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

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

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

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

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

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

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

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

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

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

comparison of statistical methods for analysis of clustered binary observations when correlated observations are obtained in a randomized controlled trial the assumption of independence among observations within cluster likely will not hold because the observations share the same cluster e g clinic physician or subject further the outcome measurements of interest are often binary the objective of this paper is to compare the performance of four statistical methods for analysis of clustered binary observations namely 1 full likelihood method 2 penalized quasi likelihood method 3 generalized estimating equation method 4 fixed effects logistic regression method the first three methods take correlations into account in inferential processes whereas the last method does not type i error rate power bias and standard error are compared across the four statistical methods through computer simulations under varying effect sizes intraclass correlation coefficients number of clusters and number of observations per cluster including large numbers 20 and 100 of observations per cluster the results show that the performance of the full likelihood and the penalized quasi likelihood methods is superior for analysis of clustered binary observations and is not necessarily inferior to that of the fixed effects logistic regression fit even when within cluster correlations are zero

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

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

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

residuated fuzzy logics with additional connectives and their validation sets in this paper we generalize the classical notions of tautology and contradiction to the case of fuzzy logic this leads to the notion of a validation set the validation set of a formula in a fuzzy logic is the set of all truth values which this formula may achieve we summarize and extend the recent results on characterizations of validation sets in various fuzzy logics