effect of boundary constraint on the frequency response of moderately thick doubly curved cross ply panels using mixed fourier solution functions abstract a hitherto unavailable analytical solution to the boundary value problem of free vibration response of shear flexible cross ply laminated doubly curved panels is presented the laminated shell theory formulation is based on the first order shear deformation theory fsdt including rotatory and surface parallel inertias the governing equations of the panel are defined by five highly coupled partial differential equations in five unknowns three displacements and two rotations the assumed solution functions for the eigen boundary value problem are selected in terms of mixed type double fourier series extensive numerical results that are presented in this study include 1 convergence characteristics of computed natural frequencies and 2 effects of length to thickness ratio radius to length ratio lamination sequence boundary constraint and shell geometry on the normalized natural frequencies of interest also numerically investigated is the highly complex interaction among bending stretching type coupling effect membrane action due to shell curvature surface parallel end constraints or lack thereof and the effects of transverse shear deformation rotatory inertias and surface parallel inertias

bayesian nonlinear model selection and neural networks a conjugate prior approach in order to select the best predictive neural network architecture in a set of several candidate networks we propose a general bayesian nonlinear regression model comparison procedure based on the maximization of an expected utility criterion this criterion selects the model under which the training set achieves the highest level of internal consistency through the predictive probability distribution of each model the density of this distribution is computed as the model posterior predictive density and is asymptotically approximated from the assumed gaussian likelihood of the data set and the related conjugate prior density of the parameters the use of such a conjugate prior allows the analytic calculation of the parameter posterior and predictive posterior densities in an empirical bayes like approach this bayesian selection procedure allows us to compare general nonlinear regression models and in particular feedforward neural networks in addition to embedded models as usual with asymptotic comparison tests

heuristics of instability and stabilization in model selection in model selection usually a best predictor is chosen from a collection hat mu cdot s of predictors where hat mu cdot s is the minimum least squares predictor in a collection mathsf u s of predictors here s is a complexity parameter that is the smaller s the lower dimensional smoother the models in mathsf u s if mathsf l is the data used to derive the sequence hat mu cdot s the procedure is called unstable if a small change in mathsf l can cause large changes in hat mu cdot s with a crystal ball one could pick the predictor in hat mu cdot s having minimum prediction error without prescience one uses test sets cross validation and so forth the difference in prediction error between the crystal ball selection and the statistician s choice we call predictive loss for an unstable procedure the predictive loss is large this is shown by some analytics in a simple case and by simulation results in a more complex comparison of four different linear regression methods unstable procedures can be stabilized by perturbing the data getting a new predictor sequence hat mu cdot s and then averaging over many such predictor sequences

approximate elasticity solution for laminated anisotropic finite cylinders this paper deals with the static response of the axisymmetric problem of arbitrarily laminated anisotropic cylindrical shells of finite length using three dimensional elasticity equations the closed cylinder is simply supported at both ends the highly coupled partial differential equations pdes are reduced to ordinary differential equations odes with variable coefficients by choosing the solution composed of trigonometric functions along the axial direction through dividing each layer into thin laminas the variable coefficients in odes become constants and the resulting equations can be solved exactly numerical examples are presented for 45 0 deg and 45 457 45 deg laminations under sinusoidal normal loading on the outer surface and uniform internal pressure from the present study it is found that although the general behavior is similar to that of isotropic shells the coupling is obvious in general and the shear effect is very important in the edge region moreover the initial curvature effect plays an essential role especially in stress distributions tatic and dynamic responses of composite laminated closed cylindrical shells and curved panels have received wide attention in recent years because of the anisotropy in composites and the presence of curvature in shell structures obtaining exact three dimensional elasticity solutions for lami nated closed cylinders and open panels subjected to general loading and arbitrary boundary conditions becomes a chal lenging task the mathematical complexity in analyzing three dimensional elasticity equations usually makes exact solutions difficult to obtain however certain problems in which a three dimensional approach can be used still exist most of these problems can be solved by assuming the solution to be composed of trigonometric functions in the axial and circumferential directions the main reason is that the partial differential equations pdes governing three di mensional problems can be reduced to one dimension al ordi nary differential equations odes with variable coefficients the solution for the resulting odes can be obtained by intro ducing the displacement potential function usually this method is used with isotropic and transversely isotropic mate rials whereas the frobenius method is used with orthotropic materials when the three dimensional elasticity solutions are available they are very useful in evaluating the accuracy of approximate results e g in the case of two dimensional shell theories for the static problem flugge and kelkar1 and yao2 ob tained an exact solution for closed isotropic long cylinders under general two dimensional surface traction using the frobenius method srinivas3 developed an exact three dimen sional solution for orthotropic finite cylinders with simply supported conditions however the numerical results are given for free vibration only varadan and bhaskar4 also performed the static stress analysis using the procedures pro posed by srinivas pagano5 obtained the stress field for a homogeneous anisotropic closed cylinder under two dimen sional surface loads in which the problems are independent of the axial coordinate however numerical results are reported only for a single orthotropic layer recently ren6 7 presented an exact solution for simply supported laminated cross ply circular cylindrical panels of infinite and finite length in the

feature selection using a piecewise linear network we present an efficient feature selection algorithm for the general regression problem which utilizes a piecewise linear orthonormal least squares ols procedure the algorithm 1 determines an appropriate piecewise linear network pln model for the given data set 2 applies the ols procedure to the pln model and 3 searches for useful feature subsets using a floating search algorithm the floating search prevents the nesting effect the proposed algorithm is computationally very efficient because only one data pass is required several examples are given to demonstrate the effectiveness of the proposed algorithm

a nine node assumed strain finite element for large deformation analysis of laminated shells an application of the element based lagrangian formulation is described for large deformation analysis of both single layered and laminated shells natural co ordinate based stresses strains and constitutive equations are used throughout the formulation of the present shell element which offers significant implementation advantages compared with the traditional lagrangian formulation in order to avoid locking phenomena an assumed strain method has been employed with judicious selection of the sampling points three strictly successive finite rotations are used to represent the current orientation of the shell normal the equivalent natural constitutive equation is derived using an explicit transformation scheme to consider the multi layer effect of laminated structures the arc length control method is used to trace complex load displacement paths several numerical analyses are presented and discussed in order to investigate the capabilities of the present shell element 1998 john wiley sons ltd

mlps mono layer polynomials and multi layer perceptrons for nonlinear modeling this paper presents a model selection procedure which stresses the importance of the classic polynomial models as tools for evaluating the complexity of a given modeling problem and for removing non significant input variables if the complexity of the problem makes a neural network necessary the selection among neural candidates can be performed in two phases in an additive phase the most important one candidate neural networks with an increasing number of hidden neurons are trained the addition of hidden neurons is stopped when the effect of the round off errors becomes significant so that for instance confidence intervals cannot be accurately estimated this phase leads to a set of approved candidate networks in a subsequent subtractive phase a selection among approved networks is performed using statistical fisher tests the series of tests starts from a possibly too large unbiased network the full network and ends with the smallest unbiased network whose input variables and hidden neurons all have a significant contribution to the regression estimate this method was successfully tested against the real world regression problems proposed at the nips2000 unlabeled data supervised learning competition two of them are included here as illustrative examples

growth of primary decompositions of frobenius powers of ideals abstract it was previously known by work of smith swanson and of sharp nossem that the linear growth property of primary decompositions of frobenius powers of ideals in rings of prime characteristic has strong connections to the localization problem in tight closure theory the localization problem has recently been settled in negative by brenner and monsky but the linear growth question is still open we study growth of primary decompositions of frobenius powers of dimension one homogeneous ideals in graded rings over fields if the ring is positively graded we prove that the linear growth property holds for non negatively graded rings we are able to show that there is a polynomial growth we present explicit primary decompositions of frobenius powers of an ideal which were known to have infinitely many associated primes having this linear growth property we also discuss some other interesting examples

on cross validation for model selection in response to zhu and rower 1996 a recent communication goutte 1997 established that leave one out cross validation is not subject to the no free lunch criticism despite this optimistic conclusion we show here that cross validation has very poor performances for the selection of linear models as compared to classic statistical tests we conclude that the statistical tests are preferable to cross validation for linear as well as for nonlinear model selection

on the roles of complementary and admissible boundary constraints in fourier solutions to the boundary value problems of completely coupled r th order pdes abstract a heretofore unavailable double fourier series based approach for obtaining non separable solution to a system of completely coupled linear r th order partial differential equations with constant coefficients and subjected to general completely coupled boundary conditions has been presented the method has been successfully implemented to solve a class of hitherto unsolved boundary value problems pertaining to free and forced vibrations of arbitrarily laminated anisotropic doubly curved thin panels of rectangular planform with arbitrarily prescribed both symmetric and asymmetric with respect to the panel centerlines admissible boundary conditions and subjected to general transverse loading existing solutions such as those due to navier or levy are based on the well known method of separation of variables such solutions represent particular solutions whenever the method of separation of variables work and when these particular solution functions fortuitously satisfy the boundary conditions for derivation of the complementary solution the complementary boundary constraints are introduced through boundary discontinuities of some of the particular solution functions and their partial derivatives such discontinuities form sets of measure zero various cases of lamination geometry and dynamic response forced and free vibrations of a class of thin anisotropic laminated shells curved panels have been shown to follow from the above six sets of boundary conditions are used to illustrate the present method for the derivation of complementary solutions navier type solutions whenever available form special cases of the present general solution

local overfitting control via leverages we present a novel approach to dealing with overfitting in black box models it is based on the leverages of the samples that is on the influence that each observation has on the parameters of the model since overfitting is the consequence of the model specializing on specific data points during training we present a selection method for nonlinear models based on the estimation of leverages and confidence intervals it allows both the selection among various models of equivalent complexities corresponding to different minima of the cost function e g neural nets with the same number of hidden units and the selection among models having different complexities e g neural nets with different numbers of hidden units a complete model selection methodology is derived

an efficient through thickness integration scheme in an unlimited layer doubly curved isoparametric composite shell element this paper presents an efficient numerical integration scheme for evaluating the matrices stiffness mass stress stiffness and thermal load for a doubly curved multilayered composite quadrilateral shell finite element the element formulation is based on three dimensional continuum mechanics theory and it is applicable to the analysis of thin and moderately thick composite shells the conventional formulation requires a 2 2 2 or 2 2 1 gauss integration per layer for the calculation of element matrices this method becomes uneconomical when a large number of layers is used owing to an excessive amount of computations the present formulation is based on explicit separation of the thickness variable from the shell surface parallel variables with the through thickness variables separated they are combined with the thickness dependent material properties and integrated separately the element matrices are computed using the integrated material matrices and only a 2 2 spatial gauss integration scheme the response results using the present formulation are identical to those obtained using the conventional formulation for a small number of layers the present method requires slightly more cpu time however for a larger number of layers numerical data are presented to demonstrate that the present formulation is an order of magnitude economical compared to the conventional scheme

frequency response of a moderately thick antisymmetric cross ply cylindrical panel using mixed type of fourier solution functions abstract a hitherto unavailable analytical solution to the boundary value problem of the free vibration response of shear flexible antisymmetric cross ply laminated cylindrical panels is presented the laminated shell theory formulation is based on the first order shear deformation theory fsdt including rotatory and surface parallel inertias the governing equations of the panel are defined by five highly coupled partial differential equations in five unknowns three displacements and two rotations the assumed solution functions for the eigen boundary value problem are selected in terms of mixed type double fourier series numerical results presented for parametric effects such as length to thickness ratio and radius to thickness ratio should serve as a bench mark for future comparison a four node shear flexible finite element is selected to compare the results with the present solution

bass numbers of local cohomology modules let a be a regular local ring of positive characteristic this paper is concerned with the local cohomology modules of a itself but with respect to an arbitrary ideal of a the results include that all the bass numbers of all such local cohomology modules are finite that each such local cohomology module has finite set of associated prime ideals and that whenever such a local cohomology module is artinian then it must be injective this last result had been proved earlier by hartshorne and speiser under the additional assumptions that a is complete and contains its residue field which is perfect the paper ends with some low dimensional evidence related to questions about whether the analogous statements for regular local rings of characteristic 0 are true

feature selection via coalitional game theory we present and study the contribution selection algorithm csa a novel algorithm for feature selection the algorithm is based on the multiperturbation shapley analysis msa a framework that relies on game theory to estimate usefulness the algorithm iteratively estimates the usefulness of features and selects them accordingly using either forward selection or backward elimination it can optimize various performance measures over unseen data such as accuracy balanced error rate and area under receiver operator characteristic curve empirical comparison with several other existing feature selection methods shows that the backward elimination variant of csa leads to the most accurate classification results on an array of data sets

a practical bayesian framework for backpropagation networks a quantitative and practical bayesian framework is described for learning of mappings in feedforward networks the framework makes possible 1 objective comparisons between solutions using alternative network architectures 2 objective stopping rules for network pruning or growing procedures 3 objective choice of magnitude and type of weight decay terms or additive regularizers for penalizing large weights etc 4 a measure of the effective number of well determined parameters in a model 5 quantified estimates of the error bars on network parameters and on network output and 6 objective comparisons with alternative learning and interpolation models such as splines and radial basis functions the bayesian evidence automatically embodies occam s razor penalizing overflexible and overcomplex models the bayesian approach helps detect poor underlying assumptions in learning models for learning models well matched to a problem a good correlation between generalization ability and the bayesian evidence is obtained

on the prediction of interlaminar shear stresses in a thick laminated general shell abstract a post processing semi analytical approach for prediction of the interlaminar shear stress distribution through the thickness of an arbitrarily laminated general shell is presented the starting point of the approach is an assumed displacement finite element analysis based on the assumptions of transverse inextensibility and layerwise constant shear angle theory lcst first the problem is posed in the context of taylor series expansions of the interlaminar shear stresses in terms of the thickness coordinate dictated by the lcst assumption and the shell curvature an exact in the context of the problem thus posed and three progressively approximate semi analytical methods for prediction of interlaminar shear stresses are then presented the throughthickness distribution of interlaminar shear stresses in an arbitrarily laminated thick plate can be obtained as a special case of the present solution numerical results are presented for two layer thin and thick tubes with simply supported edges using the cartesian like local riemann coordinate clrc approximation and are compared to the corresponding analytical solutions based on the classical lamination theory clt results for thin laminated tubes prove the accuracy of the present approach while hitherto unavailable results for a thick laminated tube are expected to serve as baseline solutions for future comparisons

model selection and validation methods for non linear systems the theory of hypothesis testing is used to select a model with the correct structure and the relation of such a method to the aic and fpe criteria is investigated parametric validation and correlation validation methods are developed for non non linear difference equation models several shortcomings of traditional methods especially when applied to non linear systems are described

local cohomology of frobenius images over graded affine algebras abstract we study the problem of bounding the exponent needed to annihilate h0m r i q where r is a characteristic p ring the main result is for the case where r is a finitely generated graded algebra over a field and it has applications in tight closure theory

sensitivity of the response of moderately thick cross ply doubly curved panels to lamination and boundary constraint i theory abstract hitherto unavailable analytical solutions to the boundary value problem of moderately thick general cross ply laminated doubly curved panels of rectangular planform subjected to various boundary conditions are presented the five highly coupled second order linear partial differential equations that characterize the deformation of such laminates are solved in part i of the paper using a recently developed double fourier series based approach together with the ss1 ss2 and ss4 types of simply supported and c4 type of clamped boundary conditions prescribed at all four edges the issues of derivation of the linear algebraic equations arising from these boundary conditions together with an efficient method of solving the complete system of linear algebraic equations convergence characteristics and other numerical results are addressed in the accompanying part ii of this investigation

fourier solution to higher order theory based laminated shell boundary value problem a complete i e particular as well as complementary fourier solution to the boundary value problem of static response under transverse load of a general cross ply thick doubly curved panel of rectangular planform is presented a boundary discontinuous double fourier series approach is used to solve a system of five partial differential equations generated by a higher order shear deformation theory based shell analysis with the ss2 type of simply supported boundary condition prescribed at all four edges unlike the conventional navier and levy type approaches which can only provide particular solutions the present method is general enough to provide the complete particular as well as the complementary solution for any arbitrary combination of admissible boundary conditions with almost equal ease the numerical accuracy of the solution is ascertained by studying the convergence characteristics of deflections and moments of cross ply spherical panels and also by comparison with the available first order shear deformation theory and classical lamination theory based analytical solutions hitherto unavailable important numerical results presented include sensitivity of the predicted response quantities of interest to lamination boundary constraint and thickness and curvature effects as well as their interactions

neural network uncertainty assessment using bayesian statistics a remote sensing application neural network nn techniques have proved successful for many regression problems in particular for remote sensing however uncertainty estimates are rarely provided in this article a bayesian technique to evaluate uncertainties of the nn parameters i e synaptic weights is first presented in contrast to more traditional approaches based on point estimation of the nn weights we assess uncertainties on such estimates to monitor the robustness of the nn model these theoretical developments are illustrated by applying them to the problem of retrieving surface skin temperature microwave surface emissivities and integrated water vapor content from a combined analysis of satellite microwave and infrared observations over land the weight uncertainty estimates are then used to compute analytically the uncertainties in the network outputs i e error bars and correlation structure of these errors such quantities are very important for evaluating any application of an nn model the uncertainties on the nn jacobians are then considered in the third part of this article used for regression fitting nn models can be used effectively to represent highly nonlinear multivariate functions in this situation most emphasis is put on estimating the output errors but almost no attention has been given to errors associated with the internal structure of the regression model the complex structure of dependency inside the nn is the essence of the model and assessing its quality coherency and physical character makes all the difference between a blackbox model with small output errors and a reliable robust and physically coherent model such dependency structures are described to the first order by the nn jacobians they indicate the sensitivity of one output with respect to the inputs of the model for given input data we use a monte carlo integration procedure to estimate the robustness of the nn jacobians a regularization strategy based on principal component analysis is proposed to suppress the multicollinearities in order to make these jacobians robust and physically meaningful

refined shear deformation models for composite laminates with finite rotations abstract for arbitrary multilayered shell structures made particularly of composite material layers a refined finite rotation theory with seven independent displacement variables is developed approximating the displacement field by a cubic series expansion of thickness coordinates this model allows a quadratic shear deformation distribution across the thickness procedures are given permitting a unique determination of the first order displacement term in the case of finite rotations kinematic relations are formulated in two alternative forms suitable for both classical and isoparametric finite element formulations the constitutive relations presented model orthotropic material properties varying arbitrarily across the thickness this third order single layer theory is then transformed by introducing further constraints into three simplified models a third order theory with five independent displacement variables a mindlin reissner type theory and a kirchhoff love type theory these four models differ however from each other essentially in the constraints imposed on the first and third order displacement variables a significant advantage for a unified finite element development finally the mindlin reissner type theory is generalized to a layer wise model being the most predictive one in dealing with local interlaminar effects the theoretical models are transformed into adequate finite shell elements and then compared by means of appropriate examples concerning their prediction capability also examples are given demonstrating their applicability to finite rotation phenomena

jacobian conditioning analysis for model validation our aim is to stress the importance of jacobian matrix conditioning for model validation wealso comment on monari and dreyfus 2002 where following rivals and personnaz 2000 it is proposed to discard neural candidates that are likely to overfit and or for which quantities of interest such as confidence intervals cannot be computed accurately in rivals and personnaz 2000 we argued that such models are to be discarded on the basis of the condition number of their jacobian matrix but monari and dreyfus 2002 suggest making the decision on the basis of the computed values of the leverages the diagonal elements of the projection matrix on the range of the jacobian or hat matrix they propose to discard a model if computed leverages are outside some theoretical bounds pretending that it is the symptom of the jacobian rank deficiency we question this proposition because theoretically the hat matrix is defined whatever the rank of the jacobian and because in practice the computed leverages of very ill conditioned networks may respect their theoretical bounds while confidence intervals cannot be estimated accurately enough two facts that have escaped monari and dreyfus s attention wealso recall the most accurate way to estimate the leverages and the properties of these estimations finally we make an additional comment concerning the performance estimation in monari and dreyfus 2002

static analysis of moderately thick finite antisymmetric angle ply cylindrical panels and shells abstract the analytical exact in the limit or strong or differential form of solutions to the bench mark problems of i axisymmetric angle ply circular cylindrical panels of rectangular planform and ii circumferentially complete circular cylindrical shells subjected to transverse load and with ss2 type simply supported boundary conditions prescribed at the edges are presented the problems investigated which were hitherto thought to be incapable of admitting analytical solutions have been solved utilizing a recently developed novel boundary discontinuous double fourier series approach for three kinematic relations which are extensions of those due to sanders love and donnell to the first order shear deformation theory fsdt numerical results presented for two layer square antisymmetric angle ply panels which demonstrate good convergence and show the effects of fiber orientation and thickness on the static response of these panels should serve as baseline solutions in the context of fsdt for future comparison with various approximate weak forms of solutions with either local e g finite element methods or global supports e g raleigh ritz galerkin

an approximate method for prediction of transverse shear stresses in a laminated shell abstract a method has been presented wherein the surface parallel stresses in a laminated shell are first computed using standard finite element formulation and then approximate transverse shear stress variation through the shell thickness is obtained utilizing the first two stress equations of equilibrium and divergence theorem numerical results have been presented for both homogeneous isotropic and laminated anisotropic cylindrical shells using the cartesian like riemann coordinate approximation and compared to the corresponding analytical solutions

orthogonal least squares methods and their application to non linear system identification abstract identification algorithms based on the well known linear least squares methods of gaussian elimination cholesky decomposition classical gram schmidt modified gram schmidt householder transformation givens method and singular value decomposition are reviewed the classical gram schmidt modified gram schmidt and householder transformation algorithms are then extended to combine structure determination or which terms to include in the model and parameter estimation in a very simple and efficient manner for a class of multivariate discrete time non linear stochastic systems which are linear in the parameters

ideals in a perfect closure linear growth of primary decompositions and tight closure this paper is concerned with tight closure in a commutative noetherian ring r of prime characteristic p and is motivated by an argument of k e smith and i swanson that shows that if the sequence of frobenius powers of a proper ideal a of r has linear growth of primary decompositions then tight closure of a commutes with localization at the powers of a single element it is shown in this paper that provided r has a weak test element linear growth of primary decompositions for other sequences of ideals of r that approximate in a certain sense the sequence of frobenius powers of a would not only be just as good in this context but in the presence of a certain additional finiteness property would actually imply that tight closure of a commutes with localization at an arbitrary multiplicatively closed subset of r work of m katzman on the localization problem for tight closure raised the question as to whether the union of the associated primes of the tight closures of the frobenius powers of a has only finitely many maximal members this paper develops through a careful analysis of the ideal theory of the perfect closure of r strategies for showing that tight closure of a specified ideal a of r commutes with localization at an arbitrary multiplicatively closed subset of r and for showing that the union of the associated primes of the tight closures of the frobenius powers of a is actually a finite set several applications of the strategies are presented in most of them it was already known that tight closure commutes with localization but the resulting affirmative answers to katzman s question in the various situations considered are believed to be new

ranking a random feature for variable and feature selection we describe a feature selection method that can be applied directly to models that are linear with respect to their parameters and indirectly to others it is independent of the target machine it is closely related to classical statistical hypothesis tests but it is more intuitive hence more suitable for use by engineers who are not statistics experts furthermore some assumptions of classical tests are relaxed the method has been used successfully in a number of applications that are briefly described

triangular finite element for analysis of thick laminated plates the development of a general triangular c0 element based on an assumed quadratic displacement potential energy approach is presented for the analysis of arbitrarily laminated thick plates the element formulation assumes transverse inextensibility and layerwise constant shear angle convergence of transverse displacement moments and stresses the effects of two different gauss quadrature schemes and comparison of the present solutions with the available analytical finite element results also form a part of the investigation furthermore numerical results indicate close agreement between the lcst layerwise constant shear angle theory and the three dimensional elasticity theory with the length or width to thickness ratio as low as 4 detailed comparison of the lcst based finite element solutions with those based on the cst constant shear angle theory and the clt classical lamination theory clearly demonstrates the superiority of the former over the latter two especially in the prediction of the distribution of the in plane displacements and stresses through the laminate thickness this paper also introduces a new non dimensionalized parameter which is shown to be a very useful measure for classification of the laminated plates and the suitability of different plate theories over various ranges of length to thickness ratio

levy type boundary fourier analysis of thick cross ply panels with negative gaussian curvature a boundary discontinuous generalized double fourier series based solution to the problem of deformation of a finite dimensional general cross ply thick doubly curved panel with negative gaussian curvature and of rectangular planform modeled using a higher order shear deformation theory is presented this spectral method is used to solve a system of five highly coupled linear partial differential equations generated by the higher order shear deformation theory based laminated shell analysis with the simply supported of type 2 boundary condition prescribed on two opposite edges whereas the remaining two edges are subjected to the simply supported of type 3 constraint the hitherto unavailable important numerical results presented include sensitivity of the predicted response quantities of interest to shell geometry negative or positive gaussian curvature lamination and thickness effects as well as their interactions

levy type boundary fourier analysis of thick clamped hyperbolic paraboloidal cross ply panels an analytical solution to the problem of deformation of a finite dimensional general cross ply thick doubly curved panel with negative gaussian curvature and of rectangular planform modeled using a higher order shear deformation theory is presented a solution methodology based on a boundary discontinuous generalized double fourier series approach is used to solve a system of five highly coupled linear partial differential equations generated by the higher order shear deformation theory based laminated shell analysis with the c4 type rigidly clamped boundary condition prescribed on two opposite edges whereas the remaining two edges are subjected to the ss3 type constraint hitherto unavailable important numerical results presented include sensitivity of the predicted response quantities of interest to applied loading shell geometry negative or positive gaussian curvature edge clamping constraints and lamination and thickness effects as well as their possible interactions comparison with the

prediction error estimation algorithm for non linear output affine systems a prediction error estimation algorithm is developed for non linear discrete time systems which can be represented by the output affine difference equation model the theory of hypothesis testing is employed to select a model with the correct structure problems relating to the use of output affine models in the identification of non linear systems are discussed and a comparison with the narmax nonlinear armax model is given