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

a topological approach to periodic oscillations related to the liebau phenomenon abstract we give some sufficient conditions for existence non existence and localization of positive solutions for a periodic boundary value problem related to the liebau phenomenon our approach is of topological nature and relies on the krasnosel ski guo theorem on cone expansion and compression our results improve and complement earlier ones in the literature

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

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

positive solutions of multi point boundary value problems at resonance abstract we establish new results on the existence of positive solutions for some multi point boundary value problems at resonance our results are based on a recent leggett williams norm type theorem due to o regan and zima we also derive a new result for a three point problem previously studied by several authors

existence of positive solutions for three point boundary value problems at resonance with the help of the theorem of a fixed point index for a proper semilinear operators established by cremins we get a existence theorem concerning the existence of positive solution for the second order ordinary differential equation of three point boundary value problems at resonance

positive solutions for a three point boundary value problem the second order three point boundary value problem x t 2x t h t f t x t t 0 1 x 0 0 x x 1 is considered under some conditions concerning the first eigenvalue of the relevant linear operator where 0 1 is a constant h t is allowed to be singular at t 0 and t 1 the existence of positive solutions is studied by means of fixed point index theory

a geometrical nonlinear eccentric 3d beam element with arbitrary cross sections abstract in this paper a finite element formulation of eccentric space curved beams with arbitrary cross sections is derived based on a timoshenko beam kinematic the strain measures are derived by exploitation of the green lagrangean strain tensor thus the formulation is conformed with existing nonlinear shell theories finite rotations are described by orthogonal transformations of the basis systems from the initial to the current configuration since for arbitrary cross sections the centroid and shear center do not coincide torsion bending coupling occurs in the linear as well as in the finite deformation case the linearization of the boundary value formulation leads to a symmetric bilinear form for conservative loads the resulting finite element model is characterized by 6 degrees of freedom at the nodes and therefore is fully compatible with existing shell elements since the reference curve lies arbitrarily to the line of centroids the element can be used to model eccentric stiffener of shells with arbitrary cross sections

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

multiple positive solutions of resonant and non resonant nonlocal boundary value problems abstract we study the existence of positive solutions for equations of the form u t f t u t a e t 0 1 when f t u 2 u 0 for u 0 for some constant 0 and for the perturbed equation u t 2 u t h t u t a e t 0 1 when h t u 0 subject to various non local boundary conditions in particular we establish existence and multiplicity of positive solutions for non perturbed boundary value problems at resonance by considering equivalent non resonant perturbed problems with the same boundary conditions

parabolic problems with nonlinear boundary conditions and critical nonlinearities we prove existence uniqueness and regularity of solutions for heat equations with nonlinear boundary conditions we study these problems with initial data in l q omega w 1 w q omega 1 q infinity or measures and with critically growing non linearities

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

positive solutions for a three point boundary value problem at resonance abstract this paper deals with the second order three point boundary value problem x t f t x t t 0 1 x 0 0 x x 1 the existence and multiplicity of positive solutions are investigated by means of the fixed point theorem in cones

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

remarks on nonlocal boundary value problems at resonance we show that it is important to allow the nonlinear term to change sign when discussing existence of a positive solution for multipoint or more general nonlocal boundary value problems in the resonant case when the nonlinear term has a fixed sign we obtain simple necessary and sufficient conditions for the existence of positive solutions

corotational total lagrangian formulation for three dimensional beamelement a corotational total lagrangian formulation of beam element is presented for the nonlinear analysis of three dimensional beam structures with large rotations but small strains the nonlinear coupling among the bending twisting and stretching deformations is considered all of the element deformations and equations are defined in body attached element coordinates three rotation parameters are proposed to determine the orientation of the element cross section two sets of element nodal parameters termed explicit nodal parameters and implicit nodal parameters are introduced the explicit nodal parameters are used in the assembly of the system equations from the element equations and chosen to be three components of the incremental translation vector and three components of the incremental rotation vector the implicit nodal parameters are used to determine the deformations of the beam element and chosen to be three components of the total displacement vector and nodal values of the three rotation parameters the element internal nodal forces corresponding to the implicit nodal parameters are obtained from the virtual work principle numerical examples are presented and compared with the numerical and experimental results reported in the literature to demonstrate the accuracy and efficiency of the proposed method hree dimensional beams are very important structural elements in all types of engineering systems in many applications these beam elements undergo finite rotations that require a nonlinear formulation to their structural analysis the development of new and efficient formulations for nonlinear analysis of beam structures has attracted the study of many researchers in recent years based on different kinematic assumptions different alternative formulation strategies and procedures to accommodate large rotation capability during the large deformation process have been presented 1 20 the kinematic assumptions used in refs 4 5 7 11 and 17 19 are based on timoshenko s hypothesis the effect of stretching bending torsion and transverse shear are taken into account

nonnegative solutions to nonlocal boundary value problems for systems of second order differential equations dependent on the first order derivatives abstract in this paper we consider nonlocal boundary value problems for systems of second order differential equations with dependence on the first order derivatives and deviating arguments by using a fixed point theorem due to avery and peterson sufficient conditions are obtained that guarantee the existence of at least three nonnegative solutions to such problems we investigate our problem both for delayed and advanced arguments i i and also for the case when i t i t t t 0 1 in all cases arguments i i can change the character on 0 1 so in some subinterval i of 0 1 they can be delayed in i and advanced in 0 1 i some remarks concern also the case when differential equations do not depend on the first order derivatives examples illustrate some results

existence and multiplicity of solutions for four point boundary value problems at resonance abstract this paper deals with the second order four point boundary value problem x t f t x t 0 t 1 x 0 ax x 1 bx where f 0 1 r r is continuous 0 1 0 a 1 1 0 b 1 a 1 b 1 a s 1 b 0 by using the coincidence degree theory the method of lower and upper solutions is established as applications some existence and multiplicity results are obtained

solvability conditions for non local boundary value problems for two dimensional half linear differential systems abstract in this paper we consider two non local boundary value problems for two dimensional half linear differential systems we prove general fredholm type theorems which allow one to derive new efficient solvability criteria for the problems studied

existence result for a singular nonlinear boundary value problem at resonance we study the existence of solutions of the second order boundary value problems u t 2u t a t g u t h t a e t 0 1 u acloc 0 1 u 0 u 1 0 where g r r is continuous a h z lloc1 0 1 01t z t dt the proof of the main result is based upon the lyapunov schmidt procedure and the connectivity properties of the solution set of parametrized families of compact vector fields

a note on multi point boundary value problems abstract multi point boundary value problems for a second order ordinary differential equation are considered in this note an existence result is obtained with the help of coincidence degree theory

a singular non local problem at resonance abstract we study a second order non local problem using the coincidence degree theory we show the existence of a solution whose derivative is singular at the right end point of the interval which is a new result for any resonant non local problem under the non local condition we find a general way to ensure that the differential operator is a fredholm operator of index zero

dynamics of the viscous cahn hilliard equation abstract we study generalized viscous cahn hilliard problems with nonlinearities satisfying critical growth conditions in w 0 1 p where is a bounded smooth domain in r n n 3 in the critical growth case we prove that the problems are locally well posed and obtain a bootstrapping procedure showing that the solutions are classical for p 2 and almost critical dissipative nonlinearities we prove global well posedness existence of global attractors in h 0 1 and uniformly with respect to the viscosity parameter l bounds for the attractors finally we obtain a result on continuity of regular attractors which shows that if n 3 4 the attractor of the cahn hilliard problem coincides in a sense to be specified with the attractor for the corresponding semilinear heat equation

positive solutions of m point boundary value problems the second order m point boundary value problem x h x f x 0 0 x 1 0 0 1 i 1m 2ai i is considered under some conditions concerning the first eigenvalue of the relevant linear operator where i 0 1 with 0 1 2 m 2 1 ai 0 with i 1m 2ai 1 h x is allowed to be singular at x 0 and x 1 the existence of positive solutions and multiple positive solutions is obtained by means of fixed point index theory similarly conclusions hold for some other m point boundary value conditions

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

on the existence of positive solution for a kind of multi point boundary value problem at resonance abstract this paper concerns the existence of positive solution for a class of second order m point boundary value problems under different resonant conditions by using the leggett williams norm type theorem due to o regan and zima we obtain the existence of positive solution an example is given to demonstrate the main results