rls laguerre lattice adaptive filtering error feedback normalized and array based algorithms this paper develops several lattice structures for rls laguerre adaptive filtering including a posteriori and a priori based lattice filters with error feedback array based lattice filters and normalized lattice filters all structures are efficient in that their computational cost is proportional to the number of taps albeit some structures require more multiplications or divisions than others the performance of all filters however can differ under practical considerations such as finite precision effects and regularization simulations are included to illustrate these facts

numerical analysis of a contact problem with wear abstract this paper represents a sequel to jureczka and ochal 2019 where numerical solution of a quasistatic contact problem is considered for an elastic body in frictional contact with a moving foundation the model takes into account wear of the contact surface of the body caused by the friction some preliminary error analysis for a fully discrete approximation of the contact problem was provided in jureczka and ochal 2019 in this paper we consider a more general fully discrete numerical scheme for the contact problem derive optimal order error bounds and present computer simulation results showing that the numerical convergence orders match the theoretical predictions

a simple approach to bifurcation and limit point calculations a simple approach is proposed to calculate the bifurcation and limit points of structures talcing into account the pre unstable behaviour by the finite element method the approach is as follows at each load step the triangular factorization of the tangent stiffness matrix is checked to determine if the matrix is positive definite or not when the tangent stiffness matrix is positive definite at a certain load step and non positive definite at the next load step the structure is considered to become unstable between the two load steps and an eigenproblem is constructed based on the difference of the tangent stiffness matrices at the two load steps the critical load and corresponding mode of the structure are then derived from solving the eigenproblem the proposed procedure is simple and economical and it can be easily incorporated into a conventional geometric nonlinear analysis computer program it is implemented in the adina program and some sample calculations are shown

numerical analysis of an elasto piezoelectric problem with damage in this paper we analyze an algorithm for the quasistatic evolution of the mechanical state of an elasto piezoelectric body with damage both damage caused by the development and the growth of internal microcracks and piezoelectric effects are included in the model the mechanical problem is expressed as an elliptic system for the displacement field coupled with a non linear parabolic partial differential equation for the damage field and a linear partial differential equation for the electric potential the variational formulation leads to a coupled system composed of two linear variational equations for the displacement field and the electric potential and a non linear parabolic variational equation for the damage field the existence of a unique weak solution is stated then a fully discrete scheme is introduced by using the finite element method to approximate the spatial variable and an euler scheme to discretize the time derivatives error estimates are derived on the approximate solutions from which the linear convergence of the algorithm is deduced under suitable regularity conditions finally some numerical simulations are performed in one two and three dimensions to demonstrate the accuracy of the scheme and the behaviour of the solution copyright 2008 john wiley sons ltd

a variational principle for finite planar deformation of straight slender elastic beams abstract the objective of this paper is to present a finite element formulation for finite deformation analysis of a slender straight elastic in plane beam the formulation is based on a modified hu washizu variational principle in which exact nonlinear kinematic equations are taken into account only the rotation in the interior of an element needs to be approximated thus the ambiguities concerning the order of polynomial approximations for different field variables e g longitudinal and lateral displacements are avoided the euler lagrange equations of this principle are among others exact kinematic and equilibrium conditions for the beam the solution capabilities are illustrated with numerical examples two different finite elements are examined with 3rd order interpolation polynomials for the rotation and with 5th order polynomials excellent convergence and accuracy of both elements is demonstrated the results indicate that the accuracy of the present elements is not notably influenced by the length of the element and the order of numerical integration if it is greater than a minimal value only one load step was sufficient in calculations to achieve the results

equilibrium problem for elastic body with delaminated t shape inclusion abstract we analyze an equilibrium problem for 2d elastic body with a t shape thin inclusion in presence of damage a part of the inclusion is elastic and the other part is a rigid one a delamination of the inclusion from the elastic body is assumed thus forming a crack between the elastic body and the inclusion nonlinear boundary conditions at the crack faces are considered to prevent a mutual penetration between the faces the damage is characterized by a positive parameter the paper provides an asymptotic analysis of the solutions as the damage parameter tends to infinity and to zero a passage to infinity of a rigidity parameter of the elastic part of the inclusion is also analyzed junction conditions are determined at the connection point between the elastic and rigid parts of the inclusion an existence theorem is proved for an inverse problem of finding displacement fields and the damage and rigidity parameters provided that a displacement of the tip point of the inclusion is known

laguerre domain adaptive filters using a tapped delay line as an adaptive fitter the complexity of the filter increases with increasing correlation length of input and reference signal the author seeks simple adaptive filter structures such that for a long correlation length only a minor complexity of the filter is needed he considers adaptive mechanisms governed by an exponentially weighted squared error criterion laguerre domain adaptive filters are introduced which lead to a tapped iir filter line these filters contain a discount factor as a free variable which makes it possible to set the memory and the number of adaptive coefficients independently convergence properties of the proposed adaptive filters are discussed

analysis of two frictional viscoplastic contact problems with damage in this work we study two quasistatic frictional contact problems arising in viscoplasticity including the mechanical damage of the material caused by excessive stress or strain and modelled by an inclusion of parabolic type the variational formulation is provided for both problems and the existence of a unique solution is proved for each of them then a fully discrete scheme is introduced using the finite element method to approximate the spatial domain and the euler scheme to discretize the time derivatives error estimates are derived and under suitable regularity assumptions the linear convergence of the algorithm is deduced finally some numerical examples are presented to show the performance of the method

a finite element method for stability problems in finite elasticity in this paper a finite element method is developed to treat stability problems in finite elasticity for this purpose the constitutive equations are formulated in principal stretches which allows a general representation of the derivatives of the strain energy function with respect to the principal stretches these results can then be used to derive an efficient numerical scheme for the computation of singular points

numerical studies of a hemivariational inequality for a viscoelastic contact problem with damage abstract this paper is devoted to the study of a hemivariational inequality modeling the quasistatic bilateral frictional contact between a viscoelastic body and a rigid foundation the damage effect is built into the model through a parabolic differential inclusion for the damage function a solution existence and uniqueness result is commented a fully discrete scheme is introduced with the time derivative of the damage function approximated by the backward finite difference and the spatial derivatives approximated by finite elements an optimal order error estimate is derived for the fully discrete scheme when linear elements are used for the velocity and displacement variables and piecewise constants are used for the damage function simulation results on numerical examples are reported illustrating the performance of the fully discrete scheme and the theoretically predicted convergence orders

quasistatic normal compliance contact problem of visco elastic bodies with coulomb friction implemented by qp and sgbem the quasistatic normal compliance contact problem of isotropic homogeneous linear visco elastic bodies with coulomb friction at small strains in kelvin voigt rheology is considered the discretization is made by a semi implicit formula in time and the symmetric galerkin boundary element method sgbem in space assuming that the ratio of the viscosity and elasticity moduli is a given relaxation time coefficient the obtained recursive minimization problem formulated only on the contact boundary has a nonsmooth cost function if the normal compliance responds linearly and the 2d problems are considered then the cost function is piecewise quadratic which after a certain transformation gets the quadratic programming qp structure however it would lead to second order cone programming in 3d problems finally several computational tests are presented and analysed with an additional discussion on numerical stability and convergence of the involved approximated poincare steklov operators

optimum laguerre networks for a class of discrete time systems an analytical approach is introduced that directly yields the optimum value of the laguerre parameter b this is achieved by minimizing the mean square error between the unit sample response of the given discrete system and that of its laguerre counterpart it is shown that laguerre networks are best suited to realized systems whose exponential unit sample responses die down rapidly

some computational aspects of the stability analysis of nonlinear structures abstract the perturbation method and the continuation method are the two most popular techniques for the solution of finite element equations that describe instability phenomena this paper presents a summary of the principles involved and describes some trends in the development of these techniques

an elastic viscoplastic quasistatic contact problem existence and uniqueness of a weak solution in this paper the contact between an elastic viscoplastic body and a deformable obstacle is studied the effect of the damage due to internal tension or compression and caused by the opening and growth of micro cracks and micro cavities is also considered the variational formulation leads to a coupled system of evolutionary equations an existence and uniqueness result is established by using approximate problems the pseudomonotone operators theory schauder fixed point theorem and a comparison result

an elastic viscoplastic quasistatic contact problem with damage abstract in this paper the contact between an elastic viscoplastic body and a deformable obstacle is studied the effect of the damage due to tension or compression is also considered the variational formulation leads to a coupled system of evolutionary equations for which an existence and uniqueness result is stated then a fully discrete scheme is introduced using the finite element method to approximate the spatial variable and an euler scheme to discretize the time derivatives error estimates are obtained and as a consequence the convergence of the algorithm is deduced finally some numerical simulations are presented to demonstrate the accuracy of the algorithm

numerical analysis and simulations of a quasistatic frictional contact problem with damage in viscoelasticity we consider a quasistatic problem which models the bilateral contact between a viscoelastic body and a foundation taking into account the damage and the friction the damage which results from tension or compression is then involved in the constitutive law and it is modelled using a nonlinear parabolic inclusion the variational problem is formulated as a coupled system of evolutionary equations for which we state the existence of a unique solution then we introduce a fully discrete scheme using the finite element method to approximate the spatial variable and the euler scheme to discretize the time derivatives error estimates are derived and under suitable regularity hypotheses the convergence of the numerical scheme obtained finally a numerical algorithm and results are presented for some two dimensional examples

blind input initial state and system identification of simo laguerre systems laguerre filters have infinite impulse responses iirs but with finite tapped delay line parameterizations this paper investigates subspace based blind identification of laguerre filter tap coefficients the internal filter state and the input given only noisy observations of the output this paper deals only with single input multiple output simo laguerre models a state space model for the simo laguerre system is derived from which blind estimation algorithms are developed as in the finite impulse response fir case the laguerre filter taps coefficients can be estimated from the column space of a certain hankel matrix constructed from noisy output observations whereas the internal state and input can be estimated from the row space by exploiting state space structure while not exactly uniquely identifiable conditions are given for which the tap coefficients the internal state and the input can be determined to within a multiplicative scalar factor

implantation of a nonlinear capability on a linear software system the present paper proposes a simple procedure which extends with minor additions an existing linear elastic program system aska to geometrically nonlinear applications involving large displacements but small strains such an attempt is of course not new numerous other techniques related to this subject are documented in a large list of publications which have appeared over the last twenty five years or so for the present purpose it suffices to quote in place of an extensive review a few pertinent papers l 8 at the same time we propose to discuss in what follows certain general principles of a geometrically nonlinear finite element analysis and their relation to the present work clearly an extension of a linear computational capability to nonlinear applications demands in the first instance a suitable incrementation procedure pertinent equations determining the so called incremental equilibrium are well known inherent to the concept of an incremental transition from a given equilibrium state to another is the notion of a tangential stiffness matrix of the structure in this context the elastic material stiffness matrix already established for a linear analysis must be supplemented by the geometrical stiffness matrix which expresses the influence of the existing stress state on the incremental condition of equilibrium of the structure simple incrementation of the nonlinear response leads to a desired linearisation of the computational process but also to inevitable accumulating deviations from the true equilibrium solution in a first attempt to remove the error imposed by the linearisation higher order incremental approximations may be employed in the limit this approach leads to a fully nonlinear formulation of the problem for large deflections and entails as a rule software concepts larstran different from those valid in a linear analysis also important in this context is the development and implementation of numerical methods for the solution of the nonlinear governing equations the literature on the subject is still growing and partial overlapping of the methods is unavoidable the treatment of geometrically nonlinear problems is based on the equilibrium condition between internal stresses and applied loads for the unknown deflected configuration of the structure elastic structures do not require a priori an incremental application of the loading which proves however advantageous in the numerical process on the other hand incremen

a quadratically convergent algorithm for the computation of stability points the application of the determinant of the tangent stiffness matrix abstract this paper presents a quadratically convergent algorithm for the computation of stability points limit and bifurcation points in the finite element formulation of the problems of the nonlinear structural mechanics one such approach was given by wriggers and coworkers comput methods appl mech engrg 70 1988 329 347 and int j numer methods engrg 30 1990 155 176 their approach employs the eigenvector equation k t 0 as the characterization of the stability point in the present paper an alternative approach is proposed which uses the equation det k t 0 as the stability point condition in combination with newton s iteration scheme this condition has so far been considered unsuitable for the implementation in the finite element analysis because it has been believed that it requires the full assembly of the derivative of the global tangent stiffness matrix which is a very costly operation objectives of our paper are i to derive a new quadratically convergent algorithm for the computation of stability points which uses the condition det k t 0 for the characterization of the stability point ii to show that the full assembly of the global tangent stiffness matrix derivative is not required and that the linearization of the determinant of the global tangent stiffness matrix can be done in an element by element fashion and iii to indicate that in terms of the number of algebraic operations memory requirements and the computer programming effort our algorithm practically equals the one based on an eigenvector equation but has the advantage of a larger radius of convergence an additional benefit of the proposed algorithm is that it can also be used without any modification as a comprehensive path following procedure to calculate regular and singular stability points the effectiveness of our algorithm is illustrated by numerical examples its convergence characteristics are compared with those of the algorithm based on the eigenvector equation we show stability analyses of elastic plastic planar frames the algorithm is of course valid generally and is not limited to this particular kind of structures

variational and numerical analysis of a quasistatic viscoelastic problem with normal compliance friction and damage we consider a model for quasistatic frictional contact between a viscoelastic body and a foundation the material constitutive relation is assumed to be nonlinear the mechanical damage of the material caused by excessive stress or strain is described by the damage function the evolution of which is determined by a parabolic inclusion the contact is modeled with the normal compliance condition and the associated version of coulomb s law of dry friction we derive a variational formulation for the problem and prove the existence of its unique weak solution we then study a fully discrete scheme for the numerical solutions of the problem and obtain error estimates on the approximate solutions

adaptive laguerre lattice filters adaptive laguerre based filters provide an attractive alternative to adaptive fir filters in the sense that they require fewer parameters to model a linear time invariant system with a long impulse response we present an adaptive laguerre lattice structure that combines the desirable features of the laguerre structure i e guaranteed stability unique global minimum and small number of parameters m for a prescribed level of modeling error with the numerical robustness and low computational complexity of adaptive fir lattice structures the proposed configuration is based on an extension to the iir case of the fir lattice filter it is a cascade of identical sections but with a single pole all pass filter replacing the delay element used in the conventional fir lattice filter we utilize this structure to obtain computationally efficient adaptive algorithms o m computations per time instant our adaptive laguerre lattice filter is an extension of the gradient adaptive lattice gal technique and it demonstrates the same desirable properties namely 1 excellent steady state behavior 2 relatively fast initial convergence comparable with that of an rls algorithm for laguerre structure and good numerical stability simulation results indicate that for systems with poles close to the unit circle where an adaptive fir model of very high order would be required to meet a prescribed modeling error an adaptive laguerre lattice model of relatively low order achieves the prescribed bound after just a few updates of the recursions in the adaptive algorithm

a kinematically exact finite element formulation of planar elastic plastic frames a finite element formulation of finite deformation static analysis of plane elastic plastic frames subjected to static loads is presented in which the only function to be interpolated is the rotation of the centroid axis of the beam one of the advantages of such a formulation is that the problem of the field consistency does not arise exact non linear kinematic relationships of the finite strain beam theory are used which assume the bernoulli hypothesis of plane cross sections finite displacements and rotations as well as finite extensional and bending strains are accounted for the effects of shear strains and non conservative loads are at present neglected yet they can simply be incorporated in the formulation because the potential energy of internal forces does not exist with elastic plastic material the principle of virtual work is introduced as the basis of the finite element formulation a generalized principle of virtual work is proposed in which the displacements rotation extensional and bending strains and the lagrangian multipliers are independent variables by exploiting the special structure of the equations of the problem the displacements the strains and the multipliers are eliminated from the generalized principle of virtual work a novel principle is obtained in which the rotation becomes the only function to be approximated in its finite element implementation it is shown that n 1 point numerical integration must be employed in conjunction with n node interpolation polynomials for the rotation and the lobatto rule is recommended regarding the integration over the cross section it is demonstrated by numerical examples that due to discontinuous integrands no integration order defined as computationally efficient yet accurate enough could be suggested the theoretical findings and a nice performance of the derived finite elements are illustrated by numerical examples

order recursive rls laguerre adaptive filtering this paper solves the problem of designing recursive least squares rls lattice or order recursive algorithms for adaptive filters that do not involve tapped delay line structures in particular an rls laguerre lattice filter is obtained

the gamma filter a new class of adaptive iir filters with restricted feedback generalized feedforward filters a class of adaptive filters that combines attractive properties of finite impulse response fir filters with some of the power of infinite impulse response iir filters are described a particular case the gamma filter generalizes widrow s adaptive transversal filter adaline to an infinite impulse response filter yet the stability condition for the gamma filter is trivial and lms adaptation is of the same computational complexity as the conventional transversal filter structure preliminary results indicate that the gamma filter is more efficient than the adaptive transversal filter the authors extend the wiener kopf equation to the gamma filter and develop some analysis tools

a general procedure for the direct computation of turning and bifurcation points we address the formulation and numerical implementation of general purpose algorithme suitable for the direct computation of stability points in non linear solid mechanics the effectiveness of the resulting algorithm is illustrated by numerical simulation that include bifurcation and loss of stability in elastoplasticity non linear rods and non linear three dimensional shells

a quasistatic contact problem for viscoelastic materials with friction and damage abstract we consider a mathematical model which describes the frictional contact between a deformable body and a foundation the process is quasistatic the material is assumed to be viscoelastic with long memory and the frictional contact is modelled with subdifferential boundary conditions the mechanical damage of the material is described by the damage function which is modelled by a nonlinear partial differential equation we derive the variational formulation of the problem which is a coupled system of a hemivariational inequality and a parabolic equation then we prove the existence of a unique weak solution to the model the proof is based on arguments of abstract stationary inclusion and a fixed point theorem

improved method for optimum choice of free parameter in orthogonal approximations we report on our investigations to choose a free parameter to minimize the error energy when approximating a given signal with orthogonal basis functions this method requires limited knowledge of the signal to be approximated and has a low computational cost

a study of incremental iterative strategies for non linear analyses the paper describes a study of incremental iterative solution techniques for geometrically non linear analyses the solution methods documented are based on a modified newton raphson approach meaning that the tangent stiffness matrix is computed at the commencement of each load step but is then held constant throughout the equilibrium iterations a consistent mathematical notation is employed in the description of the iterative and load incrementation strategies enabling the simple inclusion of several solution options in a computer program the iterative strategies investigated are iteration at constant load iteration at constant displacement iteration at constant arc length iteration at constant external work iteration at minimum unbalanced displacement norm iteration at minimum unbalanced force norm and iteration at constant weighted response the load incrementation schemes investigated include strategies based on the number of iterations required to achieve convergence in the previous load step strategies based on the current stiffness parameter and a strategy based on a parabolic approximation to the load deflection response criteria for detecting when the applied external load increment should reverse sign are described a challenging example of a circular arch exhibiting snap through load limit point behaviour and snap back displacement limit point behaviour is solved using several different iterative and load incrementation strategies the performance of the solution schemes is evaluated and conclusions are drawn

a frictionless contact problem for elastic viscoplastic materials with normal compliance and damage abstract we study a quasistatic frictionless contact problem with normal compliance and damage for elastic viscoplastic bodies the mechanical damage of the material caused by excessive stress or strain is described by a damage function whose evolution is modelled by an inclusion of parabolic type we provide a variational formulation for the mechanical problem and sketch a proof of the existence of a unique weak solution to the model we then introduce and study a fully discrete scheme for the numerical solutions of the problem an optimal order error estimate is derived for the approximate solutions under suitable solution regularity numerical examples are presented to show the performance of the method

on contact induced standing waves in rotating tires experiment and theory an experimental and theoretical study of standing waves in a rotating tire is presented a test set up for studying small balloon tires is described experimental observations of standing waves arising after a critical speed transition are presented including measurements of the spatial structure of the standing waves a simple model for the tire is developed which has a single degree of freedom at each radial location steady state solutions at any rotation speed are governed by a non linear boundary value problem which is studied in detail appropriate boundary conditions are obtained using asymptotic arguments and then used in numerical solutions the analysis is shown to agree well with the experimental observations based on the analysis a method for suppressing the standing waves is proposed and confirmed experimentally

on the interaction of frictional formulations with bifurcation phenomena in hyperelastic steady state rolling calculations a finite element formulation for hyperelastic steady state rolling of inflated tires is analyzed in particular numerical difficulties associated with enforcing frictional conditions within such a framework are discussed we focus in this work on adherent i e no slip friction formulations and in addition to analyzing the numerical difficulties associated with such problems we also study the interaction of frictional conditions with bifurcation phenomena such phenomena are observed in the context of multiple solutions both stable and unstable of the discretized system and are also manifested in the behavior of the iterative map used to solve the nonlinear algebraic system of equations

globally convergent adaptive iir filters based on fixed pole locations a new class of adaptive filters dubbed fixed pole adaptive filters fpaf s is introduced these adaptive filters have infinite impulse responses yet their adaptation exhibits provable global convergence good filter performance with a relatively small number of adapted parameters is permitted by the new filter structure thus reducing the computational burden needed to implement adaptive filters the implementation and computational complexity of the fpaf is described and its modeling capabilities are determined excitation conditions on the filter input are established that guarantee global convergence of a standard set of adaptive algorithms some methods are described for selecting the fixed pole locations based on a priori information regarding the operating environment of the adaptive filter the fpaf is tailored to applications by such a procedure enabling improved performance in examples the fpaf is shown to achieve a smaller minimum mean square error given an equal number of adapted parameters in comparison with adaptive fir filters and adaptive filters based on laguerre and kautz models

numerical analysis of a dynamic piezoelectric contact problem arising in viscoelasticity a dynamic frictionless contact problem between a viscoelastic piezoelectric body and a deformable obstacle is numerically studied in this paper the contact is modelled using the normal compliance contact condition and the linear electro viscoelastic constitutive law is employed to simulate the piezoelectric effects the variational formulation is a coupled system composed of a parabolic nonlinear variational equation for the velocity field and a linear variational equation for the electric potential an existence and uniqueness result is recalled then a fully discrete scheme is introduced based on the finite element method to approximate the spatial variable and the backward euler scheme to discretize the time derivatives error estimates are derived on the approximative solutions from which the linear convergence of the algorithm is deduced under suitable regularity conditions finally some two dimensional examples are presented to demonstrate the accuracy and the performance of the algorithm

system identification using laguerre models the traditional approach of expanding transfer functions and noise models in the delay operator to obtain linear in the parameters predictor models leads to approximations of very high order in cases of rapid sampling and or dispersion in time constants by using prior information about the time constants of the system more appropriate expansions related to laguerre networks are introduced and analyzed it is shown that the model order can be reduced compared to arx fir ar modeling by using laguerre models furthermore the numerical accuracy of the corresponding linear regression estimation problem is improved by a suitable choice of the laguerre parameter consistency error bounds persistence of excitation conditions and asymptotic statistical properties are investigated this analysis is based on the result that the covariance matrix of the regression vector of a laguerre model has a toeplitz structure

one dimensional dynamic thermoviscoelastic contact with damage abstract the problem of thermoviscoelastic dynamic contact between a rod and a rigid obstacle when the material damage is taken into account is modeled and analyzed the contact is modeled by the normal compliance condition and the stress strain constitutive equation is of kelvin voigt type the damage which describes the reduction of the load carrying capacity of the rod evolves because of the opening of microcracks as a result of tension or compression when the damage reaches a critical value at a point on the rod the material cannot carry any load and the system breaks down mathematically this is expressed by the quenching of the solution the existence of a local weak solution is established using penalization and a priori estimates

energy dependent radiative transfer equation and energy discretization the radiative transfer equation rte arises in a wide variety of applications in certain situations the energy dependence is not negligible in a series of two papers we study the energy dependent rte in this first paper of the series we focus on the well posedness analysis and energy discretization we use a mixed formulation so that the analysis covers both cases of non vanishing absorption and vanishing absorption we introduce a natural energy discretization scheme and derive an optimal order error estimate for the scheme angular discretization spatial discretization and fully discrete schemes as well as numerical simulation results are the topics of the sequel

on the determination of the optimal pole position of laguerre filters as is known in the literature at each stationary point of the squared error se curve of a laguerre filter at least one of a pair of certain laguerre coefficients weights vanishes the author describes a very efficient way to compute the derivatives of each one of these coefficients with respect to the pole position of the laguerre filter the knowledge of these derivatives makes possible the computation of high order approximations to the coefficients in question such as truncated taylor series and pade approximants the zeros of these approximations are usually good estimates of the location of the stationary points of the se curve nearer to the center of the approximation in this way the position of these stationary points in particular local minima can be estimated without resorting to a numerical search algorithm both continuous time and discrete time laguerre filters are discussed excited either by an impulse or by an arbitrary signal the authors illustrate the main results of the paper with a numerical example

folds in solutions of two parameter systems and their calculation part i this paper is concerned with paths of turning points in solutions of nonlinear systems having two parameters it is well known that these paths are solutions of a particular extended system of nonlinear equations in this paper both regular points and simple turning points in the extended system are related to the local geometry of the solution surface of the original nonlinear system a description is given of numerical methods both for solving the extended system and for calculating certain quantities which determine the local geometry of the solution surface applications to perturbed bifurcation to the formation of isolas and to the calculation of the multiplicity of solutions are also discussed numerical examples are given

damageable contact between an elastic body and a rigid foundation in this work the contact problem between an elastic body and a rigid obstacle is studied including the development of material damage which results from internal compression or tension the variational problem is formulated as a first kind variational inequality for the displacements coupled with a parabolic partial differential equation for the damage field the existence of a unique local weak solution is stated then a fully discrete scheme is introduced using the finite element method to approximate the spatial variable and an euler scheme to discretize the time derivatives error estimates are derived on the approximate solutions from which the linear convergence of the algorithm is deduced under suitable regularity conditions finally three two dimensional numerical simulations are performed to demonstrate the accuracy and the behaviour of the scheme

numerical models of steady rolling for non linear viscoelastic structures in finite deformations a lagrangian formulation of constitutive laws for a viscoelastic material based on irreversible thermodynamics is first presented these laws are expressed by a non linear differential equation governing the evolution of an internal variable then equations describing the steady rolling of an axisymmetric viscoelastic structure are obtained from the conservation laws of continuum mechanics a finite element approximation and a solution technique of the algebraic system is proposed the eiimination of the internal variable allows one to keep an elastic like algorithm with an independent solution of the viscoelastic equation numerical tests show the feasibility and the efficiency of the proposed methods in large three dimensional situations

online optimization of the time scale in adaptive laguerre based filters a new online method to optimize the free parameter in adaptive laguerre based filters is presented it is based on the minimization of a criterion that is equivalent to an upper bound for the quadratic approximation error the proposed technique presents a fast convergence and a good robustness

an optimum time scale for discrete laguerre network any discrete time stable transfer function can be expressed by a discrete time laguerre series with a chosen time scale an optimum time scale such that an index is minimized is derived this index ensures that the coefficients of higher order laguerre functions go toward zero quickly the solution derived requires the knowledge of the impulse response of the discrete plant cases of first order plants second order underdamped plants and plants with multiunit delay are also discussed

a mixed finite element method and solution multiplicity for coulomb frictional contact abstract this paper is concerned with the discrete contact problem governed by coulomb s friction law we propose and study a new technique using mixed finite elements with two multipliers in order to determine numerically critical friction coefficients for which multiple solutions to the friction problem exist the framework is based on eigenvalue problems and it allows to exhibit non uniqueness cases involving an infinity of solutions located on a continuous branch the theory is illustrated with several computations which clearly show the accuracy of the proposed method

evolutionary variational inequalities arising in viscoelastic contact problems we consider a class of evolutionary variational inequalities arising in various frictional contact problems for viscoelastic materials under the smallness assumption of a certain coefficient we prove an existence and uniqueness result using banach s fixed point theorem we then study two numerical approximation schemes of the problem a semidiscrete scheme and a fully discrete scheme for both schemes we show the existence of a unique solution and derive error estimates finally all these results are applied to the analysis and numerical approximations of a viscoelastic frictional contact problem with the finite element method used to discretize the spatial domain

on linear constraints for newton raphson corrections and critical point searches in structural f e problems the paper discusses the introduction of constraining equations in the tangential stiffness relation used to calculate the responses to different load cases in solution algorithms for non linear mechanical finite element f e problems an alternative to the normal two phase solution method is discussed this method is used to represent different iteration constraints and in conjunction with the search for critical solution points numerical tests are presented evaluating the efficiency of different iteration constraints for a model problem practically useful criteria for critical points are discussed the basic methods for search of such points and some numerical aspects are discussed and evaluated for three different problems

numerical analysis and simulations of a dynamic frictionless contact problem with damage the process of dynamic frictionless contact between a viscoelastic body and a reactive foundation which includes material damage is modelled numerically analyzed and simulated contact is modelled with the normal compliance condition the damage of the material resulting from tension or compression is described by the damage field which measures the pointwise fractional decrease in the load carrying capacity of the material the evolution of the damage is governed by a parabolic differential inclusion a fully discrete scheme for the problem is proposed and error estimates on the numerical solutions derived the scheme has been implemented and numerical simulations of the evolution of the mechanical state of the system and its material damage are presented