improving stability by change of representation in time stepping analysis of non linear beams dynamics in this paper we propose a change in the representation of the discrete motion equations in structural non linear dynamics to obtain an improvement in the stability of time numerical integrations in particular natural local state variables are indicated for a finite element approach to beam problems the results relative to newmark approximations for the variations in the displacement and velocity vectors show a significant increase in the range of stability of the time integration process and a reduction in the number of newton iterations required in the time integration steps the proposed method further preserves energy as well as the linear and angular momentum of the dynamical system copyright 2006 john wiley sons ltd

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

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

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

numerical analysis of complex instability behaviour using incremental iterative strategies the paper describes how quasi static conservative instability problems can be analysed in a multi parametric space using generalised path following procedures for augmented equilibrium problems

energy conserving algorithms for a corotational formulation standard nonlinear schemes for the the simulation of elastodynamic problems have several shortcomings when considering high speed rotations to tackle these problems we use a corotational framework and a corresponding specific linearization to design new energy conserving numerical schemes in the two dimensional case an algorithm preserving also angular momentum is presented the existence of a solution for the fully discrete setting of this algorithm is established numerical results illustrate the flexibility and efficiency of the proposed algorithms

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

on stable equivalences and blocks with one simple module using a stable equivalence due to rouquier we show that alperin s weight conjecture holds for any p block of a finite group with defect 2 whose brauer correspondent has a unique isomorphism class of simple modules

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

beam elements in instability problems this paper deals with the formulation of beam elements for the numerical analysis of instability phenomena in frame type structures total versus co rotational approaches are discussed comparatively for both two dimensional and three dimensional problems and the similarities between the two types are outlined in the context of 3d beam elements special attention is given to the parameterisation of the orthogonal transformation used to define the rotational field of the beam the technique advocated in the paper is based on the so called rotational vector this leads to symmetric stiffness matrices and avoids the need for special updating procedures for the rotational variables a set of test problems for which the critical behaviour is governed by fold cusp and butterfly catastrophes is used to assess the performances of the considered element types it is shown that analytically verified identities in element formulation also hold in numerical application the examples also show how complex instability behaviour can be reproduced by all elements where sufficient accuracy is introduced into the kinematic expressions the analytical derivation of element expressions with symbolic manipulations from stated basic assumptions is consistently used in the paper

on p blocks with abelian defect groups and inertial index 2 or 3 ii abstract let g be a finite group and b be a p block of g with an abelian defect group and inertial index 2 or 3 in this paper we determine some generalized decomposition numbers of the block b

a unified formulation of small strain corotational finite elements i theory this paper presents a unified theoretical framework for the corotational cr formulation of finite elements in geometrically nonlinear structural analysis the key assumptions behind cr are i strains from a corotated configuration are small while ii the magnitude of rotations from a base configuration is not restricted following a historical outline the basic steps of the element independent cr formulation are presented the element internal force and consistent tangent stiffness matrix are derived by taking variations of the internal energy with respect to nodal freedoms it is shown that this framework permits the derivation of a set of cr variants through selective simplifications this set includes some previously used by other investigators the different variants are compared with respect to a set of desirable qualities including self equilibrium in the deformed configuration tangent stiffness consistency invariance symmetrizability and element independence we discuss the main benefits of the cr formulation as well as its modeling limitations

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

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

higher order mitc general shell elements two mixed interpolated general shell finite elements for non linear analysis a 9 node element and a 16 node element are presented the elements are based on the mixed interpolation of tensorial components mitc approach in which the covariant strain component fields for the in plane and shear actions are interpolated and tied to the also interpolated displacement field both the 9 node element referred to as the mitc9 element and the 16 node element referred to as the mitc16 element are tested numerically and found to have high predictive capabilities

equilibrium subsets for multi parametric structural analysis the paper discusses multi parametric formulations for structural equilibrium problems by seeking subsets of equilibrium states which also fulfil extra conditions more detailed information on structural behaviour can be obtained these conditions can be related to analyses of e g critical behaviour imperfections or optimisation the paper shows a general problem setting and some interesting augmentations a solution method for the special case of one dimensional equilibrium subsets is described the algorithm is a generalisation of a path following algorithm where new methods are developed for the evaluation of the path tangent and for the isolation of special solution points examples are used to show the properties and the possibilities of the ideas

a note on olssonʼs conjecture abstract for a p block b of a finite group g with defect group d olsson conjectured that k 0 b d d where k 0 b is the number of characters in b of height 0 and d denotes the commutator subgroup of d brauer deduced olsson s conjecture in the case where d is a dihedral 2 group using the fact that certain algebraically conjugate subsections are also conjugate in g we generalize brauer s argument for arbitrary primes p and arbitrary defect groups this extends two results by robinson for p 3 we show that olsson s conjecture is satisfied for defect groups of p rank 2 and for minimal non abelian defect groups

notes on p blocks of characters of finite groups let g be a finite group and let p be a fixed prime number in this paper we shall study the numbers of irreducible characters in a p block of g with an abelian defect group and the contributions of subsections to the inner product of irreducible characters of g as is seen in 10 111 broue and puig s generalized characters which are defined in 3 are relevant for the study of p blocks with abelian defect groups they will play an important role in this paper too let k be the algebraic number field containing the gi th roots of 1 let p be a prime ideal divisor of p in k and let o be the ring of p integers in k let b be a p block and let n b be a subsection associated with b n b is a pair such that ii is a p element of g and b is a p block of c n associated with b in 3 n b is called a b g brauer element let x be an ordinary irreducible character in b the function x is the central function on g which vanishes outside the p section of rc and which is such that x x np x npe where p is a p regular element of c n and e is the block idempotent of oc n corresponding to b following i for x xi e b we denote by m xs x3 the inner product of 9 and x rnpx is equal to the inner product of 3 b and 2 by brauer and ma s orthogonality relation rnpxf is called the contribution of n b to the inner product x x by l 5b

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

an enhanced co rotational approach for large displacement analysis of plates this paper presents a new co rotational approach for the large displacement analysis of plates employing 4 noded quadrilateral flat shell elements the proposed approach benefits from i a simple local co rotational system invariant to the element nodal ordering ii the choice of the two smallest components of the nodal normal vector as global rotational degrees of freedom and iii the use of hierarchic freedoms that are unaffected by the co rotational transformations for higher order accuracy important additional benefits that arise from the aforementioned features include symmetry of the tangent stiffness matrix and complete insensitivity of the large displacement transformations to the size of the incremental step the applicability of the new approach to moderately thick as well as thin plates is illustrated by considering two alternative local formulations based on the reissner mindlin and discrete kirchhoff hypotheses several examples are finally presented which demonstrate the accuracy step insensitivity and computational benefits of the proposed co rotational approach for large displacement analysis of plate structures copyright 2005 john wiley sons ltd

on the brauer feit bound for abelian defect groups we improve the brauer feit bound on the number of irreducible characters in a p block for abelian defect groups by making use of halasi and podoski every coprime linear group admits a base of size two http arxiv org abs 1212 0199v1 7 and kessar and malle ann math 178 2 321 384 11 we also prove brauer s k b conjecture for 2 blocks with abelian defect groups of rank at most 5 and 3 blocks and 5 blocks with abelian defect groups of rank at most 3

dichromatic link invariants we investigate the skein theory of oriented dichromatic links in s3 we define a new chromatic skein invariant for a special class of dichromatic links this invariant generalizes both the two variable alexander polynomial and the twisted alexander polynomial alternatively one may view this new 1 2 invariant as an invariant of oriented monochromatic links in s x d and as such it is the exact analog of the twisted alexander polynomial we discuss basic properties of this new invariant and applications to link interchangeability for the full class of dichromatic links we show that there does not exist a chromatic skein invariant which is a mutual extension of both the two variable alexander polynomial and the twisted alexander polynomial

a mixed tetrahedral element with nodal rotations for large displacement analysis of inelastic structures summary a novel mixed four node tetrahedral finite element equipped with nodal rotational degrees of freedom is presented its formulation is based on a hu washizu type functional suitable to the treatment of material nonlinearities rotation and skew symmetric stress fields are assumed as independent variables the latter entering the functional to impose rotational compatibility and suppress spurious modes exploiting the choice of equal interpolation for strain and symmetric stress fields a robust element state determination procedure requiring no element level iteration is proposed the mixed element stability is assessed by means of an original and effective numerical test the extension of the present formulation to geometric nonlinear problems is achieved through a polar decomposition based corotational framework after validation in both material and geometric nonlinear context the element performances are investigated in demanding simulations involving complex shape memory alloy structures supported by the comparison with available linear and quadratic tetrahedrons and hexahedrons the numerical results prove accuracy robustness and effectiveness of the proposed formulation copyright 2016 john wiley sons ltd

evaluation of the constant strain triangle with drilling rotations the performance of the constant strain triangle with added drilling rotations is evaluated by solving a variety of plane test problems numerical results confirm that the new element is always superior to the standard constant strain triangle and that it is of similar accuracy to the best available alternative triangular elements of other authors it is however less accurate than some rectangular elements which include drilling rotations

geometrically nonlinear formulation for the curved shell elements this paper presents a geometrically nonlinear formulation using total lagrangian approach for the three dimensional curved shell elements the basic element geometry is constructed using the coordinates of the middle surface nodes and the mid surface nodal point normals the element displacement field is described using three translations of the mid surface nodes and the two rotations about the local axes the existing shell element formulations are restricted to small nodal rotations between two successive load increments the element formulation presented here removes such restrictions this is accomplished by retaining nonlinear nodal rotation terms in the definition of the displacement field and the consistent derivation of the element properties the formulation presented here is very general and yet can be made specific by selecting proper nonlinear functions representing the effects of nodal rotations the element properties are derived and presented in detail numerical examples are also presented to demonstrate the behaviour and the accuracy of the elements

asymptotic post buckling analysis of rectangular plates by hc finite elements the present paper extends the finite element perturbation approach already presented for pin jointed and framed structures15 to rectangular thin plates koiter s asymptotic strategy2 is coupled with a high continuity finite element discretization of the plate 22 the consistency of the discrete model is discussed from the kinematical and numerical points of view and several numerical tests are reported it appears that use of the hc elements makes the perturbation algorithm insensitive to the locking phenomenon occurring in the evaluation of the postbuckling behaviour it also allows the use of very fine discretization meshes at low computational cost

cartan matrices and brauerʼs k b conjecture ii abstract this paper continues sambale 2011 28 we show that the methods developed there also work for odd primes in particular we prove brauer s k b conjecture for defect groups which contain a central cyclic subgroup of index at most 9 as a consequence the k b conjecture holds for 3 blocks of defect at most 3 in the second part of the paper we illustrate the limits of our methods by considering an example then we use the work of kessar koshitani and linckelmann 13 and thus the classification to show that the k b conjecture is satisfied for 2 blocks of defect 5 except for the extraspecial defect group d 8 d 8 as a byproduct we also obtain the block invariants of 2 blocks with minimal nonmetacyclic defect groups some proofs rely on computer computations with gap the gap group 2008 10

finite rotation analysis and consistent linearization using projectors abstract a systematic procedure is presented that may be used to extend the capabilities of an existing linear finite element to accomodate finite rotation analysis this procedure is a generalization of the work presented in computers and structures volume 30 pp 257 267 the basis of our approach is the element independent co rotational algorithm where the element rigid body motion translations and rotations is separated from the deformational part of its total motion the variation of this co rotational relation results in a projector matrix with the property that a consistent internal force vector is invariant under its action the consistent tangent stiffness matrix is shown to depend on this invariance condition through the derivative of the projector this results in an unsymmetric tangent matrix whose anti symmetric part depends on the out of balance force vector in this paper we prove that using the symmetric part of the tangent matrix the newton iteration retains its quadratic rate of convergence this approach has been used to solve a number of large rotation test example problems the results demonstrate that it is possible to analyze structures undergoing large rotations within a general co rotational framework using simple and economical finite elements the resulting improvements in the performance of these simple elements are brought about through the use of convenient software utilities as pre and post processors to the element routines

element behavior in post critical plane frame analysis depending on the type of uni modal cuspoid catastrophe which governs the local behavior of a structure at a simple critical point correct prediction of the post critical path requires an accurat

on the choice of the linear element for corotational triangular shells the corotational formulation for triangular thin shell elements presented in a eriksson c pacoste element formulation and numerical techniques for stability problems in shells comput methods

cartan matrices and brauer s k b conjecture abstract it is well known that the cartan matrix of a block of a finite group cannot be arranged as a direct sum of smaller matrices in this paper we address the question if this remains true for equivalent matrices the motivation for this question comes from the work of kulshammer and wada 2002 10 which contains certain bounds for the number of ordinary characters in terms of cartan invariants as an application we prove such a bound in the special case where the determinant of the cartan matrix coincides with the order of the defect group in the second part of the paper we show that brauer s k b conjecture holds for 2 blocks under some restrictions on the defect group for example the k b conjecture holds for 2 blocks if the corresponding defect group is a central extension of a metacyclic group by a cyclic group the same is true if the defect group contains a central cyclic subgroup of index 8 in particular the k b conjecture holds for 2 blocks with defect at most 4 the paper is a part of the author s phd thesis

linear and geometrically nonlinear bending of isotropic and multilayered composite plates by the natural mode method abstract in the present study we apply the natural mode method and formulate an appropriate linear and geometrically nonlinear theory which is implemented on a model three node multilayered triangular facet element which incorporates the effect of transverse shear deformation and is intended for the nonlinear analysis of large and complex isotropic and composite structures in this context we discuss the derivation of the elastic and geometrical elemental stiffnesses which are based on appropriate kinematic as well as physical idealizations which constitute basic elements of the method of intelligent physical lumping subsequently we present the ariban scheme accumulation of the rigid body and natural modes for geometrically nonlinear analysis it is emphasized that both the triangular facet element and the nonlinear algorithm are developed for the analysis of large and complex structures for which higher order formal finite elements cannot provide answers inexpensivelly in addition the structure of the algorithm and its matrix language are ideally suited for modern parallel computers we conclude our study with numerical examples for isotropic and composite plates all the numerical experiments show the accuracy and potential of the developed methodology for extensive structural engineering computations

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

plastic instability of beam structures using co rotational elements in a previous paper comput methods appl mech engrg 191 2002 1755 the authors have presented a 3d co rotational elastic beam element including warping effects this formulation is now further developed in order to incorporate elasto plastic deformations the element possesses seven degrees of freedom at each node and can be used to model beams with arbitrary cross sections thus within the present approach the centroid and shear center of the cross section are not necessarily coincident the main purpose of this element is to model elasto plastic instability problems in this context two methods of branch switching are tested and discussed in the first one the bifurcation point is isolated by successive bisections and the branch switching is operated by using the eigenvector associated to the negative eigenvalue in the second one introduced by petryk an energy approach is used to select automatically the stable post bifurcation path six examples including large displacement and stability problems are used in order to assess the performances of the element

path following analysis of thin walled structures and comparison with asymptotic post critical solutions a path following non linear elastic analysis for structures composed of assemblages of flat slender elastic panels is presented the proposed path following method employs fem technology and a kinematical model to analyse these structures using a koiter asymptotic approach as a result it is possible to verify the accuracy achieved by the asymptotic method the proposed mixed path following formulation is both efficient and robust with regards to the locking extrapolation phenomenon that strongly affects compatible formulations the use of an hc finite element makes it possible to avoid the problem of the finite rotations in the space maintaining a high degree of continuity and making the numeric formulation simple and efficient copyright 2002 john wiley sons ltd

co rotational flat facet triangular elements for shell instability analyses abstract this paper investigates the formulation of co rotational flat facet triangular elements for the numerical analysis of instability phenomena in shell structures the elements have three nodes with six degrees of freedom at each node the term co rotational relates here to the provision of a local system that continuously rotates and translates with the element following mainly nour omid and rankin b nour omid and c c rankin finite rotation analysis and consistent linearization using projectors comput methods appl mech engrg 93 1991 353 384 the definition of an element resorts to a change of variables from the local frame to the global one this is done through the use of a projector matrix which relates the variations of the local displacements to the variations of the global ones by extracting the rigid body modes from the latter the main difference from the original formulation lies in the parameterization of 3d finite rotations in contrast to the paper by nour omid and rankin a parameterization based on the rotational vector is here adopted and thus an additional change of variables has to be performed as a result the rotational variables become additive and the necessity of a special updating procedure is avoided the main feature of the adopted formulation is its independence of the local assumptions used to derive the internal forces and tangent stiffness in local coordinates for a certain class of elements i e elements with the same number of nodes and degrees of freedom the main co rotational framework is the same using this property three types of local formulations are considered a set of carefully chosen test problems is used in order to assess the performances of the three element types