the finite deformation theory for beam plate and shell part v the shell element with drilling degree of freedom based on biot strain due to the facts that the spatial moment force is non conservative and the three components of the finite rotation pseudo vector are not independent the ordinary variational principle based on a functional achieving its stationary value is not suitable for the problem subject to non conservative loading the finite element method proposed in this paper is based on the virtual work principle rigid normal assumption polar decomposition and total lagrangian formulation

revised notation for partial derivatives the principle of small quantities of leibniz s notation for total derivatives is applied logically to partial derivative notation the result is the notation fdx fdy instead of the old customary fdx fdy this improvement removes serious difficulties of the old notation

hopf bifurcation and turing instability in spatial homogeneous and inhomogeneous predator prey models abstract this paper is concerned with two species spatial homogeneous and inhomogeneous predator prey models with beddington deangelis functional response for the spatial homogeneous model the asymptotic behavior of the interior equilibrium and the existence of hopf bifurcation of nonconstant periodic solutions surrounding the interior equilibrium are considered furthermore the direction of hopf bifurcation and the stability of bifurcated periodic solutions are investigated for the model with no flux boundary conditions turing instability of the interior equilibrium solution is studied in particular turing instability region regarding the parameters is established finally to verify our theoretical results some numerical simulations are also included

stress resultant geometrically nonlinear shell theory with drilling rotations part ii computational aspects abstract in this work we discuss some details of the numerical implementation of the geometrically nonlinear shell theory presented in part i two possibilities to represent finite rotations with an orthogonal matrix and with a rotation vector are examined in detail along with their mutual relationship in both spatial and material description the issues pertinent to the consistent linearization procedure corresponding to these rotation parameterizations are also carefully considered the geometrically nonlinear method of incompatible modes is extended to the nonlinear shell theory under consideration and used to provide a 4 node shell element with enhanced performance a rather extensive set of numerical examples in nonlinear elastostatics is solved in order to corroborate the non locking performance of the incompatible mode based shell elements the examples include not only analyses of simple shell structures undergoing very large displacements and rotations but also cases of strong practical interest such as non smooth shell structures and shell structures with stiffeners

conservative integration of rigid body motion by quaternion parameters with implicit constraints summary an angular momentum and energy conserving time integration algorithm for rigid body rotation is formulated in terms of the quaternion parameters and the corresponding four component conjugate momentum vector via hamilton s equations the introduction of an extended mass matrix leads to a symmetric set of eight state space equations of motion the extra inertial parameter serves as a multiplier on the kinematic constraint and it is demonstrated that convergence characteristics are improved by selecting this parameter somewhat larger than the inertial moments external loads enter these equations via the set of momentum equations initially the normalization of the quaternion array is introduced via a lagrange multiplier however this lagrange multiplier can be expressed explicitly in terms of the gradient of the external load potential and elimination of the lagrange multiplier from the final format leaves only an explicit projection applied to the external load potential gradient an algorithm is developed by forming a finite increment of the hamiltonian this procedure identifies the proper selection of increments and mean values and leads to an algorithm with conservation of momentum and energy implementation conservation properties and accuracy of the algorithm are illustrated by examples with a flying box and a spinning top copyright 2012 john wiley sons ltd

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

on the parametrization of finite rotations in computational mechanics a classification of concepts with application to smooth shells this paper concerns the computational treatment of large rotations with application to the finite element discretisation of smooth shells formulations based on various rotational parametrizations are reviewed and classified with respect to their update structure category ii is based on total rotational degrees of freedom leading to an additive update structure whereas category i relies on linearized rotational degrees of freedom leading to a multiplicative update structure based on this classification new formulations are developed among them are the rodrigues formula applied within category ii with additive update structure for the two components of the rotation vector and two successive elementary rotations in the sense of euler angles applied within category i yielding a singularity free formulation the numerical examples confirm that every rotational parametrization when applied within category ii leads to singularities whereas the application within category i enables the calculation of overall rotations unrestricted in size without any singularity

critical study of newmark scheme on manifold of finite rotations in this paper we show that the usual material form of the newmark time stepping scheme of finite rotations is only a simplified version of the correct formula this is because spin material rotation vectors angular velocity vectors and angular accelerations vectors belong to different tangential vector spaces of a manifold at separate time moments we give corrected newmark time stepping schemes for material description and for spatial description

explicit isogeometric collocation for the dynamics of three dimensional beams undergoing finite motions abstract we initiate the study of three dimensional shear deformable geometrically exact beam dynamics through explicit isogeometric collocation methods the formulation we propose is based on a natural combination of the chosen finite rotations representation with an explicit geometrically consistent lie group time integrator we focus on extending the integration scheme originally proposed for rigid body dynamics to our nonlinear initial boundary value problem where special attention is required by neumann boundary conditions the overall formulation is simple and only relies on a geometrically consistent procedure to compute the internal forces once control angular and linear accelerations of the beam cross sections are obtained from the previous time step the capabilities of the method are shown through numerical applications involving very large displacements and rotations and different boundary conditions

velocity based approach in non linear dynamics of three dimensional beams with enforced kinematic compatibility abstract in the paper we present a new finite element formulation for the dynamic analysis of geometrically exact three dimensional beams we limit our studies to implicit time integration schemes and possible approaches for increasing their robustness and numerical stability in contrast to standard displacement rotation based approach we present here a spatial and temporal discretization based on velocities and angular velocities to describe the rotational degrees of freedom quaternions are used the time integration scheme and the governing equations of the three dimensional beam are modified accordingly in the numerical implementation the galerkin type discretization is employed to obtain the finite element formulation of the problem the result of our studies is simple but accurate efficient and robust numerical model

integrating finite rotations abstract we study the integration of problems of evolution in the rotation group instead of attacking the problem in the nonlinear differential manifold so 3 pure rotational dynamics as is usually done we derive equations for the complete problem of motion translational and rotational dynamics on an extended manifold we develop a generalization of runge kutta methods that by design ensures that the solution will remain on the manifold for any choice of the tableau this is obtained through configuration updates performed via the exponential map we show how certain terms can be approximated while retaining the order of accuracy of the scheme and how the method conserves the total momentum of the system within this framework we develop two nonlinearly unconditionally stable time integration schemes that are associated with discrete laws of conservation dissipation of the total energy the dissipating algorithm generalizes to the nonlinear case the high frequency damping characteristics provided by some well known conventional methods we present numerical results to support our analysis and we develop a complete application of this methodology to the nonlinear dynamics of three dimensional rods undergoing large displacements and finite rotations under the assumption of small strains

statically and kinematically exact nonlinear theory of rods and its numerical verification abstract the entirely general nonlinear theory of rods is developed two vector equilibrium equations valid on the rod axis are derived exactly by direct integration of the mechanical balance laws of continuum mechanics over the rod cross section then the energetically conjugate exact 6 field kinematics of the rod axis is implied in an integral identity which expresses the principle of the virtual work the kinematics consists of the displacement vector of the axis describing the average translation and the proper orthogonal tensor representing the average rotation of the cross section the integral identity also suggests the required general form of the constitutive relations they are already approximate from the physical side are then the best place to make geometric approximations and abbreviations to a certain constrained theory the constitutive relations the only nonexact segment of the theory are treated here as an interchangeable element supplementing the exactly formulated principle of virtual work the solution of the nonlinear rod problem becomes nonstandard here for the configuration space is the nonlinear manifold containing the rotation group so 3 applying the finite element method the proper parameterization linearization interpolation accumulation and discretization procedures in so 3 group are discussed a library of 2 3 4 node 1 d isoparametric elements is developed and the computer program ram is worked out the presented numerical tests contain several problems of highly nonlinear plane and spatial deformations of rods with constitutive relations taken at the moment from the classical isotropic elastic beams in all the tests the developed elements in comparison with the solutions known in the literature show a good performance

innovated higher criticism for detecting sparse signals in correlated noise higher criticism is a method for detecting signals that are both sparse and weak although first proposed in cases where the noise variables are independent higher criticism also has reasonable performance in settings where those variables are correlated in this paper we show that by exploiting the nature of the correlation performance can be improved by using a modified approach which exploits the potential advantages that correlation has to offer indeed it turns out that the case of independent noise is the most difficult of all from a statistical viewpoint and that more accurate signal detection for a given level of signal sparsity and strength can be obtained when correlation is present we characterize the advantages of correlation by showing how to incorporate them into the definition of an optimal detection boundary the boundary has particularly attractive properties when correlation decays at a polynomial rate or the correlation matrix is toeplitz

an efficient mixed variational reduced order model formulation for nonlinear analyses of elastic shells summary the koiter newton method had recently demonstrated a superior performance for non linear analyses of structures compared to traditional path following strategies the method follows a predictor corrector scheme to trace the entire equilibrium path during a predictor step a reduced order model is constructed based on koiter s asymptotic post buckling theory which is followed by a newton iteration in the corrector phase to regain the equilibrium of forces in this manuscript we introduce a robust mixed solid shell formulation to further enhance the efficiency of stability analyses in various aspects we show that a hellinger reissner variational formulation facilitates the reduced order model construction omitting an expensive evaluation of the inherent fourth order derivatives of the strain energy we demonstrate that extremely large step sizes with a reasonable out of balance residual can be obtained with substantial impact on the total number of steps needed to trace the complete equilibrium path more importantly the numerical effort of the corrector phase involving a newton iteration of the full order model is drastically reduced thus revealing the true strength of the proposed formulation we study a number of problems from engineering and compare the results to the conventional approach in order to highlight the gain in numerical efficiency for stability problems this article is protected by copyright all rights reserved

a hybrid mixed model for non linear shell analysis and its applications to large rotation problems adopting an updated lagrange approach the general framework for the fully non linear analysis of curved shells is developed using a simple quadrilateral c0 model hmsh5 the governing equations are derived based on a consistent linearization of an incremental mixed variational principle of the modified hellinger reissner type with independent assumptions for displacement and strain fields emphasis is placed on devising effective solution procedures to deal with large rotations in space finite stretches and generalized rate type material models in particular a geometrically exact scheme for configuration update is developed by making use of the so called exponential mapping algorithm and the resulting element was shown to exhibit a quadratic rate of asymptotic convergence in solving practical shell problems with newton raphson type iterative schemes for the purpose of updating the spatial stress field of the element an objective generalized midpoint integration rule is utilized which relies crucially on the concept of polar decomposition for the deformation gradient and is in keeping with the underlying mixed method finally the effectiveness and practical usefulness of the hmsh5 element are demonstrated through a number of test cases involving beams plates and shells undergoing very large displacements and rotations

stability and bifurcation analysis of a stage structured predator prey model with time delay abstract in this paper we proposed and analyzed a prey predator system with stage structured for the predator population a time delay is incorporated due to the gestation for the matured predator all the possible non negative equilibria are obtained and their local as well as global behavior are studied choosing delay as a bifurcation parameter the existence of the hopf bifurcation of the system has been investigated moreover we use the normal form method and the center manifold theorem to examine the direction of the hopf bifurcation and the nature of the bifurcating periodic solution some numerical simulations are given to support the analytical results some interesting conclusions are obtained from our analysis and it is given at the end of the paper

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

generalized mixed finite element model for pre and post quasistatic buckling response of thin walled framed structures adopting an updated lagrangian approach the general framework for the fully non linear analysis of thin walled framed structures is developed using a simple two node c0 model hmb2 the governing equations are derived based on a consistent linearization of an incremental mixed variational principle of modified hellinger reissner type with independent assumptions for displacement and strain fields all coupled significant modes of deformations i e stretching bending shear torsion and warping are accounted for in the generalized beam theory employed emphasis is placed on devising effective solution procedures to deal with finite rotations in space particularly with regard to their effect on the derivations of load correction matrices corresponding to configuration dependent externally applied forces moments the effectiveness and practical usefulness of present model are demonstrated through a number of test problems involving beam assemblages undergoing large displacements and rotations in space

rich dynamics of a predator prey model with spatial motion one of the central issues in ecosystem is the influence of space on the stability of the populations as a result a predator prey model with spatial diffusion and cubic growth rate is investigated asymptotical properties of solutions of such spatial model are obtained based on comparison principle what is more we show the global stability of positive equilibrium by constructing lyapunov function we also show how predator diffuses has impact on the pattern dynamics based on numerical simulations the results may well enrich the findings in predator prey systems with spatial motions

a co rotational quasi conforming 4 node resultant shell element for large deformation elasto plastic analysis abstract a co rotational quasi conforming formulation of a 4 node stress resultant shell element is presented for non linear analysis of plate and shell structures the tangent stiffness matrix in this quasi conforming formulation is explicitly integrated this makes the element computationally efficient in incremental non linear analysis it includes drilling degrees of freedom which improves membrane behavior and allows the modeling of stiffened plates and shells it is also free of shear locking behavior the formulation of the geometrical stiffness is derived using the full definition of green strain tensor the inclusion of the bending moment and transverse shear resultant forces in the geometric stiffness allows effective analysis of stability problems of moderately thick plates and shells the stresses are accurately taken at the nodal points without extrapolation the plasticity is traced by applying the von mises yield condition and prandtl reuss flow rule to discrete points through the thickness the multi layered approach is based on equally spaced stations including extreme fibers a modified trapezoidal rule is used for the numerical integration of the constitutive relation in the plasticity part numerous tests are carried out for the non linear validation of present 4 node shell element and the results are in good agreement with references

geometrically non linear and elastoplastic three dimensional shear flexible beam element of von mises type hardening material a three dimensional elastoplastic beam element being capable of incorporating large displacement and large rotation is developed and examined elastoplastic constitutive equations are applied to the beam element based upon the assumption of small deformational strain leading to a material formulation which is completely objective for the application of stress update procedures the continuum type equations of plastic model of j2 mixed hardening are transformed into the beam equations by satisfying beam hypotheses an effective stress update algorithm is proposed to integrate elastoplastic rate equations by means of the so called multistep method which is a method of successive control of residuals on yield surfaces it avoids severe divergence when the displacement increments become large which is usual for the continuation methods material tangent stiffness matrix is derived by using consistent elastoplastic modulus resulting from the integration algorithm and is combined with geometric tangent stiffness matrix different from other elements the present element is shear flexible and can satisfy the plasticity condition in a pointwise fashion a great number of numerical examples are analysed and compared with the literature the proposed beam element is verified to be not only quite accurate but also very effective for the analyses of pre buckling and large deflection collapse of spatial framed structures

branched channel free streamlines abstract two configurations of free streamlines in a branched channel in plane incompressible potential flow are analysed for three different branch angles these cases were studied before by modi et al and sinha et al but their results are found to be incorrect the hodograph method is used producing a schwarz christoffel like integral over a semi disk region the integration is carried out using convolution number algebra which produces the potential flow in analytical form the unknown parameters in the integral are solved by iteration using the newton raphson method with the jacobian matrix approximated by a finite difference quotient matrix it is shown how a further conformal mapping of the semi disk to the full circular disk leads to the transformation of elcrat and trefethen

a formulation of the mitc4 shell element for finite strain elasto plastic analysis abstract a finite strain elasto plastic formulation is developed for the mitc4 shell element the developed formulation is based on lee s multiplicative decomposition of the deformation gradient and on the hyperelastic expression of von mises flow rule expressed in terms of hencky s strain tensor the formulation incorporates thickness stretching degrees of freedom that are condensed at the element level by imposing the classical in layer plane stress condition a symmetric and consistent tangent stiffness matrix is also developed

regularized estimation of large covariance matrices this paper considers estimating a covariance matrix of p variables from n observations by either banding the sample covariance matrix or estimating a banded version of the inverse of the covariance we show that these estimates are consistent in the operator norm as long as logp 2 n 0 and obtain explicit rates the results are uniform over some fairly natural well conditioned families of covariance matrices we also introduce an analogue of the gaussian white noise model and show that if the population covariance is embeddable in that model and well conditioned then the banded approximations produce consistent estimates of the eigenvalues and associated eigenvectors of the covariance matrix the results can be extended to smooth versions of banding and to non gaussian distributions with su ciently short tails a resampling approach is proposed for choosing the banding parameter in practice this approach is illustrated numerically on both simulated and real data

bifurcation studies on travelling wave solutions for nonlinear intensity klein gordon equation abstract in this paper we study the travelling waves for the n 1 dimensional klein gordon equation with nonlinear intensity by using the bifurcation theory and methods of planar dynamic systems with the aid of maple we obtain all bifurcations and phase portraits in the parametric space moreover we explain the reason for appearance of nonsmooth travelling waves and for persistence of smoothness of smooth travelling waves and show the existence of smooth and nonsmooth solitary and periodic waves under different regions of parametric space various sufficient conditions to guarantee the existence of the above solutions are given

large rotations revisited application of lie algebra abstract the paper presents an elementary introduction and application of lie algebra to compound groups of large rotations following an elementary overview of the foundations of lie algebra the authors discuss the rotational groups lo 3 and the exponential form of the rotation matrix these yield a practical link between the elegance of lie group theory and engineering kinematics some illustrative examples as the standard stanford manipulator indicate interesting possibilities on enlarged applications concerning robotic mechanisms vehicles and biosystems

a simplified implicit newmark integration scheme for finite rotations implicit newmark schemes for integration of finite rotations in structural and continuum mechanics typically are more complicated than those used for translational motion using euler s representation of the rotation tensor l in terms of a rotation vector f numerical integration connecting the values f n l n and f n 1 l n 1 at the beginning and end of the time step is expressed in terms of an incremental rotation vector q and the associated incremental rotation tensor l q here it is shown using backward differentiation that neglecting third order terms in q the approximation for the angular velocity w in terms of q and its time derivative has the same form as that between velocity and displacement consequently the simplified newmark scheme in terms of q w email protected has the same form as that for updating translations details of the newmark scheme and an analytical expression for the tangent stiffness tensor for the associated newton raphson iteration procedure have been presented for rigid body dynamics the resulting integration scheme has been tested on a nontrivial problem of three dimensional motion of a rigid body using a constant time step the results justify the use of the simplified newmark scheme for finite rotations

hopf bifurcation of traveling wave solutions of delayed fisher kpp equation the dynamical behavior of the traveling wave front solutions of the delayed fisher kpp equation is studied by employing the theory of functional differential equation it is found that when the delay term t comes through a threshold one equilibrium point is always unstable and there exists a periodic solution near the other equilibrium point in the traveling wave equation by using the theory of center manifold and normal form the stability of the bifurcating periodic solution which corresponds to the periodic traveling wave solution of the original equation is obtained finally some numerical simulations are also given to illustrate our results of theoretical analysis

matrix tensor notation part ii skew and curved coordinates in part i a notation called matrix tensor notation was introduced for rectilinear orthogonal coordinates part ii discusses how the same notation is equally efficient for vectors and 2nd order tensors in skew bases and skew curved coordinates without considering coordinates first vectors and 2nd order tensors are described in skew bases covariant and contravariant descriptions being distinguished similar to tensor notation a consistent interpretation of deformation and strain in terms of skew bases is given the use of the transpose symbol complicates the matrix algebra but integrates it with tensor algebra which makes it possible to interpret customary tensor equations as relations in space with all the advantages that an isomorphism with euclidean space has it is demonstrated how different metrics can be assigned arbitrarily to define higher dimensional orthogonal vectors in abstract higher dimensional space a consistent notation is given to distinguish between subspace and subbase to write higher order tensors as matrices or 2nd order tensors as vectors partial transpose is introduced which is a formal stretching operation to write any higher order tensor product operation as matrix vector product the description of the variable bases in generally curved coordinates is given in this notation together with the corresponding notation for the partial differentiation rules the vector operations grad div and curl are discussed and an almost physical notation for the christoffel symbols is given however the replacement of tensor notation for higher than second order tensors by matrix tensor notation is not feasible a version of matrix tensor notation that merges with the customary printed form is presented in an appendix further applications are deferred to part iii applying the new notation to curved coordinates in function space and the equations of mechanics projected on finite dimensional subspaces

optimal classification in sparse gaussian graphic model consider a two class classification problem where the number of features is much larger than the sample size the features are masked by gaussian noise with mean zero and covariance matrix sigma where the precision matrix omega sigma 1 is unknown but is presumably sparse the useful features also unknown are sparse and each contributes weakly i e rare and weak to the classification decision by obtaining a reasonably good estimate of omega we formulate the setting as a linear regression model we propose a two stage classification method where we first select features by the method of innovated thresholding it and then use the retained features and fisher s lda for classification in this approach a crucial problem is how to set the threshold of it we approach this problem by adapting the recent innovation of higher criticism thresholding hct we find that when useful features are rare and weak the limiting behavior of hct is essentially just as good as the limiting behavior of ideal threshold the threshold one would choose if the underlying distribution of the signals is known if only somewhat surprisingly when omega is sufficiently sparse its off diagonal coordinates usually do not have a major influence over the classification decision compared to recent work in the case where omega is the identity matrix proc natl acad sci usa 105 2008 14790 14795 philos trans r soc lond ser a math phys eng sci 367 2009 4449 4470 the current setting is much more general which needs a new approach and much more sophisticated analysis one key component of the analysis is the intimate relationship between hct and fisher s separation another key component is the tight large deviation bounds for empirical processes for data with unconventional correlation structures where graph theory on vertex coloring plays an important role

warping and in plane twist parameters in kinematics of finite rotation shells abstract the finite rotation shell equations are derived from a 3d mixed formulation with explicit rotations constitutive equations are written in terms of the relaxed biot stress and right stretch strain the shell kinematics is based on a generalised reissner hypothesis and rotations depending on the thickness coordinate the generalized reissner hypothesis includes a bubble like term for the warping of a cross section the rotations linearly vary over the thickness and are parametrised by a canonical rotation vector the components of the rotation vector can be identified as the in plane twist parameter and two warping parameters consequences of this new rotation vector for shell equations especially for rotation constraints and strain measures are examined and a comparison with the formulation which includes the in plane twist parameter is made the new rotation vector is treated as an implicit kinematical parameter and recovered from the rotation constraint hence a 6 parameter shell formulation admitting c 0 approximations is retained

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

delay induced traveling wave fronts in reaction diffusion equations of kpp fisher type this paper explores the impact of delay on the existence of traveling wave fronts in reaction diffusion equations of kpp fisher type for two such equations one being local and the other with nonlocal effect arising from the age structure of the population we show that delay can induce slow traveling wave fronts

stability and hopf bifurcation for a delayed prey predator system with diffusion effects abstract this paper is concerned with a delayed lotka volterra prey predator system with diffusion effects and neumann boundary conditions the main purpose is to investigate the stability of spatially homogeneous positive equilibrium and give the explicit formulae determining the direction and stability of hopf bifurcation by linearizing the system at positive equilibrium and analyzing the associated characteristic equation the stability of positive equilibrium and the existence of hopf bifurcation are demonstrated by means of the normal form theory and the center manifold reduction for partial functional differential equations pfdes the direction and stability of periodic solutions occurring through hopf bifurcation are determined finally in order to verify our theoretical results some numerical simulations are also included

nonlinear finite element analysis of elastic systems under nonconservative loading natural formulation part ii dynamic problems abstract the paper presents a nonlinear finite element analysis of elastic structures subject to nonconservative forces attention is focused on the stability behaviour of such systems this leads mathematically to non self adjoint boundary value problems which are of great theoretical and practical interest in particular in connection with alternative modes of instability like divergence of flutter only quasistatic effects are however considered in the present part the methodology of our theory is general but the specific thrust of the present research is directed towards the analysis of structures acted upon by displacement dependent nonconservative follower forces in a finite element formulation the analysis of geometrically nonlinear elastic systems subject to such forces gives in general rise to a contributory nonsymmetric stiffness matrix known as the load correction matrix as a result the total tangent stiffness matrix becomes unsymmetric an indication of the non self adjoint character of the problem our theory is based on the natural mode technique 1 2 3 and permits i a a simple but elegant derivation of the load correction matrix the application of the general theory as evolved in this paper is demonstrated on the beam element in space a number of numerical examples are considered including divergence and flutter types of instability for which exact analytic solutions are known the problems demonstrate the efficiency of the present finite element formulation the paper furnishes also a novel and concise formulation of finite rotations in space which may be considered as a conceptual generalization of the theory presented in 2 3

kinematically exact curved and twisted strain based beam the paper presents a formulation of the geometrically exact three dimensional beam theory where the shape functions of three dimensional rotations are obtained from strains by the analytical solution of kinematic equations in general it is very demanding to obtain rotations from known rotational strains in the paper we limit our studies to the constant strain field along the element the relation between the total three dimensional rotations and the rotational strains is complicated even when a constant strain field is assumed the analytical solution for the rotation matrix is for constant rotational strains expressed by the matrix exponential despite the analytical relationship between rotations and rotational strains the governing equations of the beam are in general too demanding to be solved analytically a finite element strain based formulation is presented in which numerical integration in governing equations and their variations is completely omitted and replaced by analytical integrals some interesting connections between quantities and non linear expressions of the beam are revealed these relations can also serve as useful guidelines in the development of new finite elements especially in the choice of suitable shape functions

bifurcation method and traveling wave solution to whitham broer kaup equation by using bifurcation method to whitham broer kaup shallow water equations bifurcation parameter sets are shown numbers of solitary waves kink waves and periodic waves are given under various parameter conditions all explicit formulas of solitary wave solutions kink wave solutions and periodic wave solutions are listed

nonlinear thin shell analysis using a curved triangular element abstract this paper describes a simple but robust curved triangular thin shell element the element has twelve degrees of freedom namely the displacement components in the corner nodes and the rotations about the element sides the element is based upon the well known facet element with constant membrane strains and constant stress couples and is augmented to take into account the influence of the changes of curvature on the membrane deformations due to the quadratic character of this influence curved geometries can be modelled in order to permit arbitrarily large rotational increments reference vectors are attached to each element side these reference vectors are updated by means of orthogonal transformations the latter are determined uniquely by the subsequent orientations of the associated element sides the changes of curvature are evaluated using these reference vectors and a corotated reference configuration to describe time independent elastoplasticity a layered shell model is applied while besseling s fraction model is adopted for each layer a number of numerical examples illustrate the performance of the element

high dimensional classification using features annealed independence rules classification using high dimensional features arises frequently in many contemporary statistical studies such as tumor classification using microarray or other high throughput data the impact of dimensionality on classifications is largely poorly understood in a seminal paper bickel and levina 2004 show that the fisher discriminant performs poorly due to diverging spectra and they propose to use the independence rule to overcome the problem we first demonstrate that even for the independence classification rule classification using all the features can be as bad as the random guessing due to noise accumulation in estimating population centroids in high dimensional feature space in fact we demonstrate further that almost all linear discriminants can perform as bad as the random guessing thus it is paramountly important to select a subset of important features for high dimensional classification resulting in features annealed independence rules fair the conditions under which all the important features can be selected by the two sample t statistic are established the choice of the optimal number of features or equivalently the threshold value of the test statistics are proposed based on an upper bound of the classification error simulation studies and real data analysis support our theoretical results and demonstrate convincingly the advantage of our new classification procedure

finite element analysis of linear and non linear planar deformations of elastic initially curved beams reference epfl article 102719view record in web of science record created on 2007 04 23 modified on 2016 08 08

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

the helicoidal modeling in computational finite elasticity part i variational formulation the finite elasticity mechanics of continua capable of a polar description is formulated by an alternative modeling to keeping position and orientation as uncoupled fields the rototranslation between two material particles can be described by a single complex tensorial quantity which is recognized to be orthogonal its linearization gives the characteristic curvature and differential vectors underlying the helicoidal modeling in both the sense of the body geometric description and the evolution of a deforming body after due introduction to dual tensors and rototranslations the polar description of the continuum is addressed with particular care to mixed differentiations of the rototranslation field then a thorough variational framework is established for the most general polar continuum under hyperelasticity hypothesis and the three field two field and one field principles are drawn and linearized the proposed modeling is expected to be profitably exploited in non linear finite element analyses of solids undergoing finite displacements rotations and strains

primal and mixed variational principles for dynamics of spatial beams a general formulation is presented for static and dynamic analysis of spatial elastic beams capable of undergoing finite rotations and small strains the tangent maps associated to the finite rotation vector are used to compute the tangent iteration matrices used to integrate implicitly the equations of motion in descriptor form a total lagrangian primal corotational method and an updated lagrangian mixed variational method are proposed to compute the tangent stiffness matrix the tangent inertia matrices including the gyroscopic and centrifugal terms are also obtained by using the tangent maps of rotation the numerical examples analyzed in this paper include static pre and postbuckling and dynamic analysis of flexible beams structures the new finite elements show a very good performance in terms of fewer number of elements used and accuracy during the simulation both for static and dynamic problems

a constrained l1 minimization approach to sparse precision matrix estimation this article proposes a constrained l1 minimization method for estimating a sparse inverse covariance matrix based on a sample of n iid p variate random variables the resulting estimator is shown to have a number of desirable properties in particular the rate of convergence between the estimator and the true s sparse precision matrix under the spectral norm is when the population distribution has either exponential type tails or polynomial type tails we present convergence rates under the elementwise l norm and frobenius norm in addition we consider graphical model selection the procedure is easily implemented by linear programming numerical performance of the estimator is investigated using both simulated and real data in particular the procedure is applied to analyze a breast cancer dataset and is found to perform favorably compared with existing methods

shape optimal design of elastic space frames with non linear response this paper describes an approach to shape optimal design of elastic planar frames with non linear response the foundation of the proposed approach forms an appropriate strategy of shape representation of the structure based on the design element technique a frame structure is treated as to be assembled from several frame design elements which in turn may consist of several appropriately joined beam finite elements the shape of each frame design element is defined by convenient functions involving bezier blending polynomials the original formulation of the beam finite element proposed by saje is modified in order to fit nicely into the context of the frame design element technique the formulation of the shape optimal design problem in a form of a problem of non linear mathematical programming and its solution by employing gradient based methods of mathematical programming are discussed briefly the theory is illustrated with two numerical examples

feature screening via distance correlation learning this article is concerned with screening features in ultrahigh dimensional data analysis which has become increasingly important in diverse scientific fields we develop a sure independence screening procedure based on the distance correlation dc sis the dc sis can be implemented as easily as the sure independence screening sis procedure based on the pearson correlation proposed by fan and lv however the dc sis can significantly improve the sis fan and lv established the sure screening property for the sis based on linear models but the sure screening property is valid for the dc sis under more general settings including linear models furthermore the implementation of the dc sis does not require model specification e g linear model or generalized linear model for responses or predictors this is a very appealing property in ultrahigh dimensional data analysis moreover the dc sis can be used directly to screen grouped predictor variables and multivariate response variables we establish

a new look into the kinematics and dynamics of finite rigid body rotations using lie group theory abstract a systematic theoretical approach is presented in an effort to provide a complete and illuminating study on kinematics and dynamics of rigid bodies rotating about a fixed point specifically this approach is based on some fundamental concepts of differential geometry with particular reference to lie group theory this treatment is motivated by the form of the configuration space corresponding to large rigid body rotation which is a differentiable manifold possessing group properties first the basic steps of the classical approach on the subject are briefly summarized then some geometrical tools are presented which are essential for supporting and illustrating the steps and findings of the new approach finally the emphasis is placed on a thorough investigation of the problem of finite rotations a key idea is the introduction of a canonical connection matching the manifold and group properties of the configuration space this proves to be sufficient and effective for performing the kinematics next following the selection of an appropriate metric the dynamics is also carried over the present approach is theoretically more demanding than the traditional treatments in engineering but brings substantial benefits in particular an elegant interpretation is provided for all the quantities with fundamental importance in both rigid body kinematics and dynamics most importantly this also leads to a correction of some misconceptions and geometrical inconsistencies in the field among other things the deeper understanding of the theoretical concepts provides powerful insight and a strong basis for the development of efficient numerical techniques in problems of solid and structural mechanics involving large rotations

global transformations of nonlinear systems recent results have established necessary and sufficient conditions for a nonlinear system of the form dot x t f x t u t g x t with f 0 0 to be locally equivalent in a neighborhood of the origin in rnto a controllable linear system we combine these results with several versions of the global inverse function theorem to prove sufficient conditions for the transformation of a nonlinear system to a linear system in doing so we introduce a technique for constructing a transformation under the assumptions that g ldot f dotg ad n 1 f ldotg span an n dimensional space and that g ldot f ldot g ad n 2 f ldotg is an involutive set

a unified co rotational framework for solids shells and beams abstract the paper describes a unified framework for applying the co rotational method to the analysis of solids shells and beams the general method stems from an unusual application of the technique which involves solid elements the proposed framework allows a formulation that is simpler than many of the earlier procedures and in addition gives a direct indication of the terms in the tangent stiffness which may be ignored

kinematics of finite rotation shells with in plane twist parameter abstract the paper concerns shell equations derived from a 3d mixed formulation with explicit rotations the constitutive equation is postulated in terms of the relaxed biot stress and right stretch strain the shell kinematics is based on the reissner hypothesis and on a constant linear approximation of the rotation tensor with respect to the thickness coordinate the rotation around the shell director is parametrized by the drill and in plane twist parameters with the latter one associated with the linear approximation the in plane twist parameter is new and hence consequences of its presence for the shell rotation constrains and strain measures are examined and compared to the formulation with the drill rotation only in the presented formulation the drill rotation is retained explicitly and can be recovered from the drill rotation constraint while the in plane twist parameter is an internal parameter of the theory in this way the enhanced shell kinematics does not increase the number of degrees of freedom of a discrete model

decay rate estimates for the quasi linear timoshenko system with nonlinear control and damping terms in this work we consider a class of quasi linear timoshenko systems with nonlinear control and damping terms we investigate the stabilization of weak solutions to the initial boundary value problem and obtain explicit decay rate estimation depending on control and damping terms

dimensionality reduction via sparse support vector machines we describe a methodology for performing variable ranking and selection using support vector machines svms the method constructs a series of sparse linear svms to generate linear models that can generalize well and uses a subset of nonzero weighted variables found by the linear models to produce a final nonlinear model the method exploits the fact that a linear svm no kernels with l1 norm regularization inherently performs variable selection as a side effect of minimizing capacity of the svm model the distribution of the linear model weights provides a mechanism for ranking and interpreting the effects of variables starplots are used to visualize the magnitude and variance of the weights for each variable we illustrate the effectiveness of the methodology on synthetic data benchmark problems and challenging regression problems in drug design this method can dramatically reduce the number of variables and outperforms svms trained using all attributes and using the attributes selected according to correlation coefficients the visualization of the resulting models is useful for understanding the role of underlying variables

generalized energy momentum method for non linear adaptive shell dynamics in the present study a generalization of the energy momentum method denoted by generalized energy momentum method applied to the non linear dynamics of shells will be developed within the framework of the generalized a method this algorithmic environment contains the unconditionally stable energy momentum method and its numerically damped version as well as the classical newmark and a methods as special cases in order to control the size of the time steps of the integration scheme with respect to accuracy and eaciency an adaptive time stepping procedure based on local a posteriori error estimation will be improved for non linear dynamical systems and applied to the proposed class of algorithms the spatial discretization is realized by an eight noded finite shell element of reissner mindlin type including an extensible shell director field permitting the application of three dimensional material laws the original formulation of this finite element will be developed for non linear dynamic analysis and adapted for the employment within the introduced energy conserving decaying time integration scheme 1999 elsevier science s a all rights reserved

goodness of fit tests via phi divergences a unified family of goodness of fit tests based on o divergences is introduced and studied the new family of test statistics s n s includes both the supremum version of the anderson darling statistic and the test statistic of berk and jones z wahrsch verw gebiete 47 1979 47 59 as special cases s 2 and s 1 resp we also introduce integral versions of the new statistics we show that the asymptotic null distribution theory of berk and jones z wahrsch verw gebiete 47 1979 47 59 and wellner and koltchinskii high dimensional probability iii 2003 321 332 birkhauser basel for the berk jones statistic applies to the whole family of statistics s n s with s 1 2 on the side of power behavior we study the test statistics under fixed alternatives and give extensions of the poisson boundary phenomena noted by berk and jones for their statistic we also extend the results of donoho and jin ann statist 32 2004 962 994 by showing that all our new tests for s 1 2 have the same optimal detection boundary for normal shift mixture alternatives as tukey s higher criticism statistic and the berk jones statistic

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

empirical bayes estimates for large scale prediction problems classical prediction methods such as fisher s linear discriminant function were designed for small scale problems in which the number of predictors n is much smaller than the number of observations n modern scientific devices often reverse this situation a microarray analysis for example might include n 100 subjects measured on n 10 000 genes each of which is a potential predictor this article proposes an empirical bayes approach to large scale prediction where the optimum bayes prediction rule is estimated employing the data from all of the predictors microarray examples are used to illustrate the method the results demonstrate a close connection with the shrunken centroids algorithm of tibshirani et al 2002 a frequentist regularization approach to large scale prediction and also with false discovery rate theory

formulation and solution of inverse spaghetti problem application to beam deployment dynamics a finite element model of the dynamics of axially moving highly flexible beams is presented the model is based on a geometrically nonlinear beam formulation that allows for large overall motions to account for the varying length of a deploying beam a moving finite element reference grid is incorporated within the nonlinear beam formulation such that the number of finite element nodes remains fixed and the finite element length is allowed to vary hamilton s law is used to formulate the equations of motion and a transient integration solution procedure is derived from a space time finite element discretization of the hamiltonian variational principle computational results of the methodology are presented for a planar inverse spaghetti problem he dynamics of axially moving beamlike structures are becoming increasingly important for the analysis of spacecraft and large space structures that deploy flexible appendages such as antenna stabilizing booms solar arrays and long trusslike structures as well as for other applications such as magnetic tape drives printing machines traveling cables and band saws an extensive amount of research has focused on the modeling of axially moving continua to analyze the dynamic behavior of such structures one of the most common models of axially moving continua that has received the most attention is the traveling string problem in what he termed the spaghetti problem carrier1 analyzed the motion of a string being accelerated upward into a fixed orifice in other works since then analytical expressions representing both linear and nonlinear vibrations of axially moving strings subject to various support conditions have been derived 2 9 the dynamics of beamlike structures traveling between or over fixed supports have also been studied to address industrial applications such as high speed tape drives and band saws 10 13 to address spacecraft applications in which antenna or other long flexible structures are deployed from a host satellite the dynamics of a cantilever beam that is ejected from a single fixed guide are modeled using bernoulli euler beam theory in ref 14 in a quite different approach the extrusion of a beam from a rotating base is modeled using a series of elastically connected rigid links in which the number of rigid links are continuously increased decreased to account for deployment retrieval of the beam 15 general formulations of axially moving bernoulli euler beam models cantilevered to a rotating rigid host body have also been developed to study the effect of appendage deployment on the attitude dynamics of orbiting spacecraft 16 20 all of these given analyses are based on an assumption of small elastic deformations with the exception of the discrete spring mass model of ref 15 all of the other models that have been referenced thus far use linear combinations of space depende nt admissible functions of a time varying length weighted by time dependen t generalized coordi

higher criticism thresholding optimal feature selection when useful features are rare and weak in important application fields today genomics and proteomics are examples selecting a small subset of useful features is crucial for success of linear classification analysis we study feature selection by thresholding of feature z scores and introduce a principle of threshold selection based on the notion of higher criticism hc for i 1 2 p let i denote the two sided p value associated with the ith feature z score and i denote the ith order statistic of the collection of p values the hc threshold is the absolute z score corresponding to the p value maximizing the hc objective i p i i p 1 i p we consider a rare weak rw feature model where the fraction of useful features is small and the useful features are each too weak to be of much use on their own hc thresholding hct has interesting behavior in this setting with an intimate link between maximizing the hc objective and minimizing the error rate of the designed classifier and very different behavior from popular threshold selection procedures such as false discovery rate thresholding fdrt in the most challenging rw settings hct uses an unconventionally low threshold this keeps the missed feature detection rate under better control than fdrt and yields a classifier with improved misclassification performance replacing cross validated threshold selection in the popular shrunken centroid classifier with the computationally less expensive and simpler hct reduces the variance of the selected threshold and the error rate of the constructed classifier results on standard real datasets and in asymptotic theory confirm the advantages of hct

on a stress resultant geometrically exact shell model part vi conserving algorithms for non linear dynamics in parts i to v of the present work the formulation and finite element implementation of a non linear stress resultant shell model are considered in detail this paper is concerned with the extension of these results to incorporate completely general non linear dynamic response of special interest here is the dynamics of very flexible shells undergoing large overall motion which conserves the total linear and angular momentum and for the hamiltonian case the total energy a main goal of this paper is the design of non linear time stepping algorithms and the construction of finite element interpolations which preserve exactly these fundamental constants of motion it is shown that only a very special class of algorithms namely a formulation of the mid point rule in conservation form exactly preserves the total linear and angular momentum for the hamiltonian case a somewhat surprising result is proved regardless of the degree of non linearity in the stored energy function a generalized mid point rule algorithm always exists which exactly conserves energy the conservation properties of a time stepping algorithm need not and in general will not be preserved by the spatial discretization precise conditions which ensure preservation of these conservation properties are derived a number of numerical simulations are presented which illustrate the exact conservation properties of the proposed methodology

finite element formulation of geometrically exact three dimensional beam theories based on interpolation of strain measures this paper presents a new finite element formulation of the geometrically exact finite strain beam theory the governing equations of the beam element are derived in which the strain vectors are the only unknown functions the consistency condition that the equilibrium and the constitutive internal force and moment vectors are equal is enforced to be satisfied at chosen points the solution is found by a collocation algorithm the linearity of the strain space not only simplifies the application of newton s method on the non linear configuration space but also leads to the strain objectivity of the proposed method the accuracy and the efficiency of the derived numerical algorithm are demonstrated by several examples c 2003 elsevier b v all rights reserved

high dimensional variable selection this paper explores the following question what kind of statistical guarantees can be given when doing variable selection in high dimensional models in particular we look at the error rates and power of some multi stage regression methods in the first stage we fit a set of candidate models in the second stage we select one model by cross validation in the third stage we use hypothesis testing to eliminate some variables we refer to the first two stages as screening and the last stage as cleaning we consider three screening methods the lasso marginal regression and forward stepwise regression our method gives consistent variable selection under certain conditions

on rigid components and joint constraints in nonlinear dynamics of flexible multibody systems employing 3d geometrically exact beam model abstract in this work we discuss the finite element implementation of the internal constraints in a three dimensional 3d geometrically exact beam model which can be formulated as holonomic constraint relationships model problems chosen for a more detailed consideration include a general joint constraint between beams and the beam connected to a rigid component appropriate modifications of the standard form of the geometrically exact beam element arrays are carried out in order to impose explicitly these kinds of constraints into time integration schemes for nonlinear dynamics consequently only the minimum number of unknowns is retained for the global set of nonlinear equations to be solved thus avoiding the use of the extra variables the lagrange multipliers and the pertinent difficulties in integrating the system of differential algebraic equations a number of numerical simulations considering dynamic analysis of multibody systems with rigid flexible components and joint constraints are presented in order to illustrate versatility of the proposed procedure

a simplified co rotational method for quadrilateral shell elements in geometrically nonlinear analysis summary this paper presents a simplified co rotational formulation for quadrilateral shell elements inheriting the merit of element independence from the traditional co rotational approach in literature with the objective of application to nonlinear analysis of civil engineering structures the authors further simply the formulation of the geometrical stiffness using the small strain assumption which is valid in the co rotational approach with the warping effects considered as eccentricities compared with the traditional element independent co rotational method the projector is neglected both in the tangent stiffness matrix and the internal force vector for simplicity in formulation meanwhile a quadrilateral flat shell element allowing for drilling rotations is adopted and incorporated into this simplified co rotational algorithm for geometrically nonlinear analysis involved with large displacements and large rotations several benchmark problems are presented to confirm the efficiency and accuracy of the proposed method for practical applications

partial correlation screening for estimating large precision matrices with applications to classification given n samples x1 x2 xn from n 0 we are interested in estimating the p p precision matrix 1 we assume is sparse in that each row has relatively few nonzeros we propose partial correlation screening pcs as a new row by row approach to estimate the i th row of 1 i p pcs uses a screen step and a clean step in the

analyses of large quasistatic deformations of inelastic bodies by a new hybrid stress finite element algorithm abstract a new hybrid stress finite element algorithm suitable for analyses of large quasistatic inelastic deformations is presented the algorithm is based upon a generalization of de veubeke s complementary energy principle the principal variables in the formulation are the nominal stress rate and spin and the resulting finite element equations are discrete versions of the equations of compatibility and angular momentum balance the algorithm produces true rates time derivatives as opposed to increments there results a complete separation of the boundary value problem for stress rate and velocity and the initial value problem for total stress and deformation hence their numerical treatments are essentially independent after a fairly comprehensive discussion of the numerical treatment of the boundary value problem we launch into a detailed examination of the numerical treatment of the initial value problem covering the topics of efficiency stability and objectivity the paper is closed with a set of examples finite homogeneous deformation problems which serve to bring out important aspects of the algorithm