wave reflection from the free end of a cylinder with an arbitrary cross section elastic wave scattering at the free end of a cylinder due to an incident monochromatic wave is investigated the cross section may have an arbitrary geometry with any number of distinct elastic rectilinear anisotropic materials comprising its planar profile the governing equations are based on a semi analytical finite element method in which the cross sectional behavior is modeled by general two dimensional finite elements with the axial dependence and time left unspecified at the outset first all the modal data for the cylinder are established two eigenproblems are posed for this purpose that are obtained by inserting a wavelike solution form into the governing equations these eigenproblems allow all propagating waves and end modes for the cylinder to be determined propagating modes are traveling waves with energy transport capabilities while the end modes are standing vibrations which in contrast do not transport any energy into the interior of the cylinder these eigendata are the basis for representing the wave reflection phenomenon at the free end the amplitudes of the traveling waves and end modes that satisfy traction free end conditions may be determined by least squares minimization or by a virtual work method four cylinders with different cross sectional geometries were considered to illustrate the analysis procedure and reveal some physical insight into the frequency dependent wave reflection phenomena in them

a mixed variational formulation based on exact intrinsic equations for dynamics of moving beams abstract a nonlinear intrinsic formulation for the dynamics of initially curved and twisted beams in a moving frame is presented the equations are written in a compact matrix form without any approximations to the geometry of the deformed beam reference line or to the orientation of the intrinsic cross section frame in accordance with previously published work when effects of warping on the dynamics and local constraints on the cross sectional deformation are ignorable the in and out of plane st venant warping displacements which are fully coupled for nonhomogeneous anisotropic beams need only be included explicitly in the determination of a suitable elastic law a two dimensional problem and need not be considered explicitly in the one dimensional equations governing global deformation in this paper it is presupposed that such an elastic law is given as a one dimensional strain energy function thus the present equations which are based on only six generalized strain variables are valid for beams with closed cross sections and for which warping is unrestrained when simplified for various special cases they agree with similar intrinsic equations in the literature although the resulting equations are newtonian in structure closely resembling euler s dynamical equations for a rigid body the formulation adheres to a variational approach throughout thus providing a link between newtonian and energy based methods in particular the present development provides substantial insight into the relationships among variational formulations in which different displacement and rotational variables are used as well as between these formulations and newtonian ones for computational purposes a compact and complete mixed variational formulation is presented that is ideally suited for development of finite element analyses finally a specialized version of the intrinsic equations is developed in which shear deformations is suppressed

a higher order beam finite element for bending and vibration problems abstract the finite element equations for a variationally consistent higher order beam theory are presented for the static and dynamic behavior of rectangular beams the higher order theory correctly accounts for the stress free conditions on the upper and lower surfaces of the beam while retaining the parabolic shear strain distribution the need for a shear correction coefficient is therefore eliminated full integration of the shear stiffness terms is shown to result in the recovery of the kirchhoff constraint for thin beams without introducing spurious locking constraints the accuracy of this formulation is demonstrated by using several numerical examples for the cases of small and large displacements for a hinged hinged beam the linear thickness shear mode frequency can be matched with the timoshenko frequency to yield a shear coefficient of 0 824 matching the bending frequencies between the two theories indicates a shear coefficient for the timoshenko theory that changes with mode number and slenderness ratio the influence of in plane inertia and slenderness ratio on the non linear frequency is examined for beams with a number of different support conditions

an intrinsic beam model based on a helicoidal approximation part i formulation the focus of the present work is directed towards the one dimensional non linear analysis of space curved and twisted beams undergoing large displacements and finite rotations according to cosserat s model a beam is intended here as a continuum generated by the rigid motion of a cross section along a curve the novelty of the proposed methodology is implied in the assumption that the reference line of the beam both in the undeformed and in the deformed configurations is a helicoid in space this formulation radically departs from the classical beam models based on polynomial interpolations of the independent fields in fact within the framework of helicoidal geometry a powerful description of space curved beam kinematics with large displacements and finite rotations can be developed furthermore the beam model developed herein can be proved to enjoy several invariance properties that make it particularly attractive for non linear analysis the formulation discussed in this work adheres to a mixed variational principle the independent fields being the generalized displacements and the sectional stress resultants in a companion paper we address the linearization of the governing weak form the finite element implementation of the proposed methodology with a novel incremental treatment of finite rotations and the development of a helicoidal model for rigid body dynamics using finite elements in time

much ado about shear correction factors in timoshenko beam theory abstract many shear correction factors have appeared since the inception of timoshenko beam theory in 1921 while rational bases for them have been offered there continues to be some reluctance to their full acceptance because the explanations are not totally convincing and their efficacies have not been comprehensively evaluated over a range of application herein three dimensional static and dynamic information and results for a beam of general both symmetric and non symmetric cross section are brought to bear on these issues only homogeneous isotropic beams are considered semi analytical finite element safe computer codes provide static and dynamic response data for our purposes greater clarification of issues relating to the bases for shear correction factors can be seen also comparisons of numerical results with timoshenko beam data will show the effectiveness of these factors beyond the range of application of elementary bernoulli euler theory an issue concerning principal shear axes arose in the definition of shear correction factors for non symmetric cross sections in this method expressions for the shear energies of two transverse forces applied on the cross section by beam and three dimensional elasticity theories are equated to determine the shear correction factors this led to the necessity for principal shear axes we will argue against this concept and show that when two forces are applied simultaneously to a cross section it leads to an inconsistency only one force should be used at a time and two sets of calculations are needed to establish the shear correction factors for a non symmetrical cross section

distributed control of spatially invariant systems we consider distributed parameter systems where the underlying dynamics are spatially invariant and where the controls and measurements are spatially distributed these systems arise in many applications such as the control of vehicular platoons flow control microelectromechanical systems mems smart structures and systems described by partial differential equations with constant coefficients and distributed controls and measurements for fully actuated distributed control problems involving quadratic criteria such as linear quadratic regulator lqr h sub 2 and h sub spl infin optimal controllers can be obtained by solving a parameterized family of standard finite dimensional problems we show that optimal controllers have an inherent degree of decentralization and this provides a practical distributed controller architecture we also prove a general result that applies to partially distributed control and a variety of performance criteria stating that optimal controllers inherit the spatial invariance structure of the plant connections of this work to that on systems over rings and systems with dynamical symmetries are discussed

a predictive control scheme for systems with variable time delay this article deals with the robust control design problem for linear time invariant systems affected by variable feedback delay constraints on the system state are considered in the system description the starting point is the construction of a predictive control law which guarantees the existence of a nonempty robust positive invariant rpi set with respect to the closed loop dynamics subsequently an iterative algorithm is proposed in order to obtain an approximation of the maximal rpi set the problem can be treated in the framework of piecewise affine systems due to the explicit formulations of the control law obtained via multiparametric programming

average consensus with packet drop communication average consensus consists in the problem of determining the average of some quantities by means of a distributed algorithm it is a simple instance of problems arising when designing estimation algorithms operating on data produced by sensor networks simple solutions based on linear estimation algorithms have already been proposed in the literature and their performance has been analyzed in detail if the communication links which allow the data exchange between the sensors have some loss then the estimation performance will degrade in this contribution the performance degradation due to this data loss is evaluated

expander graphs and their applications a major consideration we had in writing this survey was to make it accessible to mathematicians as well as to computer scientists since expander graphs the protagonists of our story come up in numerous and often surprising contexts in both fields but perhaps we should start with a few words about graphs in general they are of course one of the prime objects of study in discrete mathematics however graphs are among the most ubiquitous models of both natural and human made structures in the natural and social sciences they model relations among species societies companies etc in computer science they represent networks of communication data organization computational devices as well as the flow of computation and more in mathematics cayley graphs are useful in group theory graphs carry a natural metric and are therefore useful in geometry and though they are just one dimensional complexes they are useful in certain parts of topology e g knot theory in statistical physics graphs can represent local connections between interacting parts of a system as well as the dynamics of a physical process on such systems the study of these models calls then for the comprehension of the significant structural properties of the relevant graphs but are there nontrivial structural properties which are universally important expansion of a graph requires that it is simultaneously sparse and highly connected expander graphs were first defined by bassalygo and pinsker and their existence first proved by pinsker in the early 70s the property of being an expander seems significant in many of these mathematical computational and physical contexts it is not surprising that expanders are useful in the design and analysis of communication networks what is less obvious is that expanders have surprising utility in other computational settings such as in the theory of error correcting codes and the theory of pseudorandomness in mathematics we will encounter e g their role in the study of metric embeddings and in particular in work around the baum connes conjecture expansion is closely related to the convergence rates of markov chains and so they play a key role in the study of monte carlo algorithms in statistical mechanics and in a host of practical computational applications the list of such interesting and fruitful connections goes on and on with so many applications we will not even

integration of elastic multibody systems by invariant conserving dissipating algorithms ii numerical schemes and applications abstract this work presents a novel methodology for the dynamic analysis of general non linear multibody systems composed of rigid and deformable bodies the latter under the small strain assumption in part i we developed the 6 d compact representation and parameterization of motion for constrained bodies part ii is devoted to the design of a class of modified runge kutta rk methods dedicated to non linear dynamics these are capable of integrating on the configuration manifold and of preserving linear and angular momenta within this class of methods two second order algorithms are designed under the requirement of attaining non linear unconditional stability the energy preserving ep and energy decaying ed methods these schemes are associated with an algorithmic law of conservation and dissipation respectively of the total mechanical energy of the system together with the vanishing of the algorithmic work done by ideal time independent constraints their performances are assessed with the aid of some representative numerical applications which confirm the non conventional properties predicted in the analysis

integrating finite rotations abstract we study the integration of problems of evolution in the rotation group instead of attacking the problem in the nonlinear differential manifold so 3 pure rotational dynamics as is usually done we derive equations for the complete problem of motion translational and rotational dynamics on an extended manifold we develop a generalization of runge kutta methods that by design ensures that the solution will remain on the manifold for any choice of the tableau this is obtained through configuration updates performed via the exponential map we show how certain terms can be approximated while retaining the order of accuracy of the scheme and how the method conserves the total momentum of the system within this framework we develop two nonlinearly unconditionally stable time integration schemes that are associated with discrete laws of conservation dissipation of the total energy the dissipating algorithm generalizes to the nonlinear case the high frequency damping characteristics provided by some well known conventional methods we present numerical results to support our analysis and we develop a complete application of this methodology to the nonlinear dynamics of three dimensional rods undergoing large displacements and finite rotations under the assumption of small strains

on asymptotically correct timoshenko like anisotropic beam theory abstract this paper presents a finite element cross sectional beam analysis capable of capturing transverse shear effects the approach uses the variational asymptotic method and can handle beams of general cross sectional shape and arbitrary anisotropic material the work builds on previous works which deal with development of the classical beam theory which includes only extension torsion and bending a timoshenko like formulation is sought to achieve a refined theory with simple boundary conditions apart from some simple special cases it is shown that this problem is overdetermined however it is possible to obtain the best possible solution using the least squares minimization technique the geometrical meaning of the shear variable for this formulation is also derived results are found to be in good agreement with published results for the shear stiffness coefficients for both isotropic and anisotropic beams

on the analysis of prismatic beams using first order warping functions abstract a one dimensional theory for isotropic homogeneous beams with a general cross section is developed that utilizes both deformations in the cross section plane and warping out of the cross section plane where these deformation functions are known from saint venant s elasticity solutions for bending and flexure of a prismatic beam first order warping functions in contrast to existing technical beam theories which assume that local cross section deformations and some stresses can be neglected the present theory makes no assumption the finite element model is developed using the resulting differential equations along with a partially weak form formulation full three dimensional constitutive equations are used solutions are found using the finite element method numerical results which are presented for a wide variety of loadings and boundary conditions show that the calculated stresses and displacements are in excellent agreement with existing elasticity solutions

recent developments on the stability of systems with aperiodic sampling an overview this article presents basic concepts and recent research directions about the stability of sampled data systems with aperiodic sampling we focus mainly on the stability problem for systems with arbitrary time varying sampling intervals which has been addressed in several areas of research in control theory systems with aperiodic sampling can be seen as time delay systems hybrid systems input output interconnections discrete time systems with time varying parameters etc the goal of the article is to provide a structural overview of the progress made on the stability analysis problem without being exhaustive which would be neither possible nor useful we try to bring together results from diverse communities and present them in a unified manner for each of the existing approaches the basic concepts fundamental results converse stability theorems when available and relations with the other approaches are discussed in detail results concerning extensions of lyapunov and frequency domain methods for systems with aperiodic sampling are recalled as they allow to derive constructive stability conditions furthermore numerical criteria are presented while indicating the sources of conservatism the problems that remain open and the possible directions of improvement at last some emerging research directions such as the design of stabilizing sampling sequences are briefly discussed

stability of multiagent systems with time dependent communication links we study a simple but compelling model of network of agents interacting via time dependent communication links the model finds application in a variety of fields including synchronization swarming and distributed decision making in the model each agent updates his current state based upon the current information received from neighboring agents necessary and or sufficient conditions for the convergence of the individual agents states to a common value are presented thereby extending recent results reported in the literature the stability analysis is based upon a blend of graph theoretic and system theoretic tools with the notion of convexity playing a central role the analysis is integrated within a formal framework of set valued lyapunov theory which may be of independent interest among others it is observed that more communication does not necessarily lead to faster convergence and may eventually even lead to a loss of convergence even for the simple models discussed in the present paper

the helicoidal modeling in computational finite elasticity part ii multiplicative interpolation abstract the approximate substitute model of the position and orientation fields over a finite multi coordinate domain is built in a consistent way with the helicoidal modeling of the continuum as proposed in part i for a discrete application of variational principles in computational elasticity the set of the position and orientation referred to as oriento position is made dependent multiplicatively on the nodal values through relative rototranslations and an implicit interpolation formula is written by weighting the relative helices the proposed interpolation scheme is frame invariant and path independent and the resulting weighted average oriento position is obtained numerically a consistent linearization of the model field is carried out by developing explicit formulae for the derivatives up to third order of orthogonal tensors the parent interpolation of the orientation field which can be useful by itself in the context of classical modeling is also discussed

validation of the variational asymptotic beam sectional analysis the computer program vabs variational asymptotic beam section analysis uses the variational asymptotic method to split a three dimensional nonlinear elasticity problem into a twodimensional linear cross sectional analysis and a one dimensional nonlinear beam problem this is accomplished by taking advantage of certain small parameters inherent to beam like structures vabs is able to calculate the one dimensional cross sectional stiffness constants with transverse shear and vlasov refinements for initially twisted and curved beams with arbitrary geometry and material properties several validation cases are presented first an elliptic bar is modeled with transverse shear refinement using the variational asymptotic method and the solution is shown to be identical to that obtained from the theory of elasticity the shear center locations calculated by vabs for various cross sections agree well with those obtained from common engineering analyses comparisons with other composite beam theories prove that it is unnecessary to introduce ad hoc kinematic assumptions to build an accurate beam model for numerical validation values of the one dimensional variables are extracted from an abaqus model and compared with results from a one dimensional beam analysis using cross sectional constants from vabs furthermore point wise three dimensional stress and strain fields are recovered using vabs and the correlation with the three dimensional results from abaqus is excellent finally classical theory is shown to be insufficient for general purpose beam modeling appropriate refined theories are recommended for some classes of problems

finite element theory for curved and twisted beams based on exact solutions for three dimensional solids part 1 beam concept and geometrically exact nonlinear formulation a geometrically exact and completely consistent finite element theory for curved and twisted beams is proposed it is based on the kinematical hypothesis generally formulated for large deformation and accounts for all kinds of deformation of a three dimensional solid translational and rotational displacements of the cross sections warping of their plane and distortion of their contours the principle of virtual work is applied in a straightforward manner to all non zero six components of the strain and stress tensors expressions are given for tangent matrices of elastic inertia and external forces and specific techniques for discretization and updating are developed for the analysis of beams in inertial and non inertial frames finally the numerical properties of the finite element models are demonstrated through examples c 1998 elsevier science s a all rights reserved

the spectra of infinite hypertrees a model of regular infinite hypertrees is developed to mimic for hypergraphs what infinite trees do for graphs two notions of spectra or first eigenvalue are then examined for the infinite tree obtaining a precise value for the first notion and obtaining some estimates for the second the results indicate agreement of the first eigenvalue of the infinite hypertree with the second eigenvalue of a random hypergraph of the same degree to within logarithmic factors at least for the first notion of first eigenvalue author s abstract

advanced 3d beam element of arbitrary composite cross section including generalized warping effects summary in this paper an advanced 20 20 stiffness matrix and the corresponding nodal load vector of a member of arbitrary composite cross section is developed taking into account shear lag effects due to both flexure and torsion the case of the three dimensional beam element of arbitrary homogeneous cross section is treated as a special one the composite member consists of materials in contact each of which can surround a finite number of inclusions nonuniform warping distributions are taken into account by employing four independent warping parameters multiplying a shear warping function in each direction and two torsional warping functions ten boundary value problems with respect to the kinematical components are formulated and solved employing the analog equation method a bem based technique the aforementioned boundary value problems are formulated employing either an improved stress field arising from the correction of shear stress components or the stress field arising directly from displacement considerations the warping functions and the geometric constants including the additional ones due to warping are evaluated employing a pure bem approach that is only boundary discretization of the cross section is used numerical results are presented to illustrate the method and demonstrate its efficiency and accuracy the deviations arising from the use of the advanced 20 20 stiffness matrix and the classical 12 12 or 14 14 ones employed in commercial software packages are illustrated through examples of great practical interest moreover the influence of nonuniform warping effects necessitating the use of the aforementioned advanced stiffness matrix is also demonstrated copyright 2015 john wiley sons ltd

saint venant solutions for prismatic anisotropic beams abstract an analytical model is presented for determining the displacement and stress distributions of the saint venant extension bending torsion and flexure problems for a homogeneous prismatic beam of arbitrary section and rectilinear anisotropy the determination of the complete displacement field requires solving a coupled two dimensional boundary value problem for the local in plane deformations and warping out of the section plane the principle of minimum potential energy is applied to a discretized representation of the cross section ritz method to calculate solutions to this problem the behavior of an anisolropic beam is studied in detail using the resulting displacement and stress solutions where definitions are presented for the shear center center of twist torsion constant and a new geometric parameter the line of extension bending centers two sets of numerical results are presented to illustrate how section geometry beam length and material properties affect the behavior of a homogeneous anisotropic cantilever beam

generalized warping effect in the dynamic analysis of beams of arbitrary cross section abstract in this paper a general formulation for the nonuniform warping dynamic analysis of beams of arbitrary simply or multiply connected cross section under arbitrary external loading and general boundary conditions is presented taking into account the effects of rotary and warping inertia the nonuniform warping distributions are taken into account by employing four independent warping parameters multiplying a shear warping function in each direction and two torsional warping functions respectively which are obtained by solving the corresponding boundary value problems formulated exploiting the longitudinal local equilibrium equation a shear stress correction is also performed in order to improve the stress field arising from the employed kinematical considerations ten initial boundary value problems are formulated with respect to the displacement and rotation components as well as to the independent warping parameters and solved using the analog equation method a boundary element method based technique in combination with an appropriate time integration scheme the warping functions and the geometric constants including the additional ones due to warping are evaluated employing a pure bem approach

some remarks on the use of time varying delay to model sample and hold circuits this note revises the so called input delay approach to the control of sampled data systems with nonuniform sampling in which the sample and hold circuit is embedded into an analog system with a time varying input delay it is shown that the conservatism in calculating the maximal admissible sampling period is reduced by about 57 if the time varying delay embedding step is omitted

high degree efficient symmetrical gaussian quadrature rules for the triangle gaussian quadrature is required for the computation of matrices based on the isoparametric formulztion of the finite element method a brief review of existing quadrature rules for the triangle is given and the method for the determination of high degree efficient symmetrical rules for the triangle is discussed new quadrature rules of degree 12 20 are presented and a short fortran program is included

a method of analysis for end and transitional effects in anisotropic cylinders abstract we present a rigorous verification study and an extension to an existing semi analytical finite element formulation for analysis of end and transition effects in prismatic cylinders end and transition effects in stressed cylinders are phenomena associated with the difference between results that are predicted by the saint venant solutions and the actual point wise conditions these differences manifest themselves as self equilibrated stress states notwithstanding certain well known exceptions e g restrained torsion of open thin walled sections such effects in isotropic cylinders are usually confined to a very small neighborhood of a terminal boundary or transition zone and are typically neglected for anisotropy as in the case of most smart active and composite material systems they can persist much further into the interior of the structure and need to be quantified to design geometry transition zones and to fully understand the delamination effects in the semi analytical approach we first discretize the governing equations within the cross sectional plane of the cylinder the end solution fields satisfy the homogeneous form of the resulting semi analytical system of ordinary differential equations this leads to an algebraic eigenvalue problem and an eigenfunction expansion of the stress and displacement fields due to end effects unique to the present study we formulate a procedure to quantify the transitional effects for end to end connected cylinders for which the displacement and stress continuity along the transition interface need to be enforced the semi analytical approach has several distinct advantages i it is computationally efficient as only the cross sectional geometry is discretized ii it can be applied to arbitrary cross sectional geometries and the most general form of anisotropy and iii it yields direct measures for the decay lengths or decay rates of any end or transition solution field analytical solutions to end effect problems are scarce those that exist are for simple geometry and material constitution we use these analytical solutions as well as solutions obtained using three dimensional finite element models to verify our approach and to assess its efficiency

a modified fourier series method for the torsion analysis of bars with multiply connected cross sections a modified fourier series method is proposed for the torsion analysis of prismatic bars with multiply connected cross sections the key feature in the present approach is the combined use of polynomials and fourier series solutions unlike in the existing approaches which use the fourier series only the replacement of the zeroth harmonic terms in the fourier series solutions by carefully selected polynomials resolves the major problem of functional dependence which the direct fourier series method may pose the polynomials and fourier series solutions are selected to satisfy the governing equation exactly so that the numerical calculation is minimal the effectiveness and generality of the present method is verified through numerical examples

a new rectangular beam theory abstract a new theory for beams of rectangular cross section which includes warping of the cross sections is presented in the present work by satisfying the shear free conditions on the lateral surfaces of the beam a pair of coupled equations of motion are obtained such that no arbitrary shear coefficient is required it is shown that the uncoupled equation for the transverse displacement is the same as the corresponding equation in timoshenko beam theory provided that for the timoshenko equation the shear coefficient is taken to be 5 6 this value lies within the range of values 0 822 0 870 appearing in the literature for the beam of rectangular cross section results for two typical static examples are given for both the new theory and timoshenko beam theory these results are compared with the solutions of the comparable problems in the linear theory of elasticity for the end loaded cantilever beam the new theory predicts the same result for the neutral surface deflection as does the linear theory of elasticity while timoshenko beam theory underestimates the shear correction term by 20 for the uniformly loaded and simply supported case both beam theories provide the same overestimate of the central deflection when compared with the theory of elasticity solution

a mixed finite element for three dimensional nonlinear analysis of steel frames abstract this paper develops and demonstrates a mixed beam finite element that can represent the inelastic three dimensional stability behavior of frames composed of open walled cross section members the kinematics of deformation of the element include finite rotation and warping of the cross section due to torsion the material inelasticity is based on a two space model that includes the effect of shear stresses due to uniform torsion in addition to normal stresses due to axial force biaxial bending and bimoment initial geometric imperfections and residual stresses are accommodated the formulation is based on a two field displacement and generalized stress hellinger reissner hr variational principle the interpolation of the generalized stresses i e cross section stress resultants along the element length is based on the geometrically exact nonlinear governing differential equations of equilibrium this leads to significant improvements in the accuracy over conventional displacement based elements in problems involving highly nonlinear variations in the curvature along the member lengths due to geometric nonlinearity and or distributed plasticity effects several numerical examples involving two and three dimensional elastic and inelastic stability behavior are presented to illustrate the capabilities of the formulation

kinematically exact curved and twisted strain based beam the paper presents a formulation of the geometrically exact three dimensional beam theory where the shape functions of three dimensional rotations are obtained from strains by the analytical solution of kinematic equations in general it is very demanding to obtain rotations from known rotational strains in the paper we limit our studies to the constant strain field along the element the relation between the total three dimensional rotations and the rotational strains is complicated even when a constant strain field is assumed the analytical solution for the rotation matrix is for constant rotational strains expressed by the matrix exponential despite the analytical relationship between rotations and rotational strains the governing equations of the beam are in general too demanding to be solved analytically a finite element strain based formulation is presented in which numerical integration in governing equations and their variations is completely omitted and replaced by analytical integrals some interesting connections between quantities and non linear expressions of the beam are revealed these relations can also serve as useful guidelines in the development of new finite elements especially in the choice of suitable shape functions

resistance based performance analysis of the consensus algorithm over geometric graphs the performance of the linear consensus algorithm is studied by using a linear quadratic lq cost the objective is to understand how the communication topology influences this algorithm this is achieved by exploiting the analogy between markov chains and electrical resistive networks indeed this allows us to uncover the relation between the lq performance cost and the average effective resistance of a suitable electrical network and moreover to show that if the communication graph fulfills some local properties then its behavior can be approximated by that of a grid which is a graph whose associated lq cost is well known

on the choice of the reference frame for beam section stiffness properties abstract this work discusses the choice of a reference frame for beam section stiffness properties established concepts as the center of elasticity the center of stiffness and the center of compliance are discussed and contextualized an interpretation of univocally defined generalized strain transformations is given in terms of minimization of appropriate norms of the stiffness and compliance matrices of the beam section that univocally define special reference points transformations of generalized strain perturbations that preserve the angular strain are sought they are subsequently constrained to represent a change of reference point and further restricted to lie in the plane of the section each transformation is univocally defined and given a clear mathematical and geometrical interpretation it is recognized that transformations that decouple forces and linear strains from moments and angular strains cannot be described as a mere change of reference point

mean square performance of consensus based distributed estimation over regular geometric graphs average consensus algorithms allow one to compute the average of some agents data in a distributed way and they are used as a basic building block in many algorithms for distributed estimation load balancing formation and distributed control traditional analysis of such algorithms studies for a given communication graph the convergence rate second largest eigenvalue of the transition matrix and predicts that for many graph families performance degrades when the number of agents grows because of the longer time required to spread information however in estimation problems a growing number of sensor nodes improves the quality of the estimate to understand whether such an improvement is possible also with distributed algorithms it is important to specify a suitable performance metric depending on the specific estimation problem in which the consensus algorithm is used and to study how performance scales when both the number of iterations and the number of agents grow to infinity here we propose a simple example of a distributed estimation problem solved by average consensus and a performance index naturally arising in this context mean square estimation error mse to understand the performance limitations of sensor networks with limited range communications we consider graphs describing local interactions we give analytic results for some families of such graphs whose symmetries allow the use of suitable mathematical tools however simulations indicate that a similar behavior occurs also for random geometric graphs this suggests that the performance limitations of regular lattices are mainly due to the geometrically local interactions and not to the symmetries

non uniform warping including the effects of torsion and shear forces part ii analytical and numerical applications abstract this two part contribution presents a beam theory bt with a non uniform warping nuw including the effects of torsion and shear forces and valid for any homogeneous cross section made of isotropic elastic material in part i the governing equations of the nuw bt has been established and simplified nuw bt versions has been deduced wherein the number of degrees of freedom is reduced in this part ii these theories are used to analyze for a representative set of cross sections cs solid cs and thin walled open closed cs bi symmetric or not the elastic behavior of cantilever beams subjected to torsion or shear bending for bi symmetrical cs torsion and shear bending are analyzed separately analytical and numerical results are given for the distributions along the beam axis of the cross sectional displacements and stresses for the nuw bt and its simplified versions numerical results are also given for the three dimensional stress distributions close to the embedded section the stress predictions of the nuw bt are compared to those obtained by three dimensional finite elements computations it can be drawn from all these results indications that can help to decide when the simplified theories may be applied and hence when the warping parameters may be reduced as specified in nuw bt torsion and bending are coupled for non symmetrical cs even if the bending moments refer to the centroid while the torsional moment refers to the shear center to illustrate this coupling effect the particular example of the channel cs presented in kim and kim kim n i kim m y 2005 exact dynamic static stiffness matrices of non symmetric thin walled beams considering coupled shear deformation effects thin walled structures 43 701 734 is analyzed and the results are compared

warping displacement of timoshenko beam model abstract a refined timoshenko beam model which takes into account warping of the cross sections is presented the model extends saint venant s theory of uniform torsion to the generic loading of a beam in a coherent manner the use of kinetic and kinematic assumptions virtual work expression of full elasticity problem and the principle of virtual work in derivation brings the presentation to the usual context of engineering models a new definition of the warping displacement in terms of a variational problem is one of the outcomes boundary value problems for the stretch shear bending and torsion loading modes are also given analytic and numeric solutions to warping displacements refined constitutive equations and correction factors for circular rectangle triangle and open annular cross sections of isotropic material are compared with expressions in literature as an interesting detail shear correction factors are found to be purely geometrical quantities which contradicts many findings in literature

stability analysis of networked control systems a sum of squares approach this paper presents a sum of squares sos approach to the stability analysis of networked control systems ncss incorporating bounded time varying delays bounded time varying transmission intervals and a shared communication medium a shared communication medium imposes that per transmission only one node which consists of several actuators or sensors can access the network and transmit its corresponding data which node obtains access is determined by a network protocol we will provide mathematical models that describe these ncss and transform them into suitable hybrid systems formulations based on these hybrid systems formulations we construct lyapunov functions using sos techniques that can be solved using lmi based computations this leads to several beneficial features i we can deal with plants and controllers which are described by nonlinear piecewise polynomial differential equations ii we can allow for non zero lower bounds on the delays and transmission intervals in contrast with various existing approaches iii we allow more flexibility in the lyapunov functions thereby obtaining less conservative estimates of the maximal allowable transmission intervals mati and maximal allowable delay mad and finally iv it provides an automated method to address stability analysis problems in ncs several numerical examples illustrate the strengths of our approach

the helicoidal modeling in computational finite elasticity part i variational formulation the finite elasticity mechanics of continua capable of a polar description is formulated by an alternative modeling to keeping position and orientation as uncoupled fields the rototranslation between two material particles can be described by a single complex tensorial quantity which is recognized to be orthogonal its linearization gives the characteristic curvature and differential vectors underlying the helicoidal modeling in both the sense of the body geometric description and the evolution of a deforming body after due introduction to dual tensors and rototranslations the polar description of the continuum is addressed with particular care to mixed differentiations of the rototranslation field then a thorough variational framework is established for the most general polar continuum under hyperelasticity hypothesis and the three field two field and one field principles are drawn and linearized the proposed modeling is expected to be profitably exploited in non linear finite element analyses of solids undergoing finite displacements rotations and strains

average resistance of toroidal graphs abstract the average effective resistance of a graph is a relevant performance index in many applications including distributed estimation and control of network systems in this paper we study how the average resistance depends on the graph topology and specifically on the dimension of the graph we concentrate on d dimensional toroidal grids and we exploit the connection between resistance and laplacian eigenvalues our analysis provides tight estimates of the average resistance which are key to study its asymptotic behavior when the number of nodes grows to infinity in dimension two the average resistance diverges in this case we are able to capture its rate of growth when the sides of the grid grow at different rates in higher dimensions the average resistance is bounded uniformly in the number of nodes in this case we conjecture that its value is of order 1 d for large d we prove this fact for hypercubes and when the side lengths go to infinity

distributed estimation from relative and absolute measurements this note defines the problem of least squares distributed estimation from relative and absolute measurements by encoding the set of measurements in a weighted undirected graph the role of its topology is studied by an electrical interpretation which easily allows distinguishing between topologies that lead to small or large estimation errors the least squares problem is solved by a distributed gradient algorithm the computed solution is approximately optimal after a number of steps that does not depend on the size of the problem or on the graph theoretic properties of its encoding this fact indicates that only a limited cooperation between the sensors is necessary

brief paper stability and stabilization of aperiodic sampled data control systems using robust linear matrix inequalities stability analysis of an aperiodic sampled data control system is considered for application to networked and embedded control the stability condition is described in a linear matrix inequality to be satisfied for all possible sampling intervals although this condition is numerically intractable a tractable sufficient condition can be constructed with the mean value theorem special attention is paid to tightness of the sufficient condition for less conservative stability analysis a region dividing technique for the reduction of conservatism and generalization to stabilization are also discussed an example demonstrates the efficacy of the approach

a finite element model for a higher order shear deformable beam theory the theory for a higher order shear deformable beam model is first developed it is based on a higher order displacement model and incorporates linear and quadratic variation of transverse normal strain and transverse shearing strain respectively through the beam thickness the effects of the transverse normal and shear stresses are included in the definition of the material s constitutive law the warping of the transverse normal cross section of the beam is automatically incorporated in the mathematical model the question of selecting a shear correction coefficient as in a first order shear deformable timoshenko theory does not arise a linear two noded finite element model of this theory is introduced and developed next both static and free vibration results of this theory are presented and compared with those of euler and timoshenko theories for various boundary and loading conditions

optimal control with noisy time this paper examines stochastic optimal control problems in which the state is perfectly known but the controller s measure of time is a stochastic process derived from a strictly increasing levy process we provide dynamic programming results for continuous time finite horizon control and specialize these results to solve a noisy time variant of the linear quadratic regulator problem and a portfolio optimization problem with random trade activity rates for the linear quadratic case the optimal controller is linear and can be computed from a generalization of the classical riccati differential equation

energy preserving decaying schemes for non linear beam dynamics using the helicoidal approximation abstract we develop two unconditionally stable displacement based time stepping schemes for the non linear dynamic response of beams the first algorithm guarantees the exact discrete conservation of energy and momentum the second is associated with an energy decay inequality that achieves control of the unresolved frequencies by means of a numerical dissipation mechanism both schemes emanate from a weak form of the equations of dynamic equilibrium referred to a fixed pole space and time discretizations are based on the exponential parameterization of motion this implies that the beam reference line and the trajectories of the beam nodes are helicoids in space the exponential mapping approach allows a unified treatment of translations and rotations greatly simplifying the derivation of the algorithms and their analysis the capabilities and performance of the new schemes are demonstrated and discussed with the aid of numerical simulations

non uniform warping including the effects of torsion and shear forces part i a general beam theory this two part contribution presents a beam theory with a non uniform warping including the effects of torsion and shear forces and valid for any homogeneous cross section made of isotropic elastic material part i is devoted to the theoretical developments and part ii discusses analytical and numerical results obtained for torsion and shear bending of cantilever beams made of different kinds of cross section the theory is based on a kinematics assuming that the cross section maintains its shape and including three independent warping parameters associated to the three warping functions corresponding to torsion and shear forces starting from this displacement model and using the principle of virtual work the corresponding beam theory is derived for this theory closed form results are obtained for the cross sectional constants and the three dimensional expressions of the normal and shear stresses comparison with classical beam theories is carried out and additional effects due to the non uniformity of the warping are highlighted in particular the contributions of primary and secondary internal forces and the effect of the non symmetry of the cross section on the structural behavior of the beam are specified simplified versions of this theory wherein the number of degrees of freedom is reduced are also presented the analytical and numerical analyzes presented in part ii give responses on the quality of this non uniform beam theory and indicate also when its simplified versions could be applied

general behavior and shear center location of prismatic anisotropic beams via power series abstract the behavior of a tip loaded anisotropic cantilever beam with an arbitrary cross section is studied using saint venant s semi inverse method along with a power series solution for the local in plane and out of plane deformation warping functions the power series coefficients are determined by solving a set of variationally derived linear algebraic equations using the resulting three dimensional displacement solutions the shear deformation associated with applied tip loads is investigated as well as the shear center location two different definitions of the shear center are presented for anisotropic beams by extending existing approaches developed for isotropic sections both of the extended definitions reveal the linear dependency of the shear center location on beam length numerical results are presented for three different cross sections ellipse triangle naca 0012 airfoil and two different materials al 6061 t6 off angle high strength graphite epoxy fibers

reaching a consensus in a dynamically changing environment a graphical approach this paper presents new graph theoretic results appropriate for the analysis of a variety of consensus problems cast in dynamically changing environments the concepts of rooted strongly rooted and neighbor shared are defined and conditions are derived for compositions of sequences of directed graphs to be of these types the graph of a stochastic matrix is defined and it is shown that under certain conditions the graph of a sarymsakov matrix and a rooted graph are one and the same as an illustration of the use of the concepts developed in this paper graph theoretic conditions are obtained which address the convergence question for the leaderless version of the widely studied vicsek consensus problem

how to compute the volume in high dimension in some areas of theoretical computer science we feel that randomized algorithms are better and in some others we can prove that they are more efficient than the deterministic ones

a homogenization based theory for anisotropic beams with accurate through section stress and strain prediction this paper presents a homogenization based theory for three dimensional anisotropic beams the proposed beam theory uses a hierarchy of solutions to carefully chosen beam problems that are referred to as the fundamental states the stress and strain distribution in the beam is expressed as a linear combination of the fundamental state solutions and stress and strain residuals that capture the parts of the solution not accounted for by the fundamental states this decomposition plays an important role in the homogenization process and provides a consistent method to reconstruct the stress and strain distribution in the beam in a post processing calculation a nite element method is presented to calculate the fundamental state solutions results are presented demonstrating that the stress and strain reconstruction achieves accuracy comparable with full three dimensional nite element computations away from the ends of the beam the computational cost of the proposed approach is three orders of magnitude less than the computational cost of full three dimensional calculations for the cases presented here for isotropic beams with symmetric cross sections the proposed theory takes the form of classical timoshenko beam theory with cowper s shear correction factor and additional load dependent corrections the proposed approach provides an extension of timoshenko s beam theory that handles sections with anisotropic construction

flexure torsion behavior of prismatic beams i section properties via power series the behavior of a tip loaded cantilever beam with an arbitrary cross section is studied using saint venant s semi inverse method along with a power series solution for the out of plane flexure and torsion warping functions the power series coefficients are determined by solving a set of variationally derived linear algebraic equations for complex cross sections the calculated coefficients represented a best fit approximation to the exact warping function the resulting warping functions are used to determine the cross sectional properties torsion constant shear correction factors shear deformation coefficients and shear center location a new linear relation is developed for locating the shear center where the twist rate is zero about the line of shear centers moreover the kinematic relations for a new fully compatible one dimensional beam theory are developed numerical results are presented first to verify the approach and second to provide section data on naca four series airfoils not currently found in the literature

a weak weak formulation for large displacements beam statics a finite volumes approximation this paper addresses the problem of the numerical solution of beam statics undergoing large displacements a kinematic analysis outlines the beam geometrical model through the definition of its lagrangian co ordinate and strain parameters a definition of the stress parameters a constitutive law and an expression for the strain energy of the beam are then provided under the hypothesis of small strain the equations governing the beam equilibrium are introduced and their weak form is derived these equations are then proved to be equivalent to the primal and mixed form of principle of virtual work the numerical approximation is introduced by applying the bidiscontinuous finite elements method on the linearized weak form the weak weak formulation is attained by using the lowest interpolation order both for test and trial functions on two staggered decompositions of the space domain some numerical examples prove the capability of present formulation in handling actual problems

geometrically exact beam finite element formulated on the special euclidean group se 3 abstract this paper describes a dynamic formulation of a straight beam finite element in the setting of the special euclidean group se 3 first the static and dynamic equilibrium equations are derived in this framework from variational principles then a non linear interpolation formula using the exponential map is introduced it is shown that this framework leads to a natural coupling in the interpolation of the position and rotation variables next the discretized internal and inertia forces are developed the semi discrete equations of motion take the form of a second order ordinary differential equation on a lie group which is solved using a lie group time integration scheme it is remarkable that no parameterization of the nodal variables needs to be introduced and that the proposed lie group framework leads to a compact and easy to implement formulation some important numerical and theoretical aspects leading to a computationally efficient strategy are highlighted and discussed for instance the formulation leads to invariant tangent stiffness and mass matrices under rigid body motions and a locking free element the proposed formulation is successfully tested in several numerical static and dynamic examples

low sensitivity h filter design for linear delta operator systems with sampling time jitter this article is concerned with the problem of designing h filters for a class of linear discrete time systems with low sensitivity to sampling time jitter via delta operator approach delta domain model is used to avoid the inherent numerical ill condition resulting from the use of the standard shift domain model at high sampling rates based on projection lemma in combination with the descriptor system approach often used to solve problems related to delay a novel bounded real lemma with three slack variables for delta operator systems is presented a sensitivity approach based on this novel lemma is proposed to mitigate the effects of sampling time jitter on system performance then the problem of designing a low sensitivity filter can be reduced to a convex optimisation problem an important consideration in the design of correlation filters is the optimal trade off between the standard h criterion and the sensitivity of the transfer function with respect to sampling time jitter finally a numer

distributed control design for spatially interconnected systems this paper deals with analysis synthesis and implementation of distributed controllers designed for spatially interconnected systems we develop a state space framework for posing problems of this type and focus on systems whose model is spatially discrete in this paper analysis and synthesis results are developed for this class of systems using the l sub 2 induced norm as the performance criterion the results are stated in terms of linear matrix inequalities and are thus readily amenable to computation a special implementation of the resulting controllers is presented which is particularly attractive for distributed operation of the controller several examples are provided to further illustrate the application of the results

generalized variational principle on nonlinear theory of naturally curved and twisted beams the nonlinear behavior for naturally curved and twisted beams undergoing large displacements and rotations but small strains has been investigated in this paper an incomplete generalized variational functional for the beams with complete constrained boundaries at two ends is established by means of the lagrange multiplier method a set of equilibrium equations which takes into account the effects of transverse shear deformations as well as torsion related warping has been derived from the stationary conditions of the functional the various elastic couplings of bending twisting and or extension twisting are also included in this analysis the present theory can also be easily extended to other various incomplete constrained boundaries in case of small displacement the equilibrium equations obtained by the present theory reduce to the well known results in literature

integration of elastic multibody systems by invariant conserving dissipating algorithms i formulation abstract this work presents a novel methodology for the dynamic analysis of general non linear flexible multibody systems in part i we develop the 6 d compact representation of motion for those body models which motion may be described by a displacement field plus an independent rotation field this approach explores the fundamental properties of rigid body motion and in particular the coupled nature of linear and angular quantities in both kinematics and dynamics inspiring a novel parameterization technique based on the exponential map using the proposed approach we derive the governing equations for the case of multibody systems composed by rigid bodies and geometrically non linear beams connected by holonomic constraints these equations provide the starting point for the derivation of a class of numerical algorithms characterized by non conventional conservation properties in part ii of this work we develop the algorithms and illustrate their properties with the aid of some numerical applications

multibody implementation of finite volume c 0 beams a c 0 beam discretization based on the finite volume concept is described in the linear case this approach leads to a collocated evaluation of the stiffness matrix of the beam it proves to be intrinsically free from shear locking in the nonlinear formulation only a collocated evaluation of the elastic forces is required which dramatically simplifies the computation of the elastic contribution to the equilibrium equations the formulation is here developed for the general geometrically nonlinear case and implemented in multibody formulation the proposed approach proved to be consistent its major drawback lies in the loss of symmetry of both the linear and the linearized beam matrices for this reason the method is particularly suitable for dynamic problems like a nonlinear implicit multibody numerical approximation in which the symmetry of the matrices is not so important as it is already lost whereas the ease in the generation of the contributions to the equations can lead to faster and cheaper analyses some applications are outlined and the most relevant results are discussed

a timoshenko beam theory with pressure corrections for layered orthotropic beams a timoshenko beam theory for layered orthotropic beams is presented the theory consists of a novel combination of three key components average displacement and rotation variables that provide the kinematic description of the beam stress and strain moments used to represent the average stress and strain state in the beam and the use of exact axially invariant plane stress solutions to calibrate the relationships between all these quantities these axially invariant solutions which we call the fundamental states are also used to determine a shear strain correction factor as well as corrections to account for effects produced by externally applied loads the shear strain correction factor and the external load corrections are computed for a beam composed of isotropic layers the proposed theory yields cowper s shear correction for a single isotropic layer while for multiple layers new expressions for the shear correction factor are obtained a body force correction is shown to account for the difference between cowper s shear correction and the factor originally proposed by timoshenko numerical comparisons between the theory and finite elements results show good agreement

analysis and synthesis of state feedback controllers with timing jitter we consider a continuous time linear system with sampled constant linear state feedback control and a convex quadratic performance measure the sample times however are subject to variation within some known interval we use linear matrix inequality lmi methods to derive a lyapunov function that establishes an upper bound on performance degradation due to the timing jitter the same lyapunov function can be used in a heuristic for finding a bad timing jitter sequence which gives a lower bound on the possible performance degradation numerical experiments show that these two bounds are often close which means that our bound is tight we show how lmi methods can be used to synthesize a constant state feedback controller that minimizes the performance bound for a given level of timing jitter

beam theory for strongly orthotropic materials abstract this paper presents a displacement based model for orthotropic beams under plane linear elasticity based on the only kinematic assumption of transverse inextensibility any given axial and transverse loading as well as boundary conditions at the beam ends are considered the solution is decomposed into the principal and the residual part corresponding to the interior and the boundary problems which are obtained by series expansions of polynomial functions and eigenfunctions respectively it is proved that the proposed one dimensional theory gives both interior and boundary exact two dimensional elasticity solutions for strongly orthotropic materials i e for ratio between shear modulus and axial young modulus approaching zero for isotropic and orthotropic materials the accuracy of the beam model is also analysed and compared with that of other theories in particular the complementary energy error of the interior solution with respect to two dimensional elasticity is evaluated the asymptotic estimate of the characteristic decay length of end effects given in choi and horgan j appl mech asme 44 424 430 1977 by two dimensional analysis is reobtained and the range of validity of boundary solution is discussed the numerical results presented agree very well with exact and finite element solutions even in the neighbourhood of clamped cross sections where the solution is mainly governed by the boundary problem

exact dynamic stiffness elements based on one dimensional higher order theories for free vibration analysis of solid and thin walled structures in this paper an exact dynamic stiffness formulation using one dimensional 1d higher order theories is presented and subsequently used to investigate the free vibration characteristics of solid and thin walled structures higher order kinematic fields are developed using the carrera unified formulation which allows for straightforward implementation of any order theory without the need for ad hoc formulations classical beam theories euler bernoulli and timoshenko are also captured from the formulation as degenerate cases the principle of virtual displacements is used to derive the governing differential equations and the associated natural boundary conditions an exact dynamic stiffness matrix is then developed by relating the amplitudes of harmonically varying loads to those of the responses the explicit terms of the dynamic stiffness matrices are also presented the resulting dynamic stiffness matrix is used with particular reference to the wittrick williams algorithm to carry out the free vibration analysis of solid and thin walled structures the accuracy of the theory is confirmed both by published literature and by extensive finite element solutions using the commercial code msc nastran

large displacement analysis of naturally curved and twisted composite beams this paper presents an efficient procedure for analyzing naturally curved and twisted beams undergoing large displacements and rotations but small strains special care is taken to accurately model the structural behavior of the beam shearing deformations as well as torsion related warping are taken into account the various elastic couplings e g bending twisting or extention twisting that can arise in composite beams are also modeled in a rational fashion the equations are derived in curvilinear material coordinates and euler angles are used to represent the arbitrarily large rotations the strain energy in the beam is reduced to a quadratic expression by means of a quasilinearization procedure this expression of the strain energy is the basis for a finite element analysis of the structure and standard iteration techniques are used to obtain nonlinear solutions to the problem the predictions of this model are found to be in good agreement with the experimental results and the computational efficiency is greatly improved as compared with other available analyses

generalized beam theory applied to shear stiffness there is no consensus of opinion on the correct expressions for shear stiffness even in the apparently simple case of rectangular sections made from homogeneous isotropic material a general beam theory has been proposed which is applicable to all regular prismatic systems this has been used to find the appropriate beam like flexibilities for trusses the same approach can be used for normal beams giving values for the shear stiffnesses of various cross sections as particular results of a general theory embracing torsion binding extension and shear of regular prismatic systems