algebraic reflexivity of sets of bounded operators on vector valued lipschitz functions abstract in this paper we establish algebraic reflexivity properties of subsets of bounded linear operators acting on spaces of vector valued lipschitz functions we also derive a representation for the generalized bi circular projections on these spaces

technical communique performance of an adaptive algorithm for sinusoidal disturbance rejection in high noise the paper proposes a discrete time algorithm for the rejection of sinusoidal disturbances of unknown frequency the algorithm is adapted from an existing continuous time algorithm and the overall nonlinear system is analyzed using a linear approximation the paper shows that the noise rejection properties may be predicted using an in phase quadrature decomposition of the noise similar to the one encountered in the theory of phase locked loops estimates are obtained for the standard deviations of the plant output and of the adaptive parameters simulations validate the predictions of the analysis despite the nonlinear nature of the adaptive system and the high level of noise applied

homomorphisms between algebras of lipschitz functions with the values in function algebras abstract we give a characterization of algebra homomorphisms and isomorphisms between banach algebras of lipschitz functions with the values in unital commutative c algebras we prove that such homomorphisms are composition operators of the form and preserve some properties

algebraic reflexivity of the isometry group of some spaces of lipschitz functions abstract we show that the isometry groups of lip x d and lip x d with 0 1 for a compact metric space x d are algebraically reflexive we also prove that the sets of isometric reflections and generalized bi circular projections on such spaces are algebraically reflexive in order to achieve this we characterize generalized bi circular projections on these spaces

stabilized low order finite elements for failure and localization problems in undrained soils and foundations abstract geomaterials in general and soils in particular are highly nonlinear materials presenting a very strong coupling between solid skeleton and intersticial water in the limit of zero compressibility of water and soil grains and zero permeability which correspond to the classical undrained assumption of soil mechanics the functions used to interpolate displacements and pressures must fulfill either the babuska brezzi conditions or the much simpler patch test proposed by zienkiewicz and taylor these requirements exclude the use of elements with equal order interpolation for pressures and displacements for which spurious oscillations may appear the simplest elements with continuous pressures which can be used in 2d are the quadratic triangle and quadrilateral with linear and bilinear pressures respectively the purpose of this paper is to present a stabilization technique allowing the use of both linear triangles for displacements and pressures t3p3 and bilinear quadrilaterals q4p4 the proposed element will be applied to obtain limit loads and failure surfaces in simple boundary value problems for which analytical solutions exist

approximation design of optimal controllers for nonlinear systems with sinusoidal disturbances abstract this paper considers an infinite time optimal damping control problem for a class of nonlinear systems with sinusoidal disturbances a successive approximation approach saa is applied to design feedforward and feedback optimal controllers by using the saa the original optimal control problem is transformed into a sequence of nonhomogeneous linear two point boundary value tpbv problems the existence and uniqueness of the optimal control law are proved the optimal control law is derived from a riccati equation matrix equations and an adjoint vector sequence which consists of accurate linear feedforward and feedback terms and a nonlinear compensation term and the nonlinear compensation term is the limit of the adjoint vector sequence by using a finite term of the adjoint vector sequence we can get an approximate optimal control law a numerical example shows that the algorithm is effective and robust with respect to sinusoidal disturbances

dynamic integrated system optimization and parameter estimation for discrete time optimal control of nonlinear systems an algorithm for solving nonlinear discrete time optimal control problems with model reality differences is presented the technique uses dynamic integrated system optimization and parameter estimation disope which achieves the correct optimal solution in spite of deficiencies in the mathematical model employed in the optimization procedure a version of the algorithm with a linear quadratic model based problem implemented in the c programming language is developed and applied to illustrative simulation examples an analysis of the optimality and convergence properties of the algorithm is also presented

mixed stabilized finite element methods in nonlinear solid mechanics part i formulation abstract this paper exploits the concept of stabilized finite element methods to formulate stable mixed stress displacement and strain displacement finite elements for the solution of nonlinear solid mechanics problems the different assumptions and approximations used to derive the methods are exposed the proposed procedure is very general applicable to 2d and 3d problems implementation and computational aspects are also discussed showing that a robust application of the proposed formulation is feasible numerical examples show that the results obtained compare favorably with those obtained with the corresponding irreducible formulation

the patch test for mixed formulations this paper presents a simple extension of the patch test to mixed formulations to provide the necessary and sufficient conditions for convergence the general algebraic conditions of babuska and brezzi are given a simple form and a conceptual application of the patch tests serves to point out the instability of several well known formulations for incompressible problems the test is also applied to mixed displacement strain formulations of elasticity and limiting formulations are noted

successive approximation procedure of optimal tracking control for nonlinear similar composite systems abstract the optimal tracking control otc problem for a class of affine nonlinear composite systems with similar structure is considered by using a modeling technique the nonlinear similar composite system is first transformed into some quasi decoupled subsystems then the high order strongly coupled nonlinear two point boundary value tpbv problem is transformed into a sequence of linear decoupled tpbv problems through a successive approximation procedure the obtained otc law consists of an accurate linear term and a nonlinear compensation term which is the limit of the adjoint vector sequence a suboptimal tracking control law is obtained by truncating a finite iterative result of the adjoint vector sequence as its nonlinear compensation term

hybrid and enhanced finite element methods for problems of soil consolidation hybrid and enhanced finite element methods with bi linear interpolations for both the solid displacements and the pore fluid pressures are derived based on mixed variational principles for problems of elastic soil consolidation both plane strain and axisymmetric problems are studied it is found that by choosing appropriate interpolation of enhanced strains in the enhanced method and by choosing appropriate interpolations of strains effective stresses and enhanced strains in the hybrid method the oscillations of nodal pore pressures can be eliminated several numerical examples demonstrating the capability and performance of the enhanced and hybrid finite element methods are presented it is also shown that for some situations such as problems involving high poisson s ratio and in other related problems where bending effects are evident the performance of the enhanced and hybrid methods are superior to that of the conventional displacement based method the results from the hybrid method are better than those from the enhanced method for some situations such as problems in which soil permeability is variable or discontinuous within elements since all the element parameters except the nodal displacements and nodal pore pressures are assumed in the element level and can be eliminated by static condensation the implementations of the enhanced method and the hybrid method are basically the same as the conventional displacement based finite element method the present enhanced method and hybrid method can be easily extended to non linear consolidation problems copyright 2006 john wiley sons ltd

guaranteed cost control of affine nonlinear systems via partition of unity method we consider the problem of guaranteed cost control gcc of affine nonlinear systems in this paper firstly the general affine nonlinear system with the origin being its equilibrium point is represented as a linear like structure with state dependent coefficient matrices secondly partition of unity method is used to approximate the coefficient matrices as a result of which the original affine nonlinear system is equivalently converted into a linear like system with modeling error a gcc law is then synthesized based on the equivalent model in the presence of modeling error under certain error condition the control law ensures that the system under control is asymptotically stable as well as that a given cost function is upper bounded a suboptimal gcc law can be obtained via solving an optimization problem in terms of linear matrix inequality lmi in stead of state dependent riccati equation sdre or hamilton jacobi equations that are usually required in solving nonlinear optimal control problems finally a numerical example is provided to illustrate the validity of the proposed method

stable element free galerkin solution procedures for the coupled soil pore fluid problem it is always difficult to solve the coupled soil pore fluid problem when the soil is saturated and impermeable because this situation often results in intensive oscillations of the solutions this topic has been discussed widely in the field of the finite element method but rarely by meshless methods the element free galerkin efg method has outstanding advantages of solving this problem based on the fact that its interpolation function can be constructed flexibly by the nodes in the compact domain in this study an efg numerical model together with a stabilization technique is proposed to obtain stable solutions especially for the saturated and impermeable soil close agreement between computational results and analytical solutions for one and two dimensional examples shows that the proposed numerical model not only provides highly accurate solutions for the saturated soil with relatively high permeability but also eliminates the oscillations of the solutions very effectively for the saturated and impermeable soil furthermore the influences of the hydraulic anisotropy a typical property of two dimensional problems on the proposed stabilization technique are discussed it is suggested that the optimal distribution of the nodes of essential variables can be designed according to the relative importance of the permeability in different directions copyright c 2010 john wiley sons ltd

an efficient staggered time marching procedure for porodynamics the present work proposes a novel time marching procedure which is designed for the dynamic simulation of the coupled two phase biot equations considering the displacement pressure u p formulation the new approach provides unconditional stability and excellent efficiency due to the staggered character of the temporal discretization where equilibrium is established at time t for the u group of governing equations and at time t t for the p group of governing equations the resulting systems of equations have an improved format and can be factorized solved at significantly less computational effort when compared to standard approaches such as the generalized newmark scheme in addition the resulting new systems of equations are characterized by considerably lower condition numbers reducing correlated numerical issues unconditional stability is achieved by a consistent manipulation of the mass and compressibility matrix of the model which causes virtually no computational overhead as a byproduct of the altered compressibility matrix the method is capable of simulating incompressible and impermeable phenomena without the need for any further feats the newly developed time marching technique is implemented and tested considering different benchmark problems for comparison the commonly used newmark scheme is also applied and both direct lu decomposition and iterative gmres linear solvers are employed in order to assess the efficiency of the new technique

optimal output tracking control for nonlinear systems via successive approximation approach abstract this paper deals with the optimal output tracking control ootc problem of a class of nonlinear systems whose reference input to be tracked is produced by a generalized linear exosystem to solve the nonlinear ootc problem the nonlinear two point boundary value tpbv problem derived from the necessary conditions of the ootc problem is transformed into two decoupled iterative sequences of linear differential equations the ootc law obtained consists of accurate feedforward and feedback terms and a nonlinear compensation term the former can be found by solving a sylvester equation and a riccati equation and the latter can be approximated using a successive approximation approach saa a reduced order reference input observer is constructed to make the feedforward control law physically realizable a simulation example is employed to illustrate the validity of the results

global optimal feedback control for general nonlinear systems with nonquadratic performance criteria abstract optimal control of general nonlinear nonaffine controlled systems with nonquadratic performance criteria that permit state and control dependent time varying weighting parameters is solved classically using a sequence of linear quadratic and time varying problems the proposed method introduces an approximating sequence of riccati equations asre to explicitly construct nonlinear time varying optimal state feedback controllers for such nonlinear systems under very mild conditions of local lipschitz continuity the sequences converge globally to nonlinear optimal stabilizing feedback controls the computational simplicity and effectiveness of the asre algorithm is an appealing alternative to the tedious and laborious task of solving the hamilton jacobi bellman partial differential equation so the optimality of the asre control is studied by considering the original nonlinear nonquadratic optimization problem and the corresponding necessary conditions for optimality derived from pontryagin s maximum principle global optimal stabilizing state feedback control laws are then constructed this is compared with the optimality of the asre control by considering a nonlinear fighter aircraft control system which is nonaffine in the control numerical simulations are used to illustrate the application of the asre methodology which demonstrate its superior performance and optimality

multiplier methods for nonlinear optimal control error estimates are derived for an augmented lagrangian approximation to an optimal control problem convex control constraints are treated explicitly while a lagrange multiplier is introduced for the nonlinear system dynamics the nonlinear optimal control problem does not fit the classical theory for estimating the error in multiplier approximations since the natural coercivity assumption is formulated in a hilbert space where the cost is not differentiable this discrepancy between the function space setting needed for coercivity and that needed for differentiability is compensated for by regularity results associated with the necessary conditions the paper concludes with an analysis of the optimal penalty parameter corresponding to a given finite element discretization

a new stabilized enhanced strain element with equal order of interpolation for soil consolidation problems abstract in order to accurately model the behaviour of geostructures it is usually not possible to neglect the interaction between the soil skeleton and the pore fluid classical finite element models taking into account this interaction are formulated in terms of the displacement and pore pressure fields and are based on the assumption that the fluid acceleration relative to the soil skeleton is negligible this type of mixed problems is similar to others found in solid and fluid mechanics and might give rise to numerical instabilities unless certain requirements are met there are two classical approaches to this problem the first is usually known as the zienkiewicz taylor patch test for mixed formulations as a consequence of this test the interpolation degree of the displacement field is required to be higher than the corresponding one of the pressure field mathematically speaking this is a necessary condition for stability the second approach mathematically more involved is usually known as the bab ska brezzi inf sup condition and constitutes a sufficient condition for stability however it is possible to obtain stable formulations circumventing the interpolation degree requirement through the so called stabilization techniques these techniques were initially applied in the context of fluid mechanics and later extended to solid mechanics this article presents a new formulation in which stabilization is achieved through an approach based on the simo rifai enhanced strain element

suboptimal control for nonlinear systems a successive approximation approach abstract this paper presents a successive approximation approach saa designing optimal controllers for a class of nonlinear systems with a quadratic performance index by using the saa the nonlinear optimal control problem is transformed into a sequence of nonhomogeneous linear two point boundary value tpbv problems the optimal control law obtained consists of an accurate linear feedback term and a nonlinear compensation term which is the limit of an adjoint vector sequence by using the finite step iteration of the nonlinear compensation sequence we can obtain a suboptimal control law simulation examples are employed to test the validity of the saa

factored forms for solutions of ax xb c and x axb c in companion matrices abstract the main concern of this paper is linear matrix equations with block companion matrix coefficients it is shown that general matrix equations ax xb c and x axb c can be transformed to equations whose coefficients are block companion matrices c l x xc m diag i 0 0 and x c l xc m diag i 0 0 respectively where l and cm stand for the first and second block companion matrices of some monic r r matrix polynomials l si s 1j 0 jlj and m ti t7minus 1j 0 jmj the solution of the equat with block companion coefficients is reduced to solving vector equations sx where the matrix s is r2l r2l l max s t and enjoys some symmetry properties

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

fdm solutions to linear dynamics of porous media efficiency stability and parallel solution strategy summary this paper presents a strategy to improve the efficiency of simulations involving porous materials with linear behaviour and full saturation the method is named parallel lines finite difference and uses a method to decouple a discretised version of the governing equations allowing parallel computations as a result the complexity and the bandwidth of the global matrix are significantly reduced and hence the efficiency is improved the other advantage of the scheme is the fulfilment of the inf sup stability condition the scheme is developed to solve porous media formulations derived from the theory of porous media both the u p and u v p formulations are considered u displacement of solid p pressure of liquid and v velocity of liquid several simulations are performed to demonstrate the capabilities of the method

optimal control of nonlinear systems a recursive approach abstract in this paper we shall generalize our result 1 on the optimal control of bilinear systems to nonlinear systems adomian s decomposition is used to derive series expansions of the optimal control and state

algebraic reflexivity of isometry groups of algebras of lipschitz maps abstract we study groups of surjective linear isometries on banach algebras of lipschitz maps with values in some unital c algebras in this paper these spaces are endowed with the sum norm for the case where the c algebras are commutative whose groups of all surjective isometries are algebraically reflexive we prove that the group of all surjective isometries on the corresponding banach algebra of lipschitz maps are algebraically reflexive we also prove that the group of unital surjective isometries between matrix valued lipschitz algebras are reflexive

numerical stabilization of biot s consolidation model by a perturbation on the flow equation in this paper a stabilized finite element scheme for the poroelasticity equations is proposed this method based on the perturbation of the flow equation allows us to use continuous piecewise linear approximation spaces for both displacements and pressure obtaining solutions without oscillations independently of the chosen discretization parameters the perturbation term depends on a parameter which is established in terms of the mesh size and the properties of the material in the one dimensional case this parameter is shown to be optimal some numerical experiments are presented indicating the efficiency of the proposed stabilization technique copyright 2008 john wiley sons ltd

an iterative stabilized fractional step algorithm for finite element analysis in saturated soil dynamics abstract the discretization of the u p model for saturated porous media results in the semi discrete system of mixed type in displacements and pressures the babuska brezzi condition or the simpler patch test proposed by zienkiewicz and taylor precludes the use of elements with the equal low order of interpolation for u and p unless special stabilization techniques such as the fractional step algorithms are used the purpose of this paper is to present a modified version of the fractional step algorithm which allows much larger time step sizes than those for the existing ones the method is based on introducing an iteration algorithm the numerical experiments demonstrate the effectiveness and improved performance of the proposed modified version of the fractional step algorithm

optimal damping control and nonlinear elliptic systems optimal control for an elliptic equation when the control is the zero order coefficient of the differential operator is considered and an optimality system is derived under certain assumptions the problem is solved completely by giving the uniqueness and the constructive existence proof for the nonlinear optimality system an extension to the case when the state equation is a particular elliptic system is considered as well

an iterative method for suboptimal control of linear time delayed systems abstract this article presents a new approach for solving the optimal control problem ocp of linear time delay systems with a quadratic cost functional the proposed method can also be used for designing optimal control time delay systems with disturbance in this study the variational iteration method vim is employed to convert the original time delay optimal control problem tdocp into a sequence of nonhomogeneous linear two point boundary value problems tpbvps the optimal control law obtained consists of an accurate linear feedback term and a nonlinear compensation term which is the limit of an adjoint vector sequence the feedback term is determined by solving riccati matrix differential equation by using the finite step iteration of a nonlinear compensation sequence we can obtain a suboptimal control law finally illustrative examples are included to demonstrate the validity and applicability of the technique

wave propagation and localization problems in saturated viscoplastic geomaterials this paper presents an improved algorithm to deal with wave propagation and localization problems in saturated viscoplastic geomaterials it consists of a mixed formulation in terms of effective stress velocity and pore pressure that uses a fractional step algorithm allowing the use of equal order of interpolation for the three variables and the simplest element such as the linear triangle the viscoplastic model used is of modified cam clay type viscoplasticity results in a strong source term that deteriorates the accuracy of the two step taylor galerkin algorithm therefore a runge kutta splitting scheme has been used to deal with the source terms resulting in a better accuracy of the method copyright 2006 john wiley sons ltd

optimal sliding mode control for linear time delay systems with sinusoidal disturbances this paper develops a successive approximation approach saa of optimal sliding mode control smc for linear time delay systems with sinusoidal disturbances a sequence of two point boundary value tpbv problems with both time delay and time advance terms is derived from the optimal sliding mode design according to the saa the original tpbv problems are transformed into a sequence of linear tpbv problems without delay and advance terms the obtained smc ensures that the state trajectories reach the sliding surface in finite time and remain on it thereafter the stability of the sliding mode is proved a numerical simulation is employed to verify the effectiveness of the proposed approach

a stabilized fractional step runge kutta taylor sph algorithm for coupled problems in geomechanics abstract failure of geomaterials with pores filled with fluids is an important research area in both civil and geological engineering many finite element formulations for coupled problems present difficulties such as overestimating failure loads or mesh alignment dependence resulting on spurious failure mechanisms moreover the spaces where field variables are approximated have to fulfill additional requirements ensuring stability stress velocity pore pressure formulations in fe analysis provide accurate results for wave propagation and failure analysis however finite elements present important limitations when deformations are large the purpose of this paper is to present a stabilized fractional step sph algorithm which combines the advantages of the sph method for large deformation problems with those of the taylor galerkin algorithm used within the finite element framework

delay dependent nonfragile guaranteed cost control for nonlinear time delay systems abstract this paper concerns the nonfragile guaranteed cost control problem for a class of nonlinear dynamic systems with multiple time delays and controller gain perturbations guaranteed cost control law is designed under two classes of perturbations namely additive form and multiplicative form the problem is to design a memoryless state feedback control law such that the closed loop system is asymptotically stable and the closed loop cost function value is not more than a specified upper bound for all admissible uncertainties based on the linear matrix inequality lmi approach some delay dependent conditions for the existence of such controller are derived a numerical example is given to illustrate the proposed method

isometries between function spaces surjective isometries between some classical function spaces are investigated we give a simple technical scheme which verifies whether any such isometry is given by a homeomorphism between corresponding hausdorff compact spaces in particular the answer is positive for the c x ac 0 1 lip0 x and lip0 x spaces provided with various natural norms

brief paper sequential linear quadratic control of bilinear parabolic pdes based on pod model reduction we present a framework to solve a finite time optimal control problem for parabolic partial differential equations pdes with diffusivity interior actuators which is motivated by the control of the current density profile in tokamak plasmas the proposed approach is based on reduced order modeling rom and successive optimal control computation first we either simulate the parabolic pde system or carry out experiments to generate data ensembles from which we then extract the most energetic modes to obtain a reduced order model based on the proper orthogonal decomposition pod method and galerkin projection the obtained reduced order model corresponds to a bilinear control system based on quasi linearization of the optimality conditions derived from pontryagin s maximum principle and stated as a two boundary value problem we propose an iterative scheme for suboptimal closed loop control we take advantage of linear synthesis methods in each iteration step to construct a sequence of controllers the convergence of the controller sequence is proved in appropriate functional spaces when compared with previous iterative schemes for optimal control of bilinear systems the proposed scheme avoids repeated numerical computation of the riccati equation and therefore reduces significantly the number of odes that must be solved at each iteration step a numerical simulation study shows the effectiveness of this approach

galerkin approximations of the generalized hamilton jacobi bellman equation in this paper we study the convergence of the galerkin approximation method applied to the generalized hamilton jacobi bellman ghjb equation over a compact set containing the origin the ghjb equation gives the cost of an arbitrary control law and can be used to improve the performance of this control the ghjb equation can also be used to successively approximate the hamilton jacobi bellman equation we state sufficient conditions that guarantee that the galerkin approximation converges to the solution of the ghjb equation and that the resulting approximate control is stabilizing on the same region as the initial control the method is demonstrated on a simple nonlinear system and is compared to a result obtained by using exact feedback linearization in conjunction with the lqr design method

incompressibility without tears how to avoid restrictions of mixed formulation the severe restrictions of the babuska brezzi stability criteria permit only a limited number of interpolations for velocities displacements and pressure to be used for incompressible behaviour these restrictions preclude the use of many useful elements we show in this paper how such difficulties can be side stepped by seeking the steady state solution through the use of various time marching schemes this permits a simple iterative approach to incompressible or nearly incompressible problems of fluid mechanics or solid mechanics and provides a stimulus for the use of such procedures in metal forming flow etc

reflexivity algebraic reflexivity and linear interpolation introduction this paper was motivated by a discovery that most finite dimensional subalgebras of b h for h an infinite dimensional hilbert space are reflexive with the only obstructions to reflexivity being finite rank considerations proofs section 2 do not depend on multiplicative structure nor on topology so extend to linear subspaces of transformations in an abstract setting abstract reflexivity has been studied in 3 4 7 primarily for singly generated algebras reflexivity properties can be interpreted as linear interpolation properties and we shall adopt this point of view the results of section 2 extend in section 3 to algebraic reflexivity counterparts for countably generated algebraically linear subspaces of bounded linear transformations acting on a banach space as consequences in section 4 we obtain generalizations of two single operator results one is a multivariate version of the result due to kaplansky 10 theorem 15 that a bounded locally algebraic operator acting on a banach space is algebraic the other is a multivariate version of the result due to douglas and foias 5 for hilbert space and to hadwin 7 for a general banach space extending work of fillmore 6 that a bounded non algebraic operator acting on a banach space is topologically algebraically reflexive in section 5 we give an application kindly suggested by d hadwin concerning joint strong similarity orbits of n tupules of operators we wish to thank e azoff k davidson j erdos d hadwin j kraus c lance and a sourour for conversations and some correspon

optimal tracking control for large scale interconnected systems with time delays this paper considers an infinite horizon optimal tracking control problem for a class of large scale interconnected systems with state time delays by using the successive approximation approach two iteration sequences of vector differential equations are constructed meanwhile the large scale interconnected system is decomposed into finite decoupled subsystems the existence and uniqueness of the optimal solution is proved as well as the convergence of the solution sequence by finite iterations of the solution sequence a suboptimal tracking control law is obtained a reduced order reference input observer is designed to make the feedforward term of the optimal tracking control law physically realizable a numerical example shows that the presented algorithm is effective and easy to implement

a mixed three field fe formulation for stress accurate analysis including the incompressible limit abstract in previous works the authors have presented the stabilized mixed displacement pressure formulation to deal with the incompressibility constraint more recently the authors have derived stable mixed stress displacement formulations using linear linear interpolations to enhance stress accuracy in both linear and non linear problems in both cases the variational multi scale vms stabilization technique and in particular the orthogonal subgrid scale oss method allows the use of linear linear interpolations for triangular and tetrahedral elements bypassing the strictness of the inf sup condition on the choice of the interpolation spaces these stabilization procedures lead to discrete problems which are fully stable free of volumetric locking or stress oscillations this work exploits the concept of mixed finite element methods to formulate stable displacement stress pressure finite elements aimed for the solution of nonlinear problems for both solid and fluid finite element fe analyses the final goal is to design a finite element technology able to tackle simultaneously problems which may involve isochoric behavior preserve the original volume of the strain field together with high degree of accuracy of the stress field these two features are crucial in nonlinear solid and fluid mechanics as used in most numerical simulations of industrial manufacturing processes numerical benchmarks show that the results obtained compare very favorably with those obtained with the corresponding mixed displacement pressure formulation

an eulerian mixed formulation for viscoplastic materials abstract this paper presents an eulerian mixed formulation for viscoplastic materials the algorithm is formulated in terms of deviatoric stress velocity and hydrostatic pressure using a fractional step algorithm that allows the use of equal order of interpolation for the three variables the constitutive law is based on the viscoplasticity theory of perzyna with the von mises yield criterion the jaumann rate of cauchy stress tensor is used to ensure the objectivity of the constitutive law a splitting scheme based on a two step taylor galerkin algorithm for the advective terms plus a fourth order runge kutta scheme for the sources has been used to improve the accuracy of the method

optimal sinusoidal disturbances damping for singularly perturbed systems with time delay abstract this paper considers an optimal damping vibration control problem for linear time delay singularly perturbed systems affected by external sinusoidal disturbances by using the slow fast decomposition theory of singularly perturbed systems the system is first decomposed into a fast subsystem without time delay and a slow subsystem with time delay affected by external sinusoidal disturbances then the successive approximation approach saa and the feedforward compensation techniques are proposed to solve the slow time scale time delay optimal control problem and damp the external sinusoidal disturbances respectively the conditions of existence and uniqueness of the finite and infinite horizon feedforward and feedback composite control ffcc laws are presented and the design approaches are given the ffcc laws consist of nondelay feedback terms disturbances compensation terms and a time delay compensation term which is the limit of the solution sequence of the adjoint vector equations simulation examples indicate that the saa is valid and the ffcc laws are easy to implement and more effective with respect to damping the external sinusoidal disturbances than that of the classical feedback composite control fcc laws

triangles and tetrahedra in explicit dynamic codes for solids explicit dynamic codes which are used currently for the study of plastic deformations in impact or with some modification for metal forming suffer two serious limitations first only quadrilateral or hexahedral linear elements can be used thus limiting the possibilities of adaptive refinement and adaptive meshing second even with the use of such elements special devices such as reduced integration must be introduced to avoid locking and reduce costs these necessitate complex hour glass control mending type procedures the main difficulties are those due to the need of treatment of almost incompressible deformation modes recently similar difficulties have been overcome in the context of fluid dynamics soil dynamics and we show here how the processes introduced there can be adopted effectively to the present problem thus allowing an almost unrestricted choice of element interpolations 1998 john wiley sons ltd

adaptive remeshing for compressible flow computations an adaptive mesh procedure for improving the quality of steady state solutions of the euler equations in two dimensions is described the procedure is implemented in conjunction with a finite element solution algorithm using linear triangular elements and an explicit time stepping scheme the mesh adaptation is accomplished by regeneration using information provided by the computed solution on the current mesh the meshes produced are characterised by the appearance of stretched elements in the vicinity of one dimensional flow features and can exhibit a large variation in element size this allows solutions of enhanced quality to be produced in a computationally efficient manner