a consistent finite element formulation for linear buckling analysis of spatial beams a consistent co rotational finite element formulation and numerical procedure for the linear buckling analysis of three dimensional elastic euler beam is presented a mechanism for generating configuration dependent conservative moment is proposed and the corresponding load stiffness matrix is derived it is assumed that the prebuckling displacements and rotations of the structure and the corresponding deformations of the elements are linearly proportional to the external loading the prebuckling rotations of the structure are fixed axis rotations or small rotations and the effect of the prebuckling displacement on transformation matrix for the coordinates transformation can be ignored all coupling among bending twisting and stretching deformations for beam element is considered by consistent linearization of the fully geometrically nonlinear beam theory an inverse power method for the solution of the generalized eigenvalue problem is used to find the buckling load and buckling mode numerical examples are presented to demonstrate the accuracy and efficiency of the proposed method

revised standards for statistical evidence recent advances in bayesian hypothesis testing have led to the development of uniformly most powerful bayesian tests which represent an objective default class of bayesian hypothesis tests that have the same rejection regions as classical significance tests based on the correspondence between these two classes of tests it is possible to equate the size of classical hypothesis tests with evidence thresholds in bayesian tests and to equate p values with bayes factors an examination of these connections suggest that recent concerns over the lack of reproducibility of scientific studies can be attributed largely to the conduct of significance tests at unjustifiably high levels of significance to correct this problem evidence thresholds required for the declaration of a significant finding should be increased to 25 50 1 and to 100 200 1 for the declaration of a highly significant finding in terms of classical hypothesis tests these evidence standards mandate the conduct of tests at the 0 005 or 0 001 level of significance

bayes factors based on test statistics summary traditionally the use of bayes factors has required the specification of proper prior distributions on model parameters that are implicit to both null and alternative hypotheses i describe an approach to defining bayes factors based on modelling test statistics because the distributions of test statistics do not depend on unknown model parameters this approach eliminates much of the subjectivity that is normally associated with the definition of bayes factors for standard test statistics including the 2 f t and z statistics the values of bayes factors that result from this approach have simple closed form expressions

bifurcations and internal resonances in space curved rods abstract the paper discusses a geometrically non linear model of space curved beams the timoshenko type model is used which includes the shear effects and rotatory inertia the motion of the system is described by a non linear matrix equation which accounts for non linearities up to the second order to solve the non linear problem discretization methods based on the galerkin method are used and the resulting non linear eigenvalue problem is then solved by the continuation methods the analysis of the discretized problem allows the study of the bifurcations of solutions the post bifurcation analysis is used to explain the phenomenon of internal resonance which is of much importance in the prediction of the dynamic response of the analyzed systems the approach is illustrated by numerical examples which consider the free vibration of beams and circular arches with different boundary conditions

a multivariate two sample mean test for small sample size and missing data we develop a new statistic for testing the equality of two multivariate mean vectors a scaled chi squared distribution is proposed as an approximating null distribution because the test statistic is based on componentwise statistics it has the advantage over hotelling s t2 test of being applicable to the case where the dimension of an observation exceeds the number of observations an appealing feature of the new test is its ability to handle missing data by relying on only componentwise sample moments monte carlo studies indicate good power compared to hotelling s t2 and a recently proposed test by srivastava 2004 technical report university of toronto the test is applied to drug discovery data

a co rotational formulation for thin walled beams with monosymmetric open section abstract a consistent co rotational total lagrangian finite element formulation and numerical procedure for the geometric nonlinear buckling and postbuckling analysis of thin walled beams with monosymmetric open section is presented the element developed here has two nodes with seven degrees of freedom per node the element nodes are chosen to be located at the shear centers of the end cross sections of the beam element and the shear center axis is chosen to be the reference axis the deformations of the beam element are described in the current element coordinate system which is constructed at the current configuration of the beam element in element nodal forces all coupling among bending twisting and stretching deformations of the beam element is considered by consistent second order linearization of the fully geometrically nonlinear beam theory however the third order term of the twist rate of the beam axis is considered in element nodal forces an incremental iterative method based on the newton raphson method combined with constant arc length of incremental displacement vector is employed for the solution of nonlinear equilibrium equations the zero value of the tangent stiffness matrix determinant of the structure is used as the criterion of the buckling state a parabolic interpolation method of the arc length is used to find the buckling load numerical examples are presented to demonstrate the accuracy and efficiency of the proposed method

a consistent co rotational finite element formulation for geometrically nonlinear dynamic analysis of 3 d beams abstract a co rotational total lagrangian finite element formulation for the geometrically nonlinear dynamic analysis of spatial euler beam with large rotations but small strain is presented the nodal coordinates displacements rotations velocities accelerations and the equations of motion of the structure are defined in a fixed global set of coordinates the beam element has two nodes with six degrees of freedom per node the element nodal forces are conventional forces and moments the kinematics of beam element are defined in terms of element coordinates which are constructed at the current configuration of the beam element both the element deformation nodal forces and inertia nodal forces are systematically derived by consistent linearization of the fully geometrically nonlinear beam theory using the d alembert principle and the virtual work principle in the current element coordinates an incremental iterative method based on the newmark direct integration method and the newton raphson method is employed here for the solution of the nonlinear equations of motion numerical examples are presented to demonstrate the accuracy and efficiency of the proposed method

co rotational finite element formulation for thin walled beams with generic open section a consistent co rotational total lagrangian finite element formulation for the geometric nonlinear buckling and postbuckling analysis of thin walled beams with generic open section is presented the element developed here has two nodes with seven degrees of freedom per node the element nodes are chosen to be located at the shear centers of the end cross sections of the beam element and the shear center axis is chosen to be the reference axis the deformations of the beam element are described in the current element coordinate system constructed at the current configuration of the beam element the element nodal forces are derived using the virtual work principle the virtual rigid body motion corresponding to the virtual nodal displacements is excluded in the derivation of the element nodal forces a procedure is proposed to determine the virtual rigid body motion the way used to determine the element coordinate system and element nodal deformations corresponding to the virtual nodal displacements and that corresponding to the incremental nodal displacement are consistent in element nodal forces all coupling among bending twisting and stretching deformations of the beam element is considered by consistent second order linearization of the fully geometrically nonlinear beam theory in the derivation of the element tangent stiffness matrix the change of element nodal forces induced by the element rigid body rotations should be considered for the present method thus a stability matrix is included in the element tangent stiffness matrix an incremental iterative method based on the newton raphson method combined with constant arc length of incremental displacement vector is employed for the solution of nonlinear equilibrium equations the zero value of the tangent stiffness matrix determinant of the structure is used as the criterion of the buckling state numerical examples are presented to investigate the accuracy and efficiency of the proposed method the effect of the terms in the element nodal force and tangent stiffness matrix which will converge to zero with the decrease of element size on the convergence rate of solution and accuracy for the buckling load and nonlinear behavior of three dimensional beam structures are also investigated through numerical examples 2005 elsevier b v all rights reserved

a spatially curved beam element with warping and wagner effects this paper presents a new spatially curved beam element with warping and wagner effects that can be used for the non linear large displacement analysis of members that are curved in space the non linear behaviour of members curved in space shows that the wagner effects are substantial in the large twist rotation analysis most existing finite beam element models such as abaqus and ansys cannot predict the non linear large displacement response of members curved in space correctly because the wagner effects viz the wagner moment and the corresponding finite strain terms have not been considered in these finite beam elements as a consequence these finite beam elements do not provide correct predictions for the out of plane buckling and postbuckling behaviour of arches as well in this paper the symmetric tangent stiffness matrix has been derived based on the finite rotations parameterized by the conventional displacements the warping and wagner effects both the wagner moment and the corresponding finite strain terms and their constitutive relationship are included in the spatially curved beam element two components of the initial curvature the initial twist and their interactions with the displacements are also considered in the spatially curved beam element this ensures that the large twist rotation analysis for the members curved in space is accurate comparisons with existing experimental analytical and numerical results show that the spatially curved beam element is accurate and efficient for the non linear elastic analysis of curved members buckling and postbuckling analysis of arches and in its ability to predict large deflections and twist rotations in more arbitrarily curved members copyright 2005 john wiley sons ltd

conservative numerical methods for nonlinear strings in this article a class of numerical schemes for the simulation of nonlinear coupled longitudinal transverse string vibration is presented though there are various ways of arriving at such schemes special attention is paid here to energy conservation in nonlinear model systems and its transfer to an analogous discrete quantity in a difference scheme such exact numerical energy conservation can lead to simple global stability conditions which can be otherwise difficult to ascertain for nonlinear difference schemes in particular such conditions may be arrived at without any reliance on frequency domain concepts i e fourier or laplace transforms which are of only moderate utility in the analysis of nonlinear systems implementation details are discussed and numerical results are presented

dynamic modeling of beams with non material deformation dependent boundary conditions abstract in conventional problems of structural mechanics both kinematic boundary conditions and external forces are prescribed at fixed material points that are known in advance if however a structure may move relative to its supports the position of the imposed constraint relations generally changes in the course of motion a class of problems which inherently exhibits this particular type of non material boundary conditions is that of axially moving continua despite varying in time the positions of the supports relative to the material points of the body have usually assumed to be known a priori throughout the deformation process in previous investigations this requirement is abandoned in the present paper where the dynamic behavior of a structure is studied which may move freely relative to one of its supports as a consequence the position of such a non material boundary relative to the structure does not only change in time but also depends on the current state of deformation of the body the variational formulation of the equilibrium relations of a slender beam that may undergo large deformations is presented to this end a theory based on reissner s geometrically exact relations for the plane deformation of beams is adopted in which shear deformation is neglected for the sake of brevity before a finite element scheme is developed a deformation dependent transformation of the beam s material coordinate is introduced by which the varying positions of the constraint relations are mapped onto fixed points with respect to the new non material coordinate by means of this transformation additional convective terms emerge from the virtual work of the inertia forces whose symmetry properties turn out to be different from what has previously been presented in the literature in order to obtain approximate solutions a finite element discretization utilizing absolute nodal displacements as coordinates is subsequently used in characteristic numerical examples which give an insight into the complex dynamic behavior of problems of this type on the one hand the free vibrations of a statically pre deformed beam are investigated on the other hand an extended version of the sliding beam problem is studied

a co rotational finite element formulation for buckling and postbuckling analyses of spatial beams abstract a consistent co rotational finite element formulation and numerical procedure for the buckling and postbuckling analyses of three dimensional elastic euler beam is presented all coupling among bending twisting and stretching deformations for a beam element is considered by consistent second order linearization of the fully geometrically nonlinear beam theory however the third order terms which are relevant to the twist rate and curvature of the beam axis are also considered an incremental iterative method based on the newton raphson method combined with constant arc length of incremental displacement vector is employed for the solution of nonlinear equilibrium equations the zero value of the tangent stiffness matrix determinant of the structure is used as the criterion of the buckling state a bisection method of the arc length is proposed to find the buckling load numerical examples are presented to demonstrate the accuracy and efficiency of the proposed method and to investigate the effect of third order terms on the buckling load and postbuckling behavior of three dimensional beams

uniformly most powerful bayesian tests uniformly most powerful tests are statistical hypothesis tests that provide the greatest power against a fixed null hypothesis among all tests of a given size in this article the notion of uniformly most powerful tests is extended to the bayesian setting by defining uniformly most powerful bayesian tests to be tests that maximize the probability that the bayes factor in favor of the alternative hypothesis exceeds a specified threshold like their classical counterpart uniformly most powerful bayesian tests are most easily defined in one parameter exponential family models although extensions outside of this class are possible the connection between uniformly most powerful tests and uniformly most powerful bayesian tests can be used to provide an approximate calibration between p values and bayes factors finally issues regarding the strong dependence of resulting bayes factors and p values on sample size are discussed

liaison classes of modules abstract we propose a concept of module liaison that extends gorenstein liaison of ideals and provides an equivalence relation among unmixed modules over a commutative gorenstein ring analyzing the resulting equivalence classes we show that several results known for gorenstein liaison are still true in the more general case of module liaison in particular we construct two maps from the set of even liaison classes of modules of fixed codimension into stable equivalence classes of certain reflexive modules as a consequence we show that the intermediate cohomology modules and properties like being perfect cohen macaulay buchsbaum or surjective buchsbaum are preserved in even module liaison classes furthermore we prove that the module liaison class of a complete intersection of codimension one consists of precisely all perfect modules of codimension one

constrained relative motions in rotational mechanics the dynamical effects of imposing constraints on the relative motions of component parts in a rotating mechanical system or structure are explored it is noted that various simplifying assumptions in modeling the dynamics of elastic beams imply strain constraints i e that the structure being modeled is rigid in certain directions in a number of cases such assumptions predict features in both the equilibrium and dynamic behavior which are qualitatively different from what is seen if the assumptions are relaxed it is argued that many pitfalls may be avoided by adopting so called geometrically exact models and examples from the recent literature are cited to demonstrate the consequences of not doing this these remarks are brought into focus by a detailed discussion of the nonlinear nonlocal model of a shear free inextensible beam attached to a rotating rigid body here it is shown that linearization of the equations of motion about certain relative equilibrium configurations leads to a partial differential equation such spatially localized models are not obtained in general however and this leaves open questions regarding the way in which the geometry of a complex structure influences computational requirements and the possibility of exploiting parallelism in performing simulations a general treatment of linearization about implicit solutions to equilibrium equations is presented and it is shown that this approach avoids unintended imposition of constraints on relative motions in the models finally the example of a rotating kinematic chain shows how constraining the relative motions in a rotating mechanical system may destabilize uniformly rotating states

vibration analysis of a rotating timoshenko beam the governing equations for linear vibration of a rotating timoshenko beam are derived by the d alembert principle and the virtual work principle in order to capture all inertia e ect and coupling between extensional and exural deformation the consistent linearization of the fully geometrically non linear beam theory is used the e ect of coriolis force on the natural frequency of the rotating beam is considered a method based on the power series solution is proposed to solve the natural frequency of the rotating timoshenko beam numerical examples are studied to verify the accuracy of the proposed method and to investigate the e ect of coriolis force on the natural frequency of rotating beams with di erent angular velocity hub radius and slenderness ratio 2001 academic press

dynamics of rectangular plates undergoing prescribed overall motion a set of linear equations of motion for rectangular plates undergoing prescribed overall motion is derived in this paper two in plane stretch variables with which the in plane strain energy of the plate can be expressed in an exact quadratic form are employed and approximated to derive the equations of motion the equations of motion include motion induced stiffness variation terms which are expressed as explicit functions of the prescribed overall motion the effects of the motion induced stiffness variation terms which are neglected in the conventional linear modelling method on the dynamic response of the plate are investigated the reliability and the accuracy of the equations of motion which are derived in the present work are examined through the numerical study

a powerful bayesian test for equality of means in high dimensions abstractwe develop a bayes factor based testing procedure for comparing two population means in high dimensional settings in large p small n settings bayes factors based on proper priors require eliciting a large and complex p p covariance matrix whereas bayes factors based on jeffrey s prior suffer the same impediment as the classical hotelling t2 test statistic as they involve inversion of ill formed sample covariance matrices to circumvent this limitation we propose that the bayes factor be based on lower dimensional random projections of the high dimensional data vectors we choose the prior under the alternative to maximize the power of the test for a fixed threshold level yielding a restricted most powerful bayesian test rmpbt the final test statistic is based on the ensemble of bayes factors corresponding to multiple replications of randomly projected data we show that the test is unbiased and under mild conditions is also locally consistent we demonstrate the efficacy of the appro

co rotational formulation for geometric nonlinear analysis of doubly symmetric thin walled beams abstract a doubly symmetric thin walled beam element with open section is derived using co rotational cr total lagrangian tl formulation the effects of deformation dependent third order terms of element nodal forces on the buckling load and post buckling behavior are investigated all coupling among bending twisting and stretching deformations for beam element is considered by consistent second order linearization of the fully geometrically nonlinear beam theory however all third order terms of nodal forces which are relevant to the twist rate rate of twist rate and curvature of the beam axis are also considered an incremental iterative method based on the newton raphson method combined with constant arc length of incremental displacement vector is employed for the solution of nonlinear equilibrium equations the zero value of the tangent stiffness matrix determinant of the structure is used as the criterion of the buckling state a parabolic interpolation method of the arc length is used to find the buckling load numerical examples are presented to demonstrate the accuracy and efficiency of the proposed element and to investigate the effect of third order terms of element nodal forces on the buckling load and post buckling behavior of doubly symmetric thin walled beams

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

a two sample test for equality of means in high dimension we develop a test statistic for testing the equality of two population mean vectors in the large p small n setting such a test must surmount the rank deficiency of the sample covariance matrix which breaks down the classic hotelling t2 test the proposed procedure called the generalized component test avoids full estimation of the covariance matrix by assuming that the p components admit a logical ordering such that the dependence between components is related to their displacement the test is shown to be competitive with other recently developed methods under arma and long range dependence structures and to achieve superior power for heavy tailed data the test does not assume equality of covariance matrices between the two populations is robust to heteroscedasticity in the component variances and requires very little computation time which allows its use in settings with very large p an analysis of mitochondrial calcium concentration in mouse cardiac muscles over time and of copy number varia

liaison equivalence classes we will work in ip n 2 over an algebraically closed field the notion of liaison among subvarieties of ip was introduced in 3 we will consider here liaison in codimension two generalizing results in 4 recall therefore that two subschemes v 1 v 2 of ip that are locally cohenmacaulay and equidimensional of codimension two are said to be linked algebraically via the complete intersection x of two hypersurfaces denoted v l v z via x if d e v j x v r o v x t j they are said to be linked geometrically if i 1 and v2 in the above definition have no components in common according to 4 theorem 1 7 the two notions of linkage generate the same equivalence relation among those subschemes v which are also generically locally complete intersections we will hence consider only algebraic linkage

even linkage classes in this paper we generalize the s and af type resolutions used by martin deschamps and perrin for curves in ip3 to subschemes of pure codimension in projective space and shows that these resolutions are interchanged by the mapping cone procedure under a simple linkage via these resolutions rao s correspondence is extended to give a bijection between even linkage classes of subschemes of pure codimension two and stable equivalence classes of reflexive sheaves s satisfying hi 5 0 and ext1 ev 9 0 further these resolutions are used to extend the work of martin deschamps and perrin for cohen macaulay curves in 1p3 to subschemes of pure codimension two in ip in particular even linkage classes of such subschemes satisfy the lazarsfeld rao property and any minimal subscheme for an even linkage class links directly to a minimal subscheme for the dual class

analytical predictions of chaos in a non linear rod the resonant and chaotic conditions for non dampened non linear planar rods are developed through the chirikov criterion and the subharmonic bifurcation conditions for weakly dampened non linear planar rods are also presented through the melnikov method the analytical conditions are based on a simply supported geometrically non linear planar rod model with a specific single mode response but these conditions are applicable to geometrically non linear planar rods with different supports chaos and transient motion from chaos to periodic motion in the non linear rod are simulated through the approximate rod model and they are illustrated through the poincare mapping section

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

transverse vibrations of a rotating uniform cantilever beam with tip mass as predicted by using beam characteristic orthogonal polynomials in the rayleigh ritz method abstract natural frequencies and mode shapes of a rotating uniform cantilever beam with a tip mass are studied by using beam characteristic orthogonal polynomials in the rayleigh ritz method the set of orthogonal polynomials which satisfy the geometrical boundary conditions are generated by using the gram schmidt process the results are compared with those obtained by the myklestad method the extended galerkin method and finite element methods the variation of natural frequencies with the speed of rotation is plotted for several parameter combinations such as setting angle tip mass moment of inertia of tip mass etc mode shapes at different rotational speeds are also plotted use of orthogonal polynomials for the deflection shapes enables the computation of higher natural frequencies of any order to be accomplished without facing any numerical difficulties which is not the case when arbitrary polynomial expressions are used

on the use of non local prior densities in bayesian hypothesis tests we examine philosophical problems and sampling deficiencies that are associated with current bayesian hypothesis testing methodology paying particular attention to objective bayes methodology because the prior densities that are used to define alternative hypotheses in many bayesian tests assign non negligible probability to regions of the parameter space that are consistent with null hypotheses resulting tests provide exponential accumulation of evidence in favour of true alternative hypotheses but only sublinear accumulation of evidence in favour of true null hypotheses thus it is often impossible for such tests to provide strong evidence in favour of a true null hypothesis even when moderately large sample sizes have been obtained we review asymptotic convergence rates of bayes factors in testing precise null hypotheses and propose two new classes of prior densities that ameliorate the imbalance in convergence rates that is inherited by most bayesian tests using members of these classes we obtain analytic expressions for bayes factors in linear models and derive approximations to bayes factors in large sample settings

a consistent finite element formulation for non linear dynamic analysis of planar beam summary a co rotational finite element formulation for the dynamic analysis of planar euler beam is presented both the internal nodal forces due to deformation and the inertia nodal forces are systematically derived by consistent linearization of the fully geometrically non linear beam theory using the d almbert principle and the virtual work principle due to the consideration of the exact kinematics of euler beam some velocity coupling terms are obtained in the inertia nodal fonxs an incremental iterative method based on the newmark direct integration method and the newton raphson method is employed here for the solution of the non linear dynamic equilibrium equations numerical examples are presented to investigate the effect of the velocity coupling terms on the dynamic response of the beam structures

vibration reduction of rotating frame structure based on quadratic performance index abstract an efficient method based on quadratic performance index and lyapunov s second method is developed for the vibration reduction optimization of frame structure rotating at a constant angular velocity four optimization formulations and algorithms are studied for both low and high angular velocity these formulations consider both linear vs nonlinear dynamic models as well as direct integration and lypunov method to evaluate performance index three numerical examples are presented to compare the effectiveness of the four algorithms numerical results show that all the four optimization methods can reduce vibration at low rotating speed and find very similar optimal designs however at high rotating speed dynamic model of rotating structure must consider nonlinear axial strain in order to obtain correct dynamic response since the lyapunov s second method is not applicable for the nonlinear model and the nfti nonlinear dynamic model with nonlinear axial strain and time integration method is very inefficient the present study develops a perturbation method linearizes the nonlinear dynamic model and establishes the lnfla linearized dynamic model with nonlinear axial strain the lyapunov s second method numerical examples show the optimization method lnfla provides an efficient numerical method for vibration reduction of rotating frame structure with both low and high rotating speed

geometrically non linear beam element for dynamics simulation of multibody systems summary the main objective of the present paper is to derive an explicit expression for the stiffness term in the dynamics equations of an elastic beam based on the non linear kinematics of deformation in particular we develop a closed form expression for the non linear stiffness matrix which operates on the total elastic deformations to give the vector of internal forces the derivation begins with the description of the deformation field and the exact non linear strain4isplacement relations for a conventional beam element the strain energy is formulated in accordance with the slender beam theory and various non linear terms are identified the non linear stiffness matrix is then obtained in two stages the first step involves application of castigliano s theorem to generate the vector of nodal internal forces s from the strain energy of the element in the second step we expand s in the nodal co ordinates q using the taylor formula because of the particular form of s this expansion is exact and consists of only three terms linear quadratic and cubic it allows us to directly evaluate the respective three terms of the non linear stiffness matrix by setting the closed form expressions for the elemental matrices xg and x are provided in terms of the nodal co ordinates these were determined using the maple symbolic computation program which was also employed to generate the latex format of the results and the corresponding fortran code the paper is concluded with two numerical examples demonstrating the performance of the dynamics models incorporating the proposed non linear stiffness term the first example illustrates the response of a cantilever beam to a prescribed moment at the base the second example is modelled after an experimental planar manipulator driven by two direct drive actuators the results illustrate the differences between three dynamics models formulated with the linear second order and third order approximations for the stiffness term

karhunen loeve decomposition of coupled axial bending vibrations of beams subject to impacts abstract this work presents a study of the oscillations of a vertical slender beam clamped in its upper extreme pinned in its lower one and constrained inside an outer cylinder in its lower portion the beam is subject to distributed axial loads due to its own weight leading to geometric softening of its lower portion and thus yielding a large number of vibroimpacts with the outer cylinder this is due to the axial bending coupling often called geometric stiffening and largely discussed in the last two decades here it is accounted for by using a non linear finite element model proposed in a previous work in which non linear strain displacement relations are considered to help understand this non linear coupled vibro impact problem the karhunen loeve decomposition also known as the proper orthogonal decomposition is applied to its simulated dynamics the results show that the micro impacts accompanying the beam hole impacts and mainly due to the beam compressive softening and the reaction forces at the top and bottom positions are well represented only when using a non linear axial bending coupling it is also shown that 15 proper orthogonal modes are sufficient to reconstruct the dynamics of the impacting beam under a 3 error margin

biliaison of sheaves we define an equivalence relation among coherent sheaves on a projective variety called biliaison we prove the existence of sheaves that are minimal in a biliaison class in a suitable sense and show that all sheaves in the same class can be obtained from a minimal one using certain deformations and other basic moves our results generalize the main theorems of liaison theory of subvarieties to sheaves and provide a framework to study sheaves and subvarieties simultaneously

new predictor corrector algorithms with improved energy balance for a recent formulation of dynamic vehicle structure interaction a new class of predictor corrector algorithms is proposed to solve the complex system of differential equations that arises from a galerkin spatial discretization of the equations of motion in a recent formulation of dynamic vehicle structure interaction the applicability of the concept of a building block vehicle structure interaction model developed in our previous work where the vehicle nominal motion is not prescribed a priori but is part of the unknown motion of the system is demonstrated through the construction of a simple vehicle model in the new algorithms the presence of the accelerations of the vehicle component is eliminated in the predictor structural equations making these equations different from the corrector structural equations the special treatment of the predicted axial motion that provides an artificial damping to eliminate unstable oscillations in the numerical results as proposed in the old algorithms is avoided accurate results from numerical simulations using the new algorithms are obtained and there are no unstable oscillations that were observed in some other predictor corrector schemes the system energy balance is also better preserved compared with the old algorithms

a four node plate bending element based on mindlin reissner plate theory and a mixed interpolation this communication discusses a 4 node plate bending element for linear elastic analysis which is obtained as a special case from a general nonlinear continuum mechanics based 4 node shell element formulation the formulation of the plate element is presented and the results of various example solutions are given that yield insight into the predictive capability of the plate and shell element

nonlinear feedback control of slewing beams abstract this paper is concerned with feedback control of slewing beams it allows for the hub to have finite rotation which leads to a fully nonlinear system it uses the method of state dependent riccati equation sdre to obtain feedback control laws the model assumes finite rigid body rotations and infinitesimal small elastic displacements it considers both the classical euler bermoulli model and the timoshenko model for the beam it uses finite element method to obtain approximate equations that can be used to construct feedback control laws

a justification of nonlinear properly invariant plate theories a single asymptotic derivation of three classical nonlinear plate theories is presented in a setting which preserves the frame invariance properties of three dimensional finite elasticity by a successive scaling of the external loading on the three dimensional body the nonlinear membrane theory the nonlinear inextensional theory and the von karman equations are derived as the leading order terms in the asymptotic expansion of finite elasticity the governing equations of the nonlinear inextensional theory are of particular interest where 1 plane strain kinematics and plane stress constitutive equations are derived simultaneously from the asymptotic analysis 2 the theory can be phrased as a minimization problem over the space of isometric deformations of a surface and 3 the local equilibrium equations are identical to those arising in the one director cosserat shell model furthermore it can be concluded that with a regular single scale asymptotic expansion it is not possible to obtain a system of plate equations in which finite membrane strain and finite bending strain occur simultaneously in the leading order term of an asymptotic analysis

a two sample test for high dimensional data with applications to gene set testing we proposed a two sample test for means of high dimensional data when the data dimension is much larger than the sample size the classical hotelling s t 2 test does not work for this large p small n situation the proposed test does not require explicit conditions on the relationship between the data dimension and sample size this offers much flexibility in analyzing high dimensional data an application of the proposed test is in testing significance for sets of genes which we demonstrate in an empirical study on a leukemia data set

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

three different guises for the dynamics of a rotating beam abstract the dynamics of a flexible beam forced by a prescribed rotation around an axis perpendicular to its plane is addressed three approaches are considered two of them related with simplified theories within strength of materials and the third one using finite elasticity in the strength of materials approaches the governing equations of motion are derived by superposing the deformations and the rigid motion in the first model and in the second by stating the stationarity of the lagrangian including first and second order effects in order to capture the stiffening due to the centrifugal forces through hamilton s principle two actions are considered gravity forces pendulum and prescribed rotation comparison of the two strength of materials models with the model derived from finite elasticity is carried out predictions for the same problems interpreted in the context of the specific model are compared and it was found that sometimes they give rather different results both in the results and in the computational cost energy analyses are performed in order to obtain information about the quality of the numerical solutions the paper ends with an example of a pendulum with a finite pivot including friction and flexibility when the structural elements are sufficiently slender and the rotational speeds are low so that the resulting deformations are small the strength of material model that includes the load stiffening and the finite elasticity approach lead to similar results it can be concluded that the stiffening phenomenon is appropriately considered in the first model on the contrary when the strength of material hypothesis are not fulfilled the problem should be addressed via the finite elasticity model additionally cases with complexities such as friction at a finite pivot can only be addressed by finite elasticity