the effect of imperfect boundary conditions on the collapse behavior of anisotropic shells abstract a rigorous solution is presented for the case of stiffened anisotropic shells with general imperfections under combined axial compression internal or external pressure and torsion donnell type equations are used to describe the behavior of the layered composite shell the stiffeners are represented by smeared theory and for the discrete end rings cohen s ring equations are used the circumferential dependence is eliminated by a truncated fourier series the resulting 2 point boundary value problem is solved numerically via the parallel shooting method the nonlinear collapse behavior is studied using different combinations of axisymmetric and asymmetric imperfections comparison with koiter type imperfection predictions display the range of validity of the asymptotic results it is shown that besides initial geometric imperfections also nonuniform harmonically varying boundary conditions can have severe degrading effect on the load carrying capacity of anisotropic shells

derivation of the gross pitaevskii hierarchy for the dynamics of bose einstein condensate consider a system of n bosons on the three dimensional unit torus interacting via a pair potential n2v n xi xj where x x1 xn denotes the positions of the particles suppose that the initial data n 0 satisfies the condition where hn is the hamiltonian of the bose system this condition is satisfied if n 0 wn n 0 where wn is an approximate ground state to hn and n 0 is regular let n t denote the solution to the schrodinger equation with hamiltonian hn gross and pitaevskii proposed to model the dynamics of such a system by a nonlinear schrodinger equation the gross pitaevskii gp equation the gp hierarchy is an infinite bbgky hierarchy of equations so that if ut solves the gp equation then the family of k particle density matrices k ut ut solves the gp hierarchy we prove that as n the limit points of the k particle density matrices of n t are solutions of the gp hierarchy our analysis requires that the n boson dynamics be described by a modified hamiltonian that cuts off the pair interactions whenever at least three particles come into a region with diameter much smaller than the typical interparticle distance our proof can be extended to a modified hamiltonian that only forbids at least n particles from coming close together for any fixed n 2006 wiley periodicals inc

enhanced deterministic performance of panels using stochastic variations of geometry and material the effect of stochastic variation in material and geometric properties on structural performance is important for robust design knowledge of such effects can be acquired by applying variation pat

approximation of the vibration modes of a plate by reissner mindlin equations this paper deals with the approximation of the vibration modes of a plate modelled by the reissner mindlin equations it is well known that in order to avoid locking some kind of reduced integration or mixed interpolation has to be used when solving these equations by finite element methods in particular one of the most widely used procedures is the mixed interpolation tensorial components based on the family of elements called mitc we use the lowest order method of this family applying a general approximation theory for spectral problems we obtain optimal order error estimates for the eigenvectors and the eigenvalues under mild assumptions these estimates are valid with constants independent of the plate thickness the optimal double order for the eigenvalues is derived from a corresponding l 2 estimate for a load problem which is proven here this optimal order l 2 estimate is of interest in itself finally we present several numerical examples showing the very good behavior of the numerical procedure even in some cases not covered by our theory

noncausal inverses for linear systems suppose we are to guide a plant with a square transfer matrix through a series of way points this can be accomplished by output tracking of trajectories which are fitted together in a sufficiently smooth manner each segment of each output is prescribed in terms of a polynomial or sine function or the product thereof our technique is to compute 1 a noncausal particular solution based on the desired trajectory over each segment and the movement from one segment to the next and this particular solution consists of a particular control and a particular state trajectory and 2 a regulator to handle modeling errors disturbances etc we concentrate on the particular solution

stochastic finite element analysis of structures in the presence of multiple imprecise random field parameters the research work presents the study on non deterministic problems in the presence of the multiple imprecise random field uncertainties by extending the spectral stochastic finite element framework the standard random field is expanded to characterize the behaviour of physical model with imprecise randomness more appropriately for real engineering problems based on available sources of uncertainty the young s modulus and body force of structures are considered as imprecise random fields with bounded statistical moments mathematical expressions and solution procedure are developed to produce the uncertain but bounded statistical characteristics of responses namely interval mean value interval standard deviation and bounding distribution functions the bounding probability density and cumulative distribution of the imprecise random response are then effectively visualized by means of polynomial chaos expansion the feasibility and effectiveness of the presented method are illustrated by three numerical examples

post critical analysis of structures with a nonlinear pre buckling state in the presence of imperfections in the context of the geometrically nonlinear analysis of structures by continuation methods a technique for the determination of the imperfection sensitivity is carried out the technique is based on galerkin s reduction of equilibrium equations in the subspace of extrapolation branches emanating from the bifurcation points the pre and post critical behaviour in the neighbourhood of bifurcation points however is well approximated provided that extrapolations have a large convergence domain to this end an efficient asymptotic representation of the primary and secondary equilibrium paths and procedures that overcome the ill conditioning of the systems defined in the critical points is used here

probabilistic eigenvalue buckling analysis solved through the ratio of polynomial response surface an efficient procedure for the reliability analysis of frame structures with respect to the buckling limit state is proposed under the assumption that no imperfections are present and that the elastic parameters are uncertain and modeled as random variables the approach allows a deeper investigation of structures which are not sensitive to imperfections the procedure relies on a response surface method adopting simple ratio of polynomials without cross terms as performance function such a relationship approximates analytically the dependence between the buckling load and the basic variables furnishing a limit state equation which is very close to the exact one when a proper experimental design is adopted in this way a monte carlo simulation applied to the response surface leads to a good approximation with low computational effort several numerical examples show the accuracy and effectiveness of the method varying structural complexity correlation between basic variables and their distribution

an enhanced hybrid method for the simulation of highly skewed non gaussian stochastic fields abstract in this paper an enhanced hybrid method ehm is presented for the simulation of homogeneous non gaussian stochastic fields with prescribed target marginal distribution and spectral density function the presented methodology constitutes an efficient blending of the deodatis micaletti method with a neural network based function approximation precisely the function fitting ability of neural networks based on the resilient back propagation rprop learning algorithm is employed to approximate the unknown underlying gaussian spectrum the resulting algorithm can be successfully applied for simulating narrow banded fields with very large skewness at a fraction of the computing time required by the existing methods its computational efficiency is demonstrated in three numerical examples involving fields that follow the beta and lognormal distributions

multilayered shell finite element with interlaminar continuous shear stresses a refinement of the reissner mindlin formulation a finite element formulation for refined linear analysis of multilayered shell structures of moderate thickness is presented an underlying shell model is a direct extension of the first order shear deformation theory of reissner mindlin type a refined theory with seven unknown kinematic fields is developed i by introducing an assumption of a zig zag i e layer wise linear variation of displacement field through the thickness and ii by assuming an independent transverse shear stress fields in each layer in the framework of reissner s mixed variational principle the introduced transverse shear stress unknowns are eliminated on the cross section level at this process the interlaminar equilibrium conditions i e the interlaminar shear stress continuity conditions are imposed as a result the weak form of constitutive equations the so called weak form of hooke s law is obtained for the transverse strains transverse stress resultants relation a finite element approximation is based on the four noded isoparametric element to eliminate the shear locking effect the assumed strain variational concept is used performance of the derived finite element is illustrated with some numerical examples the results are compared with the exact three dimensional solutions as well as with the analytical and numerical solutions obtained by the classical the first order and some representative refined models copyright 2000 john wiley sons ltd

post buckling nonlinear static and dynamical analyses of uncertain cylindrical shells and experimental validation the paper presents a complete experimental validation of an advanced computational methodology adapted to the nonlinear post buckling analysis of geometrically nonlinear structures in presence of uncertainty a mean nonlinear reduced order computational model is first obtained using an adapted projection basis the stochastic nonlinear computational model is then constructed as a function of a scalar dispersion parameter which has to be identified with respect to the nonlinear static experimental response of a very thin cylindrical shell submitted to a static shear load the identified stochastic computational model is finally used for predicting the nonlinear dynamical post buckling behavior of the structure submitted to a stochastic ground motion

negative energy ground states for the l2 critical nlse on metric graphs we investigate the existence of ground states with prescribed mass for the focusing nonlinear schrodinger equation with l2 critical power nonlinearity on noncompact quantum graphs we prove that unlike the case of the real line for certain classes of graphs there exist ground states with negative energy for a whole interval of masses a key role is played by a thorough analysis of gagliardo nirenberg inequalities and by estimates of the optimal constants most of the techniques are new and suited to the investigation of variational problems on metric graphs

stochastic identification of imperfections in a submerged shell structure abstract accurate predictions of the buckling load in imperfection sensitive shell structures requires precise knowledge of the location and magnitude of any geometric imperfections in the shell e g dents this work describes a non contact approach to identifying such imperfections in a submerged shell structure by monitoring the acoustic pressure field at discrete points proximal to a shell structure excited by a cyclic membrane i e in plane loading it is noticed that parameters describing small scale denting can be identified in order to perform the identification a fluid structure model that predicts the spatio temporal pressure field is required this model is described in detail and includes the predicted effects of the imperfection on the observations a bayesian markov chain monte carlo approach is then used to generate the imperfection parameter estimates and quantify the uncertainty in those estimates additionally for cases involving the occurrence of an unknown number of dents reversible jump markov chain monte carlo rjmcmc methods are employed in this work

snap through buckling reliability analysis under spatiotemporal variability and epistemic uncertainty surrogate models often provide an effective tradeoff between accuracy and efficiency during reliability analysis with expensive physics models in snap through buckling reliability analysis a surrogate model could be built for the critical buckling load as a function of loading material properties geometry and boundary conditions however in the presence of spatiotemporal variability the response surface of the critical buckling load is often highly nonlinear and irregular thus rendering commonly used response surface type surrogate modeling strategies ineffective this paper proposes a new buckling reliability analysis method based on support vector machines for structures subjected to spatiotemporal variability and in the presence of epistemic uncertainty regarding model inputs and parameters bayesian calibration is first used to quantify the epistemic uncertainty in the modeling of spatiotemporal variability under limited data upon the modeling of spatiotemporal variability and epistemic unce

tric a simple but sophisticated 3 node triangular element based on 6 rigid body and 12 straining modes for fast computational simulations of arbitrary isotropic and laminated composite shells tric is a simple but sophisticated 3 node shear deformable isotropic and composite flat shell element suitable for large scale linear and nonlinear engineering computations of thin and thick anisotropic plate and complex shell structures its stiffness matrix is based on 12 straining modes but essentially requires the computation of a sparse 9 by 9 matrix the element formulation departs from conventional cartesian mechanics as well as previously adopted physical lumping procedures and contains a completely new implementation of the transverse shear deformation it naturally circumvents all previously imposed constraints the methodology is based on physical inspirations of the natural mode finite element method nm fem formalized through appropriate geometrical trigonometrical and engineering mathematical relations and it involves only exact integrations its stiffness mass and geometrical matrices are all explicitly derived the kinematics of the element are hierarchically decomposed into 6 rigid body and 12 straining modes of deformation a simple congruent matrix operation transforms the elemental natural stiffness matrix to the local and global cartesian coordinates the modes show explicitly how the element deforms in axial straining symmetrical and antisymmetrical bending as well as in transverse shearing the latter has only become clear in the formulation presented here and has brought about a completion of the understanding of natural modes as they apply to the triangular shell element a wide range of numerical examples substantiate the conception and purpose of the element tric fast convergence is observed in many examples

rigorous derivation of the cubic nls in dimension one we derive rigorously the one dimensional cubic nonlinear schrodinger equation from a many body quantum dynamics the interaction potential is rescaled through a weak coupling limit together with a short range one we start from a factorized initial state and prove propagation of chaos with the usual two step procedure in the former step convergence of the solution of the bbgky hierarchy associated to the many body quantum system to a solution of the bbgky hierarchy obtained from the cubic nls by factorization is proven in the latter we show the uniqueness for the solution of the infinite bbgky hierarchy

assessment of spectral representation and karhunen loeve expansion methods for the simulation of gaussian stochastic fields abstract from the wide variety of methods developed for the simulation of gaussian stochastic processes and fields two are most often used in applications the spectral representation method and the karhunen loeve k l expansion in this paper an in depth assessment on the capabilities of the two methods is presented the spectral representation method expands the stochastic field as a sum of trigonometric functions with random phase angles and or amplitudes the version having only random phase angles is used in this work a wavelet galerkin scheme is adopted for the efficient numerical solution of the fredholm integral equation appearing in the k l expansion a one dimensional homogeneous gaussian random field with two types of autocovariance function exponential and square exponential is used as the benchmark test the accuracy achieved and the computational effort required by the k l expansion and the spectral representation for the simulation of the stochastic field are investigated the accuracy obtained by the two approaches is examined by comparing their ability to produce sample functions that match the target correlation structure and the gaussian probability distribution or alternatively its low order statistical moments mean variance and skewness

a formulation of the mitc4 shell element for finite strain elasto plastic analysis abstract a finite strain elasto plastic formulation is developed for the mitc4 shell element the developed formulation is based on lee s multiplicative decomposition of the deformation gradient and on the hyperelastic expression of von mises flow rule expressed in terms of hencky s strain tensor the formulation incorporates thickness stretching degrees of freedom that are condensed at the element level by imposing the classical in layer plane stress condition a symmetric and consistent tangent stiffness matrix is also developed

the koiter newton approach using von karman kinematics for buckling analyses of imperfection sensitive structures the koiter newton approach is a reduced basis method for nonlinear structural analyses the method combines koiter s approach as a predictor step and the newton arc length technique as a corrector step to trace the entire load displacement equilibrium path of a structure in a step by step manner this computationally highly efficient and accurate solution method has recently demonstrated a superior performance in nonlinear analyses compared to standard techniques in this paper we propose an extension to buckling imperfection sensitivity analyses exploiting the method s stability and reliability we present two different modeling techniques for imperfection loads that both profit from the koiter newton approach reducing the initial computation steps to a small fraction thereof we introduce von karman kinematics which neglect some nonlinear terms of the green strain displacement relations to further increase the computational efficiency of the analysis by an essential reduction of the computation effort required to obtain higher order derivatives of the strain energy using various numerical examples and benchmark tests we demonstrate the overall high quality and performance of the proposed method

endpoint strichartz estimates we prove an abstract strichartz estimate which implies previously unknown endpoint strichartz estimates for the wave equation in dimension n 4 and the schrodinger equation in dimension n 3 three other applications are discussed local existence for a nonlinear wave equation and strichartz type estimates for more general dispersive equations and for the kinetic transport equation

derivation of the gross pitaevskii equation for the dynamics of bose einstein condensate consider a system of n bosons in three dimensions interacting via a repulsive short range pair potential n 2 v n xi xj where x x1 xn denotes the positions of the particles let hn denote the hamiltonian of the system and let n t be the solution to the schrodinger equation suppose that the initial data n 0 satisfies the energy condition h n 0 h k n n 0i c k n k for k 1 2 we also assume that the k particle density matrices of the initial state are asymptotically factorized as n we prove that the k particle density matrices of n t are also asymptotically factorized and the one particle orbital wave function solves the gross pitaevskii equation a cubic non linear schrodinger equation with the coupling constant given by the scattering length of the potential v we also prove the same conclusion if the energy condition holds only for k 1 but the factorization of n 0 is assumed in a stronger sense ams subject classification number 81v70 81t18 35q55

an efficient forward propagation of multiple random fields using a stochastic galerkin scaled boundary finite element method abstract this paper serves to extend the existing literature on the stochastic galerkin scaled boundary finite element method sgsbfem in two ways the first part of this work deals with the formulation of multiple non correlated gaussian random fields using the conventional karhunen loeve expansion technique and its forward propagation through the spectral stochastic scaled boundary finite element setting using the polynomial surface fit method in terms of the scaled boundary coordinates the advantages in adopting such a forward propagation technique in capturing the statistical moments of quantities of interest qoi across the domain are highlighted using carefully chosen linear elastic problems having large to least correlated random fields as inputs the second contribution is the extension of the proposed forward uncertainty quantification uq to take into account multiple independent random fields followed by polynomial chaos expansion pce based sensitivity analysis both the computational efficiency and the accuracy of the proposed framework under different input random field correlation settings are elaborated upon by comparing their results against that obtained using the current existing sgsbfem in the literature moreover the stochastic results are validated for all the numerical examples using the monte carlo method

stochastic inverse identification of geometric imperfections in shell structures abstract it is now widely known that the presence of geometric imperfections in shell structures constitutes an important contribution to the discrepancy between theoretical and experimentally realizable ultimate loads governed by buckling the present paper describes a method by which an actual initial imperfection field may be estimated using the service load response of a shell structure the approach requires solving a stochastic inverse problem wherein uncertainty regarding initial imperfection predictions is expressed within the context of a bayesian posterior distribution the proposed approach could be applied to condition assessment and performance evaluation activities in practice

quantum fluctuations and rate of convergence towards mean field dynamics the nonlinear hartree equation describes the macroscopic dynamics of initially factorized n boson states in the limit of large n in this paper we provide estimates on the rate of convergence of the microscopic quantum mechanical evolution towards the limiting hartree dynamics more precisely we prove bounds on the difference between the one particle density associated with the solution of the n body schrodinger equation and the orthogonal projection onto the solution of the hartree equation

a central limit theorem in many body quantum dynamics we study the many body quantum evolution of bosonic systems in the mean field limit the dynamics is known to be well approximated by the hartree equation so far the available results have the form of a law of large numbers in this paper we go one step further and we show that the fluctuations around the hartree evolution satisfy a central limit theorem interestingly the variance of the limiting gaussian distribution is determined by a time dependent bogoliubov transformation describing the dynamics of initial coherent states in a fock space representation of the system

buckling analysis of cylindrical shells with cutouts including random boundary and geometric imperfections abstract in this paper the effect of random geometric imperfections on the critical load of isotropic thin walled cylindrical shells under axial compression with rectangular cutouts is presented second moment characteristics of geometric imperfections are estimated by data of available measurements a simulation procedure based on the karhunen loeve expansion is applied for generating realizations of geometric imperfections nonlinear static finite element analyses are carried out for the calculation of the response statistics of the critical load of the cylindrical shells cumulative distribution functions of the critical load as obtained by direct monte carlo simulation are presented furthermore the individual and combined effects of random boundary and geometric imperfections on the limit loads of isotropic thin walled cylindrical shells under axial compression are also treated again second moment characteristics of these imperfections are estimated by data of available measurements of imperfections a simulation procedure also based on the karhunen loeve expansion is applied for generating realizations of both boundary and geometric imperfections a nonlinear static finite element analysis using the general purpose code stags c c rankin f a brogan w a loden h d cabiness stags structural analysis of general shells user manual lmsc p032594 version 3 0 lockheed martin missiles and space co inc palo alto ca usa 1998 is carried out for the calculation of the buckling response of the cylindrical shells finally the cumulative distribution functions of the limit load using direct monte carlo simulation are shown

the derivation of the mathbb t 3 t 3 energy critical nls from quantum many body dynamics we derive the 3d energy critical quintic nls from quantum many body dynamics with 3 body interaction in the mathbb t 3 periodic setting due to the known complexity of the energy critical setting previous progress was limited in comparison to the 2 body interaction case yielding energy subcritical cubic nls previously the only result for the 3d energy critical case was hong et al j funct anal 270 1 34 67 2016 which proved the uniqueness part of the argument in the case of small solutions in the main part of this paper we develop methods to prove the convergence of the bbgky hierarchy to the infinite gross pitaevskii gp hierarchy and separately the uniqueness of large gp solutions since the trace estimate used in the previous proofs of convergence is the false endpoint trace estimate in our setting we instead introduce a new frequency interaction analysis and apply the finite dimensional quantum de finetti theorem for the large solution uniqueness argument we discover the new hierarchical uniform frequency localization hufl property for the gp hierarchy and use it to prove a new type of uniqueness theorem the hufl property reduces to a new statement even for nls with the help of colliander et al ann math 2 167 3 767 865 2008 and ionescu and pausader duke math j 161 1581 1612 2012 which proved the global well posedness for the quintic nls this new uniqueness theorem establishes global uniqueness

rigorous derivation of the gross pitaevskii equation with a large interaction potential consider a system of n bosons in three dimensions interacting via a repulsive short range pair potential n 2 v n xi xj where x x1 xn denotes the positions of the particles let hn denote the hamiltonian of the system and let n t be the solution to the schrodinger equation suppose that the initial data n 0 satisfies the energy condition h n 0 hn n 0i cn and that the one particle density matrix converges to a projection as n then we prove that the k particle density matrices of n t factorize in the limit n moreover the one particle orbital wave function solves the time dependent gross pitaevskii equation a cubic non linear schrodinger equation with the coupling constant proportional to the scattering length of the potential v in 12 we proved the same statement under the condition that the interaction potential v is sufficiently small in the present work we develop a new approach that requires no restriction on the size of the potential

nonlinear inversion based output tracking an inversion procedure is introduced for nonlinear systems which constructs a bounded input trajectory in the preimage of a desired output trajectory in the case of minimum phase systems the trajectory produced agrees with that generated by hirschorn s inverse dynamic system however the preimage trajectory is noncausal rather than unstable in the nonminimum phase case in addition the analysis leads to a simple geometric connection between the unstable manifold of the system zero dynamics and noncausality in the nonminimum phase case with the addition of stabilizing feedback to the preimage trajectory asymptotically exact output tracking is achieved tracking is demonstrated with a numerical example and compared to the well known byrnes isidori regulator rather than solving a partial differential equation to construct a regulator the inverse is calculated using a picard like interaction when preactuation is not possible noncausal inverse trajectories can be truncated resulting in the tracking error transients found in other control schemes

derivation of the time dependent gross pitaevskii equation without positivity condition on the interaction using a new method pickl in a simple derivation of mean field limits for quantum systems 2010 it is possible to derive mean field equations from the microscopic n body schrodinger evolution of interacting particles without using bbgky hierarchies in this paper we wish to analyze scalings which lead to the gross pitaevskii equation which is usually derived assuming positivity of the interaction erdos et al in commun pure appl math 59 12 1659 1741 2006 invent math 167 515 614 2007 the new method for dealing with mean field limits presented in pickl 2010 allows us to relax this condition the price we have to pay for this relaxation is however that we have to restrict the scaling behavior of the interaction and that we have to assume fast convergence of the reduced one particle marginal density matrix of the initial wave function mu psi 0 to a pure state 0 0

quantitative derivation of the gross pitaevskii equation starting from first principle many body quantum dynamics we show that the dynamics of bose einstein condensates can be approximated by the time dependent nonlinear gross pitaevskii equation giving a bound on the rate of the convergence initial data are constructed on the bosonic fock space applying an appropriate bogoliubov transformation on a coherent state with expected number of particles mathit n the bogoliubov transformation plays a crucial role it produces the correct microscopic correlations among the particles our analysis shows that on the level of the one particle reduced density the form of the initial data is preserved by the many body evolution up to a small error that vanishes as mathit n 1 2 in the limit of large mathit n

brief parameter variations relative degree and stable inversion motivated by our prior research on automatic aircraft guidance we address stable inversion for output tracking and prove that this process is continuous with respect to parameter variations even when these variations cause a change in relative degree our earlier simulations indicated that the stable inversion process is extremely accurate and that only a linear regulator about the desired trajectory is required in the face of reasonable modeling error the principal novelty in our technique is that a differential equations point of view is taken as opposed to a state space approach on the driven zero dynamics of the system this is the situation that arises in many applications and it also enables handling the question of changes in relative degree without having to be encumbered by the change in state space dimension as the parameters change linear systems are first studied since the corresponding result is unknown next a corresponding theorem for nonlinear systems proved by using the picard process in conjunction with the result for the linear case the principal contribution of this paper is a result concerning the continuous dependence of a generalized steady state solution of nonlinear driven differential equations with respect to parameter variations which cause the order of the differential equation to change since the notion of steady state is of paramount importance to innumerable engineering situations the contents of this paper have wider scope

the stochastic finite element method past present and future a powerful tool in computational stochastic mechanics is the stochastic finite element method sfem sfem is an extension of the classical deterministic fe approach to the stochastic framework i e to the solution of static and dynamic problems with stochastic mechanical geometric and or loading properties the considerable attention that sfem received over the last decade can be mainly attributed to the spectacular growth of computing power rendering possible the efficient treatment of large scale problems this article aims at providing a state of the art review of past and recent developments in the sfem area and indicating future directions as well as some open issues to be examined by the computational mechanics community in the future

stochastic finite element analysis of shells in the present paper the stochastic formulation of the triangular composite tric facet shell element is presented using the weighted integral and local average methods the elastic modulus of the structure is considered to be a two dimensional homogeneous stochastic field which is represented via the spectral representation method as a result of the proposed derivation and the special features of the element the stochastic stiffness matrix is calculated in terms of a minimum number of random variables of the stochastic field giving a cost effective stochastic matrix under the assumption of a pre specified power spectral density function of the stochastic field it is possible to compute the response variability of the shell structure numerical tests are provided to demonstrate the applicability of the proposed methodologies

the effect of material and thickness variability on the buckling load of shells with random initial imperfections abstract the effect of material and thickness imperfections on the buckling load of isotropic shells is investigated in this paper for this purpose the concept of an initial imperfect structure is introduced involving not only geometric deviations of the shell structure from its perfect geometry but also a spatial variability of the modulus of elasticity as well as the thickness of the shell the initial geometric imperfections are described as a two dimensional uni variate 2d 1v stochastic field with statistical properties that are either based on an available data bank of measured initial imperfections or assumed in cases where no experimental data is available in order to describe the non homogeneous characteristics of the initial imperfections the spectral representation method is used in conjunction with an autoregressive moving average model with evolutionary power spectra based on a statistical analysis of the experimentally measured imperfections in cases where no experimental results is available the initial imperfections are assumed to be homogeneous and their impact on the buckling load is investigated on the basis of worst case scenarios with respect to the correlation length parameters of the stochastic fields the elastic modulus and the shell thickness are described as 2d 1v non correlated homogeneous stochastic fields while the stochastic stiffness matrix of the shell elements is formulated using the local average method the monte carlo simulation method is used to calculate the variability of the buckling load while for the determination of the limit load of the shell a stochastic formulation of the elastoplastic and geometrically non linear tric facet triangular shell element is implemented

stochastic finite element analysis of shells with combined random material and geometric properties abstract in this work an extended stochastic formulation of the triangular composite facet shell element tric is presented for the case of combined uncertain material young s modulus poisson s ratio and geometric thickness properties these properties are assumed to be described by uncorrelated two dimensional homogeneous stochastic fields the stochastic finite element analysis of shell structures is performed using the spectral representation method for the description of the random fields in conjunction with monte carlo simulation mcs for the computation of the response variability useful conclusions regarding the influence of each one of the structural parameters on the response variability are derived from the numerical tests examined

driven dynamics of time varying linear systems motivated by applications to automatic control of aircraft we consider the problem of output tracking for time varying linear systems the signals to be tracked are bounded on spl infin spl infin and our goal is to compute bounded controls and bounded state trajectories that result in the desired tracking a convolution integral representation for the desired solution is given in the literature and we show that certain integrability assumptions can be eliminated from the associated results despite the fact that our system is time varying and our signals do not necessarily have fourier transforms in the classical sense we show that computations can be carried out using generalized fourier transforms we also consider an output tracking problem in which the driven dynamical equation is an ordinary differential equation

an accurate and efficient implementation of initial geometrical imperfections in the predictor corrector reduced order modeling method abstract a predictor corrector reduced order modeling method based on koiter theory is proposed for nonlinear buckling analysis of thin walled structures with initial geometric imperfections the imperfections are implemented into the von karman kinematics and are considered using an a priori and a posteriori manners respectively in buckling analysis since the nonlinear predictor obtained from the reduced order model with imperfections provides a fairly large step size in path tracing the a priori account of imperfections still shows advantages in computational efficiency the advantages are more significant when considering a posteriori the effects of imperfections in the reduced order model of the structure without imperfections which means building once and for all by simply adding some independent imperfection terms in the reduced system the a posteriori accounts of imperfections with the first second order accuracies are developed respectively to deal with the linear nonlinear prebuckling behaviors and small large imperfection amplitudes the good performance of the proposed method in terms of reliability accuracy and computational effort is demonstrated with several examples using the linear buckling modes or measured geometric shapes as whole field geometric imperfections

elasto plastic analysis of shells with the triangular element tric tric is a simple but sophisticated three node shear deformable isotropic and composite facet shell element suitable for large scale linear and nonlinear engineering computations of thin and moderately thick anisotropic plate and complex shell structures in the present work an elasto plastic constitutive model based on the von mises yield criterion with isotropic hardening is incorporated into the element the characteristic feature of this formulation is that the nonlinear material behaviour is taken into account entirely in the natural system of the element this is achieved by transforming quantities such as equivalent plastic strain equivalent stress the expression of the yield surface and the components of flow vector from the material coordinate system to the natural coordinate system these transformations lead to simple and elegant expressions for the respective quantities in the natural system which eventually result to an efficient and cost effective treatment of the nonlinear analysis of arbitrary shells including material and geometrical nonlinearities

analysis of some low order quadrilateral reissner mindlin plate elements four quadrilateral elements for the reissner mindlin plate model are considered the elements are the stabilized mitc4 element of lyly stenberg and vihinen 1933 the min4 element of tessler and hughes 1983 the q4bl element of zienkiewicz et al 1993 and the fmin4 element of kikuchi and ishii 1999 for all elements except the q4bl element a unifying variational formulation is introduced and optimal h 1 and l 2 error bounds uniform in the plate thickness are proven moreover we propose a modified q4bl element and show that it admits the optimal h 1 and l 2 error bounds uniform in the plate thickness in particular we study the convergence behavior of all elements regarding the mesh distortion

derivation of the cubic non linear schrodinger equation from quantum dynamics of many body systems we prove rigorously that the one particle density matrix of three dimensional interacting bose systems with a short scale repulsive pair interaction converges to the solution of the cubic non linear schrodinger equation in a suitable scaling limit the result is extended to k particle density matrices for all positive integer k

accurate estimation of evolutionary power spectra for strongly narrow band random fields abstract one of the most widely used techniques for the simulation of non homogeneous random fields is the spectral representation method its key quantity is the power spectrum which characterizes the random field in terms of frequency content and spatial evolution in a mean square sense the paper at hand proposes a method for the estimation of separable power spectra from a series of samples which combines accurate spectrum resolution in space with an optimum localization in frequency for non separable power spectra it can be complemented by a joint strategy which is based on the partitioning of the space frequency domain into several sub spectra that have to be separable only within themselves characteristics and accuracy of the proposed method are demonstrated for analytical benchmark spectra whose estimates are compared to corresponding results of established techniques based on the short time fourier the harmonic wavelet and the wigner ville transforms it is then shown by a practical example from stochastic imperfection modeling in structures that in the presence of strong narrow bandedness in frequency the proposed method for separable random fields leads to a considerable improvement of estimation results in comparison to the established techniques

effect of multiple uncertain material properties on the response variability of in plane and plate structures abstract in the majority of research works on stochastic finite element analysis the main concern is put on the effect of uncertain elastic modulus on the response variability this is mainly due to the importance of this parameter in the stochastic response of structures but also to the difficulties in introducing other material and or geometrical uncertain parameters in the stochastic formulation in this paper a formulation is suggested in order to determine the response variability of in plane and plate structures with multiple uncertain material parameters i e elastic modulus and poisson s ratio to accomplish this use is made of the general equation for n th joint moment and a polynomial expansion on the coefficients of constitutive matrix for computational purposes the infinite series of stochastic sub stiffness matrices is truncated preserving sufficient accuracy to demonstrate the validity of the proposed formulation some numerical examples are provided and the results are compared with those obtained by means of classical monte carlo simulation combined with the local average scheme

buckling analysis of imperfect shells with stochastic non gaussian material and thickness properties in this paper the effect of material and thickness spatial variation on the buckling load of isotropic shells with random initial geometric imperfections is investigated to this purpose a random spatial variability of the elastic modulus as well as of the thickness of the shell is introduced in addition to the random initial geometric deviations of the shell structure from its perfect geometry the main novelty of this paper compared to previous works is that a non gaussian assumption is made for the distribution of the two aforementioned uncertain parameters i e the modulus of elasticity and the shell thickness which are described by two dimensional uni variate 2d 1v homogeneous non gaussian stochastic fields the initial geometric imperfections are described as a 2d 1v gaussian non homogeneous stochastic field with properties derived from corresponding experimental measurements numerical examples are presented focusing on the influence of the non gaussian assumption on the variability of the buckling load which is calculated by means of the monte carlo simulation method it is shown that the choice of the marginal probability distribution for the description of the material and thickness variability is crucial since it affects significantly the statistics of the buckling load of imperfection sensitive shell type structures

uncertain buckling its past present and future an authoritative review on stochastic buckling of structures was written by amazigo some quarter century ago the present review summarizes some of the developments which took place since then a brief overview of the effect of uncertainty in the initial geometric imperfections elastic moduli applied forces and thickness variation is given for the benefit of the thoughtful reader the review is of critical nature

mean field dynamics singular potentials and rate of convergence we consider the time evolution of a system of n identical bosons whose interaction potential is rescaled by n 1 we choose the initial wave function to describe a condensate in which all particles are in the same one particle state it is well known that in the mean field limit n the quantum n body dynamics is governed by the nonlinear hartree equation using a nonperturbative method we extend previous results on the mean field limit in two directions first we allow a large class of singular interaction potentials as well as strong possibly time dependent external potentials second we derive bounds on the rate of convergence of the quantum n body dynamics to the hartree dynamics

hybrid uncertain static analysis with random and interval fields abstract uncertain static analysis of an engineering structure with diverse type of non deterministic system parameter is investigated in this study unlike the traditional hybrid uncertain static analysis involving random and interval variables the concept of random and interval fields has been implemented to model the spatially dependent uncertainties associated with the system inputs a novel computational approach namely the extended unified interval stochastic sampling x uiss method is proposed to calculate the statistical characteristics i e mean and standard deviation of the extreme bounds i e lower and upper bounds of the concerned responses e g displacement and stress of engineering structure involving hybrid spatially dependent uncertainties subsequently by utilizing either parametric or nonparametric statistical analysis the probability density functions pdfs as well as the cumulative distribution functions cdfs of the extreme bounds of the concerned structural responses can be effectively established consequently the upper and lower bounds of either the concerned responses of the engineering structure at any particular percentile of probability or the structural reliability against any specified capacities can be effectively secured the applicability and effectiveness of the proposed computational analysis framework are illustrated through the numerical investigations on various examples

robust assessment of collapse resistance of structures under uncertain loads based on info gap model abstract the paper proposes a pair of novel mathematical programming based approaches which directly determine the worst collapse load limit in one case and the best limit in the other case of rigid perfectly plastic structures subjected to uncertain but bounded applied loads using an info gap model the methods take advantage of the important properties in which the worst collapse load limit defined for an uncertain static formulation is equivalent to the most favourable solution of the uncertain kinematic limit analysis problem and vice versa for the best collapse load limit the formulation for capturing the worst collapse load limit robust worst case solution takes the form as a mathematical program with equilibrium constraints that is processed using a penalty algorithm whilst that for the best collapse load limit is a standard linear programming problem the efficiency and robustness of the proposed schemes are evidenced from a number of successfully solved examples

a four node plate bending element based on mindlin reissner plate theory and a mixed interpolation this communication discusses a 4 node plate bending element for linear elastic analysis which is obtained as a special case from a general nonlinear continuum mechanics based 4 node shell element formulation the formulation of the plate element is presented and the results of various example solutions are given that yield insight into the predictive capability of the plate and shell element

stochastic finite element analysis of composite structures based on mesoscale random fields of material properties abstract the linking of microstructure uncertainty with the random variation of material properties at higher scales is of paramount importance in the framework of the stochastic finite element method sfem an efficient computational scheme has been recently proposed by the authors for the determination of mesoscale random fields for the apparent properties and of the rve size of particle reinforced composites based on computer simulated images of their microstructure the proposed approach exploits the excellent synergy of the extended finite element method xfem and monte carlo simulation in order to analyze the microstructure models and obtain statistical information probability distribution correlation structure for the apparent properties of the composite in each mesoscale size in this paper sample functions of the statistically homogeneous mesoscale random fields are generated using the spectral representation method in conjunction with translation field theory moreover micro mechanically consistent lower and upper bounds on the macroscopic response of composite structures are computed in the framework of sfem useful conclusions are derived regarding the effect of particle matrix stiffness ratio on the probabilistic characteristics of the mesoscale random fields as well as the influence of mesoscale size on the response variability

fluctuations around hartree states in the mean field regime we consider the dynamics of a large system of n interacting bosons in the mean field regime where the interaction is of order 1 n we prove that the fluctuations around the nonlinear hartree state are generated by an effective quadratic hamiltonian in fock space which is derived from bogoliubov s approximation we use a direct method in the n particle space which is different from the one based on coherent states in fock space

derivation of the two dimensional nonlinear schrodinger equation from many body quantum dynamics we derive rigorously for both r 2 and l l 2 the cubic nonlinear schrodinger equation in a suitable scaling limit from the two dimensional many body bose systems with short scale repulsive pair interactions we first prove convergence of the solution of the bbgky hierarchy corresponding to the many body systems to a solution of the infinite gross pitaevskii hierarchy corresponding to the cubic nls and then we prove uniqueness for the infinite hierarchy which requires number theoretical techniques in the periodic case

geometrically non linear behavior of structural systems with random material property an asymptotic spectral stochastic approach abstract an asymptotic spectral stochastic approach is presented for computing the statistics of the equilibrium path in the post bifurcation regime for structural systems with random material properties the approach combines numerical implementation of koiter s asymptotic theory with a stochastic galerkin scheme and collocation in stochastic space to quantify uncertainties in the parametric representation of the load displacement relationship specifically in the form of uncertain post buckling slope post buckling curvature and a family of stochastic displacement fields using the proposed method post buckling response statistics for two plane frames are obtained and shown to be in close agreement with those obtained from monte carlo simulation provided a fine enough spectral representation is used to model the variability in the random dimension

direct evaluation of the worst imperfection shape in shell buckling abstract for the evaluation of the imperfection sensitivity of elastic and elastic plastic shells a fully nonlinear finite element method has been developed that directly gives the worst imperfection shape connected to the ultimate limit load the approach uses no approximations such as asymptotical theories or computations in the deep postcritical range the key point of the method is the description of imperfections as nodal degrees of freedom at the element level these unknown quantities are implemented by isoparametric shape functions in a finite shell element including finite rotations and thickness stretch the ultimate buckling load and the corresponding worst imperfection shape is defined by two different criteria and numerically determined by an extended system of nonlinear equations in the computation of the structurally stable collapse the deflections the imperfection shape the eigenvector and the lowest possible load level are obtained the method is illustrated by several numerical examples

a posteriori initial imperfection identification in shell buckling problems the current research seeks to demonstrate that an inverse solution approach leveraging nonlinear finite element analysis with a divide and conquer type stochastic search algorithm can identify the presence of localized denting imperfections in cylindrical shell structures this imperfection field identification is achieved using rather sparse displacement measurements taken at safe service loading conditions both the existence and nature of the imperfection field present in a given shell structure instance are determined these inferred imperfections are subsequently used to make reasonably accurate predictions regarding the actual shell structure strength at ultimate loading

accurate and highly efficient algorithms for structural stationary non stationary random responses abstract an accurate and highly efficient algorithm series for structural stationary non stationary random response analysis pseudo excitation method pem is presented the algorithm series which have been developed since early 1980s applies to the random vibration analyses of structures subjected to single multiple stationary non stationary random excitations including the very attractive issue the solution of the response to non uniformly modulated evolutionary random excitations each algorithm in this series is an accurate complete quadratic combination cqc method because the cross correlation quadratic terms between the participant modes and between the excitations have both been included such algorithms are easy to use because structural stationary random response analysis is reduced to the analysis of structural harmonic response while structural non stationary random responses can be readily computed in terms of any step by step integration scheme e g newmark scheme or the precise integration method

spectral stochastic isogeometric analysis of linear elasticity abstract the stochastic isogeometric analysis of linear elasticity problem is investigated in this study the spectral stochastic analysis is introduced into isogeometric analysis iga and a novel yet robust stochastic analysis framework namely the spectral stochastic isogeometric analysis ssiga is freshly proposed unlike traditional numerical solutions of the karhunen loeve k l expansion the non uniform rational b spline nurbs and t spline basis functions are employed within the proposed framework of ssiga so the random fields acting on a continuous physical medium with complex geometry can be handled in an appropriate physically feasible and efficient fashion the polynomials chaos expansion pce is implemented to represent the stochastic structural response e g displacement strain and stress such that all corresponding statistical characteristics e g mean and standard deviation can be robustly acquired furthermore by utilizing the nonparametric statistical analysis both probability density functions pdfs and cumulative distribution functions cdfs of concerned structural displacements and stresses can be effectively established within the framework of iga by meticulously implementing the concept of the higher order k refinement the proposed ssiga provides a more legitimate and efficient stochastic computational approach for modern engineering structures which are complicated by both spatially dependent uncertainties and complex geometries

mean field evolution of fermionic mixed states in this paper we study the dynamics of fermionic mixed states in the mean field regime we consider initial states that are close to quasi free states and prove that under suitable assumptions on the initial data and on the many body interaction the quantum evolution of such initial data is well approximated by a suitable quasi free state in particular we prove that the evolution of the reduced one particle density matrix converges as the number of particles goes to infinity to the solution of the time dependent hartree fock equation our result holds for all times and gives effective estimates on the rate of convergence of the many body dynamics towards the hartree fock evolution 2015 wiley periodicals inc

application of the quadrilateral area co ordinate method a new element for mindlin reissner plate the quadrilateral area co ordinate method is used to formulate a new quadrilateral element for mindlin reissner plate bending problem firstly an independent shear field is assumed based on the locking free timoshenko s beam formulae secondly a fourth order deflection field is assumed by introducing some generalized conforming conditions thirdly the rotation field is determined by the strain displacement relations furthermore a hybrid post processing procedure is suggested to improve the stress internal force solutions following this procedure a new 4 node 12 dof quadrilateral element named ac mq4 is successfully constructed since all formulations are expressed by the area co ordinates element ac mq4 presents some different but beneficial characters when compared with other usual models numerical examples show the new element is free of shear locking insensitive to mesh distortion and possesses excellent accuracy in the analysis of both thick and thin plates it has also been demonstrated that the area co ordinate method the generalized conforming condition method and the hybrid post processing procedure are efficient tools for developing simple effective and reliable finite element models copyright 2005 john wiley sons ltd