frequency analysis of corner point supported mindlin plates by a finite difference energy method abstract the first known solution of the title problem is presented a method based on the variational procedure in conjunction with a finite difference method is used to examine the free vibration characteristics numerical studies show that the convergence is relatively slow requiring a finer mesh model in view of the symmetry of the geometry of the plate and the symmetry in the distribution of the point supports only one quarter of the plate is examined three mode types are developed to account for the full plate detailed results are given for the frequencies and mode shapes of the first six modes of each symmetry class and the effect of transverse shear deformation and rotary inertia is analyzed the validity of the results is partially demonstrated by comparing them with existing solutions based on the classical thin plate theory

partial non gaussian state space summary in this paper we suggest the use of simulation techniques to extend the applicability of the usual gaussian state space filtering and smoothing techniques to a class of nongaussian time series models this allows a fully bayesian or maximum likelihood analysis of some interesting models including outlier models discrete markov chain components multiplicative models and stochastic variance models finally we discuss at some length the use of a non gaussian model to seasonally adjust the published money supply figures

hamiltonian principle based stress singularity analysis near crack corners of multi material junctions this paper presents a new method for the stress singularity analysis near the crack corners of a multi material junctions the stress singularities near the crack corners of multi dissimilar isotropic elastic material junctions are studied analytically in terms of the methods developed in hamiltonian system the governing equations of plane elasticity in a sectorial domain are derived in hamiltonian form via variable substitution and variational principle respectively both of the methods of global state variable separation and symplectic eigenfunction expansion are used to find the analytical solution of the problem the relationships among the state vectors in different material spaces are obtained by means of coordinate transformation and consistent conditions between the two adjacent domains the expression of the original problem is thus changed into a new form where the solutions of symplectic generalized eigenvalues and eigenvectors are needed the closed form of expressions is established for the stress singularity analysis near the corner with arbitrary vertex angles numerical results are presented with several chosen angles and multi material constants to show the potential of the new method proposed a semi analytical finite element is furthermore developed for the numerical analysis of crack problems

saint venant end effects in multilayered piezoelectric laminates the saint venant end effects and stress decay in multilayered laminates of piezoelectric materials are studied a state space approach is developed in the context of generalized plane strain by means of matrix algebra and transfer matrix the characteristics of the stress decay in 2 d piezoelectric strips and laminates are examined their elastic counterparts are included as special cases evaluation of the characteristic decay length for typical materials shows that the saint venant end effects are significant it also indicates that the analysis based on the plane strain assumption is misleading

on new symplectic approach for exact bending solutions of moderately thick rectangular plates with two opposite edges simply supported the symplectic geometry method is introduced for exact bending solutions of moderately thick rectangular plates with two opposite edges simply supported the basic equations for the plates are first transferred into hamilton canonical equations the whole state variables are then separated using the method of eigenfunction expansion in the symplectic geometry typical examples for plates with selected boundary conditions are solved and exact bending solutions obtained since only the basic elasticity equations of the plates are used this method eliminates the need to pre determine the deformation function and is hence more reasonable than conventional methods numerical results were presented to demonstrate the validity and accuracy of this approach as compared to those reported in other literatures

bayesian computation via the gibbs sampler and related markov chain monte carlo methods the use of the gibbs sampler for bayesian computation is reviewed and illustrated in the context of some canonical examples other markov chain monte carlo simulation methods are also briefly described and comments are made on the advantages of sample based approaches for bayesian inference summaries

3d symplectic expansion for piezoelectric media the symplectic series expansion method is extended to three dimensional problem for transversely isotropic piezoelectric media the governing equations are first derived in hamiltonian form and symplectic eigensolutions are directly obtained through analytical method all solutions of the problem are reduced to finding eigenvalues and eigensolutions the classical st venant solutions are described by zero eigensolutions and the localized solutions are depicted by non zero eigensolutions symplectic relationships of the ortho normalization are used end conditions are rewritten by eigensolutions and a numerical scheme is formed analytically some numerical examples are given copyright 2007 john wiley sons ltd

priors and component structures in autoregressive time series models new approaches to prior specification and structuring in autoregressive time series models are introduced and developed we focus on defining classes of prior distributions for parameters and latent variables related to latent components of an autoregressive model for an observed time series these new priors naturally permit the incorporation of both qualitative and quantitative prior information about the number and relative importance of physically meaningful components that represent low frequency trends quasi periodic subprocesses and high frequency residual noise components of observed series the class of priors also naturally incorporates uncertainty about model order and hence leads in posterior analysis to model order assessment and resulting posterior and predictive inferences that incorporate full uncertainties about model order as well as model parameters analysis also formally incorporates uncertainty and leads to inferences about unknown initial values of the time series as it does for predictions of future values posterior analysis involves easily implemented iterative simulation methods developed and described here one motivating field of application is climatology where the evaluation of latent structure especially quasi periodic structure is of critical importance in connection with issues of global climatic variability we explore the analysis of data from the southern oscillation index one of several series that has been central in recent high profile debates in the atmospheric sciences about recent apparent trends in climatic indicators

the mode iii stress electric intensity factors and singularities analysis for edge cracked circular piezoelectric shafts abstract this paper introduces a new analytical method to determine the stress and electric intensity factors for edge cracked circular piezoelectric shafts using hamiltonian formalism the singularities near the crack tip are represented in terms of exponential series that can show the boundary layer effects effectively a symplectic system is established directly by introducing dual vectors in terms of the symplectic eigenfunctions the coefficients of the series are determined from the lateral boundary conditions along the crack faces and the outer boundary conditions along the exterior geometric domain the intensity factors are determined by the first two coefficients of non zero eigenvalue solutions numerical examples for various boundary conditions are given the influencing parameters on the intensity factors are investigated

a monte carlo approach to nonnormal and nonlinear state space modeling abstract a solution to multivariate state space modeling forecasting and smoothing is discussed we allow for the possibilities of nonnormal errors and nonlinear functionals in the state equation the observational equation or both an adaptive monte carlo integration technique known as the gibbs sampler is proposed as a mechanism for implementing a conceptually and computationally simple solution in such a framework the methodology is a general strategy for obtaining marginal posterior densities of coefficients in the model or of any of the unknown elements of the state space missing data problems including the k step ahead prediction problem also are easily incorporated into this framework we illustrate the broad applicability of our approach with two examples a problem involving nonnormal error distributions in a linear model setting and a one step ahead prediction problem in a situation where both the state and observational equations are nonlinear and involve unknown parameters

the wave equation approach for solving inverse eigenvalue problems of a multi connected region in r3 with robin conditions the asymptotic expansion for t of the trace of the wave kernel email protected t email protected u 1exp email protected 1 2 u where m u u 1 are the eigenvalues of the negative laplacian email protected email protected 3 b 1 x b 2 in the x 1 x 2 x 3 space where i 1 and

determination of stress intensity factors by the finite element discretized symplectic method abstract when rewriting the governing equations in hamiltonian form analytical solutions in the form of symplectic series can be obtained by the method of separation of variable satisfying the crack face conditions in theory there exists sufficient number of coefficients of the symplectic series to satisfy any outer boundary conditions in practice the matrix relating the coefficients to the outer boundary conditions is ill conditioned unless the boundary is very simple e g circular in this paper a new two level finite element method using the symplectic series as global functions while using the conventional finite element shape functions as local functions is developed with the available classical finite elements and symplectic series the main unknowns are no longer the nodal displacements but are the coefficients of the symplectic series since the first few coefficients are the stress intensity factors post processing is not required a number of numerical examples as well as convergence studies are given

large amplitude vibration of an initially imperfect moderately thick plate abstract non linear equations of motion for a transversely isotropic moderately thick plate in a general state of non uniform initial stress where the effects of transverse shear and rotary inertia are included are derived the large amplitude flexural vibration of a simply supported rectangular moderately thick plate subjected to initial stress is investigated the initial stress is taken to be a combination of a pure bending stress plus an extensional stress in the plane of the plate these equations are used to solve the vibrations problem by the galerkin method the effects of various parameters on the non linear vibration frequencies are studied

on the θ function of a riemannian manifold with boundary let be a compact riemannian manifold of dimension n with smooth boundary let 1 2 be the eigenvalues of the laplace beltrami operator with the boundary condition n 0 the associated function t n 1 exp n t has an asymptotic expansion of the form 4 t n 2 t a 0 a 1 t 1 2 a 2 t a 3 t 3 2 a 4 t 2 the values of a 0 a 1 are well known

the polarization vector and secular equation for surface waves in an anisotropic elastic half space abstract the displacement at the free surface of an anisotropic elastic half space x2 0 generated by a surface wave propagating in the direction of the x1 axis traces an elliptic path it is represented by the polarization vector a r e 1 i e 2 where e 1 e 2 are the conjugate radii of the ellipse on the polarization plane the displacement traces the ellipse in the direction from e 1 to e 2 we present explicit expressions of e 1 e 2 and the secular equation without computing the stroh eigenvalues p and the associated eigenvectors a and b after presenting the expressions for a general anisotropic elastic material the special cases are studied separately for monoclinic materials with the symmetry plane at x3 0 the secular equation and the conjugate radii e 1 e 2 are identical to that for orthotropic materials when s 16 0 but s 26 need not vanish for monoclinic materials with the symmetry plane at x1 0 e 1 is along the x1 axis while e 2 is on the plane x1 0 if the symmetry plane is at x2 0 e 1 is on the plane x2 0 while e 2 is along the negative x2 axis in both cases e 1 e 2 are the principal radii of the ellipse we also present the derivative of a r with respect to x2 the depth from the free surface that provides information on i whether the conjugate radii of the ellipse increase as x2 increases and ii whether the polarization plane rotates as x2 increases new secular equations are obtained for monoclinic materials with the symmetry plane at x1 0 or x2 0

the relationship between the beveridge nelson decomposition and other permanent transitory decompositions that are popular in economics abstract the beveridge nelson bn decomposition is a model based method for decomposing time series into permanent and transitory components when constructed from an arima model it is closely related to decompositions based on unobserved components uc models with random walk trends and covariance stationary cycles the decomposition when extended to i 2 models can also be related to non model based signal extraction filters such as the hp filter we show that the bn decomposition provides information on the correlation between the permanent and transitory shocks in a certain class of uc models the correlation between components is known to determine the smoothed estimates of components from uc models the bn decomposition can also be used to evaluate the efficacy of alternative methods we also demonstrate contrary to popular belief that the bn decomposition can produce smooth cycles if the reduced form forecasting model is appropriately specified

theory of a curved planar waveguide with robin boundary conditions a model of a thin straight strip with a uniformly curved section and with boundary requirements zeroing at the edges a linear superposition of the wave function and its normal derivative robin boundary condition is analyzed theoretically within the framework of the linear schrodinger equation and is applied to the study of the processes in the bent magnetic multilayers superconducting films and metallic ferrite filled waveguides in particular subband thresholds of the straight and curved parts of the film are calculated and analyzed as a function of the robin parameter 1 lambda with lambda being an extrapolation length entering robin boundary condition for the arbitrary robin coefficients which are equal on the opposite interfaces of the strip and for all bend parameters the lowest mode energy of the continuously curved duct is always smaller than its straight counterpart accordingly the bound state below the fundamental propagation threshold of the straight arms always exists as a result of the bend in terms of the superconductivity language it means an increased critical temperature of the curved film compared to its straight counterpart localized level dependence on the parameters of the curve is investigated with its energy decreasing with increasing bend angle and decreasing bend radius conditions of the bound state existence for the different robin parameters on the opposite edges are analyzed too in particular it is shown that the bound state below the first transverse threshold of the straight arm always exists if the inner extrapolation length is not larger than the outer one in the opposite case there is a range of the bend parameters where the curved film cannot trap the wave and form the localized mode for example for the fixed bend radius the bound state emerges from the continuum at some nonzero bend angle that depends on the difference of the two lengths lambda at the opposite interfaces various transport properties of the film such as interference blockade of the current flow at some special energies is also discussed with the special attention being paid to the transformation from the dirichlet to the neumann case as the extrapolation length lambda sweeps the positive axis

on gibbs sampling for state space models summary we show how to use the gibbs sampler to carry out bayesian inference on a linear state space model with errors that are a mixture of normals and coefficients that can switch over time our approach simultaneously generates the whole of the state vector given the mixture and coefficient indicator variables and simultaneously generates all the indicator variables conditional on the state vectors the states are generated efficiently using the kalman filter we illustrate our approach by several examples and empirically compare its performance to another gibbs sampler where the states are generated one at a time the empirical results suggest that our approach is both practical to implement and dominates the gibbs sampler that generates the states one at a time

higher dimensional inverse problem of the wave equation for a general multi connected bounded domain with a finite number of smooth mixed boundary conditions the spectral function m t j 1 exp it m j 1 2 where m j j 1 are the eigenvalues of the negative laplacian d 3 u 1 3 x u 2 in the x 1 x 2 x 3 space is studied for small t for a variety of bounded domains where

computing bayes factors by combining simulation and asymptotic approximations abstract the bayes factor is a ratio of two posterior normalizing constants which may be difficult to compute we compare several methods of estimating bayes factors when it is possible to simulate observations from the posterior distributions via markov chain monte carlo or other techniques the methods that we study are all easily applied without consideration of special features of the problem provided that each posterior distribution is well behaved in the sense of having a single dominant mode we consider a simulated version of laplace s method a simulated version of bartlett correction importance sampling and a reciprocal importance sampling technique we also introduce local volume corrections for each of these in addition we apply the bridge sampling method of meng and wong we find that a simulated version of laplace s method with local volume correction furnishes an accurate approximation that is especially useful when likelihood function evaluations are costly a simple bridge sampli

applications of numerical eigenfunctions in the fractal like finite element method the fractal like finite element method is an accurate and efficient method to determine the stress intensity factors sif around crack tips the use of a self similar mesh together with the william s eigenfunctions reduce the number of unknowns significantly the sifs are the primary unknowns and no post processing is required in all previous studies we used the analytic eigenfunction expression to perform the global transformation however the eigenfunction cannot be found analytically in general crack problems two dimensional axisymmetrical cracks are considered here the resulting static equilibrium equations in local co ordinates are non homogeneous ordinary differential equations for which the analytic eigenfunction cannot be found completely we use a finite difference method to determine all the eigenfunctions needed numerically our evaluated sif values show very close agreement with published results copyright 2004 john wiley sons ltd

a simple and efficient simulation smoother for state space time series analysis a simulation smoother in state space time series analysis is a procedure for drawing samples from the conditional distribution of state or disturbance vectors given the observations we present a new technique for this which is both simple and computationally efficient the treatment includes models with diffuse initial conditions and regression effects computational comparisons are made with the previous standard method two applications are provided to illustrate the use of the simulation smoother for gibbs sampling for bayesian inference and importance sampling for classical inference 2002 biometrika trust

eigenvalues of the laplacian for the third boundary values problem an extension to higher dimensions soit r a r b 0 0 2 une coque spherique on suppose connu exactement le spectre de valeurs propres 0 1 2 3 j quand j pour le probleme 3 u 0 dans u r 1 u r a 0 u r 2 u r b 0 ou 1 et 2 sont des constantes positives on determine la geometrie de et les impedances 1 et 2

trends and cycles in economic time series a bayesian approach trends and cyclical components in economic time series are modeled in a bayesian framework this enables prior notions about the duration of cycles to be used while the generalized class of stochastic cycles employed allows the possibility of relatively smooth cycles being extracted the posterior distributions of such underlying cycles can be very informative for policy makers particularly with regard to the size and direction of the output gap and potential turning points from the technical point of view a contribution is made in investigating the most appropriate prior distributions for the parameters in the cyclical components and in developing markov chain monte carlo methods for both univariate and multivariate models applications to us macroeconomic series are presented

singularp version finite elements for stress intensity factor computations the finite element analysis of linear elastic fracture mechanics problems is complicated by the presence of the singular and finite non singular stress distributions in the crack tip region the availability of a constant stress term in addition to the singular term in the standard h version singular finite elements is insufficient to model the finite nonsingular stress zone a p version singular finite element capable of modelling the higher order non singular stress terms in addition to the singular term and the constant term is presented the formulation for the displacement substitution technique for computing the stress intensity factors using singular p version triangular finite elements is developed unlike the standard h version formulation the stress intensity factors computed using the p version displacement substitution technique do not depend on the specific arrangement and length of the quarter point elements and require simple mesh designs as well as fewer number of degrees of freedom numerical studies comparing the convergence of the stress intensity factors computed by the p version method against other available alternatives such as the h version method and the contour integral method are presented to demonstrate the effectiveness of the present developments 1997 by john wiley sons ltd

hearing the shape of a general convex domain abstract the spectral function t j 1 exp t j where j j 1 are the eigenvalues of the laplace operator i 1 2 x i 2 in the x 1 x 2 plane is studied for a general convex domain together with an impedance condition on a part of its boundary and another impedance condition on the remaining part of that boundary

a state space formalism for piezothermoelasticity a state space formalism for electrothermoelastic analysis of a linear piezoelectric body is developed a novel feature of the formalism is that by proper grouping of the field variables and using matrix notations the three dimensional equations of piezothermoelasticity are concisely formulated into a state equation and an output equation which bear a striking resemblance to their elastic counterparts the formalism is remarkably simple with which one deals with only three vector quantities with the 13 independent electromechanical variables as their components and six submatrices that represent all the material constants for a piezoelectric material of the most general kind in this work emphasis is placed on the state space formulation and solution to the generalized plane problem exact solutions for a piezoelectric half space under a line of electromechanical loading and an infinite piezoelectric plate with an elliptical notch subjected to inplane loads are determined with relative ease in many cases piezoelectric solutions can be obtained directly from the corresponding elastic solutions by a simple replacement of the corresponding matrices on the basis of the formalism

vibration of symmetrically laminated rectangular plates considering deformation and rotatory inertia an analytical study was conducted using the galerkin technique to determine the natural frequencies and mode shapes for symmetrically laminated rectangular plates considering the effects of shear deformation and rotatory inertia two different graphite epoxy symmetric plates were used in the analysis and three different boundary conditions for each plate simply supported clamped and two opposite sides clamped two opposite sides simply supported were considered convergence characteristics comparison to classical results and the effects of length to thickness ratios were investigated the finding indicated that as the length to thickness ratios were reduced b h 3q for the first mode shear deformation effects significantly lowered the natural frequencies analysis also showed that rotatory inertia effects were very small convergence characteristics for all three boundary conditions were very good and excellent agreement with the classical solutions was achieved

meshless methods for shear deformable beams and plates abstract a meshless method is developed to analyze moderately thick and thin structures using mindlin reissner theory a uniform discretization is used to allow for efficient integration and for the shape functions to be written explicitly irregular boundaries are modeled in a straightforward manner an unmodified displacement based galerkin method is used full integration is used to evaluate all energy terms and convergence is independent of the thickness shear and membrane locking are completely eliminated pointwise at the interpolant level using cardinal splines the continuity of the splines chosen results in continuous stresses an extension to general meshless methods is given beam and plate examples show the accuracy of this method for coarse discretizations

static analysis of mindlin plates the differential quadrature element method dqem abstract the differential quadrature method dqm is a new numerical method for fast solving linear and nonlinear differential equations based on global basis functions in the present study a discrete approximate method based on the dqm the differential quadrature element method dqem is developed for the axisymmetric static analysis of moderately thick circular and annular plates described by the mindlin shear deformable theory the basic idea of the dqem is 1 to divide the whole variable domain into several sub domains elements 2 to form discretized element governing equations by applying the dqm to each element and 3 to assemble all the discretized element governing equations into the overall characteristic equations with the consideration of displacement and stress compatibility conditions between adjacent elements the annular and circular mindlin plate elements of differential quadrature dq are established the convergence characteristics of the proposed method are carefully investigated from the view points of element refinement and element grid refinement and some general regulations and suggestions on element division and element grid selection are provided a number of numerical examples are calculated and the results are compared with the corresponding exact solutions which exhibits high accuracy simplicity and applicability of the present method

on new symplectic elasticity approach for exact bending solutions of rectangular thin plates with two opposite sides simply supported abstract this paper presents a bridging research between a modeling methodology in quantum mechanics relativity and elasticity using the symplectic method commonly applied in quantum mechanics and relativity a new symplectic elasticity approach is developed for deriving exact analytical solutions to some basic problems in solid mechanics and elasticity which have long been bottlenecks in the history of elasticity in specific it is applied to bending of rectangular thin plates where exact solutions are hitherto unavailable it employs the hamiltonian principle with legendre s transformation analytical bending solutions could be obtained by eigenvalue analysis and expansion of eigenfunctions here bending analysis requires the solving of an eigenvalue equation unlike in classical mechanics where eigenvalue analysis is only required in vibration and buckling problems furthermore unlike the semi inverse approaches in classical plate analysis employed by timoshenko and others such as navier s solution levy s solution rayleigh ritz method etc where a trial deflection function is pre determined this new symplectic plate analysis is completely rational without any guess functions and yet it renders exact solutions beyond the scope of applicability of the semi inverse approaches in short the symplectic plate analysis developed in this paper presents a breakthrough in analytical mechanics in which an area previously unaccountable by timoshenko s plate theory and the likes has been trespassed here examples for plates with selected boundary conditions are solved and the exact solutions discussed comparison with the classical solutions shows excellent agreement as the derivation of this new approach is fundamental further research can be conducted not only on other types of boundary conditions but also for thick plates as well as vibration buckling wave propagation etc

the general solution of three dimensional problems in piezoelectric media abstract the governing equations of three dimensional problems in transversely isotropic piezo electric material are composed of four second order partial differential equations in which the displacement components and electric potential functions are the essential unknowns in this paper the so called general solutions of these equations are obtained with the aid of a set of new potential functions which are used to express the components of displacements and the electric potential functions as an application of the general solution the problem of a half space piezoelectrics acted by a concentrated lateral shear force is solved

vibration of shear deformable rectangular plates using a spline function rayleigh ritz approach the prediction of the natural frequencies of vibration of rectangular plates or orthotropic laminates is described through the use of b spline functions as trial functions in a rayleigh ritz approach through thickness shear deformation effects are included in the analysis and hence assumptions have to be made for the spatial variation over the plate middle surface of each of the lateral deflection and the two rotation components two versions of the spline function rayleigh ritz approach are described in one of these the deflection and rotations are represented by functions of the same polynomial order whilst in the other a lower order representation is used for each rotation component in one of the co ordinate directions it is shown in a number of applications that the former version leads to shear locking behaviour whilst the latter version avoids this behaviour and is suitable for the analysis of both thick and thin plates

on hearing the shape of rectilinear regions from complete knowledge of the eigenvalues of the negative laplacian on a bounded domain one may extract information on the geometry and the boundary conditions by analyzing the asymptotic expansion of a spectral function explicit calculations are performed for an equilateral triangular domain with dirichlet or neumann boundary conditions yielding in particular the corner angle terms in three dimensions some applications to eigenvalue problems for an equilateral triangular prism are dealt with including the solid vertex terms

an inverse problem of the wave equation for a general doubly connected region in r2 with a finite number of piecewise smooth robin boundary conditions the spectral distribution m t w 1 exp ite w 1 2 where e w w 1 are the eigenvalues of the negative laplacian d k 1 2 x k 2in the x 1 x 2 plane is studied for a variety of domains where 0

a semi analytical dqem for free vibration analysis of thick plates with two opposite edges simply supported this paper is introducing a semi analytical differential quadrature element method dqem based on first order shear deformation theory for free vibration analysis of thick plates by decomposing the plate into a series of sub domains or elements any discontinuity in geometry material properties and elastic foundations in one direction can be handled conveniently classical as well as non classical boundary conditions can be imposed one benefits of this semi analytical dqem is reducing the storage requirements and the computational efforts needed to assemble the global equations the method would also increase the computational efficiency in comparison with the finite element method fem or differential quadrature method dqm analysis of such problems the accuracy versatility stability and convergence of the algorithm are certified

vibration analysis of a thick plate with an interior cut out by a finite element method abstract plates with interior openings are often used in industrial design such as machines bridges aircraft etc many advantages can be obtained by this design such as reduced weight easy access for maintenance and an easy assembling process however when interior holes are cut from a plate structure the mechanical behavior of the structure is changed to avoid induced acoustic noise and or mechanical failure due to mechanical resonance vibration problems of such plate structures must be studied the work reported here is a study of the vibration of a plate with an interior cut out by a finite element method hamilton s variational principal and potential theory are used to derive the governing equations for a mindlin plate a quadratic element of eight nodes is used selective reduced integration is used for integration of the stiffness matrix the locking phenomenon is avoided by this particular integration technique eigenvalues and eigenvectors are calculated by subspace iteration computations are significantly reduced by this numerical technique results are compared with nagaya s work and good agreements are obtained

a finite element for variable order singularities based on the displacement formulation an element for analysis of variable order one point singularities in plane problems has been proposed the element meets all the convergence requirements viz the rigid body mode the constant strain condition and the interelement compatibility it can be easily incorporated in any package based on the displacement formulation four examples from fracture mechanics are presented to demonstrate its performance the examples involve mechanical or thermal loadings the accuracy of results in all the examples is very good

hamiltonian system based saint venant solutions for multi layered composite plane anisotropic plates this paper presents hamiltonian system based saint venant solutions for the problem of multi layered composite plane anisotropic plates a mixed energy variational principle is proposed and dual equations are derived in the symplectic space the schemes of separation of variables and eigenfunction expansion instead of the traditional semi inverse method are implemented and compatibility conditions at interfaces are formulated by dual variables by expending eigenfunctions in the subspace with zero eigenvalue an analytical solution of a cantilever composite plate is presented to illustrate the proposed approach

the boundary layer phenomena in two dimensional transversely isotropic piezoelectric media by exact symplectic expansion a separable variable method is introduced to find the exact homogeneous solutions of a two dimensional transversely isotropic piezoelectric media to handle general boundary conditions the usual method of separable variables for partial differentiation equations cannot be readily applicable due to the tangling of the unknowns and their derivatives introducing dual variables of stresses we obtain a set of first order hamiltonian equations whose eigensolutions are symplectic spanning over the solution space to cover all possible boundary conditions the solutions consist of two parts the first part is the derogative zero eigenvalue solutions of the saint venant type together with all their jordan chains the second part is the decaying non zero eigenvalue solutions describing the boundary layer effects the classical solutions are actually the zero eigenvalue solutions representing the simple extension bending equipotential field and the uniform electric displacement on the other hand the non zero eigenvalue solutions represent the localized solutions which are sensitive to the boundary conditions and are decaying rapidly with respect to the distance from the boundaries some rate of decay curves of the newly found non zero eigenvalue solutions are shown by numerical examples finally the complete boundary layer effects are quantified for the first time

completeness and nonuniqueness ofgeneral solutions of transversely isotropic elasticity abstract in this paper we give general solutions of transversely isotropic elasticity their completenessand nonuniqueness are proved we point out that famous lekhnitskii hu nowacki solutions and elliott lodge solutions are complete if the elastic region is z convex

super singular element method for two dimensional crack analysis super singular element method ssem is an accurate method devoted to stress singularity analysis accomplished by stress analysts who have little or no experience of fracture mechanics the basic i

testing for integration using evolving trend and seasonals models a bayesian approach in this paper we make use of state space models to investigate the presence of stochastic trends in economic time series a model is specified where such a trend can enter either in the autoregressive representation or in a separate state equation tests based on the former are analogous to dickey fuller tests of unit roots while the latter are analogous to kpss tests of trend stationarity we use bayesian methods to survey the properties of the likelihood function in such models and to calculate posterior odds ratios comparing models with and without stochastic trends we extend these ideas to the problem of testing for integration at seasonal frequencies and show how our techniques can be used to carry out bayesian variants of either the hegy or canova hansen test stochastic integration rules based on markov chain monte carlo as well as deterministic integration rules are used strengths and weaknesses of each approach are indicated

an inverse eigenvalue problem for a general convex domain the underlying problem is to deduce the precise shape of a membrane from the complete knowledge of the eigenvalues i for the lapace operator a cf a ax in the x1x2 plane let d g r be a simply connected bounded domain with a smooth boundary ad let us suppose that the a are the eigenvalues of the impedance problem au k o in d

bayes regression with autoregressive errors a gibbs sampling approach abstract this paper develops a practical framework for the bayesian analysis of gaussian and student t regression models with autocorrelated errors as is customary in classical estimation procedures the posteriors are conditioned on the initial observations recourse is taken to the method of gibbs sampling an iterative markovian sampling method and it is shown that the proposed approach can readily deal with high order autoregressive processes without requiring an importance sampling function or other tuning constants several examples including one with ar 4 errors are used to illustrate the ideas

an inverse problem for a general vibrating annular membrane in r3 with its physical applications further results this paper deals with the very interesting problem about the influence of the boundary conditions on the distribution of the eigenvalues of the negative laplacian in r 3 the trace of the heat semigroup q t email protected v 1 exp email protected v where m v v 1 are the eigenvalues of the negative laplacian email protected email protected b 1 email protected x b 2 in the x 1 x 2 x 3 space is studied for short time t for a general vibrating annular membrane w in r 3 together with its smooth inner bounding surface s 1 and its smooth outer bounding surface s 2 where a finite number of dirichlet neumann and robin boundary conditions on the piecewise smooth components s i i 1 m of s 1 and on the piecewise smooth components s i i m 1 n of s 2 is considered such that s email protected i 1 ms i and s email protected i m 1 ns i in this paper one may extract information on the geometry of w by analyzing the asymptotic expansions of q t for short time t some applications of q t for an ideal gas enclosed in the general vibrating annular membrane w are given we show that the asymptotic expansion of q t for short time t plays an important role in investigating the influence of the annular region w on the thermodynamic quantities of an ideal gas some applications of q t for an ideal gas enclosed in a compact n dimensional riemannian manifold are also given we show that the ideal gas cannot feel the shape of its container although it can feel some geometrical properties of it

an inverse problem for the three dimensional multi connected vibrating membrane with robin boundary conditions this paper deals with the very interesting problem about the influence of the boundary conditions on the distribution of the eigenvalues of the negative laplacian in r 3 the trace of the heat semigroup q t n 1exp t m n where m n n 1 are the eigenvalues of the negative laplacian 2 3 b 1 x b 2 in the x 1 x 2 x 3 space is studied for a general multiply connected bounded domain w in r 3 surrounded by simply connected bounded domains w j with smooth bounding surfaces s j j 1 n where a finite number of piecewise smooth robin boundary conditions on the piecewise smooth components s i i 1 k j 1 k j of the bounding surfaces s j are considered such that s j k j i 1 k j 1s i where k 0 0 some applications of q t for an ideal gas enclosed in the multiply connected bounded container w with robin boundary conditions are given we show that the asymptotic expansion of q t for short time t plays an important role in investigating the influence of the finite container w on the thermodynamic quantities of an ideal gas

dynamic analysis of frames by a two level finite element method abstract a two level finite element technique of constructing a frame super element is introduced to reduce the computational efforts for solving large scale frame problems the ordinary finite element method is used first to yield matrices for the beam members then the nodal displacements of all the nodes are related to those of a small number of selected joints master nodes in the frame by means of global finite element interpolating functions thus the order of the overall matrices is greatly reduced and the frame may be considered as a super element to be connected to other elements by means of the master nodes the accuracy of solution may be improved either with finer subdivision or by taking more master nodes inside each super element

higher dimensional inverse problem for a multi connected bounded domain with piecewise smooth robin boundary conditions and its physical applications the asymptotic expansions of the trace of the heat kernel q t email protected j 1 exp email protected j for short time t have been derived for a variety of bounded domains where l j j 1 are the eigenvalues of the negative laplace operator email protected email protected i 1 3 x i 2 in the x 1 x 2 x 3 space the dependence of q t on the connectivity of bounded domains and the boundary conditions is analyzed particular attention is given for an arbitrary multiply connected bounded domain w in r 3 together with piecewise smooth robin boundary conditions where the coefficients in these conditions are assumed to be piecewise smooth positive functions some applications of an ideal gas enclosed in the multiply connected bounded domain w are given we show that the ideal gas cannot feel the shape of its container although it can feel some geometrical properties of it

solutions for transversely isotropic piezoelectric infinite body semi infinite body and bimaterial infinite body subjected to uniform ring loading and charge abstract based on the fundamental solutions for transversely isotropic piezoelectric materials the fundamental solutions of axisymmetric problems are derived by integration and explicit expressions for three possible cases of different characteristic roots and multiple roots are all presented in the case of s 1 s 2 s 3 s 1 based on the greens functions for semi infinite piezoelectric body and bimaterial infinite piezoelectric body the greens functions for axisymmetric problems of semi infinite body and bimaterial infinite body are obtained taking pzt 4 as an example numerical computations are conducted by use of the fundamental solutions to axisymmetric problems comparison of the calculated results with those of fem shows good agreement between them

general solutions for coupled equations for piezoelectric media abstract three general solutions are obtained for the coupled dynamic equations for a transversely isotropic piezoelectric medium these solutions are expressed in terms of the two functions and f where satisfies a second degree partial differential equation and f a sixth degree partial differential equation respectively if the terms concerning the derivatives of time are removed the results become three general solutions for the corresponding equilibrium equations in which the function f can be represented by functions fi i 1 2 3 each of which satisfies a second degree partial differential equation by utilizing a generalized almansi theorem and the solution wang and zheng int j solids structures32 105 115 1995 obtained is proved to be consistent with one case of one of the three general solutions when the constants e15 e31 e33 0 the piezo electric coupling is absent then two of the solutions reduce to the elasticity general solutions for a transversely isotropie medium one of which is the result hu acta scientia sin 2 2 145 151 1953 obtained the other one has not been published last the solution in the limiting explicit form for the problem for a half space with concentrated loads at the boundary is obtained by utilizing the general solutions

three dimensional eigenfunction analysis of a crack in a piezoelectric material abstract a three dimensional analysis of a semi infinite crack embedded in a transversely isotropic piezoelectric material was performed by means of the eigenfunction expansions method the results show the characteristic 1 r singular behavior of the stress tensor in the vicinity of the crack a similar behavior is also revealed for the electric field in addition the study demonstrates that coupling or decoupling of the mechanical and electrical variables is a function of the distance to the crack tip as well as of the crack orientation

free vibration analysis of mindlin plates with linearly varying thickness abstract a method based on the variational principles in conjunction with the finite difference technique is applied to examine the free vibration characteristics of isotropic rectangular plates of linearly varying thickness by including the effects of transverse shear deformation and rotary inertia the validity of the present approach is demonstrated by comparing the results with other solutions proposed for plates with uniform and linearly varying thickness natural frequencies and mode shapes of mindlin plates with simply supported and clamped edges are determined for various values of relative thickness ratio and the taper thickness constant

bayesian non parametric signal extraction for gaussian time series abstract we consider the problem of unobserved components in time series from a bayesian non parametric perspective the identification conditions are treated as unknown and analyzed in a probabilistic framework in particular informative prior distributions force the spectral decomposition to be in an identifiable region then the likelihood function adapts the prior decompositions to the data a full bayesian analysis of unobserved components will be presented for financial high frequency data particularly a three component model long term intra daily and short term will be analyzed to emphasize the importance and the potential of this work when dealing with the value at risk analysis a second astronomical application will show how to deal with multiple periodicities

an exact symplectic geometry solution for the static and dynamic analysis of reissner plates from the mixed variational principle by selection of the variables and its dual variables the hamiltonian canonical equation for the statics and dynamics analysis of reissner plates is derived so it leads the problem to the mathematical frame of symplectic geometry and its algorithms and the exact solution for the arbitary boundary conditions is also derived by the adjoint ortho normalized symplectic expansion method

the wave equation approach to an inverse problem for a general multi connected domain in r2 with mixed boundary conditions the spectral function email protected t email protected j 1 exp email protected j 1 2 where m j j 1 are the eigenvalues of the negative laplacian email protected email protected u 1 email protected x u 2 in r 2 is studied for small t for a variety of domains where

hearing the shape of a general doubly connected domain in r3 with impedance boundary conditions the basic problem in this paper is that of determining the geometry of a general doubly connected domain in r3 together with an impedance condition on its inner bounding surface and another impedance condition on its outer bounding surface from the complete knowledge of the eigenvalues j j 1 for the three dimensional laplacian using the asymptotic expansion of the spectral function t j 1 exp t j for small positive t

buckling and vibration of laminated composite plates using various plate theories analytical and finite element solutions of the classical first order and third order laminate theories are developed to study the buckling and free vibration behavior of cross ply rectangular composite laminates under various boundary conditions

bayesian estimation of an extended local scale stochastic volatility model a new version of the local scale model of shephard 1994 is presented its features are identically distributed evolution equation disturbances the incorporation of in the mean effects and the incorporation of variance regressors a bayesian posterior simulator and a new simulation smoother are presented the model is applied to publicly available daily exchange rate and asset return series and is compared with t garch and lognormal stochastic volatility formulations using bayes factors

the simulation smoother for time series models summary recently suggested procedures for simulating from the posterior density of states given a gaussian state space time series are refined and extended we introduce and study the simulation smoother which draws from the multivariate posterior distribution of the disturbances of the model so avoiding the degeneracies inherent in state samplers the technique is important in gibbs sampling with non gaussian time series models and for performing bayesian analysis of gaussian time series