existence theorems for the dirichlet problem without growth restrictions x 0 x 1 0 x 0 x 1 0 have virtually identical growth as lx 1 co however the first problem has no solutions while the second one has one solution the essential point here is the location of zeros of polynomials y2 7 and y2 ii actually granas guenther and lee 3 have proved that the problem x g x x 0 x 1 0 has at least one solution if g has two zeros of opposite sign in this paper we shall prove the following result 0 1

on a non linear formulation for curved timoshenko beam elements considering large displacement rotation increments summary an incremental total lagrangian formulation for curved beam elements that includes the effect of large rotation increments is developed a complete and symmetric tangent stiffness matrix is obtained and the numerical results show in general an improvement over the standard formulation where the assumption of infinitesimal rotation increments is made in the derivation of the tangent stiffness matrix

a three dimensional non linear timoshenko beam based on the core congruential formulation a three dimensional geometrically non linear two node timoshenko beam element based on the total lagrangian description is derived the element behaviour is assumed to be linear elastic but no restrictions are placed on the magnitude of finite rotations the resulting element has twelve degrees of freedom six translational components and six rotational vector components the formulation uses the green lagrange strains and second piola kirchhoff stresses as energy conjugate variables and accounts for bending stretching and bending torsional coupling effects without special provisions the core congruential formulation ccf is used to derive the discrete equations in a staged manner core equations involving the internal force vector and tangent stiffness matrix are developed at the particle level a sequence of matrix transformations carries these equations to beam cross sections and finally to the element nodal degrees of freedom the choice of finite rotation measure is made in the next to last transformation stage and the choice of over the element interpolation in the last one the tangent stiffness matrix is found to retain symmetry if the rotational vector is chosen to measure finite rotations an extensive set of numerical examples are presented to test and validate the present element

finite deformation post buckling analysis involving inelasticity and contact constraints this paper is concerned with the numerical solution of large deflection structural problems involving finite strains subject to contact constraints and unilateral boundary conditions and exhibiting inelastic constitutive response first a three dimensional finite strain beam model is summarized and its numerical implementation in the two dimensional case is discussed next a penalty formulation for the solution of contact problems is presented and the correct expression for consistent tangent matrix is developed finally basic strategies for tracing limit points are reviewed and a modification of the arc length method is proposed the good performance of the procedures discussed is illustrated by means of numerical examples

a model based standardization approach that separates true bias dif from group ability differences and detects test bias dtf as well as item bias dif a model based modification sibtest of the standardization index based upon a multidimensional irt bias modeling approach is presented that detects and estimates dif or item bias simultaneously for several items a distinction between dif and bias is proposed sibtest detects bias dif without the usual type 1 error inflation due to group target ability differences in simulations sibtest performs comparably to mantel haenszel for the one item case sibtest investigates bias dif for several items at the test score level multiple item dif called differential test functioning dtf thereby allowing the study of test bias dif in particular bias dif amplification or cancellation and the cognitive bases for bias dif

on the free vibration analysis of circular plates with stepped thickness over a concentric region by the differential quadrature element method it can be seen the dqem retains all advantages of the differential quadrature method extends the applicability range of the dq method and is more convenient for treating various boundary conditions

on the use of the domain decomposition method for vibration of symmetric laminates having discontinuities at the same edge abstract a free vibration analysis of symmetrically laminated plates with mixed edge boundary conditions is presented a highly efficient and accurate domain decomposition method is employed to establish the model the original domain is first assumed to be an assemblage of small subdomains with the admissible functions of each subdomain represented by sets of orthogonal polynomials these polynomials are generated by using the gram schmidt procedure the continuity matrices resulting from the geometric compatibilities between the subdomains are used to couple the eigenvectors of adjacent subdomains the stiffness and mass matrices of each subdomain after pre and post multiplying by the respective continuity matrices are assembled to form the global stiffness and mass matrices to demonstrate this method the free vibrations of symmetrically laminated plates of various types of mixed edge boundaries are calculated

a new approach to the differential quadrature method for fourth order equations a generalized and more complete methodology for treating boundary conditions in the differential quadrature method dqm is presented this improved approach eliminates the deficiencies of the type grid arrangement which represents an approximation by applying the boundary conditions exactly two kinds of basis functions chebyshev and lagrange are used for concept demonstration it is found that the new approach cures most deficiencies of the current dqm 1997 by john wiley sons ltd

effects of approximations in analyses of beams of open thin walled cross section part ii 3 d non linear behaviour in a companion paper the effects of approximations in the flexural torsional stability analysis of beams was studied and it was shown that a second order rotation matrix was sufficiently accurate for a flexural torsional stability analysis however the second order rotation matrix is not necessarily accurate in formulating finite element model for a 3 d non linear analysis of thin walled beams of open cross section the approximations in the second order rotation matrix may introduce self straining due to superimposed rigid body motions which may lead to physically incorrect predictions of the 3 d non linear behaviour of beams in a 3 d non linear elastic plastic analysis numerical integration over the cross section is usually used to check the yield criterion and to calculate the stress increments the stress resultants the elastic plastic stress strain matrix and the tangent modulus matrix a scheme of the arrangement of sampling points over the cross section that is not consistent with the strain distributions may lead to incorrect predictions of the 3 d non linear elastic plastic behaviour of beams this paper investigates the effects of approximations on the 3 d non linear analysis of beams it is found that a finite element model for 3 d non linear analysis based on the second order rotation matrix leads to over stiff predictions of the flexural torsional buckling and postbuckling response and to an overestimate of the maximum load carrying capacities of beams in some cases to perform a correct 3 d non linear analysis of beams an accurate model of the rotations must be used a scheme of the arrangement of sampling points over the cross section that is consistent with both the longitudinal normal and shear strain distributions is needed to predict the correct 3 d non linear elastic plastic behaviour of beams copyright 2001 john wiley sons ltd

nonparametric polytomous irt models for invariant item ordering with results for parametric models it is often considered desirable to have the same ordering of the items by difficulty across different levels of the trait or ability such an ordering is an invariant item ordering iio an iio facilitates the interpretation of test results for dichotomously scored items earlier research surveyed the theory and methods of an invariant ordering in a nonparametric irt context here the focus is on polytomously scored items and both nonparametric and parametric irt models are considered

free vibration of plates by the high accuracy quadrature element method in this paper a highly accurate and rapidly converging hybrid approach is presented for the quadrature element method qem solution of plate free vibration problems the hybrid qem essentially consists of a collocation method in conjunction with a galerkin finite element technique to combine the high accuracy of the differential quadrature method dqm for the efficient solution of differential equations with the generality of the finite element formulation this results in superior accuracy with fewer degrees of freedom than conventional fem or fdm a series of numerical tests is conducted to assess the performance of the quadrature plate element in free vibration problems anisotropic and stepped thickness plates are investigated as well as mixed boundary conditions and point supports at the edges in all cases the results obtained are quite accurate

unifying differential item functioning in factor analysis for categorical data under a discretization of a normal variant the multiple group categorical factor analysis fa model and the graded response model grm are commonly used to examine polytomous items for differential item functioning to detect possible measurement bias in educational testing in this study the multiple group categorical factor analysis model mc fa and multiple group normal ogive grm models are unified under the common framework of discretization of a normal variant we rigorously justify a set of identified parameters and determine possible identifiability constraints necessary to make the parameters just identified and estimable in the common framework of mc fa by doing so the difference between categorical fa model and normal ogive grm is simply the use of two different sets of identifiability constraints rather than the seeming distinction between categorical fa and grm thus we compare the performance on dif assessment between the categorical fa and grm approaches through simulation studies on the mc fa models with their corresponding particular sets of identifiability constraints our results show that under the scenarios with varying degrees of dif for examinees of different ability levels models with the grm type of identifiability constraints generally perform better on dif detection with a higher testing power general guidelines regarding the choice of just identified parameterization are also provided for practical use

a consistent co rotational formulation for non linear three dimensional beam elements abstract this paper describes a co rotational formulation for three dimensional beams in which both the internal force vector and tangent stiffness matrix are consistently derived from the adopted strain measures the latter relate to standard beam theory but are embedded in a continuously rotating frame a set of numerical examples show that the element provides an excellent numerical performance

a rasch model for partial credit scoring a unidimensional latent trait model for responses scored in two or more ordered categories is developed this partial credit model is a member of the family of latent trait models which share the property of parameter separability and so permit specifically objective comparisons of persons and items the model can be viewed as an extension of andrich s rating scale model to situations in which ordered response alternatives are free to vary in number and structure from item to item the difference between the parameters in this model and the category boundaries in samejima s graded response model is demonstrated an unconditional maximum likelihood procedure for estimating the model parameters is developed

development of an exact dynamic stiffness matrix for free vibration analysis of a twisted timoshenko beam abstract an exact dynamic stiffness matrix for a twisted timoshenko beam is developed in this paper in order to investigate its free vibration characteristics first the governing differential equations of motion and the associated natural boundary conditions of a twisted timoshenko beam undergoing free natural vibration are derived using hamilton s principle the inclusion of a given pretwist together with the effects of shear deformation and rotatory inertia gives rise in free vibration to four coupled second order partial differential equations of motion involving bending displacements and bending rotations in two planes for harmonic oscillation these four partial differential equations are combined into an eighth order ordinary differential equation which is identically satisfied by all components of bending displacements and bending rotations this difficult task has become possible only with the help of symbolic computation next the exact solution of the differential equation is obtained in completely general form in terms of eight arbitrary constants this is followed by application of boundary conditions for displacements and forces the procedure leads to the formation of the dynamics stiffness matrix of the twisted timoshenko beam relating harmonically varying forces with harmonically varying displacements at its ends the resulting dynamic stiffness matrix is used with particular reference to the wittrick williams algorithm to compute the natural frequencies and mode shapes of a twisted timoshenko beam with cantilever end condition the exact results from the present theory are compared with numerically simulated results using simpler theories and some conclusions are drawn

differential quadrature method for nonlinear vibration of orthotropic plates with finite deformation and transverse shear effect based on the reddy s theory of plates with the effect of higher order shear deformations the governing equations for nonlinear vibration of orthotropic plates with finite deformations are presented the nonlinear free vibration is analyzed by the differential quadrature method the differential quadrature approach suggested by wang and bert is extended to handle the multiple boundary conditions of the plate a new technique is also further extended to simplify nonlinear computations and the harmonic balance method is used in deriving the equation of motion the numerical convergence and comparison studies are carried out to validate the present solutions the results show that the presented differential quadrature method is fairly reliable and valid influences of geometric and material parameters transverse shear deformations and rotation inertia as well as vibration amplitudes on the nonlinear free vibration characteristics of orthotropic plates are studied

the partial credit model and null categories a category where the frequency of responses is zero either for sampling or structural reasons will be called anull category one approach for ordered polytomous item response models is to downcode the categories i e reduce the score of each category above the null category by one thus altering the relationship between the substantive framework and the scoring scheme for items with null categories it is discussed why this is often not a good idea and a method for avoiding the problem is described for the partial credit model while maintaining the integrity of the original response framework this solution is based on a simple reexpression of the basic parameters of the model

static analysis of structures by the quadrature element method qem abstract the differential quadrature method dqm is an alternative discrete approach to solving directly the governing equations of engineering and mathematical physics since the dqm does not require the derivation of the weak forms of the governing equations like the fem it can greatly reduce formulation efforts in higher order approximation the dqm has been applied in the past to the analyses of various single structural components such as bars beams membranes and plates all of the component analyses yielded good to excellent results however previous studies were limited to simple geometries and simple boundary conditions due to the limitation of using global basis functions in the present study a domain decomposition technique for the dqm is proposed to analyse truss and frame structures where the whole structural domain is represented by a collection of simple element subdomains connected together at specific nodal points this method is named the quadrature element method qem

vibration of thin pre twisted helical beams abstract a helical beam has non zero curvature and tortuosity when there is a pre twist the frenet triad is not necessary coincident with the principal triad when an initially straight rod undergoing a large deformation it will be curved and twisted during each deformation sequence the purpose of the paper is to establish the governing equations and the associated natural boundary conditions for a pre twisted helical beam by variational principles and differential geometry although circular helix is taken as example the formulation is valid for inhomogeneous and non uniform parameters along the centerline that variable curvature and tortuosity can be treated without difficulties the method can be used to treat helical anisotropy if the pre twist rate of a ring is 0 5 we show a thick mobius ring for the first time the solution of the natural vibration problem is through chebyshev discretization and clenshaw curtis integration by means of the galerkin formulation

computational aspects of vector like parametrization of three dimensional finite rotations theoretical and computational aspects of vector like parametrization of three dimensional finite rotations which uses only three rotation parameters are examined in detail in this work the relationship of the proposed parametrization with the intrinsic representation of finite rotations via an orthogonal matrix is clearly identified careful considerations of the consistent linearization procedure pertinent to the proposed parametrization of finite rotations are presented for the chosen model problem of reissner s non linear beam theory pertaining details of numerical implementation are discussed for the simplest choice of the finite element interpolations for a 2 node three dimensional beam element a number of numerical simulations in three dimensional finite rotation analysis are presented in order to illustrate the proposed approach

a kinematically exact space finite strain beam model finite element formulation by generalized virtual work principle the present paper presents a novel finite element formulation for static analysis of linear elastic spatial frame structures extending the formulation given by simo and vu quoc a geometrically exact rod model incorporating shear and torsion warping deformation int j solids structures 27 3 1991 371 3931 along the lines of the work on the planar beam theory presented by saje a variational principle for finite planar deformation of straight slender elastic beams internat j solids and structures 26 1990 887 9001 we apply exact non linear kinematic relationships of the space finite strain beam theory assuming the bernoulli hypothesis and neglecting the warping deformations of the cross section finite displacements and rotations as well as finite extensional shear torsional and bending strains are accounted for in the formulation a deformed configuration of the beam is described by the displacement vector of the deformed centroid axis and an orthonormal moving frame rigidly attached to the cross section of the beam the position of the moving frame relative to a fixed reference frame is specified by an orthogonal matrix parametrized by the rotational vector which rotates the moving frame from an arbitrary position into the deformed configuration in one step also the incremental rotational vector is introduced which rotates the moving frame from the configuration obtained at the previous iteration step into the current configuration of the beam its components relative to the fixed global coordinate system are taken to be the rotational degrees of freedom at nodal points because in 3 d space both the axial and the follower moments are non conservative not the variational principle but the principle of virtual work has been introduced as a basis for the finite element discretization here we have proposed the generalized form of the principle of virtual work by including exact kinematic equations by means of a procedure similar to that of lagrangian multipliers this makes possible the elimination of the displacement vector field from the principle so that the three components of the incremental rotational vector field remain the only functions to be approximated in the finite element implementation of the principle other researchers on the other hand employ the three components of the incremental rotational vector field and the three components of the incremental displacement vector field as a result more accurate and efficient family of beam finite elements for the non linear analysis of space frames has been obtained a one field formulation results in the fact that in the present finite elements the locking never occurs any combination of deformation states is described equally precisely this is in contrast with the elements developed in literature where in order to avoid the locking a reduced numerical integration has to be applied which unfortunately diminishes the accuracy of the solution polynomials have been chosen for the approximation of the components of the rotational vector in this case the order of the numerical integration can rationally be estimated and the computer program can be coded in such a way that the degree of polynomials need not be limited to a particular value the newton method is used for the iterative solution of the non linear equilibrium equations in an non equilibrium configuration the tangent stiffness matrix obtained by the linearization of governing equations using the directional derivative is non symmetric even for conservative loadings only upon achieving an equilibrium state the tangent stiffness matrix becomes symmetric thus obtained tangent stiffness matrix can be symmetrized without affecting the rate of convergence of the newton method for non conservative loadings however the tangent stiffness matrix is always non symmetric the numerical examples demonstrate capability of the present formulation to determine accurately the non linear behaviour of space frames in numerical examples the out of plane buckling loads are determined and the whole pre and post critical load displacement paths of a cantilever and a right angle frame are traced these in the analysis of space beams standard verification example problems show excellent accuracy of the solution even when employing only one element to describe the displacements of the size of the structure itself the rotations of 2n and extensional strains much beyond the realistic values of linear elastic material

static analysis of frame structures by the differential quadrature element method in this paper a new version of differential quadrature method dqm is proposed and then extended to analyse frame structures the new method called the differential quadrature element method dqem retains all advantages of the earlier version of the differential quadrature method and overcomes some critical shortcomings existing in the original dqm the proposed method is however different from the quadrature element method qem proposed earlier by striz et al the methodology is explained in details herein via a differential quadrature beam element and some numerical examples are given to show the efficiency of the present method 1997 by john wiley sons ltd

on the dynamics of spatially curved and twisted rods a finite element formulation for spatially curved and twisted rods a set of governing equations consisting of equilibrium equations and strain displacement and constitutive relations are derived in terms of three translational and three rotational degrees of freedom by solving the strain displacement relations for constant and zero states of strain the rigid body and constant strain modes of the rod are obtained these displacement modes are then used as basis functions for development of a finite element model to verify the formulation and the elemental matrices three examples are analyzed for free vibrations and in each case the computed results are compared with those obtained experimentally good agreement is found for several modes of vibrations

nonlinear analysis of members curved in space with warping and wagner effects abstract the centroidal axis of a member that is curved in space is generally a space curve the curvature of the space curve is not necessarily in the direction of either of the principal axes of the cross section but can be resolved into components in the directions of both of these principal axes hence a member curved in space is primarily subjected to combined compressive biaxial bending and torsional actions under vertical or gravity loading in addition warping actions in particular may occur in curved members with an open thin walled cross section and as the deformations increase significant interactions of the compressive biaxial bending and torsional actions occur and profoundly nonlinear deformations are developed in the nonlinear range of structural response this makes the nonlinear behaviour of a member curved in space very complicated making it difficult to obtain a consistent differential equation of equilibrium for the nonlinear analysis of members curved in space in addition because torsion is one of the primary actions in these members when the torsional deformations become large the wagner effects including both wagner moment and the conjugate wagner strain terms are increasingly significant and need to be included in the nonlinear analysis this paper takes advantage of the merits of so called geometrically exact beam theory and the weak form formulation of the differential equations of equilibrium in beam theory and it develops consistent differential equations of equilibrium for the nonlinear elastic analysis of members curved in space with warping and wagner effects the application of the nonlinear differential equations of equilibrium to various problems is illustrated

objectivity of strain measures in the geometrically exact three dimensional beam theory and its finite element implementation the paper discusses the issue of discretization of the strainconfiguration relationships in the geometrically exact theory of threedimensional 3d beams which has been at the heart of most recent

vibration characteristics and transient response of shear deformable functionally graded plates in thermal environments free and forced vibration analyses for initially stressed functionally graded plates in thermal environment are presented material properties are assumed to be temperature dependent and graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents theoretical formulations are based on reddy s higher order shear deformation plate theory and include the thermal effects due to uniform temperature variation the plate is assumed to be clamped on two opposite edges with the remaining two others either free simply supported or clamped one dimensional differential quadrature technique galerkin approach and the modal superposition method are used to determine the transient response of the plate subjected to lateral dynamic loads comprehensive numerical results for silicon nitride stainless steel rectangular plates are presented in dimensionless tabular and graphical forms the roles played by the constituent volume fraction index temperature rise shape and duration of dynamic loads initial membrane stresses as well as the character of boundary conditions are studied the results reveal that when thermal effects are considered functionally graded plates with material properties intermediate to those of isotropic ones do not necessarily have intermediate natural frequencies and dynamic responses

moving least squares differential quadrature method and its application to the analysis of shear deformable plates a moving least squares differential quadrature mlsdq method is developed and employed for the analysis of moderately thick plates based on the first order shear deformation theory fsdt to carry out the analysis the governing equations in terms of the generalized displacements transverse deflection and two rotations of the plate are formulated by employing the moving least squares approximation the weighting coefficients used in the mlsdq approximation are computed through a fast computation of shape functions and their derivatives numerical examples illustrating the accuracy stability and convergence of the mlsdq method are presented effects of support size order of completeness and node irregularity on the numerical accuracy are investigated copyright 2003 john wiley sons ltd

vibrations of rods with general space curvature in this paper the equations of motion for a rod with arbitrary space curvature and cross section geometry are re examined and results showing the effects of curvature torsion and cross section shape on natural frequencies and mode shapes are presented expressions for the kinetic and potential energy functions of a curved and twisted rod are formulated in terms of centerline displacements and cross section rotations these expressions are first used to derive the equations of motion and natural boundary conditions by using hamilton s principle next the kinetic and potential energy functions are used to formulate a rayleigh ritz solution for the mode shapes and natural frequencies of helical rods with fixed fixed and fixed free ends the effects of space curvature and torsion and of cross section out of roundness on frequencies and mode shapes of fixed free helical rods are examined

the quaternion based three dimensional beam theory this paper presents the equations for the implementation of rotational quaternions in the geometrically exact three dimensional beam theory a new finite element formulation is proposed in which the rotational quaternions are used for parametrization of rotations along the length of the beam the formulation also satisfies the consistency condition that the equilibrium and the constitutive internal force and moment vectors are equal in its weak form a strict use of the quaternion algebra in the derivation of governing equations and for the numerical solution is presented several numerical examples demonstrate the validity performance and accuracy of the proposed approach c 2009 elsevier b v all rights reserved

rectangular thick plates on winkler foundation differential quadrature element solution abstract this paper deals with the static analysis of homogenous isotropic rectangular plates on winkler foundation on the basis of first order shear deformation theory an improved differential quadrature dq method called the differential quadrature element method dqem has been developed for this analysis the plates considered are subjected to a patch load or a concentrated line load which are not solvable by the global dq method the convergence and comparison studies are carried out to establish the reliability of the dqem results then the numerical results for different boundary conditions i e ssss cccc s s s s and sfsf are presented showing the parametric effects of dimensions of loading area line relative thickness ratio and elastic foundation modulus on the deflection bending and twisting moments and shear forces at selected locations most of these data are new and due to the high accuracy of the dq solution they can be useful for benchmarking future work

on measurement properties of continuation ratio models three classes of polytomous irt models are distinguished these classes are the adjacent category models the cumulative probability models and the continuation ratio models so far the latter class has received relatively little attention the class of continuation ratio models includes logistic models such as the sequential model tutz 1990 and nonlogistic models such as the acceleration model samejima 1995 and the nonparametric sequential model hemker 1996 four measurement properties are discussed these are monotone likelihood ratio of the total score stochastic ordering of the latent trait by the total score stochastic ordering of the total score by the latent trait and invariant item ordering these properties have been investigated previously for the adjacent category models and the cumulative probability models and for the continuation ratio models this is done here it is shown that stochastic ordering of the total score by the latent trait is implied by all continuation ratio models while monotone likelihood ratio of the total score and stochastic ordering on the latent trait by the total score are not implied by any of the continuation ratio models only the sequential rating scale model implies the property of invariant item ordering also we present a venn diagram showing the relationships between all known polytomous irt models from all three classes

differential quadrature element method a new approach for free vibration analysis of polar mindlin plates having discontinuities this paper presents the numerical development of the differential quadrature element method dqem for free vibration analysis of the shear deformable plates in polar coordinates this is an improvement on the global differential quadrature method dqm the formulations of the dqem for polar plate vibration element are derived in detail the convergence characteristics of the dqem for solving the free vibration of polar plates are carefully examined the reliability and flexibility of the dqem are illustrated by solving several selected example polar plates having discontinuities which are not solvable directly by the dqm the accuracy of the dqem is evaluated and verified by comparing the present numerical results with the existing exact or approximate solutions or the fem solutions computed using the software package ansys version 5 3

out of plane static analysis of circular arches by dqm the differential quadrature dq methodology introduced by the authors see comput methods appl mech engng 191 2002a 3509 int j solids struct 39 19 2002b 4927 int j numer methods engng 54 3 2003a 847 j sound vibrat 263 2 2003b 415 is employed for out of plane static analysis of circular arches under a wide spectrum of boundary conditions in addition to the classical boundary conditions elastic restraints against translation and rotation are also considered different loading conditions are examined several examples of arches with uniform continuous or stepped varying cross sections are presented to demonstrate the accuracy of the methodology the domain decomposition technique in conjunction with the present dq methodology is examined for certain cases the results are compared with those of exact solutions for several uniform or stepped sections arches and also for arches on elastic foundations accurate converged numerical solutions are obtained with only few grid points

solvability of some nonlinear boundary value problems on etablit l existence des solutions positives de problemes a deux points limites singuliers pour des equations differentielles de la forme y f t y y o o t 1

a geometrically exact rod model incorporating shear and torsion warping deformation abstract a fully nonlinear three dimensional rod model is developed that incorporates transverse shear and torsion warping deformation the geometric setting is that of a constrained body model with configuration space modeled on r3 so 3 r a differentiable manifold the proposed model incorporates the classical notion of bi moment and bi shear in a fully nonlinear geometrically exact context explicit properly invariant constitutive equations that generalize those of the linearized theory are developed the underlying variational formulation of the model is discussed and computational procedures employing a galerkin projection are addressed numerical examples are presented that illustrate the performance of the formulation

differential quadrature element method for static analysis of reissner mindlin polar plates abstract in this paper a new numerical technique the differential quadrature element method dqem has been developed for static analysis of the two dimensional polar reissner mindlin plate in the polar coordinate system by integrating the domain decomposition method ddm with the differential quadrature method dqm the detailed formulations for the sectorial dqem plate bending element and the compatibility conditions between each element are presented the convergence properties and the accuracy of the dqem for bending of thick polar plates are investigated through a number of numerical computations consequently the dqem has been successfully applied to analyze several annular sector plates with discontinuous loading and boundary conditions and cutouts to illustrate the simplicity and flexibility of this method for solving reissner mindlin plates in polar coordinate system which are not solvable directly using the differential quadrature method the numerical results are verified by the existing exact solutions or the fem solutions obtained using the software package ansys version 5 3

application of a series type method to vibration of orthotropic rectangular plates with mixed boundary conditions the object of this paper is to show an application of a series type method to the free vibration of an orthotropic rectangular plate with mixed boundary conditions the rectangular plate considered is elastically constrained or clamped along a few parts of its edge and simply supported on the remainder a frequency equation is derived to accommodate rectangular orthotropy of the plate by the extension of a previously developed method and subsequent algebraic manipulation leads to the improved equation yielding natural frequencies of the plate with very good accuracy the method is demonstrated for numerical examples where one two or three parts are constrained along the boundary of the square plate and the effects of varying constraint and orthotropic parameters on the natural frequencies and mode shapes are studied

two new approximate methods for analyzing free vibration of structural components two approximate methods which have not previously been used for structural dynamics problems are applied to the free vibration analysis of various structural components the first method is a new version of the complementary energy method it is shown to be considerably more accurate than the conventional rayleigh and rayleigh schmidt methods when applied to spatially one dimensional free vibration problems prismatic and tapered bars prismatic beams and axisymmetric motion of circular membranes the second method is the differential quadrature method introduced by bellman and his associates it is applied successfully here to all of the problems mentioned plus square membranes and circular and square plates

the finite deformation theory for beam plate and shell part iii the three dimensional beam theory and the fe formulation a finite deformation model based on the timoshenko beam theory is proposed for the three dimensional beam structures the exact green lagrangian strains are derived the finite element formulation and the corresponding algorithm are presented for the model numerical examples are given to illustrate its validity and effectiveness

on the use of the substructure method for vibration analysis of rectangular plates with discontinuous boundary conditions abstract a substructure method is presented for analysis of the free vibration of a rectangular plate with mixed edge boundary conditions the method involves the partitioning of the entire plate domain into appropriate elements to approximate the deflection function of each element by a set of admissible orthogonal polynomials the continuity conditions along the interconnecting boundaries provide the coupling between the coefficients of each element summing the strain and kinetic energies of each element and minimizing the resulting rayleigh quotient with respect to the unknown coefficients leads to the governing eigenvalue equation for the entire plate several plate problems are solved to demonstrate the applicability and accuracy of the present method where possible the results obtained are verified by comparisons with existing published values from the literature

existence theorems for a class of singular two point b v p of second order differential equations wherea b o l randf o 1 xr 2 r are continuous functions a and b are positive in 0 l and e denotes the space of boundary conditions the importance and origins of these problems can be found in granas et al 4 chap 31 see also 2 we are mainly interested in the singular case a 0 a 1 b 0 b 1 0 but our study includes the regular case a 0 and b 0 in 0 11 actually the singular case is deduced from the regular one through a sequence of regular problems

analysis of vibrating thick rectangular plates with mixed boundary constraints using differential quadrature element method a free vibration analysis of moderately thick rectangular plates with mixed boundary conditions is presented on the basis of the first order shear deformation plate theory the differential quadrature element method a highly efficient and accurate hybrid approach has been employed to establish the numerical model the complex plate domain is first decomposed into small simple continuous sub domains elements and the differential quadrature method is then applied to each continuous sub domain to solve the problems compatibility conditions are developed for the conjunction nodes on the interface boundaries of elements in order to connect the elements convergence and comparison studies are carried out to establish the reliability of the solutions the first eight frequency parameters are predicted for various types of thick rectangular plates with mixed edge constraints

the unique correspondence of the item response function and item category response functions in polytomously scored item response models the item response function irf for a polytomously scored item is defined as a weighted sum of the item category response functions icrf the probability of getting a particular score for a randomly sampled examinee of ability this paper establishes the correspondence between an irf and a unique set of icrfs for two of the most commonly used polytomous irt models the partial credit models and the graded response model specifically a proof of the following assertion is provided for these models if two items have the same irf then they must have the same number of categories moreover they must consist of the same icrfs as a corollary for the rasch dichotomous model if two tests have the same test characteristic function tcf then they must have the same number of items moreover for each item in one of the tests an item in the other test with an identical irf must exist theoretical as well as practical implications of these results are discussed

polytomous latent scales for the investigation of the ordering of items we propose three latent scales within the framework of nonparametric item response theory for polytomously scored items latent scales are models that imply an invariant item ordering meaning that the order of the items is the same for each measurement value on the latent scale this ordering property may be important in for example intelligence testing and person fit analysis we derive observable properties of the three latent scales that can each be used to investigate in real data whether the particular model adequately describes the data we also propose a methodology for analyzing test data in an effort to find support for a latent scale and we use two real data examples to illustrate the practical use of this methodology

geometrically exact thin walled beam including warping formulated on the special euclidean group se 3 abstract based on a formulation on the special euclidean group s e 3 a geometrically exact thin walled beam with an arbitrary open cross section is proposed to deal with the finite deformation and rotation issues the beam strains are based on a kinematic assumption where warping deformation and wagner effects are included such that the nonlinear behavior of a thin walled beam is predicted accurately particular under large torsion to reduce the nonlinearity of rigid motion static and dynamic equations are derived in the s e 3 framework based on the local frame approach as the value of the iteration matrix including the jacobian matrix of inertial and internal forces is invariable under arbitrary rigid motion the number of updates required during the computation process decreases sharply which drastically improves the computational efficiency furthermore the isogeometric analysis iga based on the non uniform rational b splines nurbs basis functions which promotes the integration of computer aided design cad and computer aided engineering cae is adopted to interpolate the displacement rotation and warping fields separately the interpolated strain measures satisfy the objectivity by removing the rigid motion of the reference point to obtain the symmetric jacobian matrix of internal forces the linearization operation is conducted based on the previously converged configuration a lie group s e 3 extension of the generalized time integration method is utilized to solve the equations of motion for thin walled beams finally the proposed formulation is successfully tested and validated in several static and dynamic numerical examples

an excursion into large rotations the present discourse develops an enlarged exploration of the matrix formulation of finite rotations in space initiated in 1 it is shown how a consistent but subtle matrix calculus inevitably leads to a number of elegant expressions for the transformation or rotation matrix t appertaining to a rotation about an arbitrary axis also analysed is the case of multiple rotations about fixed or follower axes particular attention is paid to an explicit derivation of a single compound rotation vector equivalent to two consecutive arbitrary rotations this theme is discussed in some detail for a number of cases semitangential rotations for which commutativity holds first proposed in 2 3 are also considered furthermore an elementary geometrical analysis of large rotations is also given finally we deduce in an appendix using a judicious reformulation of quarternions the compound pseudovector representing the combined effect of n rotations in the author s opinion the present approach appears preferable to a pure vectorial scheme and even more so to an indicial formulation and is computationally more convenient

vibration analysis of symmetrically laminated plates based on fsdt using the moving least squares differential quadrature method in this paper we adopt the first order shear deformation theory in the moving least squares differential quadrature mlsdq procedure for predicting the free vibration behavior of moderately thick symmetrically laminated composite plates the transverse deflection and two rotations of the laminate are independently approximated with the moving least squares mls approximation the weighting coefficients used in the mlsdq approximation are obtained through the fast computation of the mls shape functions and their partial derivatives the natural frequencies of vibration are computed for various laminated plates and compared with the available published results through numerical experiments the capability and efficiency of the mlsdq method for eigenvalue problems are demonstrated and the numerical accuracy and convergence are thoughtfully examined effects of the size of support order of completeness of the basis functions and node irregularity on the numerical accuracy are also investigated

spatial chaos of 3 d elastica with the kirchhoff gyrostat analogy using melnikov integrals summary the kirchhoff kinetic analogy from which the similarity between the governing equations for the static spatial equilibrium of a 3 d elastica and those for the temporal dynamics of a rigid body is constituted is revisited the melnikov integrals for detecting chaos cannot be easily formed for an elastica we shall modify the previous procedure of using the melnikov integrals for detecting temporal chaos for a gyrostat to solve the spatial chaos problem of an elastica one way to find the disturbed hamiltonian equations of the equilibrium equations of the elastica are by means of deprit s variables using the melnikov integrals the spatially chaotic deformation patterns can be resulted from the homoclinic transversal intersections of the stable and unstable manifolds at a saddle point in the poincare map when the elastica is disturbed by constant stress resultants the melnikov integrals are integrated for detecting homoclinic intersections the equations governing the evolution of the stress couples and the stress resultants are numerically integrated using the fourth runge kutta algorithms to crosscheck the analytical results the phase portraits of the poincare sections are created on a number of hyper planes to demonstrate the chaotic patterns of the stationary spatial deformations along the centreline of the elastica under weightless conditions the bounded non periodic solutions to the equilibrium of the elastica clearly show the existence of spatially chaotic deformation patterns the findings in this paper are useful in many structures in which the elastica are important examples are the mathematical modelling of the dna super coiling submarine cables and the design of the tethered satellites copyright 2004 john wiley sons ltd

an exact analytical approach to the free vibration analysis of rectangular plates with mixed boundary conditions abstract a comprehensive analytical technique is developed for the free vibration analysis of rectangular plates with discontinuities along the boundaries for illustrative purposes a solution is obtained for plates with edges partially clamped and partially simply supported and plates with edges partially and partially simply supported a vast array of first mode eigenvalues is provided for these families of plates solutions to the equations are obtained by exploiting a mathematical technique described by the author during an earlier publication it is shown that eigenvalue matrices are easily generated for a wide range of plates with discontinuities in boundary conditions

the role of non linear theories in transient dynamic analysis of flexible structures abstract transient dynamic analysis of flexible structures undergoing large motions is considered for rotating structures it is explicitly shown that appropriate account of the influence of centrifugal force on the bending stiffness requires the use of a geometrically non linear at least second order beam theory use of a first order linearized linear beam theory results in a spurious loss of bending stiffness for a rotating plane beam a set of linear partial differential equations of motion that includes all inertia effects coriolis centrifugal acceleration of revolution and coupling between extensional and flexural deformations is derived from the fully non linear beam theory by consistent linearization the analysis is subsequently extended to the more general case of a plate accomodating shear deformation and undergoing a general three dimensional rotating motion the discretization process of the resulting linear equations of motion for the beam and the plate is also discussed

an adaptive differential quadrature element method for large deformation contact problems involving curved beams with a finite number of contact points abstract contact problems involving large deformation of curved beams are difficult to analyze due to uncertainty of contact positions and strong nonlinearity a nonlinear large deformation model of curved beams is formulated in arc length coordinates a new adaptive differential quadrature element method adqem is proposed to predict contact positions of a curved beam with a finite number of contact points where a dragging method and continuity conditions are combined to determine the contact positions simulation results show that the adqem greatly improves efficiency and accuracy of the large deformation contact problem of the curved beam the number of iterations in the present method does not greatly increase with the number of contact points