co rotational beam elements with warping effects in instability problems the present paper investigates the formulation of 3d co rotational beam elements for the buckling and post buckling analysis of frame structures following pacoste and eriksson comput methods app

an exact finite rotation shell theory its mixed variational formulation and its finite element implementation a non linear shell theory including transverse shear strains with exact description of the kinematical fields is developed the strain measures are derived via the polar decomposition theorem allowing for an explicit use of a three parametric rotation tensor thus in plane rotations also called drilling degrees of freedom are included in a natural way various alternatives of the theory are derived for a special version of the theory with altogether six kinematical fields different mixed variational principles are given a hybrid finite element formulation which does not exhibit locking phenomena is developed numerical examples of shell deformation at finite rotations with excellent element performance are presented comparison with results reported in the literature demonstrates the features of the theory as well as the proposed finite element formulation

geometrically non linear 3d finite element analysis of micropolar continuum abstract in this work a 3d geometrically non linear micropolar finite element formulation based on biot like tensor representation of stresses couple stresses strains and curvature is presented the discrete approximation is based on hexahedral finite elements with lagrange interpolation for displacements and rotational spins the complete residual derivation linearisation and update are presented in detail the elements are tested against a non linear generalisation of the linear micropolar pure bending problem derived in this work and it is shown that the elements converge to the derived solution the elements are additionally tested on a combined bending and torsion problem and a well known 45 bend as a genuine problem involving large 3d rotations both also analysed in the framework of micropolar elasticity it is observed that the derived finite elements are reliable and robust in modelling finite deformation problems in micropolar elasticity exhibiting large displacements and large rotations and converge to reference geometrically non linear classical elasticity solutions for small micropolar effects with increasing micropolar effects the response becomes stiffer and the presented numerical examples may serve as benchmark problems to test geometrically non linear micropolar finite elements including those involving large 3d rotations

an objective 3d large deformation finite element formulation for geometrically exact curved kirchhoff rods the objective of this work is the development of a new finite element formulation for beams according to the kirchhoff theory of thin rods which includes the deformation states of axial tension torsion and bending the proposed formulation accounts for large deformations in three dimensional problem settings consisting of slender prismatic beams with arbitrarily curved initial geometries and arbitrary cross section shapes like in geometrically exact reissner theories the derived deformation measures are geometrically exact in the sense that they are consistent with the strong and weak form of the balance equations and the beam geometry for any configuration and for arbitrarily large translations rotations and strains a novel orthogonal interpolation strategy is applied to the triad field representing the cross section orientation in order to fulfill the kirchhoff constraint of vanishing shear strains in a strong sense and to preserve the objectivity of the spatially discretized problem the continuity requirements resulting from the corresponding weak form are fulfilled by a cubic hermite interpolation thus leading to a c1 continuous representation of the beam centerline fundamental properties such as objectivity path independence consistency and accuracy of the developed beam element are verified by means of suitable numerical examples

stability of elastic rods with self contact abstract in this paper we study the numerical stability of equilibrium configurations of an elastic rod with unilateral frictionless self contact we use a finite element method with penalty and augmented lagrangian approaches to account for the self penetration constraint the numerical solution is carried out using the arclength continuation method in the case where the energy expression satisfies some hypotheses we have proved that any isolated minimum of the continuous self contact problem is the strong limit of a sequence of local minima of the discrete problem our stability analysis is based on detecting the zeros of the determinant of a symmetrized version of the stiffness matrix and whether there is a sign change of the determinant or not

stress resultant geometrically nonlinear shell theory with drilling rotations part i a consistent formulation abstract in this work we present a consistent theoretical framework for a novel stress resultant geometrically nonlinear shell theory the main feature of the present shell theory development which stands in contrast with the classical developments in the shell theory is the presence of a rotation component around the shell normal so called drilling rotation in the description of shell finite rotations the relationship of the proposed theory with a finite deformation theory of a three dimensional continuum with independent rotation field is clearly identified the latter is shown to be an important link which facilitates the proper choice of the shell constitutive model and a proper construction of the regularized form of the theory capable of supporting the drilling rotations the corresponding linearized form of the present shell theory is discussed in the closure

element formulation and numerical techniques for stability problems in shells in the context of instability problems in shells or shell like structures the objective of the present paper is twofold primarily the paper describes how quasi static conservative instability problems can be considered in a multi parametric context where generalized path following procedures for augmented equilibrium problems are used as computational tools these allow systematic treatment of the higher dimensional solution sets generated under the variations of certain parameters deemed relevant for the given problem the efficient implementation of the above mentioned procedures requires however as an essential ingredient a non linear finite element which is not only accurate but also inexpensive to this end a systematic view on a corotational total lagrangian formulation is described the tric element of argyris and coworkers is slightly modified and introduced as core element formulation special emphasis is given to the alternative methods for treatment of finite three dimensional rotations with reference to both the element definition and solution algorithms numerical examples verify the element capabilities and the possibility to completely describe instability phenomena of large discretized models

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

the index of weighted singular integral operators with shifts and slowly oscillating data abstract let and be orientation preserving diffeomorphism shifts of r 0 onto itself with the only fixed points 0 and we establish a fredholm criterion and calculate the index of the weighted singular integral operator with shifts a i b u p c i d u p acting on the space l p r where p i s 2 are the operators associated to the weighted cauchy singular integral operator s given by s f t 1 i r t f t d with c satisfying 0 1 p 1 and u u are the isometric shift operators given by u f 1 p f u f 1 p f under the assumptions that the coefficients a b c d and the derivatives of the shifts are bounded and continuous on r and admit discontinuities of slowly oscillating type at 0 and

corotational nonlinear dynamic analysis of thin shell structures with finite rotations a new formulation for corotational nonlinear dynamic analysis of thin shell structures involving large displacements and finite rotations has been presented in this paper by introducing the kinematic description of the geometrically exact quasi static shell model to describe the motion of an arbitrary material point in a triangular shell element the new expressions for the inertial force vector and tangent inertia matrix were derived systematically the elastic deformation was handled by using the consistent symmetrizable equilibrated corotational formulation which is independent with respect to the local finite element modeling an energy momentum conserving algorithm and an energy decaying momentum conserving algorithm were developed for nonlinear dynamic analysis by applying the generalized energy momentum method in the corotational formulation three classic numerical examples including the dynamic response free motion and dynamic buckling of thin shell structures were computed to verify the ac

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

a modified corotational framework for triangular shell elements the corotational framework for triangular shell elements has been presented by different authors see the introduction the purpose of this paper is to introduce three modifications in this approach the first one is a simplified definition of the local rotations the second one is a reduction of the number of local degrees of freedom from 18 to 15 the third and principal one concerns the parameterisation of the global finite rotations a new approach based on euler parameters quaternion is proposed in particular it is shown that only three parameters are required the purpose of these three modifications is to obtain a formulation which gives the same numerical results but which is computationally more efficient than the original one this aspect is illustrated in several numerical examples

stress resultant geometrically exact form of classical shell model and vector like parameterization of constrained finite rotations summary in this work we consider the geometrically exact shell model subjected to 7nite rotations making use of rotation vector parameters for handling the corresponding constrained rotation for smooth shells a modi7cation of such a parameterization which is based on the incremental rotation vector and thus capable of avoiding the singularity problem is also discussed copyright 2001 john wiley sons ltd

treatment of reissner mindlin shells with kinks without the need for drilling rotation stabilization in an isogeometric framework this work presents a framework for the computation of complex geometries containing intersections of multiple patches with reissner mindlin shell elements the main objective is to provide an isogeometric finite element implementation which neither requires drilling rotation stabilization nor user interaction to quantify the number of rotational degrees of freedom for every node for this purpose the following set of methods is presented control points with corresponding physical location are assigned to one common node for the finite element solution a nodal basis system in every control point is defined which ensures an exact interpolation of the director vector throughout the whole domain a distinction criterion for the automatic quantification of rotational degrees of freedom for every node is presented an isogeometric reissner mindlin shell formulation is enhanced to handle geometries with kinks and allowing for arbitrary intersections of patches the parametrization of adjacent patches along the interface has to be conforming the shell formulation is derived from the continuum theory and uses a rotational update scheme for the current director vector the nonlinear kinematic allows the computation of large deformations and large rotations two concepts for the description of rotations are presented the first one uses an interpolation which is commonly used in standard lagrange based shell element formulations the second scheme uses a more elaborate concept proposed by the authors in prior work which increases the accuracy for arbitrary curved geometries numerical examples show the high accuracy and robustness of both concepts the applicability of the proposed framework is demonstrated

four node semi eas element in six field nonlinear theory of shells we propose a new four node c finite element for shell structures undergoing unlimited translations and rotations the considerations concern the general six field theory of shells with asymmetric strain measures in geometrically nonlinear static problems the shell kinematics is of the two dimensional cosserat continuum type and is described by two independent fields the vector field for translations and the proper orthogonal tensor field for rotations all three rotational parameters are treated here as independent hence as a consequence of the shell theory the proposed element has naturally six engineering degrees of freedom at each node with the so called drilling rotation this property makes the element suitable for analysis of shell structures containing folds branches or intersections to avoid locking phenomena we use the enhanced assumed strain eas concept we derive and linearize the modified hu washizu principle for six field theory of shells what makes the present approach original is the combination of eas method with asymmetric membrane strain measures based on literature we propose new enhancing field and specify the transformation matrix that accounts for the lack of symmetry to gain knowledge about the suitability of this field for asymmetric strain measures and to assess the performance of the element we solve typical benchmark examples with smooth geometry and examples involving orthogonal intersections of shell branches

a four node corotational quadrilateral elastoplastic shell element using vectorial rotational variables four node corotational quadrilateral elastoplastic shell element summary a four node corotational quadrilateral elastoplastic shell element is presented the local coordinate system of the element is defined by the two bisectors of the diagonal vectors generated from the four corner nodes and their cross product this local coordinate system rotates rigidly with the element but does not deform with the element as a result the element rigid body rotations are excluded in calculating the local nodal variables from the global nodal variables the two smallest components of each nodal orientation vector are defined as rotational variables leading to the desired additive property for all nodal variables in a nonlinear incremental solution procedure different from other existing corotational finite element formulations the resulting element tangent stiffness matrix is symmetric owing to the commutativity of the local nodal variables in calculating the second derivative of strains with respect to these variables for elastoplastic analyses the maxwell huber hencky von mises yield criterion is employed together with the backward euler return mapping method for the evaluation of the elastoplastic stress state the consistent tangent modulus matrix is derived to eliminate locking problems we use the assumed strain method several elastic patch tests and elastoplastic plate shell problems undergoing large deformation are solved to demonstrate the computational efficiency and accuracy of the proposed formulation copyright 2013 john wiley sons ltd

on the role of frame invariance in structural mechanics models at finite rotations in this work we re examine so called geometrically exact models for structures such as beams shells or solids with independent rotation field with respect to invariance under superposed rigid body motion a special attention is given to clarifying the issues pertaining to the finite element implementation which guarantees that the invariance of the continuum problem is preserved by its discrete approximation several numerical simulations dealing with finite rotations of structural models are presented in order to further illustrate and confirm the given theoretical considerations

finite rotations in dynamics of beams and implicit time stepping schemes we examine theoretical and computational aspects of three dimensional finite rotations pertinent to the dynamics of beams the model problem chosen for consideration is the reissner beam theory capable of modelling finite strains and finite rotations in geometrically exact manner special emphasis is placed on clarifying the geometry aspects finite rotation updates and the associated linearization procedure pertaining to different choices of rotation parameters the latter is shown to play an important role in constructing the optimal implementation of a time stepping scheme 1998 john wiley sons ltd

consistent quaternion interpolation for objective finite element approximation of geometrically exact beam we explore an isoparametric interpolation of total quaternion for geometrically consistent strain objective and path independent finite element solutions of the geometrically exact beam this interpolation is a variant of the broader class known as slerp the equivalence between the proposed interpolation and that of relative rotation is shown without any recourse to local bijection between quaternions and rotations we show that for a two noded beam element the use of relative rotation is not mandatory for attaining consistency cum objectivity and an appropriate interpolation of total rotation variables is sufficient the interpolation of total quaternion which is computationally more efficient than the one based on local rotations converts nodal rotation vectors to quaternions and interpolates them in a manner consistent with the character of the rotation manifold this interpolation unlike the additive interpolation of total rotation corresponds to a geodesic on the rotation manifold for beam elements with more than two nodes however a consistent extension of the proposed quaternion interpolation is difficult alternatively a quaternion based procedure involving interpolation of relative rotations is proposed for such higher order elements we also briefly discuss a strategy for the removal of possible singularity in the interpolation of quaternions proposed in i romero the interpolation of rotations and its application to finite element models of geometrically exact rods comput mech 34 2004 121 133 the strain objectivity and path independence of solutions are justified theoretically and then demonstrated through numerical experiments this study being focused only on the interpolation of rotations uses a standard finite element discretization as adopted by simo and vu quoc j c simo l vu quoc a three dimensional finite rod model part ii computational aspects comput methods appl mech engrg 58 1986 79 116 the rotation update is achieved via quaternion multiplication followed by the extraction of the rotation vector nodal rotations are stored in terms of rotation vectors and no secondary storages are required

asymptotic post buckling fem analysis using corotational formulation finite element asymptotic post buckling analysis being based on fourth order expansions of the strain energy requires that nonlinear structural modeling be accurate to same order at least with respect to the rigid motions of the elements a corotational description is proposed here as a general tool to satisfy this requirement of objectivity by referring each element to a local frame which moves rotates with the element so filtering its rigid motion in this description nonlinearity of the problem derives essentially from the change of reference from the global fixed frame to the local one the strain energy being governed by their relative rotations in finite kinematics this noticeably complicates the algebra for obtaining exact expressions of its variations quite simple basic expressions for the first four corotational derivatives of the strain energy are provided allowing the set up of a fourth order accurate asymptotic analysis starting from standard finite elements based on linear or simplified nonlinear local modelings the formulation is implemented for the analysis of 3d beam assemblages and several numerical results are presented and discussed showing the effectiveness and robustness of the proposed approach in reproducing the nonlinear equilibrium path in both cases of monomodal and coupled multimodal buckling

regular patterns in dichotomically driven activator inhibitor dynamics we investigate turing pattern formation in the presence of additive dichotomous fluctuations in the context of an extended system with diffusive coupling and fitzhugh nagumo kinetics the fluctuations vary in space and or time depending on the realization of the dichotomous switching the system is at a given time for spatial disorder at a given position in one of two possible excitable dynamical regimes each of the two excitable dynamics for itself does not support pattern formation with proper dichotomous fluctuations however the homogeneous steady state is destabilized via a turing instability we investigate the influence of different switching rates different correlation length of the spatial disorder on pattern formation we find three distinct mechanisms for slow switching existing boundaries become unstable for high rates the system exhibits effective bistability which allows for a turing instability for medium rates the fluctuations create spatial structures via a new mechanism where the influence of the fluctuations is twofold first they produce local inhomogeneities which then grow again caused by fluctuations until the whole space is covered utilizing a nonlinear map approach we show bistability of a period one and a period two orbit being associated with the steady homogeneous and the turing pattern state respectively finally for purely static dichotomous disorder we find destabilization of homogeneous steady states for finite nonzero correlation length of the disorder resulting again in turing patterns

striated populations in disordered environments with advection abstract growth in static and controlled environments such as a petri dish can be used to study the spatial population dynamics of microorganisms however natural populations such as marine microbes experience fluid advection and often grow up in heterogeneous environments we investigate a generalized fisher kolmogorov petrovsky piscounov fkpp equation describing single species population subject to a constant flow field and quenched random spatially inhomogeneous growth rates with a fertile overall growth condition we analytically and numerically demonstrate that the non equilibrium steady state population density develops a flow driven striation pattern the striations are highly asymmetric with a longitudinal correlation length that diverges linearly with the flow speed and a transverse correlation length that approaches a finite velocity independent value linear response theory is developed to study the statistics of the steady states theoretical predictions show excellent agreement with the numerical steady states of the generalized fkpp equation obtained from lattice boltzmann simulations these findings suggest that although the growth disorder can be spatially uncorrelated correlated population structures with striations emerge naturally at sufficiently strong advection

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

a 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

geometrically nonlinear dynamic formulation for three dimensional co rotational solid elements abstract this study presents a three dimensional nonlinear dynamic formulation based on a co rotational cr approach for solid elements the cr formulation is relatively efficient but it is based on the assumption of small strains during large displacement the novel idea of the present formulation involves the use of the cr formulation through a three dimensional solid element for inertial quantities in addition to an internal force vector and a stiffness matrix the present dynamic formulation is derived from lagrange s equation of motion in this procedure the cr formulation i e element independent cr is one of the most attractive features that is strongly manifested in an efficient manner consequently this obtains the governing equation of motion including motion driven inertial components physical quantities induced by the prescribed motion four examples are presented to demonstrate the accuracy of the present dynamic formulation finally the results are compared with those obtained by abaqus and the findings reveal that the proposed dynamic formulation is in good agreement with existing predictions

on finite element implementation of geometrically nonlinear reissner s beam theory three dimensional curved beam elements abstract finite element implementation of the three dimensional finite strain beam theory of reissner is considered in this work in contrast with some earlier works on the subject discussed here are the beam elements whose reference axes are arbitrary space curved lines we have shown that an improved representation of curved reference geometry significantly increases the accuracy of the results however it also makes the choice of non locking finite element interpolations somewhat more delicate a hierarchical displacement interpolation proposed here is proved to be capable of eliminating both shear and membrane locking phenomena a very satisfying non locking performance is demonstrated for a set of problems in nonlinear elasto statics

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

a consistent 3d corotational beam element for nonlinear dynamic analysis of flexible structures abstract the purpose of the paper is to present a corotational beam element for the nonlinear dynamic analysis of 3d flexible frames the novelty of the formulation lies in the use of the corotational framework i e the decomposition into rigid body motion and pure deformation to derive not only the internal force vector and the tangent stiffness matrix but also the inertia force vector and the tangent dynamic matrix as a consequence cubic interpolations are adopted to formulate both inertia and internal local terms in the derivation of the dynamic terms an approximation for the local rotations is introduced and a concise expression for the global inertia force vector is obtained to enhance the efficiency of the iterative procedure an approximate expression of the tangent dynamic matrix is adopted four numerical examples are considered to assess the performance of the new formulation against the one suggested by simo and vu quoc 1988 48 it was observed that the proposed formulation proves to combine accuracy with efficiency in particular the present approach achieves the same level of accuracy as the formulation of simo and vu quoc but with a significantly smaller number of elements

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

isogeometric collocation for three dimensional geometrically exact shear deformable beams abstract we extend the isogeometric collocation method to the geometrically nonlinear beams an exact kinematic formulation able to represent three dimensional displacements and rotations without any restriction in magnitude is presented without the introduction of the moving frame concept a displacement based formulation is adopted full linearization of the strong form of the governing equations is derived consistently with the underlying geometric structure of the configuration manifold incremental rotations are parametrized through eulerian rotation vectors and configuration updates are performed by means of the exponential map numerical tests demonstrate that the proposed combination of isogeometric collocation method with the chosen rotations parametrization results in an efficient computational scheme able to model complex problems with high accuracy

geometrically nonlinear shell element for hygrothermorheologically simple linear viscoelastic composites a triangular flat shell element for large deformation analysis of linear viscoelastic laminated composites is presented hygrothermorheologically simple materials are considered for which a change in the hygrothermal environment results in a horizontal shifting of the relaxation moduli curves on a log time scale in addition to the usual hygrothermal loads recurrence relations are developed and implemented for the evaluation of the viscoelastic memory loads the nonlinear deformation process is computed using an incremental iterative approach with the newton raphson method used to find the incremental displacements in each step the presented numerical examples consider the large deformation and stability of linear viscoelastic structures under deformation independent mechanical loads deformation dependent pressure loads and thermal loads unlike elastic structures that have a single critical load value associated with a given snapping of buckling instability phenomenon viscoelastic structures will usually exhibit a particular instability for a range of applied loads over a range of critical times both creep buckling and snap through examples are presented here in some cases viscoelastic results are also obtained using the quasielastic method in which load history effects are ignored and time varying viscoelastic properties are simply used in a series of elastic problems the presented numerical examples demonstrate the capability and accuracy of the formulation

locking free isogeometric collocation formulation for three dimensional geometrically exact shear deformable beams with arbitrary initial curvature abstract this paper presents a displacement based and a mixed isogeometric collocation formulations for three dimensional geometrically exact shear deformable beams with arbitrarily curved initial geometry strong forms of both formulations are consistently linearized with respect to the underlying configuration manifold high efficiency is achieved by using a geometrically consistent kinematic model in which incremental rotations are parametrized through the spatial rotation vector several numerical tests demonstrate that the proposed mixed formulation is totally locking free for any choice of approximation degree mixed formulation also exhibits higher robustness in the incremental iterative algorithm elimination of shear locking and low computational cost assured by the combination of isogeometric collocation with a consistent kinematic model result in a very efficient accurate and geometrically powerful method able to handle geometrically complex beam problems

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

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

geometrically exact theory for contact interactions of 1d manifolds algorithmic implementation with various finite element models abstract the intuitive understanding of contact between bodies is based on the geometry of adjoining bodies a more sophisticated approach of an advanced analysis including the application of various numerical methods is to take advantage of the geometry of an analyzed object and describe the problem in the best coordinate system the best coordinate system to describe contact interaction in all its geometrical details is a coordinate system attached to the geometrical features of contacting bodies this leads to a systematical analysis of geometrical situations leading to contact pairs surface to surface line to surface point to surface line to line point to line each contact pair is inherited with a special coordinate system based on its geometrical properties the current contribution is concentrating on contact between 1d manifolds in 3d space this is the majority of edge to edge beam to beam cable to edge etc contact cases the geometrically exact curve to curve contact approach is then systematically combined together with various finite element approaches classical finite elements isogeometric beam finite elements and also with a new developed solid beam approach examples illustrating the diversity of various finite element combinations e g within knot mechanics are shown

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

spatial patterns induced purely by dichotomous disorder we study conditions under which spatially extended systems with coupling in the manner of swift and hohenberg exhibit spatial patterns induced purely by the presence of quenched dichotomous disorder complementing the theoretical results based on a generalized mean field approximation we also present numerical simulations of particular dynamical systems that exhibit the proposed phenomenology

total lagrangian reissner s geometrically exact beam element without singularities in this paper we introduce a new reissner s geometrically exact beam element which is based on a total lagrangian updating procedure the element has the rotation vector as the dependent variable and the singularity problems at the rotation angle 2 and its multiples are passed by the change of parametrization on the rotation manifold the beam formulation has several benefits such as all the unknown vectors belong to the same tangential vector space no need for secondary storage variables the path independence in the static case any standard time integration algorithm may be used and the symmetric stiffness copyright 2006 john wiley sons ltd

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

the linearized three dimensional beam theory of naturally curved and twisted beams the strain vectors formulation this paper presents the equations of the linearized geometrically exact three dimensional beam theory of naturally curved and twisted beams a new finite element formulation for the linearized theory is proposed in which the strain vectors are the only unknown functions the linear form of the consistency condition that the equilibrium and the constitutive internal force and moment vectors are equal is enforced to be satisfied at chosen points an arbitrary curved and twisted axis of the beam is taken into account which demands proper consideration of the non linearity of spatial rotations the accuracy and the efficiency of the derived numerical algorithm are demonstrated by comparing present numerical results with various analytical and numerical results

on the choice of finite rotation parameters in this work we discuss some aspects of the three dimensional finite rotations pertinent to the formulation and computational treatment of the geometrically exact structural theories among various possibilities to parameterize the finite rotations special attention is dedicated to a choice featuring an incremental rotation vector some computational aspects pertinent to the implementation of the newton iterative scheme and the newmark time stepping algorithm applied to solving these problems are examined representative numerical simulations are presented in order to illustrate the performance of the proposed formulation

a large rotation finite element analysis of 3d beams by incremental rotation vector and exact strain measure with all the desirable features abstract different strategies based on rotation vector and exact strain measure have been proposed over the years for analyzing flexible bodies undergoing arbitrary large rotations to avoid the singularity of the vector like parametrization the interpolation of the incremental rotation vector is the most popular approach in this context even if this leads to path dependence and numerical instability i e error accumulation it is also non objective although both objectivity and path independence are recovered with h and p refinement corotational approaches do not have these drawbacks even though the geometrically exact model is achieved by mesh refinement in this work we develop a novel strategy which uses the incremental nodal rotation vectors to define corotational nodal rotations which are then interpolated for the evaluation of the nonlinear strains this choice makes the approach singularity free allows for additive updates within each increment and preserves all the features of the theoretical problem for any mesh and interpolation rotational variables objectivity exact strain measure path independence and symmetric stiffness matrix for conservative loads this last property is a consequence of the direct differentiation of the relation between local and global rotations whose compact form also makes a simple and general definition of the internal forces and the tangent stiffness for any order of interpolation possible in addition we show how the common approach of interpolating incremental vectors can be made stable by a simple updating procedure based on local rotations carried out at the end of each increment in order to avoid cumulative errors geometrically exact 3d beams are considered as a demonstrative example an iterative strategy based on mixed integration points is used to solve the nonlinear discrete equations efficiently

an algebra of pseudodifferential operators with slowly oscillating symbols let v mathbb r denote the banach algebra of absolutely continuous functions of bounded total variation on mathbb r and let mathcal b p be the banach algebra of bounded linear operators acting on the lebesgue space l p mathbb r for 1 p infty we study the banach algebra mathfrak a subset mathcal b p generated by the pseudodifferential operators of zero order with slowly oscillating v mathbb r valued symbols on mathbb r boundedness and compactness conditions for pseudodifferential operators with symbols in l infty mathbb r v mathbb r are obtained a symbol calculus for the non closed algebra of pseudodifferential operators with slowly oscillating v mathbb r valued symbols is constructed on the basis of an appropriate approximation of symbols by infinitely differentiable ones and by use of the techniques of oscillatory integrals as a result the quotient banach algebra mathfrak a pi mathfrak a mathcal k where mathcal k is the ideal of compact operators in mathcal b p is commutative and involutive an isomorphism between the quotient banach algebra mathfrak a pi of pseudodifferential operators and the banach algebra widehat mathfrak a of their fredholm symbols is established a fredholm criterion and an index formula for the pseudodifferential operators a in mathfrak a are obtained in terms of their fredholm symbols