first and second order necessary conditions for stochastic optimal controls abstract the main purpose of this paper is to establish the first and second order necessary optimality conditions for stochastic optimal controls using the classical variational analysis approach the control system is governed by a stochastic differential equation in which both drift and diffusion terms may contain the control variable and the set of controls is allowed to be nonconvex only one adjoint equation is introduced to derive the first order necessary condition while only two adjoint equations are needed to state the second order necessary conditions for stochastic optimal controls

pointwise second order necessary optimality conditions for the mayer problem with control constraints this paper is devoted to second order necessary optimality conditions for the mayer optimal control problem when the control set u is a closed subset of mathbb r m we show that in the absence of endpoint constraints if an optimal control bar u cdot is singular and integrable then for almost every t such that bar u t is in the interior of u both the goh and a generalized legendre clebsch condition hold true moreover when the control set is a convex polytope similar conditions are verified on the tangent subspace to u at bar u t for almost all t s such that bar u t lies on the boundary partial u of u the same conditions are valid also for u having a smooth boundary at every t where bar u cdot is singular and locally lipschitz and bar u t in partial u in the presence of a smooth endpoint constraint these second order necessary optimality conditions are satisfied whenever the mayer problem is calm and the maximum principle is abnormal if it is

use of higher order shape functions in the scaled boundary finite element method the scaled boundary finite element method is a novel semi analytical technique whose versatility accuracy and efficiency are not only equal to but potentially better than the finite element method and the boundary element method for certain problems this paper investigates the possibility of using higher order polynomial functions for the shape functions two techniques for generating the higher order shape functions are investigated in the first the spectral element approach is used with lagrange interpolation functions in the second hierarchical polynomial shape functions are employed to add new degrees of freedom into the domain without changing the existing ones as in the p version of the finite element method to check the accuracy of the proposed procedures a plane strain problem for which an exact solution is available is employed a more complex example involving three scaled boundary subdomains is also addressed the rates of convergence of these examples under p refinement are compared with the corresponding rates of convergence achieved when uniform h refinement is used allowing direct comparison of the computational cost of the two approaches the results show that it is advantageous to use higher order elements and that higher rates of convergence can be obtained using p refinement instead of h refinement copyright 2005 john wiley sons ltd

distance estimates to feasible controls for systems with final point constraints and second order necessary optimality conditions abstract we prove an inverse mapping theorem on a metric space of controls that allows to control final points of trajectories of a nonlinear system more precisely our result provides local distance estimates of arbitrary controls from feasible ones as an application we derive second order necessary optimality conditions for l 1 local minima for the mayer optimal control problem with a general control constraint u r m state constraints described by inequalities and final point constraints possibly having empty interior thanks to this inverse mapping theorem we first get a second order variational inequality as a necessary optimality condition then the separation theorem leads in a straightforward way to second order necessary conditions

on the use of nurbs based discretizations in the scaled boundary finite element method for wave propagation problems abstract we discuss the application of non uniform rational b splines nurbs in the scaled boundary finite element method sbfem for the solution of wave propagation problems at rather high frequencies we focus on the propagation of guided waves along prismatic structures of constant cross section comparisons are made between nurbs based discretizations and high order spectral elements in terms of the achievable convergence rates we find that for the same order of shape functions nurbs can lead to significantly smaller errors compared with lagrange polynomials the difference becomes particularly important at very high frequencies where spectral elements are prone to instabilities furthermore we analyze the behavior of nurbs for the discretization of curved boundaries where the benefit of exact geometry representation becomes crucial even in the low frequency range

superstatistical distributions from a maximum entropy principle we deal with a generalized statistical description of nonequilibrium complex systems based on least biased distributions given some prior information a maximum entropy principle is introduced that allows for the determination of the distribution of the fluctuating intensive parameter beta of a superstatistical system given certain constraints on the complex system under consideration we apply the theory to three examples the superstatistical quantum mechanical harmonic oscillator the superstatistical classical ideal gas and velocity time series as measured in a turbulent taylor couette flow

plate spectral elements based upon reissner mindlin theory plate bending spectral elements based upon the reissner mindlin theory is developed for a rectangular plate numerical comparison studies for static and eigenvalue problems demonstrate the excellent performance and robustness of the present method the improvement in accuracy and computational efficiency in comparison with low order plate bending elements is remarkable and suggests that the proposed approach is an alternative to existing schemes

first and second order necessary conditions for control problems with constraints second order necessary conditions are developed for an abstract nonsmooth control problem with mixed state control equality and inequality constraints as well as a constraint of the form g x u e if where f is a closed convex set of a banach space with nonempty interior the inequality constraints g s x u 0 depend on a parameter s belonging to a compact metric space s the equality constraints are split into two sets of equations k x u 0 and h x u 0 where the first equation is an abstract control equation and h is assumed to have a full rank property in u the objective function is maxtet f t x u where t is a compact metric space f is upper semicontinuous in t and lipschitz in x u the results are in terms of a function a that disappears when the parameter spaces t and s are discrete we apply these results to control problems governed by ordinary differential equations and having pure state inequality constraints and control state equality and inequality constraints thus we obtain a generalization and extension of the existing results on this problem

linked interpolation for reissner mindlin plate elements part ii a simple triangle the formulation and shape functions given in part i are extended to develop a simple plate bending triangle with good performance in both thin and thick situations indeed its performance is better than that of other nine dof elements and its computer implementation simpler when used with selective reduced integration the element produces identical results as that of xu 1 2 to save space details given in part i are not repeated and some results are also presented in the figures of part i

the scaled boundary finite element method in structural dynamics the scaled boundary finite element method is extended to solve problems of structural dynamics the dynamic stiffness matrix of a bounded finite domain is obtained as a continued fraction solution for the scaled boundary finite element equation the inertial effect at high frequencies is modeled by high order terms of the continued fraction without introducing an internal mesh by using this solution and introducing auxiliary variables the equation of motion of the bounded domain is expressed in high order static stiffness and mass matrices standard procedures in structural dynamics can be applied to perform modal analyses and transient response analyses directly in the time domain numerical examples for modal and direct time domain analyses are presented rapid convergence is observed as the order of continued fraction increases a guideline for selecting the order of continued fraction is proposed and validated high computational efficiency is demonstrated for problems with stress singularity

the conjugate point condition for smooth control sets abstract in this paper we present for optimal control problems with smooth control constraints second order necessary conditions stated in terms of conjugate points and a riccati type equation we show explicitly how to construct a set of feasible directions and how to derive the corresponding accessory problem

pq adaptive solid finite elements for three dimensional plates and shells this article presents a pq adaptive finite element procedure for three dimensional computation of thin walled structures like plates and shells the approach is based on a hexahedral element with high order shape functions the polynomial degree of the shape functions in the three spatial directions of the element is adjusted by means of an adaptive procedure to this end a hierarchical error indicator is applied to automatically control the polynomial degree q in thickness and p in the in plane direction of plate and shell like structures the efficiency and reliability of the proposed adaptive method is demonstrated using two numerical examples

an edge based smoothed finite element method es fem with stabilized discrete shear gap technique for analysis of reissner mindlin plates abstract an edge based smoothed finite element method es fem for static free vibration and buckling analyses of reissner mindlin plates using 3 node triangular elements is studied in this paper the calculation of the system stiffness matrix is performed by using the strain smoothing technique over the smoothing domains associated with edges of elements in order to avoid the transverse shear locking and to improve the accuracy of the present formulation the es fem is incorporated with the discrete shear gap dsg method together with a stabilization technique to give a so called edge based smoothed stabilized discrete shear gap method es dsg the numerical examples demonstrated that the present es dsg method is free of shear locking and achieves the high accuracy compared to the exact solutions and others existing elements in the literature

a stabilization procedure for the quadrilateral plate element with one point quadrature a stabilization procedure is developed for controlling the kinematic modes of the four node bilinear quadrilateral element when single point quadrature is used these kinematic modes manifest themselves by spatial oscillations or singularity of the total stiffness in this stabilization procedure additional generalized strains are defined which are activated by the kinematic modes these generalized modes are furthermore not activated by rigid body motions regardless of the shape of the quadrilateral by using a scaling law developed in an earlier paper the stabilization parameters are defined so they do not adversely affect the element s performance several problems which are subject to kinematic modes are presented to illustrate the performance of this stabilization procedure for linear problems

a smoothed finite element method for plate analysis a quadrilateral element with smoothed curvatures for mindlin reissner plates is proposed the curvature at each point is obtained by a non local approximation via a smoothing function the bending stiffness matrix is calculated by a boundary integral along the boundaries of the smoothing elements smoothing cells numerical results show that the proposed element is robust computational inexpensive and simultaneously very accurate and free of locking even for very thin plates the most promising feature of our elements is their insensitivity to mesh distortion

perturbation expansion for option pricing with stochastic volatility abstract we fit the volatility fluctuations of the s p 500 index well by a chi distribution and the distribution of log returns by a corresponding superposition of gaussian distributions the fourier transform of this is remarkably of the tsallis type an option pricing formula is derived from the same superposition of black scholes expressions an explicit analytic formula is deduced from a perturbation expansion around a black scholes formula with the mean volatility the expansion has two parts the first takes into account the non gaussian character of the stock fluctuations and is organized by powers of the excess kurtosis the second is contract based and is organized by the moments of moneyness of the option with this expansion we show that for the dow jones euro stoxx 50 option data a hedging strategy is close to being optimal

efficient computation of order and mode of three dimensional stress singularities in linear elasticity by the boundary finite element method the boundary finite element method bfem a novel semi analytical boundary element procedure solely relying on standard finite element formulations is employed for the investigation of the orders and modes of three dimensional stress singularities which occur at notches and cracks in isotropic halfspaces as well as at free edges and free corners of layered plates after a comprehensive literature review and a concise introduction to the standard three dimensional bfem formulation for the static analysis of general unbounded structures we demonstrate the application of the bfem for the computation of the orders and modes of two dimensional and three dimensional stress singularities for several classes of problems within the framework of linear elasticity special emphasis is placed upon the investigation of stress concentration phenomena as they occur at straight free edges and at free corners of arbitrary opening angles in composite laminates in all cases the bfem computations agree excellently with available reference results the required computational effort is found to be considerably lower compared to e g standard finite element method fem computations in the case of free laminate corners numerous new results on the occurring stress singularities are presented it is found that free corner problems generally seem to involve a more pronounced criticality than the corresponding free edge situations

a unified 3d based technique for plate bending analysis using scaled boundary finite element method summary this paper presents a unified technique for solving the plate bending problems by extending the scaled boundary finite element method the formulation is based on the three dimensional governing equation without enforcing the kinematics of plate theory only the in plane dimensions are discretised into finite elements any two dimensional displacement based elements can be employed the solution along the thickness is expressed analytically by using a matrix function the proposed technique is consistent with the three dimensional theory and applicable to both thick and thin plates without exhibiting the numerical locking phenomenon moreover the use of higher order spectral elements allows the proposed technique to better represent curved boundaries and to achieve high accuracy and fast convergence numerical examples of various plate structures with different thickness to length ratios demonstrate the applicability and accuracy of the proposed technique copyright 2012 john wiley sons ltd

linked interpolation for reissner mindlin plate elements part i a simple quadrilateral in most plate elements using the reissner mindlin assumptions the interpolations used for the lateral displacements w and the rotation involve the independent representation of each variable by its nodal values usually with identical interpolations to ensure a higher order of expansion for displacement w its representation is linked in the present paper with both sets of nodal variables conditions necessary for the use of such expansions are established here and the paper shows the development of a linear quadrilateral element q4bl whose performance and robustness are good although it possesses one singularity if only three degrees of freedom are prescribed in part ii we apply the identical formulation to develop a triangular element t3bl which performs equally well and is fully robust

optimality conditions for a constrained control problem this paper is devoted to the study of necessary or sufficient second order conditions for a weak local minimum in an optimal control problem the problem is stated in the mayer form and includes equality constraints both on the endpoints and on the state control trajectory the second order conditions are stated through an associated linear quadratic problem

transition from lognormal to χ2 superstatistics for financial time series abstract share price returns on different time scales can be well modelled by a superstatistical dynamics here we provide an investigation which type of superstatistics is most suitable to properly describe share price dynamics on various time scales it is shown that while 2 superstatistics works well on a time scale of days on a much smaller time scale of minutes the price changes are better described by lognormal superstatistics the system dynamics thus exhibits a transition from lognormal to 2 superstatistics as a function of time scale we discuss a more general model interpolating between both statistics which fits the observed data very well we also present results on correlation functions of the extracted superstatistical volatility parameter which exhibits exponential decay for returns on large time scales whereas for returns on small time scales there are long range correlations and power law decay

higher order mitc general shell elements two mixed interpolated general shell finite elements for non linear analysis a 9 node element and a 16 node element are presented the elements are based on the mixed interpolation of tensorial components mitc approach in which the covariant strain component fields for the in plane and shear actions are interpolated and tied to the also interpolated displacement field both the 9 node element referred to as the mitc9 element and the 16 node element referred to as the mitc16 element are tested numerically and found to have high predictive capabilities

optimum problems with certain lower semicontinuous set valued constraints in this paper we provide a complete analysis of second order admissible variations to inequality type constraints that are given in terms of lower semicontinuous set valued functions whose images are closed convex sets with nonempty interior as an application we consider optimization problems where such constraints are present and we deduce second order necessary conditions for optimality

the p version of the finite element method for three dimensional curved thin walled structures in this paper we present an implementation of a three dimensional p version for structural problems of solids with almost arbitrarily curved surfaces applying the blending function method complex structures can often be modelled by a few p elements being the basis for a higher order approximation numerical examples will demonstrate that the p version with anisotropic ansatz spaces allows to predict the structural behaviour of three dimensional plates and shells with approximately the same amount of degrees of freedom as in the two dimensional case yet significantly more accurate due to the three dimensional model furthermore it is advantageous to compute complex structures exclusively with three dimensional discretizations as no special elements are needed to model the transition from dimensionally reduced formulations like plates or shells to fully three dimensional solid elements using the p version with anisotropic ansatz spaces the whole structure can be efficiently discretized with solid elements even if the aspect ratio of the elements becomes very large copyright 2001 john wiley sons ltd

noise intensity fluctuation in langevin model and its higher order fokker planck equation abstract in this paper we investigate a langevin model subjected to stochastic intensity noise sin which incorporates temporal fluctuations in noise intensity we derive a higher order fokker planck equation hfpe of the system taking into account the effect of sin by the adiabatic elimination technique stationary distributions of the hfpe are calculated by using the perturbation expansion we investigate the effect of sin in three cases a parabolic and quartic bistable potentials with additive noise b a quartic potential with multiplicative noise and c a stochastic gene expression model we find that the existence of noise intensity fluctuations induces an intriguing phenomenon of a bimodal to trimodal transition in probability distributions these results are validated with monte carlo simulations

possible generalization of boltzmann gibbs statistics with the use of a quantity normally scaled in multifractals a generalized form is postulated for entropy namelys q k 1 i 1 w p i q q 1 whereq characterizes the generalization andp i are the probabilities associated withw microscopic configurations w the main properties associated with this entropy are established particularly those corresponding to the microcanonical and canonical ensembles the boltzmann gibbs statistics is recovered as theq 1 limit

a three node mindlin plate element with improved transverse shear abstract a displacement methodology for mindlin elements recently employed in the development of an efficient four node quadrilateral min4 is the basis for a three node explicitly integrated triangular element min3 the approach herein referred to as anisoparametric is founded upon two kinematic requirements that are auxiliary to the standard convergence criteria the initial complete quadratic deflection field is constrained by continuous shear edge constraints to achieve an isoparametric like three node configuration much success of the element is due to an innovative shear correction factor concept several numerical experiments are performed in the linear elasto static regime to ascertain the element performance

from time series to superstatistics complex nonequilibrium systems are often effectively described by a statistics of a statistics in short a superstatistics we describe how to proceed from a given experimental time series to a superstatistical description we argue that many experimental data fall into three different universality classes chi2 superstatistics tsallis statistics chi2 inverse superstatistics and log normal superstatistics we discuss how to extract the two relevant well separated superstatistical time scales tau and t the probability density of the superstatistical parameter beta and the correlation function for beta from the experimental data we illustrate our approach by applying it to velocity time series measured in turbulent taylor couette flow which is well described by log normal superstatistics and exhibits clear time scale separation

a new plate bending element based on orthogonal polynomials expansion of the curvature field a new approach to derive finite elements for the thin plate model is presented the proposed method approximates compatible kirchhoff formulations by means of orthogonal polynomials expansion of the curvature field depending only on the element boundary traces with respect to the compatible formulation the proposed method produces elements that beneficially underestimate the deformation energy a simple triangular element is developed and investigated from both the theoretical and the numerical point of view and numerically compared with other two well known elements copyright 2007 john wiley sons ltd

an implementation of the hp version of the finite element method for reissner mindlin plate problems reissner mindlin plate theory is still a topic of research in finite element analysis one reason for the continuous development of new plate elements is that it is still difficult to construct elements which are accurate and stable against the well known shear locking effect in this paper we suggest an approach which allows high order polynomial degrees of the shape functions for deflection and rotations a balanced adaptive mesh refinement and increase of the polynomial degree in an hp version finite element program is presented and it is shown in numerical examples that the results are highly accurate and that high order elements show virtually no shear locking even for very small plate thickness

necessary second order conditions for a weak local minimum in a problem with endpoint and control constraints abstract one of the first steps towards necessary second order optimality conditions in problems with constraints was taken by dubovitskii and milyutin in 1965 they offered a scheme that was very effective in smooth optimization problems but seemed to be not suitable for applications in problems with pointwise control constraints in this article we consider a modification of the dubovitskii milyutin scheme which allows to derive necessary second order conditions for a weak local minimum in optimal control problems with a finite number of endpoint constraints of equality and inequality type and with pointwise control constraints of inequality type given by smooth functions assuming that the gradients of active control constraints are linearly independent we provide rather straightforward proof of these conditions for a measurable and essentially bounded optimal control

dynamical modelling of superstatistical complex systems abstract we show how to construct the optimum superstatistical dynamical model for a given experimentally measured time series for this purpose we generalise the superstatistics concept and study a langevin equation with a memory kernel whose parameters fluctuate on a large time scale we show how to construct a synthetic dynamical model with the same invariant density and correlation function as the experimental data as a main example we apply our method to velocity time series measured in high reynolds number turbulent taylor couette flow but the method can be applied to many other complex systems in a similar way

variational approach to second order optimality conditions for control problems with pure state constraints for optimal control problems with set valued control constraints and pure state constraints we propose new second order necessary optimality conditions in addition to the usual second order derivative of the hamiltonian these conditions contain extra terms involving second order tangents to the set of feasible trajectory control pairs at the extremal process under consideration the second order necessary optimality conditions of the present work are obtained by using a variational approach in particular we present a new second order variational equation this approach allows us to make direct proofs as opposed to the classical way of obtaining second order necessary conditions by using an abstract infinite dimensional optimization problem no convexity assumptions on the constraints are imposed and optimal controls are required to be merely measurable

tsallis thermostatics as a statistical physics of random chains in this paper we point out that the generalized statistics of tsallis havrda charvat can be conveniently used as a conceptual framework for statistical treatment of random chains in particular we use the path integral approach to show that the ensuing partition function can be identified with the partition function of a fluctuating oriented random loop of arbitrary length and shape in a background scalar potential to put some meat on the bare bones we illustrate this with two statistical systems schultz zimm polymer and relativistic particle further salient issues such as the projective special linear group psl 2 r transformation properties of tsallis inverse temperature parameter and a grand canonical ensemble of fluctuating random loops related to the tsallis havrda charvat statistics are also briefly discussed

a semi analytical curved element for linear elasticity based on the scaled boundary finite element method summary this work introduces a semi analytical formulation for the simulation and modeling of curved structures based on the scaled boundary finite element method sbfem this approach adapts the fundamental idea of the sbfem concept to scale a boundary to describe a geometry until now scaling in sbfem has exclusively been performed along a straight coordinate that enlarges shrinks or shifts a given boundary in this novel approach scaling is based on a polar or cylindrical coordinate system such that a boundary is shifted along a curved scaling direction the derived formulations are used to compute the static and dynamic stiffness matrices of homogeneous curved structures the resulting elements can be coupled to general sbfem or fem domains for elastodynamic problems computations are performed in the frequency domain results of this work are validated using the global matrix method and standard finite element analysis copyright 2016 john wiley sons ltd

necessary optimality conditions for local minimizers of stochastic optimal control problems with state constraints the main purpose of this work is to establish some first and second order necessary optimality conditions for local minimizers of stochastic optimal control problems with state constraints the control may affect both the drift and the diffusion terms of the systems and the control regions are allowed to be nonconvex a stochastic inward pointing condition is proposed to ensure the normality of the corresponding necessary conditions

asymptotics of superstatistics superstatistics are superpositions of different statistics relevant for driven nonequilibrium systems with spatiotemporal inhomogeneities of an intensive variable e g the inverse temperature they contain tsallis statistics as a special case we develop here a technique that allows us to analyze the large energy asymptotics of the stationary distributions of general superstatistics a saddle point approximation is developed which relates this problem to a variational principle several examples are worked out in detail

investigation of bending behavior for laminated composite magneto electro elastic cylindrical shells subjected to mechanical or electric magnetic loads abstract due to the multidisciplinary nature for the solution of magneto electro elastic mee shell structures developing a novel and accurate computational model is both essential and necessary for the practical engineering the scaled boundary finite element method sbfem is a semi analytical technique in which only the surfaces or boundaries of the computational domain need to be discretized while an analytical formulation can be derived in the radial direction of the surrounding area these advanced features enable the spatial dimension to be reduced by one while the accuracy of the proposed algorithm is maintained in this paper a novel semi analytical numerical model based on the sbfem is developed for the bending analysis of the laminated mee cylindrical shells under the mechanical or electric magnetic potential loads according to the three dimensional 3d magneto electro elasticity theory the magneto electro mechanical coupling equations and the associated boundary conditions in terms of the mechanical displacement as well as the electrical and magnetical potentials are derived in the scaled boundary coordinate system using the weighted residual method the analytical expressions for the generalized displacement and internal nodal force fields are determined by applying the state space method and have been solved by means of the precise integration technique pit comparisons between the present numerical results for limiting conditions and solutions available in the published work have been carried out to demonstrate the convergence and accuracy of this approach at the same time by utilizing the proposed mechanics the influences of the aspect ratio and stacking configuration on the through thickness bending behaviors of the laminated mee cylindrical shells are studied in detail

superpositions of probability distributions probability distributions which can be obtained from superpositions of gaussian distributions of different variances v ensuremath sigma 2 play a favored role in quantum theory and financial markets such superpositions need not necessarily obey the chapman kolmogorov semigroup relation for markovian processes because they may introduce memory effects we derive the general form of the smearing distributions in v which do not destroy the semigroup property the smearing technique has two immediate applications it permits simplifying the system of kramers moyal equations for smeared and unsmeared conditional probabilities and can be conveniently implemented in the path integral calculus in many cases the superposition of path integrals can be evaluated much easier than the initial path integral three simple examples are presented and it is shown how the technique is extended to quantum mechanics

transitions between superstatistical regimes validity breakdown and applications abstract superstatistics is a widely employed tool of non equilibrium statistical physics which plays an important role in analysis of hierarchical complex dynamical systems yet its canonical formulation in terms of a single nuisance parameter is often too restrictive when applied to complex empirical data here we show that a multi scale generalization of the superstatistics paradigm is more versatile allowing to address such pertinent issues as transmutation of statistics or inter scale stochastic behavior to put some flesh on the bare bones we provide a numerical evidence for a transition between two superstatistics regimes by analyzing high frequency minute tick data for share price returns of seven selected companies salient issues such as breakdown of superstatistics in fractional diffusion processes or connection with brownian subordination are also briefly discussed

numerical solutions for magneto electro elastic laminated plates resting on winkler foundation or elastic half space abstract this article investigates the bending response performances of the magneto electro elastic mee laminated plates resting on the winkler foundation or the elastic half space subjected to a transverse mechanical loading by assuming that the foundation is not electrically and magnetically conductive the scaled boundary finite element method sbfem based on the three dimensional 3d theory of elasticity is applied for both the simulation of the mee laminated plate and the elastic half space the sbfem model considers the generalized displacement involving the elastic displacement electric potential and magnetic potential as the nodal degree of freedom for the mee laminated plates and only the in plane of the mee laminated plate or the boundary of the elastic half space needs to be discretized leading to reduce the spatial dimension by one furthermore in the sbfem the governing equations can be solved by using an analytical approach in the radial direction of the scaled coordinate system so that it is particularly suitable for the simulation of the elastic half space for the winkler foundation plate system the global stiffness coupling governing equation that includes the interaction between the mee laminated plate and the winkler foundation is derived directly from the 3d elasticity equations of the mee laminated plate by assuming that the foundation reactions are proportional to the transverse displacements of the plate structure while for the mee laminated plate half space system the whole domain is divided into three sub domains including the mee laminated plate structure the near and semi infinite far foundation systems based on the sub structure method and then the stiffness matrix of each sub domain can be determined by means of the sbfem as a result the global stiffness equation of the plate half space system can be assembled according to the principle of the degree of freedom matching at the same nodes the numerical results obtained for limiting cases by using the proposed method were compared with the published works and showed excellent agreements with the solutions based on the analytical and numerical approaches so that the accuracy and applicability of the proposed formulations for the analysis of the interaction problems between the mee laminated plate and the winkler foundation or elastic half space can be verified moreover several numerical examples with various material properties geometries stacking sequences aspect ratios and supported boundary conditions were presented to show the effects of which on the responses of the plate foundation system

superstatistics from a different perspective abstract in this paper we elaborate on the recently proposed superstatistics formalism c beck e g d cohen physica a 322 2003 267 used to interpret unconventional statistics their interpretation is that unconventional statistics in dynamical systems arise as weighted averages of the ordinary statistics obeyed by these systems over a statistical distribution of background configurations due to fluctuations intrinsic to the background in this paper we suggest that the same picture can arise because of the intrinsic dynamics of the system the dynamics of the system and the background hence concur together to determine the overall final statistics differently evolving systems embedded within the same background can yield different statistical distributions some simple examples are provided among them a toy model able to yield a power law distribution also some recent independent results are quoted that appear to support this viewpoint

strong local minimizers in optimal control problems with state constraints second order necessary conditions this paper is devoted to second order necessary optimality conditions for strong local minima for a mayer type optimal control problem with a general control constraint u subset mathbb r m a

first and second order optimality conditions for a strong local minimum in control problems with pure state constraints in this paper first and second order optimality conditions for a strong local minimum are presented for optimal control problems with pure state set inclusion constraints the first order condition is of pontryagin type while the second order condition is of the form of an accessory problem associated with the strong local minimality this latter condition contains an extra term reflecting the presence of the pure state constraints

second order necessary conditions in pontryagin form for optimal control problems in this article we state and prove first and second order necessary conditions in pontryagin form for optimal control problems with pure state and mixed control state constraints we say that a lagrange multiplier of an optimal control problem is a pontryagin multiplier if it is such that pontryagin s minimum principle holds and we call optimality conditions in pontryagin form those which only involve pontryagin multipliers our conditions rely on a technique of partial relaxation and apply to pontryagin local minima

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

bistable stochastic processes in the q exponential family abstract stochastic bistable systems whose stationary distributions belong to the q exponential family are investigated using two approaches i the langevin model subjected to additive and quadratic multiplicative noise and ii the superstatistical model previously the bistable langevin model has been analyzed under linear multiplicative noise whereas this paper reports on quadratic multiplicative noise which is more physically meaningful the stationary distribution of the langevin model under quadratic multiplicative noise which agrees with that derived by the maximum tsallis entropy method is found to be qualitatively different from its counterpart under linear multiplicative noise we also show that the stationary distribution of the superstatistical model is the same as that of the langevin model whereas their transient properties described in terms of mean first passage times mfpts are qualitatively different

a scaled boundary polygon formulation for elasto plastic analyses this study presents a novel scaled boundary polygon formulation to model elasto plastic material responses in structures the polygons have flexible mesh generation capabilities and are more accurate than standard finite elements especially for problems with cracks and notches shape functions of arbitrary n sided polygons are constructed using the scaled boundary finite element method these shape functions are conforming and linearly complete when modeling a crack strain singularities are analytically modeled without enrichment standard finite element procedures are used to formulate the stiffness matrix and residual load vector the nonlinear material constitutive matrix and the internal stresses are approximated locally in each polygon by a polynomial function the stiffness matrix and the residual load vector are matrix power integrals that can be evaluated analytically even when a strain singularity is present standard nonlinear equation solvers e g the modified newton raphson algorithm are used to obtain the nonlinear response of the structure the proposed formulation is validated using several numerical benchmarks

normality of the maximum principle for nonconvex constrained bolza problems we consider a bolza optimal control problem with state constraints it is well known that under some technical assumptions every strong local minimizer of this problem satisfies first order necessary optimality conditions in the form of a constrained maximum principle in general the maximum principle may be abnormal or even degenerate and so does not provide a sufficient information about optimal controls in the recent literature some sufficient conditions were proposed to guarantee that at least one maximum principle is nondegenerate cf a v arutyanov s m aseev investigation of the degeneracy phenomenon of the maximum principle for optimal control problems with state constraints siam j control optim 35 1997 930 952 f rampazzo r b vinter a theorem on existence of neighbouring trajectories satisfying a state constraint with applications to optimal control ima 16 4 1999 335 351 f rampazzo r b vinter degenerate optimal control problems with state constraints siam j control optim 39 4 2000 989 1007 our aim is to show that actually conditions of a similar nature guarantee normality of every nondegenerate maximum principle in particular we allow the initial condition to be fixed and the state constraints to be nonsmooth to prove normality we use j yorke type linearization of control systems and show the existence of a solution to a linearized control system satisfying new state constraints defined in turn by linearization of the original set of constraints along an extremal trajectory

on the accuracy of p version elements for the reissner mindlin plate problem this paper addresses the question of accuracy of p version finite element formulations for reissner mindlin plate problems three model problems a circular arc a rhombic plate and a geometrically complex structure are investigated whereas displacements and bending moments turn out to be very accurate without any post processing even for very coarse meshes the quality of shear forces computed from constitutive equations is poor it is shown that significantly improved results can be obtained if shear forces are computed from equilibrium equations instead a consistent computation of second derivatives of the shape functions is derived 1998 john wiley sons ltd

the p version of the finite element method in the p version of the finite element method the triangulation is fixed and the degree p of the piecewise polynomial approximation is progressively increased until some desired level of precision is reached in this paper we first establish the basic approximation properties of some spaces of piecewise polynomials defined on a finite element triangulation these properties lead to an a priori estimate of the asymptotic rate of convergence of the p version the estimate shows that the p version gives results which are not worse than those obtained by the conventional finite element method called the h version in which h represents the maximum diameter of the elements when quasi uniform triangulations are employed and the basis for comparison is the number of degrees of freedom furthermore in the case of a singularity problem we show under conditions which are usually satisfied in practice that the rate of convergence of the p version is twice that of the h version with quasi uniform mesh inve

a p version mitc finite element method for reissner mindlin plates with curved boundaries we consider the approximation of reissner mindlin plates with curved boundaries using a p version mitc finite element method we describe in detail the formulation and implementation of the method and emphasize the need for a piola type map in order to handle the curved geometry of the elements the results of our numerical computations demonstrate the robustness of the method and suggest that it gives near exponential convergence when the error is measured in the energy norm for the robust computation of quantities of engineering interest such as the shear force the proposed method yields very satisfactory results without the need for any additional post processing comparisons are made with the standard finite element formulation with and without post processing

the computation of dispersion relations for three dimensional elastic waveguides using the scaled boundary finite element method abstract in this paper a numerical approach for the computation of dispersion relations for three dimensional waveguides with arbitrary cross section is proposed the formulation is based on the scaled boundary finite element method sbfem it is an extension of the approach previously derived for plate structures it is shown that the wavenumbers of guided waves in a waveguide can be obtained as the eigenvalues of the z matrix which is well known in the sbfem the hamiltonian properties of this matrix are utilized to derive an efficient way to compute the group velocities of propagating waves as eigenvalue derivatives the cross section of the waveguide is discretized using higher order spectral elements it is discussed in detail how symmetry axes can be utilized to reduce computational costs in order to sort the solutions at different frequencies a mode tracking algorithm is proposed based on the pade expansion

nonsmooth optimum problems with constraints this paper develops second order necessary conditions for nonsmooth infinite dimensional optimization problems with banach space valued equality and real valued inequality constraints another constraint in the form of a closed convex set is also present the objective function is the maximum over a parameter of functions f t z that are lipschitz in z and upper semicontinuous in t the inequality constraints g s z depend on a parameter s the technique we use is a generalization of that of dubovitskii and milyutin the second order conditions obtained here are in terms of a certain function sigma that disappears when the parameters and a certain set that derives from the given convex set are absent the presence of the function sigma and that set is due to the envelope like effect discovered by kawasaki

the scaled boundary finite element method alias consistent infinitesimal finite element cell method for elastodynamics the scaled boundary finite element method alias the consistent infinitesimal finite element cell method is developed starting from the governing equations of linear elastodynamics only the boundary of the medium is discretized with surface finite elements yielding a reduction of the spatial dimension by one no fundamental solution is necessary and thus no singular integrals must be evaluated general anisotropic material is analysed without any increase in computational effort boundary conditions on free and fixed surfaces and on interfaces between different materials are enforced exactly without any discretization this method is exact in the radial direction and converges to the exact solution in the finite element sense in the circumferential directions for a bounded medium symmetric static stiffness and mass matrices with respect to the degrees of freedom on the boundary result without any additional assumption a stress singularity is represented very accurately as the condition on the boundary in the vicinity of the point of singularity is satisfied without spatial discretization

a class of mixed assumed strain methods and the method of incompatible modes a three field mixed formulation in terms of displacements stresses and an enhanced strain field is presented which encompasses as a particular case the classical method of incompatible modes within this frame work incompatible elements arise as particular compatible mixed approximations of the enhanced strain field the conditions that the stress interpolation contain piece wise constant functions and be l2 ortho gonal to the enhanced strain interpolation ensure satisfaction of the patch test and allow the elimination of the stress field from the formulation the preceding conditions are formulated in a form particularly convenient for element design as an illustration of the methodology three new elements are developed and shown to exhibit good performance a plane 3d elastic plastic quad an axisymmetric element and a thick plate bending quad the formulation described herein is suitable for non linear analysis

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

pointwise second order necessary optimality conditions and second order sensitivity relations in optimal control abstract this paper is devoted to pointwise second order necessary optimality conditions for the mayer problem arising in optimal control theory we first show that with every optimal trajectory it is possible to associate a solution p of the adjoint system as in the pontryagin maximum principle and a matrix solution w of an adjoint matrix differential equation that satisfy a second order transversality condition and a second order maximality condition these conditions seem to be a natural second order extension of the maximum principle we then prove a jacobson like necessary optimality condition for general control systems and measurable optimal controls that may be only partially singular and may take values on the boundary of control constraints finally we investigate the second order sensitivity relations along optimal trajectories involving both p and w