on finite strain micromorphic elastoplasticity abstract in the micromorphic continuum theory of eringen it was proposed that microstructure of materials could be represented in a continuum framework using a micro deformation tensor governing micro element deformation in addition to the deformation gradient governing macro element deformation the paper formulates finite strain micromorphic elastoplasticity based on micromorphic continuum mechanics in the sense of eringen multiplicative decomposition into elastic and plastic parts of the deformation gradient and micro deformation are assumed and the clausius duhem inequality is formulated in the intermediate configuration b to analyze what stresses elastic deformation measures and plastic deformation rates are used defined in the constitutive equations the resulting forms of plastic and internal state variable evolution equations can be viewed as phenomenological at their various scales i e micro continuum and macro continuum the phenomenology of inelastic mechanical material response at the various scales can be different but for demonstration purposes j2 flow plasticity is assumed for each of three levels of plastic evolution equations identified with different stress internal state variables and material parameters all evolution equations and a semi implicit time integration scheme are formulated in the intermediate configuration for future coupled lagrangian finite element implementation a simpler two dimensional model for anti plane shear kinematics is formulated to demonstrate more clearly how such model equations simplify for future finite element implementation

mechanics of granular materials the discrete and the continuum descriptions juxtaposed abstract in recent years a discussion could be followed where the pros and cons of the applicability of the cosserat continuum model to granular materials were debated bardet j p vardoulakis i 2001 the asymmetry of stress in granular media int j solids struct 38 353 367 kruyt n p 2003 static and kinematics of discrete cosserat type granular materials int j solids struct 40 511 534 bagi k 2003 discussion on the asymmetry of stress in granular media int j solids struct 40 1329 1331 bardet j p vardoulakis i 2003a reply to discussion by dr katalin bagi int j solids struct 40 1035 kuhn m 2003 discussion on the asymmetry of stress in granular media int j solids struct 40 1805 1807 bardet j p vardoulakis i 2003b reply to dr kuhn s discussion int j solids struct 40 1809 ehlers w ramm e diebels s d addetta g a 2003 from particle ensembles to cosserat continua homogenization of contact forces towards stresses and couple stresses int j solids struct 40 6681 6702 chang c s kuhn m r 2005 on virtual work and stress in granular media int j solids struct 42 3773 3793 the authors follow closely this debate and try with this paper to provide a platform where the various viewpoints could find their position we consider an ensemble of rigid arbitrarily shaped grains as a set with structure we establish a basic mathematical framework which allows to express the balance laws and the action reaction laws for the discrete system in a global form through the concepts of part granular surface separately additive function and flux the independent variable in the balance laws is then the arbitrary part of the assembly rather than the single grain a parallel framework is constructed for cosserat continua by applying the axiomatics established by noll w 1959 the foundation of classical mechanics in the light of recent advances in continuum mechanics in the axiomatic method with special reference to geometry and physics north holland publishing co amsterdam pp 266 281 gurtin m e williams w o 1967 an axiomatic foundation of continuum thermodynamics arch rat mech anal 26 83 117 gurtin m e martins l c 1976 cauchy s theorem in classical physics arch rat mech anal 60 305 324 the comparison between the two realisations suggests the microscopic interpretation for some features of cosserat mechanics among which the asymmetry of the cauchy stress tensor and the couple stress

material symmetries of micropolar continua equivalent to lattices some aspects concerning the identification of continuum coarse models from fine discrete models are discussed the preservation of the mechanical power in the transition from the microscopic to the macroscopic description is required a procedure based on the equivalence of the virtual power provides a natural way to select the continuum satisfying this requirement having the advantages of an integral procedure it gives good results if the coarse model is a multifield continuum with strain fields compatible with those of the fine model in this situation both models share the same material symmetry group this is shown with reference to rigid particle systems in particular the symmetry group of the discrete material is defined and its transformation into that of an equivalent micropolar continuum is studied in detail numerical analyses are also performed to investigate the effect of change in the material symmetries

the asymmetry of stress in granular media here we show that the average stress in granular media which is defined from virtual work may be asymmetric in the absence of contact moments we specify the circumstances and amplitude of stress asymmetry and calculate the corresponding couple stress and first stress moment we also show that the average stress is always symmetric when it is alternately defined by using statics and no contact moment the stress asymmetry which results from external moments has an amplitude that decreases with the volume size the present analysis applies to two and three dimensional particles of arbitrary shapes the asymmetric stress couple stress and first stress moment are analytically calculated in a particular example with cylindrical and spherical particles

statics and kinematics of discrete cosserat type granular materials a theoretical framework is presented for the statics and kinematics of discrete cosserat type granular materials in analogy to the force and moment equilibrium equations for particles compatibility equations for closed loops are formulated in the two dimensional case for relative displacements and relative rotations at contacts by taking moments of the equilibrium equations micromechanical expressions are obtained for the static quantities average cauchy stress tensor and average couple stress tensor in analogy by taking moments of the compatibility equations micromechanical expressions are obtained for the infinitesimal kinematic quantities average rotation gradient tensor and average cosserat strain tensor in the two dimensional case alternatively these expressions for the average cauchy stress tensor and the average couple stress tensor are obtained from considerations of the equivalence of the continuum force and couple traction vectors acting on a plane and the resultant of the discrete forces and couples acting on this plane in analogy the expressions for the average rotation gradient tensor and the average cosserat strain tensor are obtained from considerations of the change of length and change of rotation of a line element in the two dimensional case it is shown that the average particle stress tensor is always symmetrical contrary to the average stress tensor of an equivalent homogenized continuum finally discrete analogues of the virtual work and complementary virtual work principles from continuum mechanics are derived

mixed formulation and locking in path following nonlinear analysis abstract the arc length riks strategy has rapidly become a standard tool for path following analysis of nonlinear structures due to its theoretical ability to surpass limit points the aim of this paper is to show that the failures in convergence that are occasionally experienced are not related to proper defects of the algorithm but come from a subtle locking effect intrinsic to the nonlinear nature of the problem as a consequence its sanitization has to be pursued within a reformulation of the structural model the use of a mixed stress displacement variant of the algorithm in particular appears very promising in this respect the topic is discussed with reference to the analysis of nonlinear frames using a mixed version of the nonlinear beam model discussed in 39 it is shown that with no extra computational cost and only a minor modification in coding with respect to a purely compatible formulation it is possible to achieve a noticeable improvement in convergence and a real gain in both computational time and overall robustness of the algorithm

weighted sensitivity minimization general plants in h and rational weights abstract for general plants in h and rational weighting functions the problem of computing the weighted h optimal sensitivity is considered a general formula is derived for a function whose singularities determine the optimal sensitivity 6 a determinantal expression for the optimal sensitivity is then deduced and related to a conjecture of zhou and khargonekar

asymptotic analysis of heterogeneous cosserat media abstract the present work deals with the development of homogenization procedures for periodic heterogeneous linear elastic cosserat media it is resorted to asymptotic methods classically used in periodic homogenization it is shown that the nature of the homogeneous equivalent medium depends on the hierarchy of three characteristic lengths the size l of the heterogeneities the cosserat intrinsic lengths l c of the constituents and the typical size l of the considered structure when l and l c are comparable and much smaller than l the effective medium is proved to be a cauchy continuum with volume couples whereas the case l c l leads to a cosserat effective medium finite element simulations are provided in the case of a fiber matrix composite for a large range of characteristic lengths l c and for two different volume fractions reference calculations involving every heterogeneity are compared to the response obtained using a homogeneous equivalent medium the results confirm the predicted hierarchy of models and also show that a cosserat effective medium still provide a good estimation when all characteristic lengths have the same order of magnitude

constitutive relation for a particulate medium with the effect of particle rotation abstract the constitutive behavior of granular assemblies is investigated taking into account the effect of particle rotation continuum fields are assumed by tensorial polynomial expansion for the discrete variables namely particle displacements and rotations the strain measures for the packing are obtained from the particle displacement and rotation from the principle of virtual work the stress measures for the packing are expressed in terms of the contact forces the contact moments and the geometric measures for the packing structure the derived stress strain relationship is then evaluated by an example of a randomly packed assembly of circular disks loaded in two different conditions deformation of the packing calculated from the constitutive equations is compared with the results obtained from the discrete method of computer simulation to show the applicability of the method

multilevel approach for brick masonry walls part i a numerical strategy for the nonlinear analysis a numerical strategy based on a multilevel approach is presented for the nonlinear analysis of brick masonry walls as in plane prototypes of large masonry structures the strategy is based on an iterative scheme which uses two different local and global modelings of the masonry mechanics contemporarily the former is the reference mechanical model and is defined at the fine scale of the bricks and mortar joints and describes their nonlinear mechanical interaction including damage evolution and friction toughness phenomena the latter is a linearized finite element approximation of the previous model defined at the rough scale of the wall and used to accelerate the iteration the proposed iterative scheme proves to be efficient and robust in both linear and nonlinear contexts

micro mechanical analysis of deformation characteristics of three dimensional granular materials the deformation characteristics of idealized granular materials have been studied from the micro mechanical viewpoint using bagi s three dimensional micro mechanical formulation for the strain tensor bagi k 1996 mechanics of materials 22 165 177 this formulation is based on the delaunay tessellation of space into tetrahedra the set of edges of the tetrahedra can be divided into physical contacts and virtual contacts between particles bagi s formulation expresses the continuum macro scale strain as an average over all edges of their relative displacements between two successive states and the complementary area vectors this latter vector is a geometrical quantity determined from the set of edges i e from the structure of the particle packing results from discrete element method simulations of isotropic and triaxial loading of a three dimensional polydisperse packing of spheres have been used to investigate statistics of the branch vectors and complementary area vectors of edges subdivided into physical and virtual contacts and of the relative displacements of edges the investigated statistics are probability density functions and averages over groups of edges with the same orientation it is shown that these averages can be represented by second order fourier series in edge orientation edge orientations are distributed isotropically contrary to contact orientations the average lengths of the branch vectors and the normal component of the complementary area vectors are distributed isotropically with respect to the edge orientation and their average values are related to each other and to the volume fraction of the assembly the other two components of the complementary area vector are zero on average the total deformation of the assembly as given by the average of the relative displacements of the edges of the delaunay tessellation follows the uniform strain prediction however neither the deformation of the physical contact network nor of the virtual contact network has this property the average relative displacement of physical edges in the normal direction determined by the branch vector is smaller than that according to the uniform strain assumption while that of virtual contacts is larger this is caused by the high interparticle stiffness that hinders compression the reverse observation holds for the tangential component of the relative displacement vector the contribution of the deformation of the empty space between physical contacts to the continuum macro scale strain tensor is therefore very important for the understanding and the prediction of the macro scale deformation of granular materials

comparative study of different discrete element models and evaluation of equivalent micromechanical parameters abstract comparative studies of different discrete element models of a rock type material are presented the discrete element formulation employs spherical particles with the cohesive interaction model combining linear elastic behaviour with brittle failure numerical studies consisted in simulation of the uniaxial compression test two cylindrical specimens with particle size distributions yielding different degree of heterogeneity have been used macroscopic response produced by different discrete element models has been compared the main difference between the compared models consists in the evaluation of micromechanical constitutive parameters two approaches are compared in the first approach the contact stiffness and strength parameters depend on the local particle size while in the second approach global uniform contact parameters are assumed for all the contacting pairs in function of average geometric measures characterizing the particle assembly the size dependent contact parameters are calculated as functions of geometric parameters characterizing each contacting particle pair as geometric scaling parameters the arithmetic and harmonic means as well as the minimum of the radii of two contacting particles are considered two different models with size dependent contact parameters are formulated the performance of these models is compared with that of the discrete element model with global uniform contact parameters equivalence between the models with size dependent and uniform contact parameters has been checked in search of this equivalence different methods of evaluation of global uniform parameters have been studied the contact stiffness has been evaluated in terms of the average radius of the particle assembly or in terms of the averages of the arithmetic and harmonic means of the contact pair radii the geometric parameters used in the evaluation of the contact stiffness in the size dependent models the uniform contact strengths have been determined as functions of the averages of radii squares squares of arithmetic radii means or squares of minimum radii of the contacting pairs for the more homogenous specimen the models with local size dependent parameters and models with global uniform parameters give similar response the models with uniform parameters evaluated according to the averages of the geometric parameters used in the evaluation of local parameters ensure better agreement with the respective models with size dependent parameters than the models with uniform parameters evaluated according to the particle radii simulations using the more heterogenous specimen reveal differences between the considered models there are significant differences in stress strain curves as well as in the failure pattern the models with local size dependent parameters are more sensitive to the change of heterogeneity than the model with global uniform parameters

multilevel approach for brick masonry walls part ii on the use of equivalent continua abstract this work investigates the possibility of using equivalent continua within a multilevel strategy for the analysis of brick masonry walls as prototypes for the in plane behavior of masonry buildings this strategy proposed and discussed in detail in part i of the same paper lies in an iterative solution scheme which uses two levels local and global of description the former accounts for the interaction between the single bricks the latter modeled as a coarse finite element discretization accounts for global interactions within the same finite element format and strategy the paper compares the performances of schemes implementing the identification procedures based on equivalent continua with those implementing the algebraic re parametrization of the local model proposed in part i the former while suitable for a synthetic representation of masonry behavior does not prove to be convenient for a multilevel solution strategy

non linear micropolar and classical continua for anisotropic discontinuous materials non linear cosserat and cauchy anisotropic continua equivalent to masonry like materials like brick block masonry jointed rocks granular materials or matrix particle composites are presented an integral procedure of equivalence in terms of mechanical power has been adopted to identify the effective elastic moduli of the two continuous models starting from a lagrangian system of interacting rigid elements non linear constitutive functions for the interactions in the lagrangian system are defined in order to take into account both the low capability to carry tension and the friction at the interfaces between elements the non linear problem is solved through a finite element procedure based on the iterative adjustment of the continuum constitutive tensor due to the occurrence of some limit situation involving the contact actions of the discrete model differences between the classical and the micropolar model are investigated with the aid of numerical analyses carried out on masonry walls made of blocks of different size the capability of the micropolar continuum to discern unlike the classical continuum the behaviour of systems made of elements of different size is pointed out it is also shown that for anisotropic materials even in the elastic case the micropolar solution in general does not tend to the classical solution when the size of the elements vanishes 2002 elsevier science ltd all rights reserved

linear control theory with an h 0e optimality criterion this expository paper sets out the principal results in bf h infty control theory in the context of continuous time linear systems the focus is on the mathematical theory rather than computational methods

singular values and vectors of a class of hankel operators abstract this paper considers the problem of determining the singular values and vectors of the class of hankel operators whose symbol can be written in the form w where is inner and w is rational we will obtain a new and simplified proof of the fact conjectured in 17 and first proved in 9 that the zeros of a certain determinantal expression coincide with the hankel singular values we will also show how this expression can be used to generate the singular vectors

weighted sensitivity minimization for delay systems in this note we discuss the h infty sensitivity minimization problem for linear time invariant delay systems while the unweighted case reduces to simple nevanlinna pick interpolation the weighted case turns out to be much more complicated and demands certain functional analytic techniques for its solution

on the parametrization of the suboptimal solutions in generalized interpolation abstract we apply methods previously developed to give a explicit parametrization of the suboptimal solutions to the standard h generalized interpolation problem this gives in particular a simple parametrization of all the suboptimal controllers of the standard sensitivity minimization problem

generalized bridging domain method for coupling finite elements with discrete elements abstract the concurrent coupling of finite elements and discrete elements is an effective dof reduction methodology for reproducing the granular flow phenomenon as discrete element method does in this paper we present a novel coupling strategy named the generalized bridging domain method this method introduces independent functions to weight the material properties of the continuum and those of the discrete element model and then the equilibrium of each new model is guaranteed by imposing compensation forces the compensation force of continuum is determined by force and displacement compatibility requirements of continuum with respect to discrete elements and vice versa utilizing different weighting functions four typical coupling methods the bridging domain method edge to edge coupling separate domain coupling and separate edge coupling are obtained additionally a new integration algorithm with multiple time steps is developed for the separate edge coupling the numerical performance of the separate domain coupling where displacement compatibility condition of continuum and that of discrete elements are individually enforced by the lagrange multiplier method has been investigated in detail results of several numerical examples show that the separate domain coupling outperforms other methods in avoiding spurious reflection and the separate edge coupling is effective enough for coupling finite elements with discrete elements due to the truncation of high frequency waves there exists energy loss but at an acceptable level if the waves can be resolved by the macroscopic finite element model

homogenization of interlocking masonry structures using a generalized differential expansion technique in this paper a micromorphic continuum is derived for the homogenization of masonry structures with interlocking blocks this is done by constructing a continuum which maps exactly the kinematics of the corresponding discrete masonry structure and has the same internal and kinetic energy for any virtual translational and rotational field the obtained continuum is an anisotropic micromorphic continuum of second order the enriched kinematics of micromorphic continua allows to model microelement systems undergoing both translations and rotations the homogenization technique applied here excludes averaging and keeps all the necessary information of the discrete structure therefore all the dispersion curves of the discrete system are reproduced in the continuum model

a mixed solution strategy for the nonlinear analysis of brick masonry walls the paper presents a discrete mechanical model for masonry walls based on a lagrangean description where each brick is described as a rigid body and each mortar joint as an interface element constitutive assumptions characterized by elasticity damage and friction are associated to the joints only a numerical solution strategy based on a mixed path following approach in terms of stresses strains displacements damage and load parameters is proposed for avoiding convergence problems related to the joint softening behaviour some numerical results are also presented showing the robustness and effectiveness of this proposal

on decoupling the h optimal sensitivity problem for products of plants abstract in this note we show how to solve the h optimal sensitivity problem for a siso plant p s p 1 s p 2 s given the solutions for p 1 s p 2 s this allows us to solve the problem for systems of the form e hs p 0 s where p 0 s is the transfer function of a stable lti finite dimensional system

discrete derivatives and symmetries of difference equations we show with an example of the discrete heat equation that for any given discrete derivative we can construct a nontrivial leibniz rule suitable for finding the symmetries of discrete equations in this way we obtain a symmetry lie algebra defined in terms of shift operators isomorphic to that of the continuous heat equation

approximation of stable systems by laguerre filters laguerre methods are used to develop concrete techniques and results for approximating stable infinite dimensional systems both hankel norm and l approximation by laguerre filters are studied the infimum of the hankel norm approximation error when the system is approximated by laguerre filters of given maximum order is given by the norm of a certain shifted hankel operator and the best laguerre filter to approximate the system is obtained essentially from the associated eigenproblem for the shifted hankel operator hankel optimal laguerre filters are here called cf laguerre filters as there is a certain connection to the caratheodory fejer interpolation problem and typically provide near best solutions to related l approximation problems a time domain compressed laguerre shift method for solving certain nehari problems for delay systems is used to determine analytically the achievable hankel error norms and thus also to obtain bounds for the achievable l error norm for delay systems a result on a laguerre filter approximation problem in the hilbert schmidt norm is given as well

some remarks on optimal interpolation abstract we give in this note very simple new formula for the optimal solution of a generalized interpolation problem which arises in the weighted sensitivity h minimization for distributed systems this is based on our work on skew toeplitz operators from 2

new time type and space type non standard quantum algebras and discrete symmetries starting from the classical r matrix of the non standard or jordanian quantum deformation of the sl 2 algebra new triangular quantum deformations for the real lie algebras so 2 2 so 3 1 and iso 2 1 are simultaneously constructed by using a graded contraction scheme these are realized as deformations of conformal algebras of 1 1 dimensional spacetimes time and space type quantum algebras are considered according to the generator that remains primitive after deformation either the time or the space translation respectively furthermore by introducing differential difference conformal realizations these families of quantum algebras are shown to be the symmetry algebras of either a time or a space discretization of 1 1 dimensional wave and laplace equations on uniform lattices the relationship with the known lie symmetry approach to these discrete equations is established by means of twist maps

stress strain relationship for granular materials based on the hypothesis of best fit abstract stress strain relationships of a granular system are derived based on the premise that the mean field of displacement is the best fit of actual particle displacements based on the best fit hypothesis two fundamental relationships are derived 1 the average strain as a function of contact displacements and 2 the mean field of contact force as a function of stress these two relationships lead to a stress strain law without the kinematic constraint of uniform strain for an assembly with isotropic packing structure closed form stress strain relationships are explicitly derived in which the modulus can be determined from the inter particle stiffness the difference between the derived stress strain relationship and that derived from voigt hypothesis is discussed the effect of fabric variation is illustrated in the theory discrete element analyses are also performed and the results are used to compare with the estimated moduli from the proposed theory in the comparison the solution bounds for granular assembly system are illustrated

on the h optimal sensitivity problem for systems with delays in this paper we extend some of the results of ieee trans automat control ac 31 1986 pp 763 766 to more general delay systems in particular we analyze the effect of the interaction of delays and nonminimum phase zeros on the h infty optimal weighted sensitivity

elastic properties of isotropic discrete systems connections between geometric structure and poisson s ratio abstract the use of discrete material representation in numerical models is advantageous due to the straightforward way it takes into account material heterogeneity and randomness and the discrete and orientated nature of cracks unfortunately it also restricts the macroscopic poisson s ratio and therefore narrows its applicability the paper studies the poisson s ratio of a discrete model analytically it derives theoretical limits for cases where the geometry of the model is completely arbitrary but isotropic in the statistical sense it is shown that the widest limits are obtained for models where normal directions of contacts between discrete units are parallel with the vectors connecting these units any deviation from parallelism causes the poisson s ratio limits to shrink a comparison of the derived equations to the results of the actual numerical model is presented it shows relatively large deviations from the theory because the fundamental assumptions behind the theoretical derivations are largely violated in systems with complex geometry the real shrinking of the poisson s ratio limit is less severe compared to that which is theoretically derived

umbral calculus difference equations and the discrete schrodinger equation in this paper we discuss umbral calculus as a method of systematically discretizing linear differential equations while preserving their point symmetries as well as generalized symmetries the method is then applied to the schrodinger equation in order to obtain a realization of nonrelativistic quantum mechanics in discrete space time in this approach a quantum system on a lattice has a symmetry algebra isomorphic to that of the continuous case moreover systems that are integrable superintegrable or exactly solvable preserve these properties in the discrete case

feedback and optimal sensitivity model reference transformations multiplicative seminorms and approximate inverses in this paper the problem of sensitivity reduction by feedback is formulated as an optimization problem and separated from the problem of stabilization stable feedback schemes obtainable from a given plant are parameterized salient properties of sensitivity reducing schemes are derived and it is shown that plant uncertainty reduces the ability of feedback to reduce sensitivity the theory is developed for input output systems in a general setting of banach algebras and then specialized to a class of multivariable time invariant systems characterized by n times n matrices of h infty frequency response functions either with or without zeros in the right half plane the approach is based on the use of a weighted seminorm on the algebra of operators to measure sensitivity and on the concept of an approximate inverse approximate invertibility of the plant is shown to be a necessary and sufficient condition for sensitivity reduction an indicator of approximate invertibility called a measure of singularity is introduced the measure of singularity of a linear time invariant plant is shown to be determined by the location of its right half plane zeros in the absence of plant uncertainty the sensitivity to output disturbances can be reduced to an optimal value approaching the singularity measure in particular if there are no right half plane zeros sensitivity can be made arbitrarily small the feedback schemes used in the optimization of sensitivity resemble the lead lag networks of classical control design some of their properties and methods of constructing them in special cases are presented

on the nehari problem for a certain class of l functions appearing in control theory ii abstract in this paper we generalize the results of c foias and a tannenbaum j functional analysis 74 1987 146 159 on the classical nehari problem to a much broader class of operators we relate our results to the computation of the discrete spectrum for a certain class of contractions which appear frequently in control engineering applications

symmetries of the wave equation in a uniform lattice the symmetries of discrete versions of a class of equations that includes klein gordon and wave equations on a two dimensional grid are studied they close the same lie algebra as the corresponding continuous equations the relationship to difference special functions is also given

a micromechanical model for a non linear elastic granular material based on local equilibrium conditions abstract a micromechanical model is developed to study the non linear elastic stress strain relation of a homogenous isotropic granular solid consisting of a random package of identical elastic spheres with contacts equally distributed in all directions in order to obtain the effective tangent elastic moduli of the random packing subject to an isotropic pressure the equilibrium of each particle is imposed in an approximate way and the strain energy of a representative volume element containing a huge number of particles is determined to this aim a variational approach is adopted by decomposing the displacement field into the sum of a mean field and a fluctuation field it is shown that the elastic moduli so determined differ considerably from the values obtained by using classical homogenization procedures based on the uniform strain voigt hypothesis and are in closer agreement with the experimental results

on h optimal sensitivity theory for siso feedback systems this paper deals with the design of feedback controllers which minimize the h infty norm of the sensitivity function suitably weighted this approach to the theory of feedback design was introduced by zames 1 and developed by zames and francis 2 in this paper the theory of sarason 3 is applied to the determination of the optimal weighted sensitivity function and an upper bound on its norm the problem of achieving small sensitivity over a specified frequency band is studied and the effect of nonminimum phase is elucidated finally a method is introduced for handling plant poles and zeros on the imaginary axis

analysis of three dimensional micro mechanical strain formulations for granular materials evaluation of accuracy an important objective of recent research on micro mechanics of granular materials is to develop macroscopic constitutive relations in terms of micro mechanical quantities at inter particle contacts although the micro mechanical formulation of the stress tensor is well established the corresponding formulation for the strain tensor has proven to be much more evasive still being the subject of much discussion in this paper we study various micro mechanical strain formulations for three dimensional granular assemblies following the work of bagi in two dimensions bagi 2006 all of these formulations are either based on an equivalent continuum approach or follow the best fit approach their accuracy is evaluated by comparing their results using data from discrete element method simulations on periodic assemblies to the macroscopic deformation it is found that bagi s formulation bagi 1996 which is based on the delaunay tessellation of space is the most accurate furthermore the best fit formulation based on particle displacements only did unexpectedly well in contrast to previously reported results for two dimensional assemblies

on hankel operators associated with a class of non toeplitz operators the classical nehari theorem 7 p 43 gives the distance from a bounded measurable function cp on the unit circle t to h the algebra of bounded measurable functions on t with zero negative fourier coefficients the distance is the norm of the hankel operator defined by cp this result was followed by the result of hartman 7 p 61 giving the distance from cp to the algebra h c generated by h and the continuous functions on t as the essential norm of the hankel operator defined by rp as was shown by adamjan arov and krein 11 these two results are extremal cases of the following result if r denotes the rational functions on t with no more than n poles counting multiplicities in the interior of t then the distance from cp to h r is given by the nth s number of the hankel operator defined by cp in this paper we present operator theoretic analogues of these results we define for an operator t acting on the hilbert sequence h2 of square summable complex sequences a sequence of operators on h which when it converges converges to a hankel operator h t in the case where t is a toeplitz operator h t is the classical hankel operator associated with t we give a necessary and sufficient condition for the existence of h t and show that h t exists for a large class of non toeplitz operators we then define the corresponding operator theoretic analogues to the above function theoretic results in terms of the s numbers of the hankel operator h t associated with t note that since h t is in fact a hankel operator in the classical sense all these numbers can be computed using the algorithms of foias tannenbaum s a problem closely related to the problem discussed here was studied by barria and halmos s the relationship between the two problems is discussed in detail in 9 1 oc22 1236190 3 00

on large deformation granular strain measures for generating stress strain relations based upon three dimensional discrete element simulations abstract generating stress strain relations based upon three dimensional discrete element simulations for hierarchical multiscale constitutive modeling of granular materials at finite strain requires measures of stress and strain in the reference and current configurations the cauchy stress tensor calculated from interparticle forces and branch vectors resulting from discrete element simulations is well established but the various finite strain definitions existing in the literature are not as well studied or accepted thus the paper develops seven finite strain measures in three dimensions cartesian coordinates assumed two are calculated in the reference configuration and five are calculated in the current configuration in the process a time integrated deformation gradient is formulated with which the cauchy stress tensor can be mapped to either the kirchhoff stress first piola kirchhoff stress or second piola kirchhoff stress the difficulty in calculating strain measures for granular materials is the discrete particulate nature of the materials in the paper strain measures are motivated by the equivalent continuum method but are extended to finite strain in three dimensions simulations are conducted to test the finite strain measures and it is found that these strain measures are independent of rigid body rotation of a particle assembly granular cauchy stress is also calculated for these discrete element simulations to be able to plot stress strain curves in the current configuration finally two numerical examples with large deformation are simulated 1 cavity expansion and 2 pile penetration and their results are analyzed

stabilization and sensitivity for eventually time invariant systems abstract this paper studies the stability and minimal sensitivity of a time varying system which as time passes becomes more and more time invariant

invariant manifolds in mechanics i the general construction of coarse theories from fine theories la theorie dite fine fournit potentiellement des informations tres detaillees sur le comportement du materiau et generalement plus d informations que necessaire tandis que la theorie dite grossiere donne des informations brutes plus accessibles qui peuvent etre suffisantes dans des circonstances donnees presentation d une methode permettant de deduire les theories grossieres des theories fines

sensitivity minimization for arbitrary siso distributed plants abstract in this note we write down an explicit formula for the computation of the optimal sensitivity of an arbitrary single input single output linear invariant distributed plant we moreover discuss the uniqueness of the optimal compensator and work out a design example

on the weighted sensitivity minimization problem for delay systems we consider the h optimal sensitivity problem for delay systems in particular we consider computation of inf w q q h jr where w s is any function in rh jr and in h jr is any inner function we derive a new explicit solution in the pure delay case where e sh h 0

an interpolation problem associated with h optimal design in systems with distributed input lags the symbol for infinity appears as superscript in title where indicated by the word infinity in brackets

nehari problems and equalizing vectors for infinite dimensional systems for a class of infinite dimensional systems we obtain a simple frequency domain solution for the suboptimal nehari extension problem the approach is via j spectral factorization and it uses the concept of an equalizing vector moreover the connection between the equalizing vectors and the nehari extension problem is given

a finite element with micro scale effects for the linear analysis of masonry brickwork in this paper we present a two dimensional finite element able to describe local effects in the linear analysis of periodic brickwork modelled as a lagrangean system of rigid bodies interacting by point elastic interfaces particular emphasis is given to the description and the implications of the continuum modelling of the lagrangean system before the finite element discretization is performed

a polynomial approach to hankel norm and balanced approximations abstract a new unified approach to problems of hankel norm and balanced approximations is presented which is based on a combination of polynomial algebra and the geometry of invariant subspaces contrary to state space methods where contact with external properties of systems is indirect the approach presented yields new insights into basic properties of hankel norm approximation and balanced realizations several approximation results are interpreted geometrically in terms of projections also duality results in this area are printed out

analytic system problems and j lossless coprime factorization for infinite dimensional linear systems abstract this paper extends the coprime factorization approach to the synthesis of internally stabilizing controllers satisfying an h norm bound to a class of systems with irrational transfer matrices using the coprime factorization description the h control problem can be reduced to two stable analytic system problems such problems have solutions if and only if a certain j lossless factorization exists the full h synthesis problem is shown to be equivalent to the solution of two nested j lossless factorizations if the irrational transfer matrix has a state space realization then the known state space formulas for the h control problem may be recovered using the relationship between j lossless factorizations and solutions of riccati equations however the results derived here are valid for a larger class of infinite dimensional systems

symmetries and conditional symmetries of differential difference equations two different methods of finding lie point symmetries of differential difference equations are presented and applied to the two dimensional toda lattice continuous symmetries are combined with discrete ones to obtain various reductions to lower dimensional equations in particular to differential equations of the delay type the concept of conditional symmetries is extended from purely differential to differential difference equations and shown to incorporate backlund transformations

continuum modeling of periodic brickwork continuum models of periodic masonry brickwork viewed at a micro level as a discrete system are identified within the frame of linearized elasticity the accuracy of various identification schemes is investigated for standard and micropolar continua which are directly compared with the help of some numerical benchmarks for different loading conditions that induce periodic and non periodic deformation states it is shown that periodic deformation states of brickwork are exactly reproduced by both continua provided that a suitable identification scheme is adopted for non periodic states micropolar continuum is shown to better reproduce the discrete solutions due to its capability to take scale effects into account both continua are asymptotically equivalent as the characteristic length of the discrete system tends to zero while providing an upper and a lower bound of the discrete solution

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

quantum symmetries of q difference equations a general method is presented to determine the symmetry operators of linear q difference equations it is applied to q difference analogs of the helmoltz heat and wave equations in diverse dimensions the symmetries are found to generate q deformations of classical lie algebras the method of separation of variables is used to obtain solutions which are seen to involve many basic special functions this allows the derivation of various identities and formulas for these q functions