advantages of the mixed format in geometrically nonlinear analysis of beams and shells using solid finite elements summary the paper deals with two main advantages in the analysis of slender elastic structures both achieved through the mixed stress and displacement format with respect to the more commonly used displacement one i the smaller error in the extrapolations usually employed in the solution strategies of nonlinear problems and ii the lower polynomial dependence of the problem equations on the finite element degrees of freedom when solid finite elements are used the smaller extrapolation error produces a lower number of iterations and larger step length in path following analysis and a greater accuracy in koiter asymptotic method to focus on the origin of the phenomenon the two formats are derived for the same finite element interpolation the reduced polynomial dependence improves the koiter asymptotic strategy in terms of both computational efficiency accuracy and simplicity copyright 2016 john wiley sons ltd

transmitter optimization for the multi antenna downlink with per antenna power constraints this paper considers the transmitter optimization problem for a multiuser downlink channel with multiple transmit antennas at the base station in contrast to the conventional sum power constraint on the transmit antennas this paper adopts a more realistic per antenna power constraint because in practical implementations each antenna is equipped with its own power amplifier and is limited individually by the linearity of the amplifier assuming perfect channel knowledge at the transmitter this paper investigates two different transmission schemes under the per antenna power constraint a minimum power beamforming design for downlink channels with a single antenna at each remote user and a capacity achieving transmitter design for downlink channels with multiple antennas at each remote user it is shown that in both cases the per antenna downlink transmitter optimization problem may be transformed into a dual uplink problem with an uncertain noise this generalizes previous uplink downlink duality results and transforms the per antenna transmitter optimization problem into an equivalent minimax optimization problem further it is shown that various notions of uplink downlink duality may be unified under a lagrangian duality framework this new interpretation of duality gives rise to efficient numerical optimization techniques for solving the downlink per antenna transmitter optimization problem

a method of optimal control of non linear stochastic systems with non quadratic criteria abstract the derivation of optimal non linear feedback control laws for non linear systems with non quadratic performance criteria is presented by using statistical linearization the validity of this method is shown by analytical and numerical examples of first and second order duffing type non linear systems in the case of stationary control the approximate optimal non linear control laws can be analytically obtained only by solving riccati type algebraic equations the significances of the optimal non linear control and the non quadratic criterion including the fourth order term of the state variable are discussed

path integration of the duffing rayleigh oscillator subject to harmonic and stochastic excitations this paper is focused on the duffing rayleigh oscillator subject to harmonic and stochastic excitations using path integration based on the gauss legendre integration scheme first applying methods of harmonic balance and multiple scales to the deterministic case the stabilities of the responses can be analyzed then the steady state periodic solution of probability density can be captured via path integration at the same time the changes of probability density induced by the intensities of harmonic and stochastic excitations are discussed in three cases

control of non linear stochastic sampled data systems with non quadratic criteria by equivalent lq modelling abstract the control of non linear stochastic sampled data systems with non quadratic performance criteria is approached by development of an equivalent linear system quadratic criterion model using equivalent linearization the resulting control algorithm requires updating as the system trajectory evolves due to the dependence of the equivalent lq model on the trajectory an example illustrates the method and provides comparison with the actual optimal control and the simpler standard lq control based on neglecting the non linear and non quadratic terms altogether

noncooperative eigencoding for mimo ad hoc networks a new noncooperative eigencoding algorithm is introduced for multiple input multiple output mimo ad hoc networks the algorithm performs generalized waterfilling with respect to its transmit covariance matrix and the receive node covariance matrix both of which can be estimated locally a cooperative algorithm is also developed as a benchmark in simulations simulation results show that the noncooperative algorithm performance is close to that of the cooperative method and is much better than greedy optimization a game theoretic interpretation of the algorithm is also provided

stochastic averaging of strongly non linear oscillators under combined harmonic and white noise excitations abstract a stochastic averaging procedure of strongly non linear oscillators subject to external and or parametric excitations of both harmonic and white noise forces is developed by using the so called generalized harmonic functions the procedure is applied to a duffing oscillator with hardening stiffness under both external harmonic excitation and external and parametric excitations of white noises the averaged fokker planck kolmogrov equation is solved by using the path integration method based on the stationary joint probability density of amplitude and phase obtained by using the stochastic averaging and the path integration the stochastic jump of the duffing oscillator under combined harmonic and white noise excitations and its bifurcation as the system parameters frequency ratio strength of the non linearity amplitude of harmonic excitation and intensity of white noise change are examined for the first time

exact stationary solutions of averaged equations of stochastically and harmonically excited mdof quasi linear systems with internal and or external resonances abstract the exact stationary solutions of the averaged equations of stochastically and harmonically excitedndegree of freedom quasi linear systems withminternal and or external resonances are obtained as functions of bothnindependent amplitudes andmcombinations of phase angles to make the solutions more general the equivalent stochastic systems of the averaged equations are obtained by using the differential forms and exterior differentiation by considering the periodic boundary conditions with respect tomcombinations of phase angles the probability potentials of the exact stationary solutions of the equivalent stochastic systems are expanded into anm fold harmonic series ofmcombinations of phase angles and the exact stationary solutions are obtained for the case where the averaged equations belong to the class of stationary potential to examples are given to illustrate the application of the proposed procedure

the role of symmetry in the post buckling behaviour of structures symmetry plays an integral role in the post buckling analysis of elastic structures we show that the post buckling response of engineering systems with given symmetry properties can be described u

how to get around a simple quadratic fold we analyse from a theoretical point of view a computational technique previously introduced 2 5 for tracing branches of solutions of nonlinear equations near simple quadratic folds

almost sure stability of dynamical systems under combined harmonic and stochastic excitations abstract the almost sure asymptotic stability and the associated sample behavior of mechanical and structural systems under combined harmonic and stochastic excitations are examined the method of extended stochastic averaging developed by the author is used to obtain a lower dimensional markov processes for multi degree of freedom structures subjected to both harmonic and stochastic excitations provided that the intensities of these excitations are small the approach in this paper formulated for the study of almost sure asymptotic stability is based on the well developed concept of lyapunov exponents the largest lyapunov exponent is obtained explicitly by using the lower dimensional approximate ito equations the results from this analysis are applied to study the almost sure asymptotic stability of uncoupled flapping motion of rotor blades in forward flight under the effect of atmospheric turbulence

response of nonlinear systems in probability domain using stochastic averaging determination of probability density function pdf of the response for strongly nonlinear single degree of freedom system subjected to both multiplicative and additive random excitations using stochastic averaging technique is faced with few difficulties firstly the size of excitations should be small such that the response of the system converges weakly to a markov process secondly the excitations should preferably be broad banded so that the analytical results are reasonably accurate and finally the nonlinear functions should be integrable if closed formed expressions for the result are desired the above issues are examined in the paper with a view to show a limiting values of the size parameter of excitations for which stochastic averaging technique can be applied to obtain reasonable estimates of pdf and mean square value of response b the effect of the nature of the frequency contents of excitation on the response and c the use of the stochastic averaging method employing generalized harmonic functions for nonintegrable functions representing the dynamic system it is shown that the stochastic averaging procedure provides results which compare very well with those obtained from simulation analysis not only for wide band excitations but also for narrow band excitations for a wide range of the size parameter of excitation further the procedure can be easily implemented for highly irregular functions by employing a numerical scheme with fft

influence of the noise spectrum on the anomalous diffusion in a stochastic system we use an effective markovian description to study the long time behavior of a nonlinear second order langevin equation with a gaussian noise when dissipation is neglected the energy of the system grows as with time a power law with an anomalous scaling exponent that depends both on the confining potential and on the high frequency distribution of the noise the asymptotic expression of the probability distribution function in phase space is calculated analytically the results are extended to the case where small dissipative effects are taken into account

extrapolation locking and its sanitization in koiter s asymptotic analysis abstract this paper shows that the fem implementation of koiter s asymptotic method w t koiter on the stability of elastic equilibrium 1970 ph d thesis delft 1945 english transl nasa tt f10 883 1967 affdl tr70 25 outlined by casciaro et al finite element asymptotic analysis of slender elastic structures a simple approach int j num meth eng 35 1992 1397 1426 provides accurate and reliable results in the critical and post critical analysis of non linear elastic structures care however does have to be taken in implementing apparently minor details to avoid locking effects which adversely affect accuracy and which can destroy the method reliability as the effects related to the finite element interpolation have been discussed before this paper focuses on the non linear locking due to the use implicit in the method of finite distance extrapolations within this scope it is shown that perturbation algorithms based on compatible formulations can imply a strong critical and post critical locking when analysing structures characterized by high stiffness ratios in the presence of moderate pre critical rotations on the contrary perturbation algorithms based on independent extrapolations of displacements and stresses furnish reliable results in excellent agreement with those provided by step by step analysis at a small fraction of its computational cost

stochastic averaging based on generalized harmonic functions for energy harvesting systems abstract a stochastic averaging method is proposed for nonlinear vibration energy harvesters subject to gaussian white noise excitation the generalized harmonic transformation scheme is applied to decouple the electromechanical equations and then obtained an equivalent nonlinear system which is uncoupled to an electric circuit the frequency function is given through the equivalent potential energy which is independent of the total energy the stochastic averaging method is developed by using the generalized harmonic functions the averaged ito equations are derived via the proposed procedure and the fokker planck kolmogorov fpk equations of the decoupled system are established the exact stationary solution of the averaged fpk equation is used to determine the probability densities of the amplitude and the power of the stationary response the procedure is applied to three different type duffing vibration energy harvesters under gaussian white excitations the effects of the system parameters on the mean square voltage and the output power are examined it is demonstrated that quadratic nonlinearity only and quadratic combined with properly cubic nonlinearities can increase the mean square voltage and the output power respectively the approximate analytical outcomes are qualitatively and quantitatively supported by the monte carlo simulations

mixed formulation and locking in path following nonlinear analysis abstract the arc length riks strategy has rapidly become a standard tool for path following analysis of nonlinear structures due to its theoretical ability to surpass limit points the aim of this paper is to show that the failures in convergence that are occasionally experienced are not related to proper defects of the algorithm but come from a subtle locking effect intrinsic to the nonlinear nature of the problem as a consequence its sanitization has to be pursued within a reformulation of the structural model the use of a mixed stress displacement variant of the algorithm in particular appears very promising in this respect the topic is discussed with reference to the analysis of nonlinear frames using a mixed version of the nonlinear beam model discussed in 39 it is shown that with no extra computational cost and only a minor modification in coding with respect to a purely compatible formulation it is possible to achieve a noticeable improvement in convergence and a real gain in both computational time and overall robustness of the algorithm

stochastic stability of quasi non integrable hamiltonian systems abstract an n degree of freedom quasi non integrable hamiltonian system is first reduced to an ito equation of one dimensional averaged hamiltonian by using the stochastic averaging method developed by the first author and his coworkers the necessary and sufficient conditions for the asymptotic stability in probability of the trivial solution of the quasi non integrable hamiltonian system are then obtained approximately by examining the sample behaviors of the one dimensional diffusion process of the square root of averaged hamiltonian at the two boundaries a system of linearly and non linearly coupled two non linearly damped oscillators subject to parametric excitations of gaussian white noises is employed as an example to illustrate the procedure and the effects of non linear damping and non linear coupling on the stability are analyzed in detail

stochastic averaging of strongly non linear oscillators under bounded noise excitation abstract a stochastic averaging method for strongly non linear oscillators under external and or parametric excitation of bounded noise is proposed by using the so called generalized harmonics functions the method is then applied to study the primary resonance of duffing oscillator with hardening spring under external excitation of bounded noise the stochastic jump and its bifurcation of the system are observed and explained by using the stationary probability density of amplitude and phase subsequently the method is applied to study the dynamical instability and parametric resonance of duffing oscillator with hardening spring under parametric excitation of bounded noise the primary unstable region is delineated by evaluating the lyapunov exponent of linearized system and the response and jump of non linear system around the unstable region are examined by using the sample functions and stationary probability density of amplitude and phase

a numerical analysis of infinitesimal mechanisms the paper presents a numerical algorithm based on koiter s theory of the elastic stability for detecting the order of infinitesimal mechanisms i e kinematically indeterminate systems of pin jointed bars in cases of one degree of indeterminacy the algorithm improves in terms of computational simplicity and efficiency an analogous algorithm proposed by salerno in 1992 this is shown to be due to the vanishing of the terms higher than the third order of the asymptotic expressions of the energy owing to the use of the green strain measure and a mixed displacement and stress formulation of the problem moreover the proposed algorithm is able to provide a correct definition of mechanism in cases of several degrees of indeterminacy mainly for structures like those first studied by connelly and servatius in 1994 which the paper will treat in depth

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

a nonlinear beam finite element for the post buckling analysis of plane frames by koiter s perturbation approach abstract a nonlinear finite element of plane beam oriented to koiter s perturbation analysis of frames is presented the locking problem arising in the calculation of the post critical curvature is thoroughly examined and solved at the continuum level by means of a suitable definition of the kinematic settings the proposed strain measures are lagrangian and rationally founded geometrically exact the exact solutions of the critical problem have been chosen as shape functions of the finite element so obtaining an immediately convergent finite element in the calculation of the critical load and of the post critical slope

asymptotic post buckling fem analysis using corotational formulation finite element asymptotic post buckling analysis being based on fourth order expansions of the strain energy requires that nonlinear structural modeling be accurate to same order at least with respect to the rigid motions of the elements a corotational description is proposed here as a general tool to satisfy this requirement of objectivity by referring each element to a local frame which moves rotates with the element so filtering its rigid motion in this description nonlinearity of the problem derives essentially from the change of reference from the global fixed frame to the local one the strain energy being governed by their relative rotations in finite kinematics this noticeably complicates the algebra for obtaining exact expressions of its variations quite simple basic expressions for the first four corotational derivatives of the strain energy are provided allowing the set up of a fourth order accurate asymptotic analysis starting from standard finite elements based on linear or simplified nonlinear local modelings the formulation is implemented for the analysis of 3d beam assemblages and several numerical results are presented and discussed showing the effectiveness and robustness of the proposed approach in reproducing the nonlinear equilibrium path in both cases of monomodal and coupled multimodal buckling

optimal feedback control of strongly non linear systems excited by bounded noise abstract a strategy for non linear stochastic optimal control of strongly non linear systems subject to external and or parametric excitations of bounded noise is proposed a stochastic averaging procedure for strongly non linear systems under external and or parametric excitations of bounded noise is first developed then the dynamical programming equation for non linear stochastic optimal control of the system is derived from the averaged ito equations by using the stochastic dynamical programming principle and solved to yield the optimal control law the fokker planck kolmogorov equation associated with the fully completed averaged ito equations is solved to give the response of optimally controlled system the application and effectiveness of the proposed control strategy are illustrated with the control of cable vibration in cable stayed bridges and the feedback stabilization of the cable under parametric excitation of bounded noise

first passage failure of quasi integrable hamiltonian systems under time delayed feedback control a procedure for studying the first passage failure of quasi integrable hamiltonian systems under time delayed feedback control is proposed the stochastic averaging method for quasi integrable hamiltonian systems under time delayed feedback control is firstly introduced a backward kolmogorov equation governing the conditional reliability function and a set of generalized pontryagin equations governing the conditional moments of first passage time are then established the conditional reliability function the conditional probability density and moments of first passage time are obtained by solving the backward kolmogorov equation and generalized pontryagin equations with suitable initial and boundary conditions an example is given to illustrate the proposed procedure and the results from digital simulation are obtained to verify the effectiveness of the proposed procedure the effects of time delay in feedback control forces on the conditional reliability function conditional probability density and moments of first passage time are analyzed

interactive buckling analysis with finite strips on presente un procede semi analytique pour l etude de phenomenes de flambage interactif dans des structures de plaques prismatiques la methode combine les concepts de bandes finies et la theorie des interactions de modes

averaging method using generalized harmonic functions for strongly non linear oscillators abstract an averaging method in which generalized harmonic functions are used is applied to study the approximate solutions of the strongly non linear oscillators g x e x and g x ef x t where g x is an arbitrary non linear function the method gives the approximate solutions in terms of generalized harmonic functions these functions are also periodic and are exact solutions of strongly non linear differential equations some phenomena considered include limit cycles of strongly non linear autonomous oscillators and steady state response of strongly non linear oscillators subject to weak harmonic excitation the procedure is simple and easy to apply

stochastic averaging of quasi integrable hamiltonian systems with delayed feedback control abstract a stochastic averaging method for quasi integrable hamiltonian systems with time delayed feedback control is proposed first a quasi integrable hamiltonian system with delayed feedback control subjected to gaussian white noise excitations is formulated and then transformed into ito stochastic differential equations without time delay then the averaged ito stochastic differential equations for the system are derived and the stationary solution of the averaged fokker planck kolmogorov fpk equation associated with the averaged ito equations is obtained for both non resonant and resonant cases finally three examples are worked out in detail to illustrate the application and effectiveness of the proposed method and the effect of time delayed feedback control on the response of the systems

finite element asymptotic analysis of slender elastic structures a simple approach an asymptotic method directly derived from koiter s theory and suitable for the solution of elastic buckling problems and its natural adaptation to a numerical solution by means of a finite element technique are presented here the order of the extrapolation of the equilibrium equations has been intentionally kept very low because attention has been entirely devoted to all those features theoretical definitions eigenproblem numerical techniques suitable fem implementation which make such an approach competitive with respect to the classic step by step methods for plane frames and 3d pin jointed trusses the performances of the algorithm numerical accuracy and computational cost are compared with those of riks are length method

dual methods for nonconvex spectrum optimization of multicarrier systems the design and optimization of multicarrier communications systems often involve a maximization of the total throughput subject to system resource constraints the optimization problem is numerically difficult to solve when the problem does not have a convexity structure this paper makes progress toward solving optimization problems of this type by showing that under a certain condition called the time sharing condition the duality gap of the optimization problem is always zero regardless of the convexity of the objective function further we show that the time sharing condition is satisfied for practical multiuser spectrum optimization problems in multicarrier systems in the limit as the number of carriers goes to infinity this result leads to efficient numerical algorithms that solve the nonconvex problem in the dual domain we show that the recently proposed optimal spectrum balancing algorithm for digital subscriber lines can be interpreted as a dual algorithm this new interpretation gives rise to more efficient dual update methods it also suggests ways in which the dual objective may be evaluated approximately further improving the numerical efficiency of the algorithm we propose a low complexity iterative spectrum balancing algorithm based on these ideas and show that the new algorithm achieves near optimal performance in many practical situations

optimal bounded control of first passage failure of strongly non linear oscillators under combined harmonic and white noise excitations a procedure for designing the optimal bounded control of strongly non linear oscillators under combined harmonic and white noise excitations for minimizing their first passage failure is proposed first a stochastic averaging method for strongly non linear oscillators under combined harmonic and white noise excitations using generalized harmonic functions is introduced then the dynamical programming equations and their boundary and final time conditions for the control problems of maximizing reliability and of maximizing mean first passage time are formulated from the averaged ito equations by using the dynamical programming principle the optimal control law is derived from the dynamical programming equations and control constraint finally the conditional reliability function the conditional probability density and mean of the first passage time of the optimally controlled system are obtained from solving the backward kolmogorov equation and pontryagin equation an example is given to illustrate the proposed procedure and the results obtained are verified by using those from digital simulation

stochastic jump and bifurcation of a duffing oscillator under narrow band excitation abstract the variance of the displacement the probability densities of the displacement velocity and amplitude and the joint probability density of the displacement and velocity of the stationary response of a duffing oscillator to narrow band gaussian random excitation for a number of combinations of the parameters of the oscillator and excitation obtained from digital simulation are presented based on these results the stochastic jump and bifurcation of the system are examined it is shown that for each combination of the parameters all the statistics of the stationary response are unique and independent of initial conditions in a certain domain of the parameter space there are two more probable motions in the stationary response and jumps may occur the jump is a transition from one more probable motion to another or vice versa outside of this domain the stationary response is either nearly gaussian or like a diffused limit cycle as the parameters cross the boundary of the domain the qualitative behavior of the stationary response changes and it is a special kind of bifurcation it is pointed out that some previous results and explanations on this problem are incorrect

koiter s analysis of thin walled structures by a finite element approach summary this paper refers to the analysis of the postbuckling behaviour of thin walled structures by means of an asymptotic approach based on a finite element implementation of koiter s non linear theory of instability the analysis has been accomplished by using the following assumptions i the structure is described as an assemblage of flat slender rectangular panels ii a non linear kirchhoff type plate theory is used to model each panel iii hc finite elements discretization is used iv linear and quadratic extrapolations are assumed for the fundamental and the postbuckling paths respectively v multimodal buckling is considered and vi imperfection sensitivity analysis is performed in both multimodal and monomodal form based on the steepest descent path criterion several numerical results are presented and discussed comparisons with numerical solution obtained by standard incremental codes are given which show the accuracy and reliability of the proposed approach

how to improve efficiency and robustness of the newton method in geometrically non linear structural problem discretized via displacement based finite elements abstract in this paper we show how to significantly improve the robustness and the efficiency of the newton method in geometrically non linear structural problems discretized via displacement based finite elements the strategy is based on the relaxation of the constitutive equations at each integration point this leads to an improved iterative scheme which requires a very low number of iterations to converge and can withstand very large steps in step by step analyses the computational cost of each iteration is the same as the original newton method the impressive performances of the proposal are shown by many numerical tests in geometrically non linear analysis the proposed strategy called mip newton seems worthy to replace the standard newton method in any finite element code based on displacement formulations its implementation in existing codes is very easy

smooth postbuckling stresses by a modified finite element method exact postbuckling stresses usually vary fairly smoothly unfortunately finite element postbuckling stresses tend to be much less well behaved the result is that second order postbuckling constants determined by the finite element method may be highly inaccurate the reason is that in finite element solutions transverse displacements associated with the buckling fields furnish too rapidly varying postbuckling strain contributions while the postbuckling axial or membrane displacements contribute strain components that are sufficiently smooth thus creating an internal postbuckling strain and stress mismatch the present study suggests a modified finite element method that handles the problem which is a special example of membrane locking by introducing the postbuckling strains as independent variables in general the method provides rather complicated finite element expressions however by a suitable choice of interpolating functions the resulting finite element equations themselves may be found to be the usual ones and yet provide smooth postbuckling stresses and therefore good values of the postbuckling constants

coordinated linear precoding in downlink multicell mimo ofdma networks we consider coordinated linear precoding in downlink multicell multiple input multiple output orthogonal frequency division multiple access mimo ofdma systems where multiple base stations bss coordinate to mitigate the co channel interference two nonconvex rate optimization problems with per cell power constraints are addressed weighted sum rate maximization wsrm and maximizing the weighted sum of the minimal user rates mwsmr of the coordinated cells we propose two iterative algorithms to achieve suboptimal solutions for the wsrm problem one attempts to solve the karush kuhn tucker kkt conditions of the problem and the other is an alternating maximization algorithm based on the idea of the classical blahut arimoto algorithm the distributed implementations of the two algorithms are also discussed moreover an iterative algorithm based on alternating maximization is proposed to solve the mwsmr problem finally simulation results are presented to demonstrate the effectiveness of the proposed algorithms

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

nonconventional stochastic resonance it is argued on the basis of linear response theory lrt that new types of stochastic resonance sr are to be anticipated in diverse systems quite different from the one most commonly studied to date which has a static double well potential and is driven by a net force equal to the sum of periodic and stochastic terms on this basis three new nonconventional forms of sr are predicted sought found and investigated both theoretically and by analogue electronic experiment a in monostable systems b in bistable systems with periodically modulated noise and c in a system with coexisting periodic attractors in each case it is shown that lrt can provide a good quantitative description of the experimental results for sufficiently weak driving fields it is concluded that sr is a much more general phenomenon than has hitherto been appreciated

averaging method for quasi integrable hamiltonian systems abstract a deterministic averaging method for quasi integrable hamiltonian systems is proposed to predict the approximate response of many degree of freedom autonomous or non autonomous strongly nonlinear systems the form and dimension of the averaged equations depend on the number of degree of freedom and the number of resonant relations of the associated hamiltonian systems in non resonant case the averaged equations for n action variables or n independent integrals of motion are derived in resonant case the averaged equations for n action variables and combinations of angle variables are derived two examples are given to illustrate the application of the proposed method it is shown that the analytical results agree well with those from numerical solution even for systems with very strong nonlinearity

instabilities in moving bands under random tension fluctuation flexural instabilities in moving bands under random tension fluctuation are investigated the discretized equations of flexural motion represent a gyroscopic system with randomly varying stiffness explicit stability conditions based on the mean square amplitudes are established by employing a stochastic averaging procedure the effect of mean band speed on the band stability is discussed

mixed formulation in koiter analysis of thin walled beams abstract the paper extends the asymptotic mixed formulation proposed in g garcea g salerno sanitizing of locking in koiter perturbation analysis through mixed formulation fourth world congress on computational mechanics buenos aires argentina 1988 g garcea g salerno r casciaro comput methods appl mech engrg 180 1 2 1999 137 167 to structures composed of an assemblage of flat slender elastic panels the same type of structure has already been investigated in a d lanzo g garcea r casciaro int j numer methods engrg 38 1995 2325 2345 a d lanzo g garcea int j numer methods engrg 39 1996 3007 3031 with a compatible formulation and using the usual hypothesis of negligible precritical rotations in order to avoid the extrapolation locking see also g garcea g a trunfio r casciaro comput methods appl mech engrg 165 1 4 1998 137 167 produced by the high axial to flexural stiffness ratio of the panels the use of a mixed formulation provides a consistent way of eliminating the extrapolation locking without introducing ad hoc approximations it is thus both reliable and accurate when combined with a quadratic strain displacement relationship as presented here it gives zero fourth order energy variations further computational simplifications and a natural linearization of the eigenvalue problem required by the buckling analysis an extensive numerical testing shows the effectiveness and robustness of the proposed approach

koiter analysis of folded structures using a corotational approach the paper deals with geometrically nonlinear finite element analysis of folded plate and shell structures a koiter asymptotic approach is proposed based on the reuse of a linear element in the nonlinear context through a corotational formulation the corotational approach represents a simple and effective way to satisfy the basic requirement of koiter analysis i e full objectivity in the finite element modeling in fact starting simply from a suitable linear finite element and implementing the corotational algebra proposed in garcea et al 2009 zagari 2009 lead to objective explicit expressions for the first four variations of the strain energy which are needed by asymptotic analysis the shell element used here is the flat shell quadrangular element with 4 nodes and 6 dofs per node proposed in madeo et al 2012 and called miss 4 a mixed element based on the reissner mindlin plate theory with an allman like quadratic interpolation for displacements and an equilibrated isostatic interpolation for the stress resultants the element is free from locking and spurious zero energy modes so it appears a suitable candidate for nonlinear corotational analysis the results of the numerical validation show the effectiveness and accuracy of the proposed approach and its excellent overall robustness for both mono and multi modal buckling problems also in the presence of strong nonlinear pre critical behavior

asymptotic post buckling analysis of rectangular plates by hc finite elements the present paper extends the finite element perturbation approach already presented for pin jointed and framed structures15 to rectangular thin plates koiter s asymptotic strategy2 is coupled with a high continuity finite element discretization of the plate 22 the consistency of the discrete model is discussed from the kinematical and numerical points of view and several numerical tests are reported it appears that use of the hc elements makes the perturbation algorithm insensitive to the locking phenomenon occurring in the evaluation of the postbuckling behaviour it also allows the use of very fine discretization meshes at low computational cost

on the choice of the linear element for corotational triangular shells the corotational formulation for triangular thin shell elements presented in a eriksson c pacoste element formulation and numerical techniques for stability problems in shells comput methods

an isogeometric formulation of the koiter s theory for buckling and initial post buckling analysis of composite shells abstract numerical formulations of the koiter theory allow the efficient prediction through a reduced model of the behavior of shell structures when failure is dominated by buckling in this work we propose an isogeometric version of the method based on a solid shell model a nurbs interpolation is employed on the middle surface of the shell to accurately describe the geometry and the high continuity typical of the displacement field in buckling problems and to directly link the cad model to the structural one a linear interpolation is then adopted through the thickness together with a modified generalized constitutive matrix which allows us to easily eliminate thickness locking and model multi layered composites reduced integration schemes which take into account the continuity of the shape functions are used to avoid interpolation locking and make the integration faster a mixed integration point strategy makes it possible to transform the displacement model into a mixed stress displacement one required by the koiter method to obtain accurate predictions without introducing stress interpolation functions the result is an efficient numerical tool for buckling and initial post buckling analysis of composite shells characterized by a low number of dofs and integration points and by a simple and quick construction of the reduced model

interactive buckling in thin walled beams i theory abstract a method is derived for the analysis of mode interaction in thin walled elastic beams a nonlinear plate theory is employed for the plate segments of the beam in which the exact nonlinear expressions are used for the middle surface strain measures but the bending measures are linearized the beam is subjected to a combination of axial compression and a constant bending moment and it is assumed to be simply supported at the ends in the calculation of the total potential energy the influence of the prebuckling deformations is neglected the finite strip method is used with the transverse variation of all three displacement components described by cubic polynomials in the arc length the nonlinear mode interaction is analysed by means of koiter s asymptotic theory of stability some applications of the method to representative problems are presented in a subsequent paper by the authors this shows that significant mode interaction and imperfection sensitivity occur in these structures

study of the duffing rayleigh oscillator subject to harmonic and stochastic excitations by path integration in this paper the duffing rayleigh oscillator subject to harmonic and stochastic excitations is investigated via path integration based on the gauss legendre integration formula the method can successfully capture the steady state periodic solution of probability density function this path integration method using the periodicity of the coefficient of associated fokker planck kolmogorov equation is extended to deal with the averaged stationary probability density and is efficient to computation meanwhile the changes of probability density caused by the intensities of harmonic and stochastic excitations are discussed in three cases through the instantaneous probability density and the averaged stationary probability density

stochastic response and bifurcation of periodically driven nonlinear oscillators by the generalized cell mapping method the stochastic response of nonlinear oscillators under periodic and gaussian white noise excitations is studied with the generalized cell mapping based on short time gaussian approximation gcm stga method the solutions of the transition probability density functions over a small fraction of the period are constructed by the stga scheme in order to construct the gcm over one complete period both the transient and steady state probability density functions pdfs of a smooth and discontinuous sd oscillator are computed to illustrate the application of the method the accuracy of the results is verified by direct monte carlo simulations the transient responses show the evolution of the pdfs from being gaussian to non gaussian the effect of a chaotic saddle on the stochastic response is also studied the stochastic p bifurcation in terms of the steady state pdfs occurs with the decrease of the smoothness parameter which corresponds to the deterministic pitchfork bifurcation

mode jumping and attractive paths in multimode elastic buckling this paper summarizes a part of the first author s ph d thesis completely devoted to multimode elastic buckling within an fem strategy the theoretical arguments unfold among critical points on radial paths the unique post critical paths variationally defined algebraic characterizations proposition demonstrations and so on by aiming to prove that the complexity of the phenomenon of multimode buckling secondary bifurcations post critical attractive paths can be theoretically explained 1997 by john wiley sons ltd

on nonlinear beam models from the point of view of computational post buckling analysis abstract the buckling and post buckling analysis of elastic planar frames is considered and the use of geometrically exact beam models is thereby advocated it is shown that usual technical beam models fail to predict correctly the curvature of the post buckling curve at bifurcation even for standard problems of elastic stability theory it is also argued that versatile and efficient computational procedures for bifurcation analysis of general planar frames are to be based on unconstrained beam models some remarks on finite element representation of nonlinear beam models are passed in conclusion

technical communique asymptotic lyapunov stability with probability one of quasi integrable hamiltonian systems with delayed feedback control the asymptotic lyapunov stability with probability one of multi degree of freedom mdof quasi integrable and nonresonant hamiltonian systems with time delayed feedback control subject to multiplicative parametric excitation of gaussian white noise is studied first the time delayed feedback control forces are expressed approximately in terms of the system state variables without time delay and the system is converted into ordinary quasi integrable and nonresonant hamiltonian system then the averaged ito stochastic differential equations are derived by using the stochastic averaging method for quasi integrable hamiltonian systems and the expression for the largest lyapunov exponent of the linearized averaged ito equations is derived finally the necessary and sufficient condition for the asymptotic lyapunov stability with probability one of the trivial solution of the original system is obtained approximately by letting the largest lyapunov exponent to be negative an example is worked out in detail to illustrate the above mentioned procedure and its validity and to show the effect of the time delay in feedback control on the largest lyapunov exponent and the stability of the system

explanation on the importance of narrow band random excitation characters in the response of a cantilever beam a detailed theoretical investigation into the first and second mode response of a parametrically excited slender cantilever beam where the narrow band random excitation characters are taken into consideration is presented the method of multiple scales is used to determine a uniform first order expansion of the solution of the nonlinear integro differential equations the first order moment frequency and force response data curves of a specimen beam tested by other investigators are obtained further comparisons have been made and results show that whether the first order moment frequency response data curves or the first order moment force response data curves of the first two modes are all in agreement with other investigators experimental results furthermore the stochastic jump and bifurcation have been investigated for the first modal parametric principal resonance by using the stationary joint probability of amplitude and phase results show that stochastic jump occurs mainly in the region of triple valued solution for the frequency response domain if the bandwidth is a variable and others keep constant the basic phenomena indicate that the most probable motion is around the higher branch when the bandwidth is smaller whereas the most probable motion gradually approaches the lower one when the bandwidth becomes higher if the excitation central frequency f is a variable and others keep constant the basic phenomena imply that the higher is f the more probable is the jump from the higher branch to the lower one once f exceeds an certain value for the force response domain there is a region of excitation acceleration a within which the joint probability density has two peaks an upper peak and a lower peak results show that the upper peak decreases while the lower peak increases as the value of a decreases

path following analysis of thin walled structures and comparison with asymptotic post critical solutions a path following non linear elastic analysis for structures composed of assemblages of flat slender elastic panels is presented the proposed path following method employs fem technology and a kinematical model to analyse these structures using a koiter asymptotic approach as a result it is possible to verify the accuracy achieved by the asymptotic method the proposed mixed path following formulation is both efficient and robust with regards to the locking extrapolation phenomenon that strongly affects compatible formulations the use of an hc finite element makes it possible to avoid the problem of the finite rotations in the space maintaining a high degree of continuity and making the numeric formulation simple and efficient copyright 2002 john wiley sons ltd

cooperative multi cell mimo downlink precoding with finite alphabet inputs this work investigates the design of linear precoders in cooperative multi cell mimo downlink coverage for finite alphabet source signals traditional design of multi cell mimo downlink precoder relies on gaussian input assumption which may lead to performance loss when true data inputs consist of discrete non gaussian symbols this work presents optimized precoders for finite alphabet input by maximizing the sum rate under per base station power constraints specifically we propose two distributed algorithms a finite alphabet signal gaussian interference gradient projection algorithm and a block diagonalization alternating optimization algorithm while supporting interference cancellation our numerical results demonstrate considerable performance gain in terms of approximate transmission data rate as well as decoded bit error rate over precoding schemes designed by using the non realistic gaussian input assumption