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

shear flexible models for spatial buckling of thin walled curved beams the governing non linear finite element equations for the spatial stability analysis of curved beams using a simple two noded model are derived based on the incremental form of a mixed variational principle with independent discretization for its generalized strain field and the reference line displacements as well as cross sectional warping and bending twisting rotations the formulation is valid for both open and closed type thin walled sections and this is accomplished by the use of a kinematic description based on a generalized beam theory in which shear deformation due to both flexural and warping torsional actions is accounted for the effect of finite rotations in space is included resulting in a second order accurate geometric stiffness matrix and ensuring that all significant instability modes can be predicted finally the results obtained in a number of numerical simulations for lateral torsional bifurcation buckling of circular arches are presented to illustrate the model effectiveness and practical usefulness and to provide explanations for the source of discrepancies noted in the results obtained in previous investigations

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

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

host parasite models on graphs the behavior of two interacting populations hosts and parasites is investigated on cayley trees and scale free networks in the former case analytical and numerical arguments elucidate a phase diagram for the susceptible infected susceptible model whose most interesting feature is the absence of a tricritical point as a function of the two independent spreading parameters for scale free graphs the parasite population can be described effectively by its dynamics in a host background this is shown both by considering the appropriate dynamical equations and by numerical simulations on barab asi albert networks with the major implication that in the thermodynamic limit the critical parasite spreading parameter vanishes some implications and generalizations are discussed

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

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

self organized packs selection in predator prey ecosystems received 19 july 2005 revised manuscript received 3 october 2005 published 23 february 2006we present a lattice model of a system of predators of ve kinds competing for prey the predators aregrouped in packs and characterized by two parameters the energy spent on hunting and energy gained by thekill the success of hunting depends on the actual competition among predators found near a prey wedetermine via monte carlo simulations the numbers of predators of each kind as a function of time and thedistribution of the size of their packs we show that the ratio of the energy spent by the competing predatorsdetermines their fate the energy gain plays only a secondary role we show also that the system self organizesitself into groups of predators living in well de ned packs which size depends on the energy spent the mostpreferred size dependence on the energy spent follows a very simple power law we present also a mean eld type approach to the problem and we discuss the differences in the results obtained by the two methods showing in particular that the simulation approach produces more reliable results doi 10 1103 physreve 73 021913 pacs number s 87 23 cc 87 23 kg 05 10 ln 87 23 n

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 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

finite element analysis of two and three dimensional elasto plastic frames the natural approach abstract the paper presents a finite element analysis of large deformations in elasto plastic frames attention is focused on the step by step analysis of the nonlinear behaviour of such structures advantage is taken of the so called natural formulation in terms of the generalised cross sectional forces limit state functions applying to different loading conditions and frame geometries are implemented into a computer program a number of test examples illustrate practical applications

formulation of geometrically non linear problems in the spatial reference frame this paper presents a new formulation for geometrically non linear problems and their numerical treatment by the p version of the finite element method the formulation is characterized by a weak form based on the spatial representation of the equilibrium equations a deformed geometry mapped by the displacement field a natural description for non conservative loads that keeps the symmetry of the equations and a direct non incremental iterative algorithm to solve the equations the paper is concerned only with problems for which the solution is unique i e the load displacement curves are single valued and the strains are small examples are presented 1997 by john wiley sons ltd

effective modelling of spatial buckling of beam assemblages accounting for warping constraints and rotation dependency of moments a simple two noded finite element model for the three dimensional buckling analysis of beam assemblages is developed the underlying generalized beam theory employed accounts for all coupled significant modes of deformations including stretching bending shear and torsion as well as warping its mixed formulation is of the two field type utilizing linear and constant interpolants for displacements and strain fields due considerations are given to the effect off inite rotations in space on the non linear kinematic descriptions as well as the configuration dependent behaviour of externally applied moment vectors of the conservative and non conservative types the performance of the model and particularly the accuracy of its geometric and load correction stiffnesses is assessed in a fairly complete set of numerical simulations

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

dynamics of competing predator prey species abstract we study the predator prey model described by the lotka volterra equations n s goel et al rev mod phys 43 1971 231 these coupled non linear differential equations are solved numerically and compared with monte carlo simulations spectral analysis of the data indicate the presence of a fixed set of frequencies and the absence of power law behaviour features introduced to make the model more realistic such as age structures and ageing are found to have no qualitative effect

improved prediction in the presence of multicollinearity abstract in this paper monte carlo techniques are used to examine the performance of several estimators for the linear statistical model under a squared error of prediction loss measure when the data are multicollinear under this measure of performance the stein like rules that shrink toward the principal components estimator perform very well relative to other minimax estimators for alternative specifications of the characteristics root spectrum the sampling performance of a non minimax pretest rule is also considered

on generalized ridge regression estimators under collinearity and balanced loss in regression analysis ridge estimators are often used to alleviate the problem of multicollinearity ridge estimators have traditionally been evaluated using the risk under quadratic loss criterion which places sole emphasis on estimators precision here we consider the balanced loss function a zellner in s s gupta j o berger eds statistical decision theory and related topics vol v springer new york 1994 p 377 which incorporates a measure for the goodness of fit of the model as well as estimation precision by adopting this loss we derive and numerically evaluate the risks of the feasible generalized ridge and the almost unbiased feasible generalized ridge estimators we show that in the case of severe multicollinearity the feasible generalized ridge estimator often produces the greatest risk reductions even if a relatively heavy weight is given to goodness of fit in the balanced loss function

nonlinear analysis and elastic plastic load carrying behaviour of thin walled spatial beam structures with warping constraints an analysis of the elastic plastic load carrying behaviour of thin walled spatial beam structures is presented it is based on a beam theory valid for large displacements and rotations which admits arbitrary cross sections curved axes initial imperfections a general material description and which fully accounts for the influence of warping constraints as well as the stress history dependence of the elastic plastic shear moduli an incremental updated lagrangian viewpoint is adopted in the derivation of the basic beam equations from a generalized variational principle and in the numerical solution procedure the displacement finite element approach is followed the associated tangential stiffness matrices are obtained by direct numerical integration of the governing incremental differential equations rather than through the use of shape functions in connection with a virtual work principle applications of the theory are given in which the influence of the loading configuration material parameters geometric nonlinearities and warping constraints on the load carrying behaviour and on the bifurcation and ultimate loads of thin walled beam structures is explored

inadmissibility of the stein rule estimator under the balanced loss function in this paper the risk of the stein rule sr estimator is compared with that of the improved stein rule estimator using the stein variance srsv estimator under the balanced loss function it is shown that the srsv estimator dominates the sr estimator even if the loss function is extended to the blf also our numerical results show that the srsv estimator dominates the ols estimator when the weight of precision of estimation is larger than about half and vice versa