persistency of excitation for nonminimal models of systems having purely deterministic disturbances all results to date on the question of persistency of excitation depend on the model being minimal thus the results do not apply to systems having purely deterministic disturbances since these automatically give rise to uncontrollable modes on the unil circle this note presents new results on persistency of excitation applicable to nonminimal models of systems having purely deterministic disturbances

a stabilized conforming nodal integration for galerkin mesh free methods domain integration by gauss quadrature in the galerkin mesh free methods adds considerable complexity to solution procedures direct nodal integration on the other hand leads to a numerical instability due to under integration and vanishing derivatives of shape functions at the nodes a strain smoothing stabilization for nodal integration is proposed to eliminate spatial instability in nodal integration for convergence an integration constraint ic is introduced as a necessary condition for a linear exactness in the mesh free galerkin approximation the gradient matrix of strain smoothing is shown to satisfy ic using a divergence theorem no numerical control parameter is involved in the proposed strain smoothing stabilization the numerical results show that the accuracy and convergent rates in the mesh free method with a direct nodal integration are improved considerably by the proposed stabilized conforming nodal integration method it is also demonstrated that the gauss integration method fails to meet ic in mesh free discretization for this reason the proposed method provides even better accuracy than gauss integration for galerkin mesh free method as presented in several numerical examples copyright 2001 john wiley sons ltd

the natural element method in solid mechanics the application of the natural element method nem 1 2 to boundary value problems in two dimensional small displacement elastostatics is presented the discrete model of the domain consists of a set of distinct nodes n and a polygonal description of the boundary in the natural element method the trial and test functions are constructed using natural neighbour interpolants these interpolants are based on the voronoi tessellation of the set of nodes n the interpolants are smooth c 1 everywhere except at the nodes where they are c 0 in one dimension nem is identical to linear nite elements the nem interpolant is strictly linear between adjacent nodes on the boundary of the convex hull which facilitates imposition of essential boundary conditions a methodology to model material discontinuities and non convex bodies cracks using nem is also described a standard displacement based galerkin procedure is used to obtain the discrete system of linear equations application of nem to various problems in solid mechanics which include the patch test gradient problems bimaterial interface and a static crack problem are presented excellent agreement with exact analytical solutions is obtained which exemplies the accuracy and robustness of nem and suggests its potential application in the context of other classes of problems crack growth plates and large deformations to name a few 1998 john wiley sons ltd

nonlinear oscillations in the rolling motion of euler s disk the fixed points of the dynamical system describing the rolling motion of a uniform disk or a uniform circular hoop on a rough horizontal plane without dissipation are analyzed all fixed points of the system are stated to be steady motion states which are either saddle points or centers the spectral analysis of the sound amplitude time series emitted by a toy of the rolling disk shows that the similar nonlinear oscillations are expected in the motion with dissipation if under adiabatic approximation a finite time singularity occurs the bifurcation in the disk motion can appear

meshfree and finite element nodal integration methods nodal integration can be applied to the galerkin weak form to yield a particle type method where stress and material history are located exclusively at the nodes and can be employed when using meshless or finite element shape functions this particle feature of nodal integration is desirable for large deformation settings because it avoids the remapping or advection of the state variables required in other methods to a lesser degree nodal integration can be desirable because it relies on fewer stress point evaluations than most other methods in this work aspects regarding stability consistency efficiency and explicit time integration are explored within the context of nodal integration both small and large deformation numerical examples are provided copyright 2007 john wiley sons ltd

rls parameter convergence with overparametrized models abstract this paper through the concept of quotient space generalizes the rls parameter convergence results obtained previously using the lyapunov type function approach 14 1 12 7 to overparameterized systems the system signals do not have to be quasi stationary as assumed by ljung 10 and a priori knowledge of the degree of overparameterization is not required the excitation condition is the weakest possible and it is shown that under this excitation condition limiting set of parameter estimates always belongs to a set h each element of which contains the irreducible plant model plus a monic common factor polynomial it is further shown that the common factor polynomials defined by the limiting set of parameter estimates are quantitatively related to the initial conditions of the algorithm for example if the condition number of the initial covariance matrix is unity then the limiting set of parameter estimates is the singleton on h closest to the initial parameter estimate

remarks on persistency of excitation for nonminimal models of systems having purely deterministic disturbances a persistency of excitation result for nonminimal models of systems having purely deterministic disturbances has been given recently in 1 in this note we give a direct and simple proof for the case of bounded signals of the result of 1 and show via a counterexample that an assumption on system signals boundedness which does not appear in 1 is necessary when arbitrary unbounded signals are allowable finally we give a proper persistency of excitation result which does not require signal boundedness for the case when the system input consists of a bounded external signal and of a constant coefficient feedback component

complementary energy principle for elastodynamics free of volumetric locking abstract this paper proposes a complementary energy principle for elastodynamic problems in doing so the stresses and the inertial forces that satisfy the equilibrium equations a priori are chosen as basic variables and then the complementary variational formulation is established by weakly enforcing the kinematic constraints the eventual formulation is posed to be an integral equation with respect to the time dimension and can be easily applied to free and forced vibration analysis in addition the volumetric locking free property inherent in the complementary energy principle is addressed numerical study on a rectangular plate is performed to validate the proposed complementary energy principle as well as to verify the featured locking free property moreover extensions of the dynamic complementary energy principle to tackle visco elastodynamics and stokes flows are also presented

reproducing kernel particle methods for large deformation analysis of non linear structures abstract large deformation analysis of non linear elastic and inelastic structures based on reproducing kernel particle methods rkpm is presented the method requires no explicit mesh in computation and therefore avoids mesh distortion difficulties in large deformation analysis the current formulation considers hyperelastic and elasto plastic materials since they represent path independent and path dependent material behaviors respectively in this paper a material kernel function and an rkpm material shape function are introduced for large deformation analysis the support of the rkpm material shape function covers the same set of particles during material deformation and hence no tension instability is encountered in the large deformation computation the essential boundary conditions are introduced by the use of a transformation method the transformation matrix is formed only once at the initial stage if the rkpm material shape functions are employed the appropriate integration procedures for the moment matrix and its derivative are studied from the standpoint of reproducing conditions in transient problems with an explicit time integration method the lumped mass matrices are constructed at nodal coordinate so that masses are lumped at the particles several hyperelasticity and elasto plasticity problems are studied to demonstrate the effectiveness of the method the numerical results indicated that rkpm handles large material distortion more effectively than finite elements due to its smoother shape functions and consequently provides a higher solution accuracy under large deformation unlike the conventional finite element approach the nodal spacing irregularity in rkpm does not lead to irregular mesh shape that significantly deteriorates solution accuracy no volumetric locking is observed when applying non linear rkpm to nearly incompressible hyperelasticity and perfect plasticity problems further model adaptivity in rkpm can be accomplished simply by adding more points in the highly deformed areas without remeshing

on computing upper and lower bounds on the outputs of linear elasticity problems approximated by the smoothed finite element method verification of the computation of local quantities of interest e g the displacements at a point the stresses in a local area and the stress intensity factors at crack tips plays an important role in improving the structural design for safety in this paper the smoothed finite element method sfem is used for finding upper and lower bounds on the local quantities of interest that are outputs of the displacement field for linear elasticity problems based on bounds on strain energy in both the primal and dual problems one important feature of sfem is that it bounds the strain energy of the structure from above without needing the solutions of different subproblems that are based on elements or patches but only requires the direct finite element computation upper and lower bounds on two linear outputs and one quadratic output related with elasticity the local reaction the local displacement and the j integral are computed by the proposed method in two different examples some issues with sfem that remain to be resolved are also discussed

free surface fluid dynamics on moving domains this paper presents a lagrangian approach for the simulation of two dimensional free surface flows along with a systematic validation fluid flow is traditionally modeled using an eulerian description in association with finite differences and more recently finite elements free surface flow introduces new difficulties in connection with the time dependence of the domain the proposed approach sets a framework for meshfree and finite element formulations it is extended to two phase media in preisig and zimmermann m preisig th zimmermann two phase free surface fluid dynamics on moving domains j comput phys 229 7 2010 2740 2758 in this paper triangular finite elements and a remeshing procedure to avoid excessive element distortion are chosen for their robustness convergence of the lagrangian description is analyzed and compared to results obtained with an eulerian description the equivalence of the two formulations for confined flows is demonstrated numerically illustrations include stratified flow flow over a backward facing step propagation of a solitary wave and dam break meshfree formulations will be addressed in separate papers c 2010 elsevier b v all rights reserved

global stability of adaptive pole placement algorithms this paper presents direct and indirect adaptive control schemes for assigning the closed loop poles of a single input single output system in both the continuous and discrete time cases the resulting closed loop system is shown to be globally stable when driven by an external reference signal consisting of a sum of sinusoids in particular persistent excitation of the potentially unbounded closed loop input output data and hence convergence of a sequential least squares identification algorithm is proved the results are applicable to standard sequential least squares and least squares with covariance reset

stabilization and positioning control of a rolling disk by using the bogdanov takens bifurcation abstract on the basis of bogdanov takens bifurcation we obtain two nonlinear control laws for stabilization and positioning of a rolling disk on a horizontal plane at a desired set point the first control law is applied to reach a set of predetermined points from previously calculated initial conditions which unavoidably implies a small position error to overcome this problem a second procedure based on a nonlinear inverse control law is examined by using adequate leaning tilting and rolling moments the system satisfies nonholonomic constraints it is underactuated and the analysis of the bogdanov takens bifurcation provides the admissible parameter values to reach the desired set point our analysis allows stabilization and positioning of the rolling disk through small control torques neglecting the internal servomechanism dynamics with adequate reaction forces satisfying the nonholonomic conditions the results of the analytical calculations are verified by full numerical simulations

dynamics of an eccentric disk on a curved surface abstract this paper investigates the dynamic behavior of an eccentric disk rolling on a curve of arbitrary shape and then on a curve defined as a cubic function comparisons are made to a disk without eccentricity and the related point mass approximation the curve is subject to sinusoidal base excitation and the system is considered from the perspective of a potential well problem where escape is possible on one side the equations of motion are derived using a roll without slip constraint and the behavior is investigated by means of approximate analytical solutions numerically simulated frequency and amplitude sweeps and by considering the basins of attraction when initial conditions or forcing parameters are varied

locking free numerical methods for nearly incompressible elasticity and incompressible flow on moving domains abstract considerable effort is invested in the development of meshless methods under the claim that such methods have superior performance as compared to standard finite elements this claim is often justified by poor performance of finite elements in situations where the mesh undergoes large distortion and by a better ability of meshless methods to deal with the incompressibility constraint in this paper these claims are investigated on a series of problems in incompressible elasticity and incompressible fluid flow a standard displacement formulation and a mixed formulation with stabilization to circumvent the lbb condition are used the equations are integrated using stabilized nodal integration as well as gauss quadrature in the displacement formulation nodal integration effectively removes locking while in the mixed formulation no stabilization is required nodal integration on median dual cells is preferred over voronoi cells due to computational efficiency on very irregular nodal sets finite element and sibson shape functions perform equally well both when using gauss quadrature as well as nodal integration

globally stable and exponentially convergent adaptive control in this paper three new adaptive control strategies for linear discrete time single input single output plants are proposed they enable globally stable and exponentially convergent adaptive controllers to be designed based on various approaches such as pole placement and optimal lq the principle idea of the strategies proposed is to apply a fixed parameter control law while the estimates of the plant parameters leave some appropriately chosen region the persistency of excitation of some external signals is crucial for the stability analysis of an overall adaptive system

a geometric structure preserving discretization scheme for incompressible linearized elasticity abstract in this paper we present a geometric discretization scheme for incompressible linearized elasticity we use ideas from discrete exterior calculus dec to write the action for a discretized elastic body modeled by a simplicial complex after characterizing the configuration manifold of volume preserving discrete deformations we use hamilton s principle on this configuration manifold the discrete euler lagrange equations are obtained without using lagrange multipliers the main difference between our approach and the mixed finite element formulations is that we simultaneously use three different discrete spaces for the displacement field we explicitly derive the governing equations for the two dimensional case where the discrete spaces for the displacement field are constructed by p 1 polynomials over primal meshes for incompressibility constraint p 0 polynomials over dual meshes for the kinetic energy and p 1 polynomials over support volumes for the elastic energy and the discrete space of the pressure field is constructed by p 0 polynomials over primal meshes we test the efficiency and robustness of this geometric scheme using some numerical examples in particular we do not see any volume locking and or checkerboarding of pressure in our numerical examples this suggests that our choice of discrete solution spaces is compatible

a novel reduced basis method with upper and lower bounds for real time computation of linear elasticity problems abstract this paper presents a novel reduced basis method for analyzing problems of linear elasticity in a systematical rapid and reliable fashion for solutions with both upper and lower bounds to the exact solution in the form of energy norm or compliance output the lower bound of the solution output is obtained form the well known reduced basis method based on the galerkin projection used in the finite element method which is termed as gp rbm for the upper bound a new reduced basis approach is developed by the combination of the reduced basis method and a smoothed galerkin projection used in the linearly conforming point interpolation method and it is thus termed as sgp rbm to examine the present sgp rbm we first conduct a theoretical study on the very important upper bound property reduced basis models for both gp rbm and sgp rbm are constructed with the aid of an asymptotic error estimation and greedy adaptive procedure the gp rbm and the newly proposed sgp rbm are applied to analyze a cantilever beam with an oblique crack to verify the proposed rbm technique in terms of accuracy convergence bound properties and computational savings both theoretical analysis and numerical results have demonstrated that the present method is a very efficient method for real time solutions providing exact output bounds

exponential convergence of adaptive identification and control algorithms output and equation error adaptive identification algorithms are shown to be exponentially convergent under a deterministic or stochastic persistently exciting or spanning condition on the system inputs together with several other standard conditions an adaptive control algorithm is shown to be exponentially convergent under a deterministic or stochastic persistently exciting condition on the reference trajectory together with some standard conditions

chaotic phenomena triggering the escape from a potential well this paper explores the manner in which a driven mechanical oscillator escapes from the cubic potential well typical of a metastable system close to a fold the aim is to show how the well known atoms of dissipative dynamics saddle node folds period doubling flips cascades to chaos boundary crises etc assemble to form molecules of overall response hierarchies of cusps incomplete feigenbaum trees etc particular attention is given to the basin of attraction and the loss of engineering integrity that is triggered by a homoclinic tangle the latter being accurately predicted by a melnikov analysis after escape chaotic transients are shown to conform to recent scaling laws analytical constraints on the mapping eigenvalues are used to demonstrate that sequences of flips and folds commonly predicted by harmonic balance analysis are in fact physically inadmissible

a finite point method in computational mechanics applications to convective transport and fluid flow the paper presents a fully meshless procedure fo solving partial differential equations the approach termed generically the finite point method is based on a weighted least square interpolation of point data and point collocation for evaluating the approximation integrals some examples showing the accuracy of the method for solution of adjoint and non self adjoint equations typical of convective diffusive transport and also to the analysis of compressible fluid mechanics problem are presented

persistency of excitation in the presence of possibly unbounded signals this note develops an explicit characterization of the concept of persistency of excitation for time invariant linear systems in the presence of possibly unbounded signals this result can be used to establish exponential convergence for a range of adaptive control algorithms a feature of our proof is a particular technique for dealing with the initial condition response