an efficient implementation of stress resultant plasticity in analysis of reissner mindlin plates reference epfl article 102718view record in web of science record created on 2007 04 23 modified on 2016 08 08

partially implicit schemes for the numerical solutions of some non linear differential equations as numerical methods are one of the main tools used to discover the non linear behaviour characteristics of continuous dynamical systems a study on the use of numerical schemes which delineate the true physics from numerical artefact is desirable as a step in that direction partially implicit rational schemes based on first order methods and a second order method are derived and analysed from the point of view of dynamical systems for a scalar autonomous ordinary differential equation the second order method is developed by taking a linear combination of first order methods though implicit in nature the methods are applied explicitly the approach adopted is extended to obtain numerical schemes for the solution of a class of reaction diffusion partial differential equations the methods are tested on differential equations with cubic and quadratic reaction terms it is found that for certain sets of initial conditions the first order partially implicit schemes converge monotonically to the correct fixed points for all time steps unlike the euler method and the second order method in other words for the same steady state solution the associated domain of attraction of the discrete problem and its continuous counterpart are exactly the same however for other initial conditions it is found that the domains of attraction of the second order method mimic more closely the domains of attraction of the continuous differential equations the comparative study of the various explicit runge kutta methods of orders 2 6 shows that it is the discretized form with its specific algebraic form recursive relation which are the source of spurious steady state solutions and numerical chaos from these methods it is found however that the use in general of fifth order runge kutta methods is seen to be preferred to other runge kutta methods as they have an extended stability range in particular the fifth order lawson method which has a far superior range of stability than the other runge kutta methods

a plasticity model and algorithm for mode i cracking in concrete summary a class of plasticity models which utilize rankine s principal stress yield locus is formulated to simulate cracking in concrete and rock under monotonic loading conditions the formulation encompasses isotropic and kinematic hardenindsoftening rules and incremental flow theory as well as total deformation theory formats are considered an euler backward algorithm is used to integrate the stresses and internal variables over a finite loading step and an explicit expression is derived for a consistently linearized tangent stiffness matrix associated with the euler backward scheme particular attention is paid to the corner regime that is when the two major principal stresses become equal a detailed comparison has been made of the proposed plasticity based crack formulations and the traditional fixed and rotating smeared crack models for a homogeneously stressed sample under a non proportional loading path a comparison between the flow theory based plasticity crack models and experimental data has been made for a single edge notched plain concrete specimen under mixed mode loading conditions

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

a return mapping algorithm for a class of cyclic plasticity models a return mapping algorithm for a class of cyclic plasticity models is presented the constitutive model includes a quadratic yield criterion and multi component formulations of non linear isotropic and kinematic hardening thus both initially isotropic and anisotropic materials can be described and a proper description of the hysteresis loops and the cyclic hardening response of materials under cyclic loading is obtained the return mapping algorithm employs the closest point projection scheme in combination with a decomposition method to obtain an efficient and robust integration of the constitutive model the consistent tangent operator is derived in closed form and is found to be unsymmetric due to the non linear evolution of the kinematic hardening terms the accuracy and robustness of the algorithm are assessed through numerical examples

stable splitting scheme for general form of associated plasticity including different scales of space and time an efficient implementation of the operator split procedure for boundary value solution with plastic flow computation is presented for a general form of associated plasticity model we start with the general form of phenomenological model of plasticity where the yield criterion is not restricted to a simple quadratic form and the elasticity tensor does not have constant entries we then turn to the multi scale model of plasticity which employs the fine scale representation of the plastic deformation along with the homogenization procedure for stress computation we also visit the plasticity model with rate sensitive plastic response where plastic flow computation is carried out at fine scale in time we proved herein the sufficient and necessary conditions for the proposed operator split procedure to converge for any such general form of associated plasticity moreover we presented a systematic manner for constructing the main ingredients for the plastic flow computation and the global newton s iteration such as the consistent elastoplastic tangent

explicit finite difference methods for non linear dynamic systems froude s pendulum abstract numerical schemes based on first order methods and a second order method are developed and analysed for solving the non linear froude s pendulum system the second order method is developed by taking a linear combination of three first order methods though implicit in nature with the resulting improvements in stability the methods are applied explicitly these methods are extended to a more general second order ordinary differential equation stability of the numerical methods is approached from the point of view of dynamical systems it is found that the methods are stable under the same conditions as those required by the linearized schemes in the neighbourhood of constant stable fixed points of the underlying initial value problem for the second order method this result is found to hold for any chosen value of the step length a major advantage of using the second order method is the absence of solutions to the discrete finite difference equation that do not correspond to the continuous dynamical system this contrasts starkly with the runge kutta methods which are found to produce solutions that converge to a false asymptote or wrong solutions in a deceptively smooth manner if the step length is not rightly chosen a selection of examples are carried out on the non linear froude s pendulum system to illustrate the differing predictions obtained by the methods

clairvoyant and adaptive signal detection in non gaussian clutter a data dependent threshold interpretation this paper addresses the problem of signal detection in correlated non gaussian clutter modeled as a spherically invariant random process the optimum strategy to detect a constant signal with either known or unknown complex amplitude embedded in correlated gaussian clutter is given by comparing the whitening matched filter output with a fixed threshold when the clutter is non gaussian the performance of the matched filter sensibly degrades the optimum strategy is the classical whitening matched filter output compared with a data dependent threshold this interpretation provides a deeper insight into the structure of the optimum detector and allows us to single out a family of suboptimum detectors based on a polynomial approximation of the data dependent threshold they are easy to implement and have performance that is really close to the optimal the adaptive implementation of the polynomial detectors is also investigated and their performance is analyzed by means of monte carlo simulation for various clutter scenarios

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

a displacement like finite element model for j2 elastoplasticity variational formulation and finite step solution abstract the displacement like finite element formulation for finite step j2 elastoplasticity is revisited in this paper the classical computational strategy according to which plastic loading is tested at the gauss points of each element and an independent return mapping algorithm is performed for given incremental displacements is consistently derived from a suitably discretized version of a min max variational principle the sequence of solution phases to be performed within each load step adopting a full newton s method is illustrated in detail and the importance of a correct update of the plastic strains is emphasized it is further shown that in order to increase the rate of convergence and the stability properties of the newton s method the consistent elastoplastic tangent operator must be exploited even at the first iteration of each load step subsequent to the first yielding of the structural model this is in contrast with the traditional implementation according to which the elastic operator is used at the first iteration of each load step the effectiveness of the present approach is shown by a set of numerical examples referred to plane strain problems

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

bootstrap based detection of signals with unknown parameters in unspecified correlated interference a detection scheme that uses estimators for signal frequency amplitude and phase to detect signals in correlated interference is proposed the scheme does not require training data but uses the bootstrap to estimate the distribution of the test statistic under the null hypothesis directly from the received data simulation results are provided that confirm the detector performance for correlated gaussian and non gaussian interference and the consistency of the estimators the detector asymptotically maintains the preset level of false alarm and a detection rate of 100 is achievable at 5 db signal to noise ratio snr for sample sizes as small as 500 data points the case where the arrival time of the signal is unknown is also treated simulation results showing the performance of the detector when it is suitably extended to handle this case are given

the cfar adaptive subspace detector is a scale invariant glrt the constant false alarm rate cfar matched subspace detector cfar msd is the uniformly most powerful invariant test and the generalized likelihood ratio test glrt for detecting a target signal in noise whose covariance structure is known but whose level is unknown previously the cfar adaptive subspace detector cfar asd or adaptive coherence estimator ace was proposed for detecting a target signal in noise whose covariance structure and level are both unknown and whose covariance structure is estimated with a sample covariance matrix based on training data we show here that the cfar asd is glrt when the test measurement is not constrained to have the same noise level as the training data as a consequence this glrt is invariant to a more general scaling condition on the test and training data than the well known glrt of kelly 1986

finite elastoplastic deformations of space curved membranes abstract under restriction of an isotropic elastic response of deformed lattice a covariant theory of finite elastoplasticity is developed in principal axes of a pair of deformation tensors in material description the tensor pair consists of the plastic deformation tensor and the total deformation cauchy green tensor the proposed theory is applied to elastoplastic membranes whose reference and current configurations can be arbitrary space curved surfaces pressure insensitive von mises yield criterion and isotropic hardening are considered as a model problem with a particular form of the strain energy function given in terms of elastic principal stretches through an explicit enforcement of the plane stress condition we arrive at a reduced two dimensional problem representation which is set in the membrane tangent plane numerical implementation details are given to show an important role of the operator split methodology in simplifying the state update computation and the computation of the consistent tangent modulus a set of numerical examples illustrates the performance of the presented theory and indicates some of the possible areas of application

dynamical approach study of spurious steady state numerical solutions of nonlinear differential equations i the dynamics of time discretization and its implications for algorithm development in computational fluid dynamics abstract the goal of this paper is to utilize the theory of nonlinear dynamics approach to investigate the possible sources of errors and slow convergence and nonconvergence of steady state numerical solutions when using the time dependent approach for nonlinear hyperbolic and parabolic partial differential equations terms this interdisciplinary research belongs to a subset of a new field of study in numerical analysis sometimes referred to as the dynamics of numerics and the numerics of dynamics at the present time this new interdisciplinary topic is still the property of an isolated discipline with all too little effort spent in pointing out an underlying generality that could make it adaptable to diverse fields of applications this is the first of a series of research papers under the same topic our hope is to reach researchers in the fields of computational fluid dynamics cfd and in particular hypersonic and combustion related cfd by simple examples in which the exact solutions of the governing equations are known the application of the apparently straightforward numerical technique to genuinely nonlinear problems can be shown to lead to incorrect or misleading results one striking phenomenon is that with the same initial data the continuum and its discretized counterpart can asymptotically approach different stable solutions this behavior is especially important for employing a time dependent approach to the steady state since the initial data are usually not known and a freestream condition or an intelligent guess for the initial conditions is often used with the unique property of the different dependence of the solution on initial data for the partial differential equation and the discretized counterpart it is not easy to delineate the true physics from numerical artifacts when numerical methods are the sole source of solution procedure for the continuum part i concentrates on the dynamical behavior of time discretization for scalar nonlinear ordinary differential equations in order to motivate this new yet unconventional approach to algorithm development in cfd and to serve as an introduction for parts 11 and iii of the same series of research papers

chaos in numerical analysis of ordinary differential equations abstract the discretisation of the ordinary nonlinear differential equation d y d t y 1 y by the entral difference scheme is studied for fixed mesh size in the usual numerical computation this method produces some ghost solution for the long range calculation regarding this discretisation as a dynamical system in r2 these pathological behaviors are shown to be a kind of chaos in the dynamical system for any mesh size moreover some combination of the central difference scheme and the euler s scheme is studied for the above equation it gives some motivation for henon s model the usual discretisation of a second order differential equation are studied also it gives some chaotic behaviors numerically which is similar to the behavior of the orbits of the system of differential equations proposed by henon heiles

finite difference schemes having the correct linear stability properties for all finite step sizes iii abstract we construct a class of finite difference schemes for two coupled first order ordinary differential equations such that the difference equations have the correct linear stability properties for all finite values of the step size the differential equations considered are assumed to have only a single real fixed point a major consequence of such schemes is the absence of elementary numerical instabilities illustrations of such schemes are given for the duffing and van der pol equations

matched subspace detectors we formulate a general class of problems for detecting subspace signals in subspace interference and broadband noise we derive the generalized likelihood ratio glr for each problem in the class we then establish the invariances for the glr and argue that these are the natural invariances for the problem in each case the glr is a maximal invariant statistic and the distribution of the maximal invariant statistic is monotone this means that the glr test glrt is the uniformly most powerful invariant detector we illustrate the utility of this finding by solving a number of problems for detecting subspace signals in subspace interference and broadband noise in each case we give the distribution for the detector and compute performance curves

central difference scheme and chaos abstract the existence of chaotic orbits is proved for area preserving diffeomorphisms of the plane defined by polynomials of degree two derived from the discretized logistic equation

turbulence in multistep methods for initial value problems solving a scalar initial value problem with a numerical k step scheme amounts to iterating a k dimensional discrete dynamical system in this paper we investigate regular and chaotic behaviour of some dynamical systems associated with adams bashforth formulas applied to a simple nonlinear test equation

a unified approach to spurious solutions introduced by time discretization part i basic theory the asymptotic states of numerical methods for initial value problems are examined in particular spurious steady solutions solutions with period 2 in the timestep and spurious invariant curves

on a class of constitutive equations in viscoplasticity formulation and computational issues the viscoplastic constitutive model is formulated based on the existence of the dissipation potential which embodies the notion of the gauge minkowski function of the convex set a perturbation method is used for a solution of stiff differential equations characterizing the associated problem of evolution it relies on a discrete formulation of viscoplasticity which results from the regularized version of the principle of maximum plastic dissipation the operator split methodology and the newton raphson method are used to obtain the numerical solution of the discretized equations of evolution the consistent tangent modulus is expressed in a closed form as a result of the exact linearization of the discretized evolution equations for several variants of the flow potential function including some representative stiff functional forms numerical tests of the integration algorithm based on iso error maps are provided finally a numerical example is presented to illustrate the robustness and the effectiveness of the proposed approach

stress resultant plasticity for shells revisited in this work we revisit the stress resultant elastoplastic geometrically exact shell finite element formulation that is based on the ilyushin shapiro two surface yield function with isotropic and kinematic hardening the main focus is on implicit projection algorithms for computation of updated values of internal variables for stress resultant shell elastoplasticity four different algorithms are derived and compared three of them yield practically identical final results yet they differ considerably in computational efficiency and implementation complexity since they solve different sets of equations and they use different procedures that choose active yield surfaces one algorithm does not provide acceptable accuracy it turns out that the most simple and straightforward algorithm performs surprisingly well and efficiently several numerical examples are presented to illustrate the ilyushin shapiro stress resultant shell formulation and the numerical performance of the presented integration algorithms