nonlinear panel flutter by finite element method les equations non lineaires sont calculees a partir de considerations energetiques et la force d etirement non lineaire est formulee en termes de deplacement transversal seul

the evolution of a batch immigration death process subject to counts a bivariate batch immigration death process is developed to study the degree to which the fundamental structure of a hidden stochastic process can be inferred purely from counts of escaping individuals this question is of immense importance in fields such as quantum optics where externally based radiation elucidates the nature of the underlying electromagnetic radiation process batches of i immigrants enter the population at rate qi and each individual dies independently at rate general expressions are developed for the population size cumulants and probabilities together with those for the associated counting process the strong link between these two structures is highlighted through two specific examples involving k batch immigration for i k and schoenberg batch immigration over i 2m m 0 1 2 and shows that high quality inferences on the hidden population process can be inferred purely from externally counted observations

shape sensitivity analysis and shape optimization in planar elasticity using the element free galerkin method abstract this paper demonstrates that the element free galerkin efg method can be successfully used in shape design sensitivity analysis and shape optimization for problems in 2d elasticity the continuum based variational equations for displacement sensitivities are derived and are subsequently discretized this approach allows one to avoid differentiating the efg shape functions the present formulation that employs a penalty method for imposing the essential boundary conditions can be easily extended to 3d and or non linear problems numerical examples are presented to show the capabilities of the current approach for calculating sensitivities the flexibility of the efg method that eliminates the element connectivity requirement of the finite element method fem permits solving shape optimization problems without re meshing the problem of shape optimization of a fillet is used to demonstrate this fact smoother stresses and better accuracy for points close to the boundary allow for a better efg solution compared to published results using the fem the boundary element method bem or the boundary contour method bcm furthermore for the efg approach grid optimization appears unnecessary

markov branching processes with instantaneous immigration markov branching processes with instantaneous immigration possess the property that immigration occurs immediately the number of particles reaches zero i e the conditional expectation of sojourn time at zero is zero in this paper we consider the existence and uniqueness of such a structure we prove that if the sum of the immigration rates is finite then no such structure can exist and we provide a necessary and sufficient condition for existence for the case in which this sum is infinite study of the uniqueness problem shows that for honest processes the solution is unique

a note on parameter effects curvature abstract the parameter effects curvature measure proposed by bates and watts 1980 is examined for a growth model and the fieller creasy problem exact confidence regions are constructed and compared to linear approximation regions for the growth model the agreement between the regions is good despite high curvature in the fieller creasy problem it is shown that the agreement can be quite poor despite low curvature

flutter analysis of laminated curvilinear stiffened plates this paper proposes the use of curvilinear stiffeners as a mechanism to control supersonic panel flutter to account for transverse shear deformation the plate and stiffeners are modeled according to the first order shear deformation theory and timoshenko beam theory respectively the chebyshev polynomials are the basis of the deflection and rotation functions in the ritz method the aeroelastic load is formulated according to the first order high mach number approximation to linear potential flow theory the minimum potential energy and hamilton s principle are used to solve the problem plots of frequency versus aerodynamic pressure and damping versus aerodynamic pressure are used to determine the critical aerodynamic pressure and hence to predict flutter of various isotropic and composite stiffened and unstiffened plates the results for the flutter of straight stiffened plates are validated through comparison with published papers several numerical examples are discussed for which parametric st

curvature measures for multiresponse regression models a multiresponse model presented in this study is two fold first a nonuniformity measure is developed to measure the validity of the approximation of the determinant contours by generalised least squares contours secondly curvature measures similar to those of bates watts are calculated for the generalised least squares model to evaluate the validity of the linear approximation of the model functions in a neighbourhood of the parameter estimates

dual and feller reuter riley transition functions abstract in this paper we investigate duality and feller reuter riley frr property of continuous time markov chains ctmcs a criterion of dual q functions is given in terms of their q matrices for a dual q matrix q a necessary and sufficient conditions for the minimal q function to be a frr transition function are also given finally by using dual technique we give a criterion of frr q functions when q is monotone

vibration of plate with curvilinear stiffeners using mesh free method the element free galerkin method which is based on the moving least squares approximation is developed for vibration analysis of unitized structures e g a plate with curvilinear stiffeners the plate and stiffeners are modeled using the first order shear deformation theory and timoshenko beam theory respectively the moving least squares approximation does not satisfy the delta function property consequently an approximation method e g the well known penalty method must be used for imposing essential boundary conditions a key benefit of using element free galerkin for the vibration analysis of a stiffened panel is that the locations and curvatures of the stiffeners can be changed without modifying the plate nodes numerical results for different stiffeners configurations and boundary conditions are presented all results are verified using the commercial finite element software ansys excellent agreement is seen in all cases a comparison of the present formulations with other available results for stiffened plates is also made the mesh free approach yields highly accurate results for the plates with curvilinear stiffeners

a differential quadrature analysis of vibration for rectangular stiffened plates abstract structures consisting of thin plates stiffened by a system of ribs or diaphragms form a class of structural elements of practical importance in various engineering applications a differential quadrature analysis of free vibration of plates with eccentric stiffeners is presented the plate and the stiffeners are treated separately simultaneous governing differential equations are derived from the plate dynamic equilibrium the stiffener dynamic equilibrium and equilibrium and compatibility conditions along the interface of a plate segment and a stiffener the plate and the stiffeners have displacements in three dimensions shear forces and in plane forces in the plate are considered to satisfy the compatibility at the interface of a plate segment and a stiffener meanwhile in plane inertia effects in the plate and in the stiffener are ignored the application of the differential quadrature method is demonstrated by three examples a simply supported plate with central eccentric stiffener a clamped square plate with central eccentric stiffener and a double ribbed plate with all edges clamped the natural frequencies are compared with the experimental results and with the results obtained by finite element analysis very good agreement was found

continuum based stiffened composite shell element for geometrically nonlinear analysis a continuum based laminated stiffened shell element is used to investigate the static geometrically nonlinear response of composite shells the element is developed from a three dimensional continuum element based on the incremental total lagrangian formulation the newton raphson method or modified riks method is used to trace the nonlinear equilibrium path a number of sample problems of unstiffened and stiffened shells are presented to show the accuracy of the present element and to investigate the nonlinear response of laminated composite plates and shells inite element analyses of the large displacement the ories are based on the principle of virtual work or the associated principle of stationary potential energy horrigmoe and bergan1 presented classical variational principles for non linear problems by considering incremental deformations of a continuum a survey of various principles in incremental form in different reference configurations such as the total lagran gian and updated lagrangian formulations is presented by wiinderlich 2 in the total lagrangian description all static and kinematic variables are referred to the initial configura tion finite element models based on such formulations have been used in the analysis of arch and shell instability prob lems 3 6 a special numerical technique must be adopted to trace the path of the load deflection curve near the limit point i e critical buckling load and in the postbuckling region because the stiffness matrix in the vicinity of the limit point is nearly singular and the descending branch of the load deflec tion curve in the postbuckling region is characterized by a negative definite stiffness matrix many methods have been proposed to solve limit point problems among these are the simple methods of suppressing equilibrium iterations 7 8 the introduction of artificial spring 3 the displacement control method 7 8 and the constant arc length method of riks 11 12 reviews of these most commonly used techniques are con tained in refs 13 and 14 among these methods the modified riks method appears to be the most effective in conjunction with the finite element method many investigators11 15 have used this method in its original or modified form to determine the pre and postbuckling behavior of various types of struc tures such as arches shells and domes in most of these works only isotropic material was considered very few works of the nonlinear buckling analysis of laminated com posite structures are reported in the literature 16 when solving the problems of shells with stiffeners by the finite element method a beam element whose displacement pattern is compatible with that of the shell is required in analyzing eccentrically stiffened cylindrical shell kohnke and schnobrich17 proposed a 16 deg of free dom dof isotropic beam finite element that has displacements compatible with

likelihood ratio testing of variance components in the linear mixed effects model using restricted maximum likelihood this paper reports the results of an extensive monte carlo study of the distribution of the likelihood ratio test statistic using the value of the restricted likelihood for testing random components in the linear mixed effects model when the number of fixed components remains constant the distribution of this test statistic is considered when one additional random component is added the distribution of the likelihood ratio test statistic computed using restricted maximum likelihood is compared to the likelihood ratio test statistic computed from the usual maximum likelihood the rejection proportion is computed under the null hypothesis using a mixture of chi square distributions the restricted likelihood ratio statistic has a reasonable agreement with the maximum likelihood test statistic for the parameter combinations considered the rejection proportions are in most cases less than the nominal 5 level for both test statistics though on average the rejection proportions for reml are closer to the nominal level than for ml

buckling and static analysis of curvilinearly stiffened plates using mesh free method with the advancement s being made in manufactu ring technology it is now possible to manufacture panels with arbitrary curvilinear stiffeners a plate with curvilinear stiffener s can in some cases yield a desired structural response but with a lower mass in this paper the element free galerkin efg method is employed for buckling and static analysis of stiffened plates the formulation allows the placeme nt of any number of arbitrarily curvilinear stiffeners within a plate the first order shear deformation theory fsdt is used to model the behav ior of the plate and the stiffener moving least squares mls approximation is used to construct the shape function s one of the major difficulties in the implementation of some mesh free methods is the imposition of essential boundary conditions as the appro ximations do not pass through the nodal parameter values in this research the penalty method is used for satisfying the boundary conditions using a meshfree method sets free the user from providing a nodal line on the plate along every stiffener this i s very beneficial for performing optimization studies several numerical examples using both straight and curvilinear stiffener s are obtained and compared with those available in the literature and those obtained using ansys this demonstrate s the validit y of th e presented approach

stochastic comparability and dual q functions in this paper we discuss the relationship and characterization of stochastic comparability duality and feller reuter riley transition functions which are closely linked with each other for continuous time markov chains a necessary and sufficient condition for two feller minimal transition functions to be stochastically comparable is given in terms of their density q matrices only moreover a necessary and sufficient condition under which a transition function is a dual for some stochastically monotone q function is given in terms of again its density q matrix finally for a class of q matrices the necessary and sufficient condition for a transition function to be a feller reuter riley transition function is also given

nonlinear panel flutter using high order triangular finite elements a 54 degree of freedom high order triangular plate finite element extended for geometrically nonlinear static and dynamic analysis is used to formulate and analyze the supersonic nonlinear panel flutter problems the finite element formulation is based on kirchhoffs theory of thin plates the quasisteady aerodynamic theory is used numerical solution procedures are presented the limit cycle oscillation analyses are performed for twodimensional and square panels with all edges simply supported and clamped respectively the effects of in plane compressive force mass ratio and in plane edge stress free condition are considered stress distributions for the limit cycle oscillation of a two dimensional panel are plotted for the case of panels under static pressure differential the results for the steady mean amplitude and flutter dynamic pressure are obtained for the twodimensional and square panels respectively the effect of biaxial in plane compressive stress for a simply supported square panel is studied and boundaries among the flat and stable region dynamically stable buckled region and the limit cycle oscillation region are found alternative analytical and numerical solutions are available for most of the examples for comparison and all are in excellent agreement

surfaces generated by moving least squares methods an analysis of moving least squares m l s methods for smoothing and interpolating scattered data is presented in particular theorems are proved concerning the smoothness of interpolants and the description of m l s processes as projection methods some properties of compositions of the m l s projector with projectors associated with finiteelement schemes are also considered the analysis is accompanied by examples of univariate and bivariate problems

integrated semigroups and integrated solutions to abstract cauchy problems abstract concepts which have been developed in the theory of weakly continuous semigroups on dual banach spaces are extended to integrated semigroups the relation to integrated solutions of homogeneous and inhomogeneous abstract cauchy problems is established the results are illustrated for the wave equation in l2 rm

45 years of orthogonal polynomials a view from the wings this is an informal and rather personal report on what a bit player observed happening on stage in this ongoing drama we call orthogonal polynomials

buckling and free vibration analyses of stiffened plates using the fsdt mesh free method this paper presents a mesh free galerkin method for the free vibration and stability analyses of stiffened plates via the first order shear deformable theory fsdt the model of a stiffened plate is formed by 1 regarding the plate and the stiffener separately 2 imposing displacement compatible conditions between the plate and the stiffener so that displacement fields of the stiffener can be expressed in terms of the mid surface displacement of the plate and 3 superimposing the strain energy of plate and stiffener because there are no meshes used in this method the stiffeners can be placed anywhere on the plate and need not be placed along the mesh lines several numerical examples are computed by this method to show its accuracy and convergence the present results demonstrate good agreement with the existing solutions given by other researchers and the ansys influences of support size and order of the complete basis functions on the numerical accuracy are also investigated

c semigroups and the cauchy problem abstract we extend the definition of generator to c semigroups that may not be exponentially bounded where the range of c may not be dense we then characterize linear operators a for which the associated abstract cauchy problem has a unique solution for every initial value in the domain of another operator b without assuming that the domain of a is dense or the solutions are exponentially bounded we also give hille yosida type characterizations of generators that may not be densely defined

accounting for intrinsic nonlinearity in nonlinear regression parameter inference regions joint confidence and likelihood regions for the parameters in nonlinear regression models can be defined using the geometric concepts of sample space and solution locus using a quadratic approximation to the solution locus instead of the usual linear approximation it is shown that these inference regions correspond to ellipsoids on the tangent plane at the least squares point accurate approximate inference regions can be obtained by mapping these ellipsoids into the parameter space and measures of the effect of intrinsic nonlinearity on inference can be based on the difference between the tangent plane ellipsoids and the sphere which would be obtained using a linear approximation

quasi stationary distributions for discrete state models this paper contains a survey of results related to quasi stationary distributions which arise in the setting of stochastic dynamical systems that eventually evanesce and which may be useful in describing the long term behaviour of such systems before evanescence we are concerned mainly with continuous time markov chains over a finite or countably infinite state space since these processes most often arise in applications but will make reference to results for other processes where appropriate next to giving an historical account of the subject we review the most important results on the existence and identification of quasi stationary distributions for general markov chains and give special attention to birth death processes and related models the question of under what circumstances a quasi stationary distribution given its existence is indeed a good descriptor of the long term behaviour of a system before evanescence is addressed as well we conclude with a discussion of computational aspects with more details given in a web appendix accompanying this paper

flutter analysis of stiffened laminated composite plates and shells in supersonic flow the equation of motion of the present problem is formulated using hamilton s principle then using the finite element method along with three dimensional degenerated shell elements and three dimensional degenerated curved beam elements the equation of motion is discretized the characteristic equation to study the flutter instability of the present problem is obtained from the previous finite element equation of motion

modelling hearing thresholds in the elderly this paper concerns a linear mixed effects repeated measures model in the analysis of a large data set with over 17 000 observations in a longitudinal study of pure tone hearing perception in the elderly the repeated measurements are described by fixed and random components in the model the fixed effects include the age at entry time of follow up a quadratic component in natural logarithm of frequency a component to allow for participants with hearing impairments as well as interaction terms between age and frequency and between impairment and frequency the random factors include a term for subject a time component and a frequency component the analysis shows that hearing impaired individuals have similar patterns of hearing loss over time but on average have higher hearing thresholds than normal individuals estimation of the random effects in the model by restricted maximum likelihood reml using the newton raphson method made possible the analysis of this large data set with speed and efficiency

maximizing generalized linear mixed model likelihoods with an automated monte carlo em algorithm summary two new implementations of the em algorithm are proposed for maximum likelihood fitting of generalized linear mixed models both methods use random independent and identically distributed sampling to construct monte carlo approximations at the e step one approach involves generating random samples from the exact conditional distribution of the random effects given the data by rejection sampling using the marginal distribution as a candidate the second method uses a multivariate t importance sampling approximation in many applications the two methods are complementary rejection sampling is more efficient when sample sizes are small whereas importance sampling is better with larger sample sizes monte carlo approximation using random samples allows the monte carlo error at each iteration to be assessed by using standard central limit theory combined with taylor series methods specifically we construct a sandwich variance estimate for the maximizer at each approximate e step this suggests a rule for automatically increasing the monte carlo sample size after iterations in which the true em step is swamped by monte carlo error in contrast techniques for assessing monte carlo error have not been developed for use with alternative implementations of monte carlo em algorithms utilizing markov chain monte carlo e step approximations three different data sets including the infamous salamander data of mccullagh and nelder are used to illustrate the techniques and to compare them with the alternatives the results show that the methods proposed can be considerably more efficient than those based on markov chain monte carlo algorithms however the methods proposed may break down when the intractable integrals in the likelihood function are of high dimension

column continuous transition functions abstract a column continuous transition function is by definition a standard transition function p t whose every column is continuous for t 0 in the norm topology of bounded sequence space l we will prove that it has a stable q matrix and that there exists a one to one relationship between column continuous transition functions and increasing integrated semigroups on l using the theory of integrated semigroups we give some necessary and sufficient conditions under which the minimal q function is column continuous in terms of its generator of the markov semigroup as well as its q matrix furthermore we will construct all column continuous q functions for a conservative single exit and column bounded q matrix q as applications we find that many interesting continuous time markov chains ctmcs say feller reuter riley processes monotone processes birth death processes and branching processes etc have column continuity

analysis of thin shells by the element free galerkin method a meshless approach to the analysis of arbitrary kirchhoff shells by the element free galerkin efg method is presented the shell theory used is geometrically exact and can be applied to deep shells the method is based on moving least squares approximant the method is meshless which means that the discretization is independent of the geometric subdivision into finite elements the satisfaction of the c1 continuity requirements is easily met by efg since it requires only c1 weights therefore it is not necessary to resort to mindlin reissner theory or to devices such as discrete kirchhoff theory the requirements of consistency are met by the use of a polynomial basis of quadratic or higher order a subdivision similar to finite elements is used to provide a background mesh for numerical integration the essential boundary conditions are enforced by lagrange multipliers membrane locking which is due to different approximation order for transverse and membrane displacements is removed by using larger domains of influence with the quadratic basis and by using quartic polynomial basis which can prevent membrane locking completely it is shown on the obstacle course for shells that the present technique performs well

supersonic flutter analysis of stiffened laminated plates subject to thermal load abstract flutter analysis of stiffened laminated plates has been performed the purpose of this study is to analyze the flutter characteristics of stiffened plates subject to thermal load the first order shear deformable plate and timoshenko beam theories are used for the finite element modelling of a skin panel and stiffeners respectively the von karman non linear strain displacement relation is used to account for large deflections first order piston theory is used for modelling aerodynamic loads the newton raphson iteration method and complex eigenvalue solver with the lum ntf approximation method are used to obtain the postbuckled deflection and flutter information respectively the guyan reduction method and mode tracing procedure are employed for an efficient analysis the effects of various parameters such as the stiffening scheme lamination angle boundary conditions and temperature gradient on flutter characteristics are investigated through some numerical examples from these examples it can be shown that the selection of a proper stiffening scheme results in great improvements of flutter characteristics of laminated panels without introducing considerable weight penalty

on the existence of a quasistationary measure for a markov chain we consider a markov chain on a locally compact metric space with an absorbing set necessary and sufficient conditions are provided for the existence of a quasistationary probability distribution

subgeometric ergodicity for continuous time markov chains abstract in this paper subgeometric ergodicity is investigated for continuous time markov chains several equivalent conditions based on the first hitting time or the drift function are derived as the main theorem in its corollaries practical drift criteria are given for l ergodicity and computable bounds on subgeometric convergence rates are obtained for stochastically monotone markov chains these results are illustrated by examples

existence and uniqueness criteria for conservative uni instantaneous denumerable markov processes until now denumerable markov processes with instantaneous states have not been extensively considered and so in this paper we present a detailed examination of the conservative uni instantaneous cui case we determine criteria for the existence and uniqueness of a specific cui pregenerator and consider the general problem of constructing cui processes

multiresponse estimation with special application to linear systems of differential equations we present a multiresponse estimation procedure for parameters of systems described by as the procedure features a generalized gauss newton algorithm for optimizing the determinant criterion efficient evaluation of the expectation function and its derivatives directly from the reaction network or compartment diagram automatic determination of starting values and eficient computational procedures for handling linear constraints on the responses

newton raphson and em algorithms for linear mixed effects models for repeated measures data abstract we develop an efficient and effective implementation of the newton raphson nr algorithm for estimating the parameters in mixed effects models for repeated measures data we formulate the derivatives for both maximum likelihood and restricted maximum likelihood estimation and propose improvements to the algorithm discussed by jennrich and schluchter 1986 to speed convergence and ensure a positive definite covariance matrix for the random effects at each iteration we use matrix decompositions to develop efficient and computationally stable implementations of both the nr algorithm and an em algorithm laird and ware 1982 for this model we compare the two methods em vs nr in terms of computational order and performance on two sample data sets and conclude that in most situations a well implemented nr algorithm is preferable to the em algorithm or em algorithm with aitken s acceleration the term repeated measures refers to experimental designs where there are several individuals and several

flutter analysis of cantilevered quadrilateral plates abstract in this paper the title problem is solved by using a numerical method involving an integral equation technique and a normal mode method linear plate theory has been used for computing the strain energy and kinetic energy of the plate piston theory has been used to describe the aerodynamic pressure distribution numerical work has been done and convergence of the solution has been studied results have also been obtained for various cases and compared with those of other investigators

criteria for feller transition functions abstract this paper presents some conditions for the minimal q function to be a feller transition function for a given q matrix q we derive a sufficient condition that is stated explicitly in terms of the transition rates furthermore some necessary and sufficient conditions are derived of a more implicit nature namely in terms of properties of a system of equations or inequalities and in terms of the operator induced by the q matrix the criteria lead to some perturbation results these results are applied to birth death processes with killing yielding some sufficient and some necessary conditions for the feller property directly in terms of the rates an essential step in the analysis is the idea of associating the feller property with individual states

correction factors for f ratios in nonlinear regression summary multiplicative correction factors are derived for the limiting f distributions of two test statistics for parameter subsets in nonlinear regression the factors depend on the first and second derivatives of the model and are related to measures of intrinsic nonlinearity an example is given for which the correction is substantial a similar factor is obtained for the lack of fit test in nonlinear regression

nonlinear mixed effects models for repeated measures data we propose a general nonlinear mixed effects model for repeated measures data and define estimators for its parameters the proposed estimators are a natural combination of least squares estimators for nonlinear fixed effects models and maximum likelihood or restricted maximum likelihood estimators for linear mixed effects models we implement newton raphson estimation using previously developed computational methods for nonlinear fixed effects models and for linear mixed effects models two examples are presented and the connections between this work and recent work on generalized linear mixed effects models are discussed

applications of feller reuter riley transition functions a feller reuter riley function is a markov transition function whose corresponding semigroup maps the set of the real valued continuous functions vanishing at infinity into itself the aim of this paper is to investigate applications of such functions in the dual problem markov branching processes and the williams matrix the remarkable property of a feller reuter riley function is that it is a feller minimal transition function with a stable q matrix by using this property we are able to prove that in the theory of branching processes the branching property is equivalent to the requirement that the corresponding transition function satisfies the kolmogorov forward equations associated with a stable q matrix it follows that the probabilistic definition and the analytic definition for markov branching processes are actually equivalent also by using this property together with the resolvent decomposition theorem a simple analytical proof of the williams existence theorem with respect to the williams matrix is obtained the close link between the dual problem and the feller reuter riley transition functions is revealed it enables us to prove that a dual transition function must satisfy the kolmogorov forward equations a necessary and sufficient condition for a dual transition function satisfying the kolmogorov backward equations is also provided

a relative off set orthogonality convergence criterion for nonlinear least squares an orthogonality convergence criterion using relative offset is proposed this criterion is compared to currently used criteria and its advantages are discussed