concept of the switch on time t on and the switch off time t off and their determination and bound estimation is developed owing to the implicit linearity superposition formulae for the stress response are discovered as an example the exact constitutive solutions for circular paths based on the superposition formulae are obtained and t on and t off are determined

output regulation for general linear heterodirectional hyperbolic systems with spatially varying coefficients abstract this article presents a backstepping solution to the output regulation problem for general linear heterodirectional hyperbolic systems with spatially varying coefficients the disturbances can act at both boundaries distributed in domain or at the output to be controlled the latter is defined at a boundary distributed or pointwise in domain and has not to be available for measurement by utilizing backstepping coordinates it is shown that all design equations are explicitly solvable this allows a simple determination of a state feedback regulator that is implemented by a reference and a disturbance observer furthermore an easy evaluation of the existence conditions for the resulting output feedback regulator is possible in terms of the plant transfer behaviour in order to facilitate the parameterization of the regulator the resulting closed loop dynamics is directly related to the design parameters the proposed backstepping based design of the output feedback regulator is demonstrated for an unstable heterodirectional 4 4 hyperbolic system

infinite dimensional continuous time linear systems stabilityand structure analysis the question of exponential and asymptotic stability of infinite dimensional continuous time state space systems is investigated it is shown that every par balanced realization is asymptotically stable conditions are given for par balanced input normal or output normal ealizations to be asymptotically and or exponentially stable the boundedness of the system operators is also studied examples of delay systems are given to illustrate the theory

conditions for robustness and nonrobustness of thestability of feedback systems with respect to small delays inthe feedback loop it has been observed that for many stable feedback control systems the introduction of arbitrarily small time delays into the loop causes instability in this paper we present a systematic frequency domain treatment of this phenomenon for distributed parameter systems we consider the class of all matrix valued transfer functions which are bounded on some right half plane and which have a limit at spinfty along the real axis such transfer functions are called regular under the assumption that a regular transfer function is stabilized by unity output feedback we give sufficient conditions for the robustness and for the nonrobustness of the stability with respect to small time delays in the loop these conditions are given in terms of the high frequency behavior of the open loop system moreover we discuss robustness of stability with respect to small delays for feedback systems with dynamic compensators in particular we show that if a plant with infinitely many poles in the closed right half plane is stabilized by a controller then the stability is not robust with respect to delays we show that the instability created by small delays is itself robust to small delays three examples are given to illustrate these results

a lie poisson bracket formulation of plasticity and the computations based on the lie group so n abstract in this paper we develop a generalized hamiltonian formulation of a perfectly elastoplastic model which is a typical dissipative system on the cotangent bundle of the yield manifold a lie poisson bracket is used to construct the differential equations system the stress trajectory is a coadjoint orbit on the poisson manifold under a coadjoint action by the lie group so n the plastic differential equation is an affine non linear system of which a finite dimensional lie algebra can be constructed and the superposition principle is available for this system accordingly we can construct numerical schemes to automatically preserve the yield surface for perfect plasticity for isotropic hardening material as well as for an anisotropic elastic plastic model then we describe an anisotropic elastic plastic material model without entering the work hardening range and deforming under a specified dissipation rate which can be achieved through a stress dependent feedback control law of strain rate

consistent tangent operators for rate independent elastoplasticity abstract it is shown that for problems involving rate constitutive equations such as rate independent elastoplasticity the notion of consistency between the tangent stiffness operator and the integration algorithm employed in the solution of the incremental problem plays a crucial role in preserving the quadratic rate of asymptotic convergence of iterative solution schemes based upon newton s method within the framework of closest point projection algorithms a methodology is presented whereby tangent operators consistent with this class of algorithms may be systematically developed to wit associative j 2 flow rules with general nonlinear kinematic and isotropic hardening rules as well as a class of non associative flow rules are considered the resulting iterative solution scheme preserves the asymptotic quadratic convergence characteristic of newton s method whereas use of the socalled elastoplastic tangent in conjunction with a radial return integration algorithm a procedure often employed results in newton type of algorithms with suboptimal rate of convergence application is made to a set of numerical examples which include saturation hardening laws of exponential type

the optimized schwarz method with a coarse grid correction optimized schwarz methods osms use robin transmission conditions across the subdomain interfaces the robin parameter can then be optimized to obtain the fastest convergence a new formulation is presented with a coarse grid correction the optimal parameter is computed for a model problem on a cylinder together with the corresponding convergence factor which is smaller than that of classical schwarz methods a new coarse space is presented suitable for osm numerical experiments illustrating the effectiveness of osm with a coarse grid correction both as an iteration and as a preconditioner are reported

on the numerical treatment of finite deformations in elastoviscoplasticity abstract this paper deals with the generalization of a geometric linear viscoplastic model to finite strains and its numerical application we owe the original formulation of the applied model to perzyna and chaboche it includes nonlinear isotropic and kinematic hardening as well as a nonlinear rate dependence the constitutive equations are integrated numerically in the context of a finite element formulation from theoretical considerations it is known that in the case of vanishing viscosity or slow processes rate independent plasticity arises as an asymptotic limit accordingly the numerical formulation includes this property in fact the stress algorithm corresponding to viscoplasticity is reduced to the asymptotic limit in a most simple way namely by setting the viscosity parameter equal to zero furthermore it is shown that the numerical integration of the constitutive model involves the solution of only one nonlinear equation for one scalar unknown this even applies to a sum of armstrong frederick terms the algorithm incorporates the inelastic incompressibility on the level of the gau points numerical computations of examples taken from metal forming technology show the physical significance of the model and the reliability of the numerical algorithm these calculations have been carried out by means of the finite element program psu

some computational aspects of large deformation rate dependent plasticity problems abstract the governing equations for a finite element formulation of boundary value problems for large deformation metal forming processes are derived using a principle of virtual work formulated in a lagrangian reference system the updated lagrangian method is used to simplify the equations the resulting nonlinear equilibrium equations are solved using newton s method a constitutive model for large deformation rate dependent plasticity is developed the model incorporates a one parameter implicit integration operator for stability and accuracy the stressrate strain rate relation is written in terms of the jaumann rate of stress numerous example problems are solved to demonstrate the effectiveness of the numerical algorithms

implementation of cyclic plasticity models based on a general form of kinematic hardening this paper deals with implementation of cyclic plastic constitutive models in which a general form of strain hardening and dynamic recovery is employed to represent the multilinear as well as non linear evolution of back stress first in order to incorporate such a general form of kinematic hardening in finite element methods successive substitution and its convergence are discussed for implicitly integrating stress moreover a new expression of consistent tangent modulus is derived by introducing a set of fourth rank constitutive parameters into discretized kinematic hardening then the constitutive parameters introduced are specified in three cases of the general form of kinematic hardening the three cases have distinct capabilities of simulating ratcheting and cyclic stress relaxation numerical examples are given to verify the convergence in successive substitution and the new expression of consistent tangent stiffness error maps for implicitly integrating stress under non proportional as well as proportional loading are also given to show that the multilinear case of the general form provides high accuracy even if strain increment is very large copyright 2002 john wiley sons ltd

root locii for systems defined on hilbert spaces the root locus is an important tool for analyzing the stability and time constants of linear finite dimensional systems as a parameter often the gain is varied however many systems are modelled by partial differential equations or delay equations these systems evolve on an infinite dimensional space and their transfer functions are not rational in this paper a rigorous definition of the root locus for infinite dimensional systems is given and it is shown that the root locus is well defined for a large class of infinite dimensional systems as for finite dimensional systems any limit point of a branch of the root locus is a zero however the asymptotic behavior can be quite different from that for finite dimensional systems this point is illustrated with a number of examples it is shown that the familiar pole zero interlacing property for collocated systems with a hermitian state matrix extends to infinite dimensional systems with self adjoint generator this interlacing property is also shown to hold for collocated systems with a skew adjoint generator

a return mapping algorithm for plane stress elastoplasticity an unconditionally stable algorithm for plane stress elastoplasticity is developed based upon the notion of elastic predictor return mapping plastic corrector enforcement of the consistency condition is shown to reduce to the solution of a simple nonlinear equation consistent elastoplastic tangent moduli are obtained by exact linearization of the algorithm use of these moduli is essential in order to preserve the asymptotic rate of quadratic convergence of newton methods the accuracy of the algorithm is assessed by means of iso error maps the excellent performance of the algorithm for large time steps is illustrated in numerical experiments

shape design sensitivity analysis of viscoplastic structures abstract design sensitivity analysis of nonlinear viscoplastic structures is developed in the continuum form starting from hamilton s principle constitutive models based on internal variable theory are incorporated in response analysis such models are described by a set of first order nonlinear differential equations with respect to time and some of them allow development of the yield surface the direct variation method is employed to obtain the sensitivity of the response discretization of the analysis and sensitivity equations and computer implementation aspects are discussed the discretized equations are implemented into a computer program and two numerical examples are solved to demonstrate the theory in the numerical examples only material nonlinearity under quasi static loading history is considered and the explicit integration method is employed to integrate the constitutive equations and their design variations the accuracy and efficiency of the developed sensitivity analysis are compared with the central finite difference method cyclic loading and loading rate effects are studied and discussed to show the general applicability of the developed sensitivity formulation

fast and robust numerical solution of the richards equation in homogeneous soil we derive and analyze a solver friendly finite element discretization of a time discrete richards equation based on kirchhoff transformation it can be interpreted as a classical finite element discretization in physical variables with nonstandard quadrature points our approach allows for nonlinear outflow or seepage boundary conditions of signorini type we show convergence of the saturation and in the nondegenerate case of the discrete physical pressure the associated discrete algebraic problems can be formulated as discrete convex minimization problems and therefore can be solved efficiently by monotone multigrid methods in numerical examples for two and three space dimensions we observe l 2 convergence rates of order mathcal o h 2 and h 1 convergence rates of order mathcal o h as well as robust convergence behavior of the multigrid method with respect to extreme choices of soil parameters

best robin parameters for optimized schwarz methods at cross points optimized schwarz methods are domain decomposition methods in which a large scale pde problem is solved by subdividing it into smaller subdomain problems solving the subproblems in parallel and iterating until one obtains a global solution that is consistent across subdomain boundaries fast convergence can be obtained if robin conditions are used along subdomain boundaries provided that the robin parameters p are chosen correctly in the case of second order elliptic problems such as the poisson equation it is well known for two subdomain problems without overlap that the optimal choice is p o h 1 2 where h is the mesh size with the resulting method having a convergence factor of rho 1 o h 1 2 however when cross points are present i e when several subdomains meet at a single point this choice leads to a divergent method in this article we show for a model problem that convergence can occur only if p o h 1 at the cross point thus a different scaling of the ro

a study of type i intermittency of a circular differential equation under a discontinuous right hand side abstract in this paper we study a circular differential equation under a discontinuous periodic input developing a quadratic differential equations system on s 1 and a linear differential equations system in the minkowski space m 3 the symmetry groups of these two systems are respectively pso o 2 1 and so o 2 1 the poincare circle map is constructed exactly and a critical value c of the parameter is identified depending on of the input amplitude the equation may exhibit periodic subharmonic or quasiperiodic motions when varies from c to c there undergoes an inverse tangent bifurcation consequently the resultant poincare circle map offers one route to the quasiperiodicity via a type i intermittency in the parameter range of c the orbit generated by the poincare circle map is either m periodic or quasiperiodic when n m is a rational or an irrational number

bilinear transformation of infinite dimensional state space systems and balanced realizations of nonrational transfer functions the bilinear transform maps the open right half plane to the open unit disk and is therefore a suitable tool for carrying over results for continuous time systems to discrete time systems and vice versa corresponding state space formulae are widely used and well understood for the case of finite dimensional systems in this paper infinite dimensional generalizations of these formulae are studied for a general class of infinite dimensional state space systems in particular it is shown that reachability and observability are carried over and that the reachability and observability gramians are preserved under this transformation young showed that a wide class of nonrational discrete time transfer functions admit a balanced state space representation it is shown that this result carries over to the continuous time situation via the bilinear transformation

a time integration method for the viscoelastic viscoplastic analyses of polymers and finite element implementation the present study introduces a time integration algorithm for solving a non linear viscoelastic viscoplastic ve vp constitutive equation of isotropic polymers the material parameters in the constitutive models are stress dependent the algorithm is derived based on an implicit time integration method computational inelasticity springer new york 1998 within a general displacement based finite element fe analysis and suitable for small deformation gradient problems schapery s integral model is used for the ve responses while the vp component follows the perzyna model having an overstress function a recursive iterative method int j numer meth engng 2004 59 25 45 is employed and modified to solve the ve vp constitutive equation an iterative procedure with predictor corrector steps is added to the recursive integration method a residual vector is defined for the incremental total strain and the magnitude of the incremental vp strain a consistent tangent stiffness matrix as previously discussed in ju j eng mech 1990 116 1764 1779 and simo and hughes computational inelasticity springer new york 1998 is also formulated to improve convergence and avoid divergence available experimental data on time dependent and inelastic responses of high density polyethylene are used to verify the current numerical algorithm the time integration scheme is examined in terms of its computational efficiency and accuracy numerical fe analyses of microstructural responses of polyethylene reinforced with elastic particle are also presented copyright 2009 john wiley sons ltd

accuracy and stability of integration algorithms for elastoplastic constitutive relations an analysis of accuracy and stability of algorithms for the integration of elastoplastic constitutive relations is carried out in this paper reference is made to a very general internal variable formulation of plasticity and to two families of algorithms that generalize the well known trapezoidal and midpoint rules to fit the present context other integration schemes such as the radial return mean normal and closest point procedures are particular cases of this general formulation the meaning of first and second order accuracy in the presence of the plastic consistency condition is examined in detail and the criteria derived are used to identify two second order accurate members of the proposed algorithms a general methodology is also derived whereby the numerical stability properties of integration schemes can be systematically assessed with the aid of this methodology the generalized midpoint rule is seen to have far better stability properties than the generalized trapezoidal rule finally numerical examples are presented that illustrate the performance of the algorithms

transfer function models for distributed parameter systems with impedance boundary conditions abstracta transfer function description is derived for a general class of linear distributed parameter systems dependent on time and one spatial variable suitable functional transformations are the laplace transformation for the time variable and the sturm liouville transformation for the space variable a practical problem is the determination of the eigenfunctions of the sturm liouville transformation since these depend on the type and the parameters of the boundary conditions this contribution shows that the design of a transfer function model can be separated from the correct treatment of the boundary conditions the presented approach exhibits strong parallels to state feedback techniques from control theory examples for an electrical transmission line demonstrate how terminations with arbitrary complex impedances can be considered without redesigning the transmission line model

time varying and adaptive integral control of infinite dimensional regular linear systems with input nonlinearities closing the loop around an exponentially stable single input single output regular linear system subject to a globally lipschitz nondecreasing actuator nonlinearity and compensated by an integral controller with time dependent gain k t is shown to ensure asymptotic tracking of a constant reference signal r provided that a the steady state gain of the linear part of the system is positive b the reference value r is feasible in an entirely natural sense and c the function t mapsto k t monotonically decreases to zero at a sufficiently slow rate this result forms the basis of a simple adaptive control strategy that ensures asymptotic tracking under conditions a and b

exponential stability of coupled beams with dissipative joints a frequency domain approach two examples of coupled euler bernoulli beams with a dissipative joint are considered the joint placements that lead to exponential stability for these systems are characterized the technique used shows input output stability of a related controlled observed system and then shows that in these examples input output stability implies exponential stability in the first example the energy dissipation arises from a discontinuity in the shear at the joint in the second example the energy dissipation arises from a discontinuity in the bending moment at the joint the analysis of this system involves a complete spectrum analysis of the zero dynamics of the associated controlled observed system

integration methods for complex plastic constitutive equations abstract this paper shows new results concerning the finite element computations with complex plastic and viscoplastic constitutive equations the integration procedure then needs special numerical treatments when a large number of internal variables are present or for stiff non linearities implicit and explicit integration methods are compared the general solution proposed can be applied either in plasticity or in viscoplasticity for isotropic or anisotropic materials several options are proposed in the numerical scheme and for the completion step for the semi implicit scheme numerical tests are performed in order to compare the relative performances of the various approaches

transfer functions of regular linear systems part i characterizations of regularity we recall the main facts about the representation of regular linear systems essentially that they can be described by equations of the form x t ax t bu t y t cx t du t like finite dimensional systems but now a b and c are in general unbounded operators regular linear systems are a subclass of abstract linear systems we define transfer functions of abstract linear systems via a generalization of a theorem of foures and segal we prove a formula for the transfer function of a regular linear system which is similar to the formula in finite dimensions the main result is a simple to state but hard to prove necessary and sufficient condition for an abstract linear system to be regular in terms of its transfer function other conditions equivalent to regularity are also obtained the main result is a consequence of a new tauberian theorem which is of independent interest

on the numerical algorithm for isotropic kinematic hardening with the armstrong frederick evolution of the back stress the algorithmic consistency conditions are derived which yield the plastic loading index for the combined isotropic kinematic hardening plasticity with the armstrong frederick evolution equation for the back stress rate independent elastic plastic and rate dependent viscoelastic plastic and elastic viscoplastic material models are all encompassed by the analysis the directions of the plastic and viscoplastic increments of strain are determined from a developed numerical algorithm in conjunction with the radial return method numerical evaluations are presented to compare the predictions of various models under cyclic loading in simple shear the effects of different material parameters on stress response are discussed 2002 elsevier science b v all rights reserved

large simple shear and torsion problems in kinematic hardening elasto plasticity with logarithmic rate abstract large simple shear and torsion problems in plasticity have been the object of a large number of papers sophisticated schemes have been developed e g j appl mech 50 1983 561 that overcome problems encountered cf e g j mech phys solids 48 2000 2231 int j solids struct 37 2000 5037 this paper substantially uses the logarithmic rate acta mechanica 124 1997a 89 which is equally based on strong mathematical and physical principles and therefore may contrast to classical approaches of cited kinds stress responses to large simple shear and torsional deformations in elastoplastic bodies are studied by applying the self consistent kinematic hardening j 2 flow model based on the logarithmic tensor rate recently established by these authors int j plasticity 15 1999 479 the application of the logarithmic stress rate in the elastic rate equation of hypoelastic type results in an exact finite hyperelastic solution in terms of hencky s logarithmic strain the plastic solution is composed of two parts the back stress and the effective stress the kirchhoff stress reduced by the back stress it is shown that the evolution equation of the back stress with the logarithmic rate is integrable to deliver a closed form relation between the back stress and hencky s logarithmic strain and the current stress moreover the effective stress is shown to be governed by a first order nonlinear ordinary differential equation with a small dimensionless material parameter multiplying the highest derivative for which the initial condition is related to the elastic plastic transition and prescribed in terms of the just mentioned small parameter a singular perturbation solution for the just mentioned equation is derived by utilizing the method of matched expansions with the analytical solution derived it is possible to make a detailed study of the coupling effect of material properties including the elastic yielding and hardening properties on elastic plastic responses for the large deformations at issue it is demonstrated that merely with three commonly known classical material constants i e the elastic shear modulus the initial tensile yield stress and the hardening modulus the simple kinematic hardening j 2 flow model with the logarithmic rate may supply satisfactory explanations for salient features of complex behaviour in experimental observation

convergence and stability properties of minimal polynomial and reduced rank extrapolation algorithms the minimal polynomial and reduced rank extrapolation algorithms are two acceleration of convergence methods far sequences of vectors in a recent survey these methods were tested and compared with the scalar vector and topological epsilon algorithms and were observed to be more efficient than the latter it was also observed that the two methods have similar convergence properties the purpose of the present work is to analyze the convergence and stability properties of these methods and to show that they are bona fide acceleration methods when applied to a class of vector sequences that includes those sequences obtained from systems of linear equations by using matrix iterative methods

rotations stress rates and strain measures in homogeneous deformation processes abstract the article draws the distinction between homogeneous and pure homogeneous deformation in the latter mode an orthogonal triad can be identified the principal axes which remain orthogonal throughout the deformation an appropriate strain measure in such processes is that of logarithmic strain furthermore its material derivative equals the rate of deformation tensor in homogeneous processes the deformation gradient tensor is unsymmetric and there is no triad which remains orthogonal throughout this often leads to a description of the actual deformation by means of the polar decomposition theorem the material derivative of the tensor logorithm is no longer simply related to the rate of deformation tensor and this is exemplified herein as a result of material rotation the stress components will vary and constitutive equations which involve stress rate must be formulated to compensate for the rotation a number of objective stress rates are examined herein and employed in a constitutive equation describing a hypoelastic solid the effect of stress rate on the evolution of stresses in the deforming solid is demonstrated for the case when the body undergoes simple rectilinear shear

lie symmetries of finite strain elastic perfectly plastic models and exactly consistent schemes for numerical integrations abstract for finite strain elastic perfectly plastic models the use of non spinning objective stress rates leads to cubic degree non linear differential equations as well as the coupling of deviatoric and volumetric constitutive equations the governing equations reduce to quadratic non linearity and the coupling disappears when spinning objective stress rates are used in order to effectively deal with these non linearities we first convert the non linear constitutive equations into a lie type system x ax a so 5 1 for x in the minkowski spacetime m 5 1 which has an indefinite metric g of signature 5 1 however for spinning objective stress rates a merely depends on t through deformation history and the above equation reduces to a time varying linear system the new representation admits a lie symmetry of the proper orthochronous lorentz group soo 5 1 in the plastic phase in terms of x the yield condition is transformed to a null cone condition x t gx 0 in m 5 1 due to this nullity we thus assign a quaternionic hermitian matrix to represent x and convert the six dimensional system to a more economic lower dimensional quaternionic two component spinor system q q sl 2 h in the two dimensional spinor space the lie symmetry is found to be sl 2 h the mapping of which onto soo 5 1 is derived in addition to the mapping between so 5 1 and sl 2 h an isomorphic mapping between sl 2 h and su 4 is also established the latter of which generates the group su 4 finally according to these lie symmetries the numerical schemes preserving the group properties are developed which satisfy the consistency condition 1 exactly for every time step without iterations at all

transfer functions for infinite dimensional systems in this paper we study three definitions of the transfer function for an infinite dimensional system the first one defines the transfer function as the expression c si a 1 b d in the second definition the transfer function is defined as the quotient of the laplace transform of the output and input with initial condition zero in the third definition we introduce the transfer function as the quotient of the input and output when the input and output are exponentials we show that these definitions always agree on the right half plane bounded to the left by the growth bound of the underlying semigroup but that they may differ elsewhere

the 2 lagrange multiplier method applied to nonlinear transmission problems for the richards equation in heterogeneous soil with cross points we formulate the 2 lagrange multiplier method for the richards equation in heterogeneous soil this allows a rigorous formulation of a discrete version of the richards equation on subdomain decompositions involving cross points using kirchhoff transformation the individual subdomain problems can be transformed into convex minimization problems and solved efficiently using a monotone multigrid method we discuss and compare weak formulations of the time discrete and fully discretized multidomain problem it is shown that in the case of two subdomains when solving the resulting discrete system with a richardson iteration the new method is equivalent to a parallel version of the nonlinear robin method for the richards equation proposed in h berninger and o sander comput vis sci 13 2010 pp 187 205 we give numerical results for a problem with realistic soil parameters

riccati equations for stable well posed linear systems the generic case under the generic assumption that zero is in the resolvent set of the generator we show that the optimal control problem for a stable well posed linear system is equivalent to a control problem for its reciprocal system which has bounded generating operators consequently the operator x that defines the optimal cost satisfies a riccati equation with bounded operators previous results needed various regularity assumptions to obtain x as a solution to a riccati equation resembling that in the finite dimensional theory

space time domain decomposition for two phase flow between different rock types in previous work e ahmed s ali hassan c japhet m kern and m vohralik a posteriori error estimates and stopping criteria for space time domain decomposition for two phase flow between different rock types the smai journal of computational mathematics 5 2019 pp 195 227 https doi org 10 5802 smai jcm 47 a space time domain decomposition method was proposed for two phase ow in a porous medium composed of two different rock types so that the capillary pressure field is discontinuous at the interface between the rocks for this nonlinear and degenerate parabolic problem with nonlinear and discontinuous transmission conditions on the interface the optimized schwarz waveform relaxation method oswr with robin or ventcell transmission conditions was considered a guaranteed and fully computable a posteriori error estimate was derived which in particular took into account the domain decomposition error in this paper we provide a mathematical and numerical analysis of this space time domain decomposition method in the robin case complete numerical approximation is achieved by a finite volume scheme in space and the lowest order discontinuous galerkin method in time we prove the existence of a weak solution of the two phase ow subdomain problem with robin boundary conditions by analyzing the convergence of the finite volume scheme the domain decomposition algorithm is based on the solution of space time nonlinear subdomain problems over the whole time interval allowing for different time steps in dfferent parts of the domain adapted to the physical properties of each subdomain and we show that such an algorithm is well defined numerical experiments on three dimensional problems with different rock types illustrate the performance of the domain decomposition method

the choice of objective rates in finite elastoplasticity general results on the uniqueness of the logarithmic rate a eulerian rate formulation of finite elastoplasticity is a composite one composed of a rate equation for elastic behaviour and a flow rule for plastic behaviour as well as an evolution equation for hardening behaviour in which objective eulerian tensor rates are used among a large variety of objective rates actually infinitely many how to choose suitable ones has been one of the crucial points in finite elastoplasticity it is realized that the foregoing composite formulation of elastoplasticity should fulfil certain consistency criteria in order to avoid inconsistencies or contradictions these criteria narrow the choice of objective rates these authors bruhns and co workers and xiao and co workers have recently introduced the self consistency criterion in a composite formulation of elastoplasticity the rate equation intended for characterization of elastic behaviour should be exactly integrable to deliver an elastic relation it has been demonstrated in the work of the aforementioned authors that if a composite formulation of elastoplasticity with objective rates is required to fulfil the just stated self consistency criterion as it should be then the newly discovered logarithmic rate is the only possible choice among all objective corotational rates including the zaremba jaumann rate and the green naghdi rate etc in the afore mentioned result non corotational rates including oldroyd rates cotter rivlin rate and truesdell rate etc are not taken into consideration in general it is the main goal of this paper to further establish the uniqueness of the logarithmic rate among all corotational and non corotational objective rates essential to the attainment of this goal is the use of the yielding stationarity criterion the vanishing of the stress rate implies that the yield function is stationary it is shown that the just stated criterion is necessary for a composite eulerian rate formulation of finite elastoplasticity to be consistent and means that the stress rate must be a corotational rate the main goal of this article is thus attained by combining the just stated result and the established result stated before

output regulation for coupled linear parabolic pides abstract this paper presents a backstepping based solution of the output regulation problem for coupled parabolic partial integro differential equations pides with spatially varying coefficients and distinct diffusion coefficients the considered setup assumes in domain as well as boundary disturbances while the output to be controlled can be defined distributed in domain pointwise in domain or at the boundaries and need not be measured by assuming a finite dimensional signal model which may also be non diagonalizable a systematic solution of the output regulation problem is presented by making use of observer based feedforward control existence conditions for the corresponding regulator are formulated in terms of the plant transfer behaviour for the resulting closed loop system exponential stability with a prescribed decay rate is verified the regulator design for two unstable coupled parabolic pides demonstrates the results of the paper

a priori error estimates for a mixed finite element discretization of the richards equation a mixed finite element discretization is applied to richards equation a nonlinear possibly degenerate parabolic partial differential equation modeling water flow through porous medium the equation is considered in its pressure formulation and includes both variably and fully saturated flow regime characteristic for such problems is the lack in regularity of the solution to handle this we use a time integrated scheme we analyze the scheme and present error estimates showing its convergence

two level domain decomposition methods with lagrange multipliers for the fast iterative solution of acoustic scattering problems we present two different but related lagrange multiplier based domain decomposition dd methods for solving iteratively large scale systems of equations arising from the finite element discretization of high frequency exterior helmholtz problems the proposed methods are essentially two distinct extensions of the regularized finite element tearing and interconnecting feti method to indefinite or complex problems the first method employs a single lagrange multiplier field to glue the local solutions at the subdomain interface boundaries the second method employs two lagrange multiplier fields for that purpose the key ingredients of both of these feti methods are the regularization of each subdomain matrix by a complex lumped mass matrix defined on the subdomain interface boundary and the preconditioning of the global interface problem by a coarse second level problem constructed with planar waves we show numerically that both methods are scalable with respect to the mesh size the subdomain size and the wavenumber but that the feti method with a single lagrange multiplier field labeled feti h h for helmholtz in this paper delivers superior computational performances we apply the feti h method to the parallel solution on a 24 processor origin 2000 of an acoustic scattering problem with a submarine shaped obstacle and report performance results that highlight the unique efficiency of this dd method for the solution of high frequency acoustic scattering problems

robustness and continuity of the spectrum for uncertain distribution parameter systems we analyze the spectrum of a class of abstract partial differential equations with boundary feedback control if we interpret the feedback as a perturbation then we obtain a robustness radius for spectrum placement we obtain continuity of the spectrum using this radius and rouche s theorem we exploit extensively recent developments in the representation theory for abstract linear systems especially regular systems we also analyze ill posed systems by interchanging the roles of input and output we apply these results to a wave equation and an ill posed beam equation

condition number estimates for the nonoverlapping optimized schwarz method and the 2 lagrange multiplier method for general domains and cross points the optimized schwarz method and the closely related 2 lagrange multiplier method are domain decomposition methods which can be used to parallelize the solution of partial differential equations although these methods are known to work well in special cases e g when the domain is a square and the two subdomains are rectangles the problem has never been systematically stated nor analyzed for general domains with general subdomains the problem of cross points when three or more subdomains meet at a single vertex has been particularly vexing we introduce a 2 lagrange multiplier method for domain decompositions with cross points we estimate the condition number of the iteration and provide an optimized robin parameter for general domains we hope that this new systematic theory will allow broader utilization of optimized schwarz and 2 lagrange multiplier preconditioners

a new look into the kinematics and dynamics of finite rigid body rotations using lie group theory abstract a systematic theoretical approach is presented in an effort to provide a complete and illuminating study on kinematics and dynamics of rigid bodies rotating about a fixed point specifically this approach is based on some fundamental concepts of differential geometry with particular reference to lie group theory this treatment is motivated by the form of the configuration space corresponding to large rigid body rotation which is a differentiable manifold possessing group properties first the basic steps of the classical approach on the subject are briefly summarized then some geometrical tools are presented which are essential for supporting and illustrating the steps and findings of the new approach finally the emphasis is placed on a thorough investigation of the problem of finite rotations a key idea is the introduction of a canonical connection matching the manifold and group properties of the configuration space this proves to be sufficient and effective for performing the kinematics next following the selection of an appropriate metric the dynamics is also carried over the present approach is theoretically more demanding than the traditional treatments in engineering but brings substantial benefits in particular an elegant interpretation is provided for all the quantities with fundamental importance in both rigid body kinematics and dynamics most importantly this also leads to a correction of some misconceptions and geometrical inconsistencies in the field among other things the deeper understanding of the theoretical concepts provides powerful insight and a strong basis for the development of efficient numerical techniques in problems of solid and structural mechanics involving large rotations

using comparison theorem to compare corotational stress rates in the model of perfect elastoplasticity abstract for the simple shear problem of a perfectly elastoplastic body we convert the non linear governing equations into a third order linear differential system then into a second order linear differential system and further into a sturm liouville equation thus sturm s comparison theorem can be employed and extended to compare the simple shear responses based on different objective corotational stress rates it is proved that the rates of jaumann green naghdi sowerby chu xiao bruhns meyers and lee mallett wertheimer render non oscillatory stress responses with the jaumann equation as a sturm majorant for the other four equations for an objective corotational stress rate with the general plane spin a sufficient non oscillation criterion is found to be that the plane spin must not exceed the shear strain rate

quadratic optimal control of stable well posed linear systems we consider the infinite horizon quadratic cost minimization problem for a stable time invariant well posed linear system in the sense of salamon and weiss and show that it can be reduced to a spectral factorization problem in the control space more precisely we show that the optimal solution of the quadratic cost minimization problem is of static state feedback type if and only if a certain spectral factorization problem has a solution if both the system and the spectral factor are regular then the feedback operator can be expressed in terms of the riccati operator and the riccati operator is a positive self adjoint solution of an algebraic riccati equation this riccati equation is similar to the usual algebraic riccati equation but one of its coefficients varies depending on the subspace in which the equation is posed similar results are true for unstable systems as we have proved elsewhere

comparison of some stress rates abstract this paper introduces a new derivation rule by means of which two new stress rates are defined furthermore the paper compares five stress rates jaumann s truesdell s green naghdi s sowerby chu s and durban baruch s for simple shear elastic elastic perfectly plastic and elastic plastic hardening isotropic kinematic and combined material models are considered different solutions have already been published for these cases except for sowerby chu and durban baruch time derivatives using the new derivation rule the new rate form of the hyperelastic doyle ericksen formula is obtained taking advantage of the sowerby chu stress rate a new constitutive equation for hypoelastic material is given

optimized schwarz methods optimized schwarz methods are a new class of schwarz methods with greatly enhanced convergence properties they converge uniformly faster than classical schwarz methods and their convergence rates dare asymptotically much better than the convergence rates of classical schwarz methods if the overlap is of the order of the mesh parameter which is often the case in practical applications they achieve this performance by using new transmission conditions between subdomains which greatly enhance the information exchange between subdomains and are motivated by the physics of the underlying problem we analyze in this paper these new methods for symmetric positive definite problems and show their relation to other modern domain decomposition methods like the new finite element tearing and interconnect feti variants

well posedness and exact controllability of fourth order schrodinger equation with boundary control and collocated observation in this paper we study the well posedness and exact controllability of a system described by a fourth order schrodinger equation on a bounded domain of mathbb r n n geqslant 2 with boundary control and collocated observation the neumann boundary control problem is first discussed it is shown that the system is well posed in the sense of d salamon this implies the exponential stability of the closed loop system under proportional output feedback control the well posedness result is then generalized to the dirichlet boundary control problem in particular in order to conclude feedback stabilization from well posedness we discuss the exact controllability with the dirichlet boundary control which is similar to the neumann boundary control case in addition we show that both systems are regular in the sense of g weiss and their feedthrough operators are zero

efficient and accurate explicit integration algorithms with application to viscoplastic models several explicit integration algorithms with self adative time integration strategies are developed and investigated for efficiency and accuracy these algorithms involve the runge kutta second order the lower runge kutta method of orders one and two and the exponential integration method the algorithms are applied to viscoplastic models put forth by freed and verrilli and bodner and partom for thermal mechanical loadings including tensile relaxation and cyclic loadings the large amount of computations performed showed that for comparable accuracy the efficiency of an integration algorithm depends significantly on the type of application loading however in general for the aforementioned loadings and viscoplastic models the exponential integration algorithm with the proposed self adaptive time integration strategy worked more or comparably efficiently and accurately than the other integration algorithms using this strategy for integrating viscoplastic models may lead to considerable savings in computer time better efficiency without adversely affecting the accuracy of the results this conclusion should encourage the utilization of viscoplastic models in the stress analysis and design of structural components

robust state feedback regulator design for general linear heterodirectional hyperbolic systems the topic of this paper is the backstepping based solution of the robust state feedback regulation problem for general linear heterodirectional hyperbolic systems with spatially varying coefficients thereby a large class of outputs is considered i e mixed distributed and pointwise in domain or boundary outputs the state feedback regulator design is based on the boldsymbol p copy internal model principle this results in a stabilization problem for a cascade of boldsymbol m p boundary controlled transport partial differential equations pdes with boldsymbol p ordinary differential equations odes for this a systematic backstepping approach is presented in which all design equations are explicitly solvable in backstepping coordinates furthermore the solvability conditions for the considered output regulation problem can be evaluated in closed form utilizing the plant transfer behavior robust output regulation is verified for nondestabilizing model uncertainties and unknown disturbance input locations a boldsymbol 4 times 4 hyperbolic system with uncertain transport velocities and couplings in the transport pdes illustrates the results of this paper

internal symmetry groups for the drucker prager material model of plasticity and numerical integrating methods abstract internal symmetries for the drucker prager material model and numerical methods based on them are investigated here we first convert the non linear constitutive equations to a lie type system x a x t x where a sl 5 2 r is a lie algebra of the special orthochronous pseudo linear group sl 5 2 r the underlying space of drucker prager model in the plastic phase is a pseudo sphere in the pseudo riemann manifold which is locally a pseudo euclidean space e 7 5 2 and whose metric tensor is indefinite having signature 5 2 and also depends on the temporal component then we split the drucker prager yield condition into two sub yield conditions which together with two integrating factors idea led us to derive two lie type systems in the product space m 5 1 m 1 1 the lie algebra is the direct sum so 5 1 so 1 1 and the symmetry group is thus soo 5 1 soo 1 1 these results are essential from computational aspect based on these symmetry groups exponential mappings are developed which update stress points exactly on the yield surface at every time increment without any iteration as an example the results calculated by using the two different group preserving schemes are compared to that calculated by the runge kutta scheme together with the newton raphson iterative solution of a non linear algebraic equation which enforcing the consistency condition

on the characterization of admissible control and observation operators abstract in this note we give a short proof of a recent result in 2 integral equations operator theory 25 1996 182 198 which characterizes the admissibility of unbounded observation operators in linear infinite dimensional control theory moreover we present the analogous result for the admissibility of unbounded control operators

infinite dimensional linear systems with unbounded control and observation a functional analytic approach abstract the object of these notes is to develop a unifying framework for the functional analytic representation of infinite dimensional linear systems with unbounded input and output operators on the basis of the general approach new results are derived on the wellposedness of feedback systems and on the linear quadratic control problem the implications of the theory for large classes of functional and partial differential equations are discussed in detail keywords representation of infinite dimensional systems semigroups boundary control feedback linear quadratic control

finite time output regulation for linear 2 2 hyperbolic systems using backstepping this contribution presents the backstepping design of output feedback regulators for boundary controlled linear 2 2 hyperbolic systems that achieve regulation in finite time it is assumed that the disturbances can act in domain at both boundaries and at the output to be controlled the latter need not be available for measurement and consists of in domain pointwise distributed or boundary outputs firstly a solution of the finite time state feedback regulator problem is given on the basis of the regulator equations they are formulated in backstepping coordinates so that a solution is attainable in closed form this leads to a very straightforward regulator design for 2 2 hyperbolic systems with a general class of outputs then a finite dimensional reference observer that converges in finite time is introduced which consists of two observers and a delay this result is extended to the backstepping design of finite time disturbance observers for 2 2 hyperbolic systems with a collocated measurement in particular two backstepping disturbance observers are determined so that after introducing a delay the disturbance model and plant states can be estimated in finite time hence by combining the state feedback regulator with these observers a finite time output feedback regulator is obtained for the state feedback regulator and the disturbance observer existence conditions are derived in terms of the plant transfer behaviour a simple example with an in domain pointwise and distributed output illustrates the theoretical results

on the modelling of non linear kinematic hardening at finite strains with application to springback comparison of time integration algorithms the paper discusses the derivation and the numerical implementation of a finite strain material model for non linear kinematic and isotropic hardening the kinematic hardening component represents a continuum extension of the classical rheological model of armstrong frederick kinematic hardening in addition a comparison between several numerical algorithms for the integration of the evolution equations is conducted in particular a new form of the exponential map that preserves the plastic volume and the symmetry of the internal variables as well as two modifications of the backward euler scheme are discussed finally the applicability of the model for springback prediction is demonstrated by performing simulations of the draw bending process and a comparison with experiments the results show an excellent agreement between simulation and experiment copyright 2007 john wiley sons ltd

second order accurate integration algorithms for von mises plasticity with a nonlinear kinematic hardening mechanism abstract two second order numerical schemes for von mises plasticity with a combination of linear isotropic and nonlinear kinematic hardening are presented the first scheme is the generalized midpoint integration procedure originally introduced by ortiz and popov in 1985 detailed and applied here to the case of armstrong frederick nonlinear kinematic hardening the second algorithm is based on the constitutive model exponential based reformulation and on the integration procedure previously introduced by the authors in the context of linearly hardening materials there are two main targets to the work firstly we wish to extensively test the generalized midpoint procedure since in the scientific literature no thorough numerical testing campaign has been carried out on this second order algorithm secondly we wish to extend the exponential based integration technique also to nonlinear hardening materials a wide numerical investigation is carried out in order to compare the performance of the two methods

backstepping design of robust state feedback regulators for linear 2 times 2 hyperbolic systems this technical note deals with the robust output regulation problem for boundary controlled linear 2 times 2 hyperbolic systems thereby the output to be controlled can be located at one of the boundaries or is a pointwise in domain output by utilizing the internal model principle a state feedback regulator is determined for a finite dimensional signal model describing the exogenous signals this amounts to stabilizing a hyperbolic pde ode cascade coupled at an intermediate point for this a systematic backstepping method is developed to determine the stabilizing state feedback controller the solvability of the considered output regulation problem can easily be verified on the basis of the nominal plant transfer behaviour for non destabilizing model uncertainties the robustness of the achieved output regulation is verified an uncertain hyperbolic system with an in domain output illustrates the results of the technical note

the suboptimal nehari problem for well posed linear systems we solve the suboptimal nehari problem for a transfer function that has a state space realization as a system stable input output and input output stable well posed linear system we obtain an explicit solution in terms of the state space parameters