a priori error estimation of a four node reissner mindlin plate element for elasto dynamics abstract the explicit finite element method for transient dynamics of linear elasticity by reissner mindlin plate model is introduced for clamped rectangular plate the a priori error estimates are derived for the four node bathe dvorkin element for fixed thickness the convergence rates of deflection rotation and their velocities measured both in h 1 norm and l 2 norm can possibly all be optimal under certain conditions in some cases the numerical examples show that the convergence rate stays optimal for a certain range of thickness in other cases however the deterioration in rate of convergence and even locking may occur to the velocity terms

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

a computational method for frictional contact problem using finite element method a numerical procedure is developed for the solution of the two dimensional frictional contact problems with coulomb s law of friction the formulation for this procedure is reduced to a complementarity problem the contact region is separated into stick and slip regions and the contact stress can be solved systematically by applying the solution technique of the complementarity problem

approximation of the vibration modes of a plate by reissner mindlin equations this paper deals with the approximation of the vibration modes of a plate modelled by the reissner mindlin equations it is well known that in order to avoid locking some kind of reduced integration or mixed interpolation has to be used when solving these equations by finite element methods in particular one of the most widely used procedures is the mixed interpolation tensorial components based on the family of elements called mitc we use the lowest order method of this family applying a general approximation theory for spectral problems we obtain optimal order error estimates for the eigenvectors and the eigenvalues under mild assumptions these estimates are valid with constants independent of the plate thickness the optimal double order for the eigenvalues is derived from a corresponding l 2 estimate for a load problem which is proven here this optimal order l 2 estimate is of interest in itself finally we present several numerical examples showing the very good behavior of the numerical procedure even in some cases not covered by our theory

on a non linear formulation for curved timoshenko beam elements considering large displacement rotation increments summary an incremental total lagrangian formulation for curved beam elements that includes the effect of large rotation increments is developed a complete and symmetric tangent stiffness matrix is obtained and the numerical results show in general an improvement over the standard formulation where the assumption of infinitesimal rotation increments is made in the derivation of the tangent stiffness matrix

a new hybrid mixed variational approach for reissner mindlin plates the misp model a valuable variational approach for plate problems based on the reissner mindlin theory is presented the new misp mixed shear projected approach is based on the hellinger reissner variational principle with a particular representation of transversal shear forces and transversal shear strains the approximations of the shear forces are derived from those of the bending moments using the corresponding equilibrium relations the shear strains are defined in terms of the edge tangential strains that are projected on the element degrees of freedom two finite elements are developed on the misp approach basis 3 node triangular element misp3 and 4 node quadrilateral element misp4 both elements can be considered as the most simple among the existent mixed elements a modified misp model with a derived 4 node element is also presented numerical experiments are presented which show that the misp elements do not exhibit shear locking and give excellent results for thick and thin plates they also pass the patch test for a general triangle and quadrilateral 1998 john wiley sons ltd

multilayered shell finite element with interlaminar continuous shear stresses a refinement of the reissner mindlin formulation a finite element formulation for refined linear analysis of multilayered shell structures of moderate thickness is presented an underlying shell model is a direct extension of the first order shear deformation theory of reissner mindlin type a refined theory with seven unknown kinematic fields is developed i by introducing an assumption of a zig zag i e layer wise linear variation of displacement field through the thickness and ii by assuming an independent transverse shear stress fields in each layer in the framework of reissner s mixed variational principle the introduced transverse shear stress unknowns are eliminated on the cross section level at this process the interlaminar equilibrium conditions i e the interlaminar shear stress continuity conditions are imposed as a result the weak form of constitutive equations the so called weak form of hooke s law is obtained for the transverse strains transverse stress resultants relation a finite element approximation is based on the four noded isoparametric element to eliminate the shear locking effect the assumed strain variational concept is used performance of the derived finite element is illustrated with some numerical examples the results are compared with the exact three dimensional solutions as well as with the analytical and numerical solutions obtained by the classical the first order and some representative refined models copyright 2000 john wiley sons ltd

a discontinuous galerkin method for nonlinear shear flexible shells abstract in this paper a discontinuous galerkin method for a nonlinear shear flexible shell theory is proposed that is suitable for both thick and thin shell analysis the proposed method extends recent work on reissner mindlin plates to avoid locking without the use of projection operators such as mixed methods or reduced integration techniques instead the flexibility inherent to discontinuous galerkin methods in the choice of approximation spaces is exploited to satisfy the thin plate compatibility conditions a priori a benefit of this approach is that only generalized displacements appear as unknowns we take advantage of this to craft the method in terms of a discrete energy minimization principle thereby restoring the rayleigh ritz approach in addition to providing a straightforward and elegant derivation of the discrete equilibrium equations the variational character of the method could afford numerous advantages in terms of mesh adaptation and available solution techniques the proposed method is exercised on a set of benchmarks and example problems to assess its performance numerically and to test for shear and membrane locking

an unsymmetric 4 node 8 dof plane membrane element perfectly breaking through macneal s theorem summary among numerous finite element techniques few models can perfectly without any numerical problems break through macneal s theorem any 4 node 8 dof membrane element will either lock in in plane bending or fail to pass a c0 patch test when the element s shape is an isosceles trapezoid in this paper a 4 node plane quadrilateral membrane element is developed following the unsymmetric formulation concept which means two different sets of interpolation functions for displacement fields are simultaneously used the first set employs the shape functions of the traditional 4 node bilinear isoparametric element while the second set adopts a novel composite coordinate interpolation scheme with analytical trail function method in which the cartesian coordinates x y and the second form of quadrilateral area coordinates qacm ii s t are applied together the resulting element us atfq4 exhibits amazing performance in rigorous numerical tests it is insensitive to various serious mesh distortions free of trapezoidal locking and can satisfy both the classical first order patch test and the second order patch test for pure bending furthermore because of usage of the second form of quadrilateral area coordinates qacm ii the new element provides the invariance for the coordinate rotation it seems that the behaviors of the present model are beyond the well known contradiction defined by macneal s theorem copyright 2015 john wiley sons ltd

general prolongations and x t depending pseudopotentials for the kdv equation given an exterior differential system on a manifold m we study general prolongations of the system on a locally trivial fiber bundle m m by a cartan ehresmann connection we characterize such prolongations for the system associated with the kdv equation without any assumption of x t independence the partial lie algebra discovered by wahlquist estabrook j math phys 16 1 1975 appears by this way as an intrinsic tool simple analytic pseudopotentials are classified up to diffeomorphism

an effective two dimensional frictional contact model for arbitrary curved geometry a finite element model is developed on the basis of a variational formulation of the perturbed lagrange type and the classical coulomb law of friction for the analysis of frictional contact problems in two dimensions the model accounts for all geometric kinematic non linearities associated with large sliding motions as well as arbitrary contact surface curvatures explicit forms for the contact force and tangent stiffness operators and a penalty type format is utilized in the implementation an extensive number of numerical simulations are used to demonstrate the effectiveness and practical usefulness of the model

field and edge consistency synthesis of a 4 noded quadrilateral plate bending element in this paper we demonstrate the use of two conceptual13 principles the field consistency requirement and the edge 13 consistency requirement as the basis for deriving a 4 noded13 quadrilateral plate bending element based on mindlin plate13 theory using jacobean transformations only the derivation is now free of the use of such devices as strain interpolation points and hrennikoff strain reference lines etc which have been the basis for many recent formulations of this element the shear strain constraints are now consistently defined within the element dornain and tangential shear strains are consistently matched at element boundaries so that there is no locking even13 under extreme distortion e g even when two nodes are collapsed so that the quadrilateral becomes a triangle numerical experiments show that this synthesis produces an element that should be identical to other recent formulations of this element based on tensorial transformations or on shear constraint condensation on the edges but now given a more complete and formal logical basis

on convergence of nonconforming convex quadrilateral finite elements agq6 the 4 node quadrilateral membrane elements agq6 i and ii are two novel incompatible models formulated by the quadrilateral area coordinate method qacm in this paper the sufficient conditions for their convergence are established it is further shown theoretically that the convergence in the energy norm is linear and the convergence in the l2 norm is quadratic provided that certain geometric conditions are met requiring asymptotically parallelograms meshes to be used the necessity of conditions is also discussed the results of numerical examples completely confirm the theoretical findings

a formulation of the mitc4 shell element for finite strain elasto plastic analysis abstract a finite strain elasto plastic formulation is developed for the mitc4 shell element the developed formulation is based on lee s multiplicative decomposition of the deformation gradient and on the hyperelastic expression of von mises flow rule expressed in terms of hencky s strain tensor the formulation incorporates thickness stretching degrees of freedom that are condensed at the element level by imposing the classical in layer plane stress condition a symmetric and consistent tangent stiffness matrix is also developed

a coupled alpha fem for dynamic analyses of 2d fluid solid interaction problems abstract an alpha finite element method using triangular elements fem t3 which combines the node based smoothed fem ns fem t3 and standard fem t3 with a scale factor 0 1 is extended to the dynamic analysis of 2d fluid solid interaction problems based on the pressure displacement formulation the gradient smoothing technique based on a part of the smoothing domains associated with the nodes of the triangles is used to smooth both the gradient of pressure and gradient of displacement this gradient smoothing technique can provide proper softening effect and thus improve significantly the accuracy of solution of coupled system some numerical examples have been presented to illustrate the effectiveness and stability of the fem t3 0 6 compared with some existing methods for 2d fluid solid interaction problems

frictional contact problems of kinked cracks modelled by a boundary integral method a numerical method is presented for the solution of two dimensional crack problems including the effects of crack kinks and frictional contact between crack faces the method is based on an integral equation for the resultant forces along a crack coulomb friction between contacting crack surfaces is taken into account the numerical implementation is demonstrated by considerations of surface and sub surface piece wise straight line cracks in a half plane numerical results are presented to illustrate the efficiency and the reliability of the presented method

semitoric integrable systems on symplectic 4 manifolds let m be a symplectic 4 manifold a semitoric integrable system on m is a pair of smooth functions j h c m r for which j generates a hamiltonian s 1 action and the poisson brackets j h vanish we shall introduce new global symplec tic invariants for these systems some of these invariants encode topological or geometric aspects while others encode analytical information about the singularities and how they stand with respect to the system our goal is to prove that a semitoric system is completely determined by the invariants we introduce

an isostatic assumed stress triangular element for the reissner mindlin plate bending problem the paper describes a new assumed stress triangular element for reissner mindlin plates called tip3 with three nodes and three degrees of freedom per node the kinematics is constructed by means of the so called linked interpolation ruled by technically significant degrees of freedom i e one transversal displacement and two rotations per node without using additional bubble modes the static representation starts from a moment shear uncoupled polynomial approximation and is constrained to satisfy some equilibrium conditions in order to reduce the stress parameters to a minimum number the resulting element is locking free presents correct rank and passes the bending patch test even for very thin plates the good performances of the element are demonstrated by several comparisons with other triangular plate elements available in the literature copyright 2007 john wiley sons ltd

a new discontinuous galerkin method for kirchhoff love shells abstract discontinuous galerkin methods dg have particular appeal in problems involving high order derivatives since they provide a means of weakly enforcing the continuity of the unknown field derivatives this paper proposes a new discontinuous galerkin method for kirchhoff love shells considering only the membrane and bending response the proposed one field method utilizes the weak enforcement in such a way that the displacements are the only unknowns while the rotation continuity is weakly enforced this work presents the formulation of the new discontinuous galerkin method for linear elastic shells demonstrates the consistency and stability of the proposed framework and establishes the method s convergence rate after a description of the formulation implementation into a finite element code these properties are demonstrated on numerical applications

a reduced integration solid shell finite element based on the eas and the ans concept geometrically linear problems in this paper a new reduced integration eight node solid shell finite element is presented the enhanced assumed strain eas concept based on the hu washizu variational principle requires only one eas degree of freedom to cure volumetric and poisson thickness locking one key point of the derivation is the taylor expansion of the inverse jacobian with respect to the element center which closely approximates the element shape and allows us to implement the assumed natural strain ans concept to eliminate the curvature thickness and the transverse shear locking the second crucial point is a combined taylor expansion of the compatible strain with respect to the center of the element and the normal through the element center leading to an efficient and locking free hourglass stabilization without rank deficiency hence the element requires only a single integration point in the shell plane and at least two integration points in thickness direction the formulation fulfills both the membrane and the bending patch test exactly which has to the authors knowledge not yet been achieved for reduced integration eight node solid shell elements in the literature owing to the three dimensional modeling of the structure fully three dimensional matenal models can be implemented without additional assumptions

a unified 3d based technique for plate bending analysis using scaled boundary finite element method summary this paper presents a unified technique for solving the plate bending problems by extending the scaled boundary finite element method the formulation is based on the three dimensional governing equation without enforcing the kinematics of plate theory only the in plane dimensions are discretised into finite elements any two dimensional displacement based elements can be employed the solution along the thickness is expressed analytically by using a matrix function the proposed technique is consistent with the three dimensional theory and applicable to both thick and thin plates without exhibiting the numerical locking phenomenon moreover the use of higher order spectral elements allows the proposed technique to better represent curved boundaries and to achieve high accuracy and fast convergence numerical examples of various plate structures with different thickness to length ratios demonstrate the applicability and accuracy of the proposed technique copyright 2012 john wiley sons ltd

correction to inverse spectral theory for semiclassical jaynes cummings systems we explain why theorem b in the original article does not follow from the main result of this paper theorem a while we conjecture that theorem b should nevertheless be true in this erratum we prove a slightly weaker version of it

semi global symplectic invariants of the spherical pendulum abstract we compute the semi global symplectic invariants near the focus focus point of the spherical pendulum a modified birkhoff normal form procedure is presented to compute the expansion of the hamiltonian near the focus focus point in eliasson variables combining this with explicit formulas for the action we find the semi global symplectic invariants near the focus focus point introduced by v ng c 2003 32 we show that the birkhoff normal form at the focus focus point is the inverse of a complete elliptic integral over a vanishing cycle we close with some remarks about the pendulum for which the invariants can be related to theta functions in a beautiful way

constructing integrable systems of semitoric type let m be a connected symplectic 4 manifold a semitoric integrable system on m essentially consists of a pair of independent real valued smooth functions j and h on m for which j generates a hamiltonian circle action under which h is invariant in this paper we give a general method to construct starting from a collection of five ingredients a symplectic 4 manifold equipped a semitoric integrable system then we show that every semitoric integrable system on a symplectic 4 manifold is obtained in this fashion in conjunction with the uniqueness theorem proved recently by the authors this gives a classification of semitoric integrable systems on 4 manifolds in terms of five invariants

unification of ernst equation backlund transformations using a modified wahlquist estabrook technique the three known backlund transformations for the ernst equation are derived using a modification of the wahlquist estabrook prolongation procedure the modification requires that the equation to be studied be cast into a set of differential forms and their exterior derivatives such that all coefficients are constant a cc ideal analysis of the resulting equations produces 16 solutions composed of the three basic transformations combined with identity and other essentially trivial transformations the group structure of the transformations is discussed a backlund transformation already known for the ernst maxwell equations can be found by the same method promising generalizations are mentioned

prolongation structures of a higher order nonlinear schrodinger equation a higher order schrodinger equation containing parameters which is used to describe pulse propagation in optical fibres is shown to admit an infinite dimensional prolongation structure for exactly four combinations of the parameters besides the classical nls equation for each of these cases the structure of the resulting prolongation algebra is determined explicitly for the first three cases the prolongation algebra is essentially a sub algebra of a1 1 the fourth case turns out to be sub algebra of the twisted kac moody algebra a2 2 using vector field representations related systems of differential equations for the pseudo potential functions are given for each of the cases the cases found here correspond exactly to the derived nls equations i and ii the hirota equation and the equation recently considered by sasa and satsuma 1991 the result of this paper strongly indicates that the considered higher order nls equation is completely integrable for precisely these four cases

the robinson trautman type iii prolongation structure contains k_2 the minimal prolongation structure for the robinson trautman equations of petrov type iii is shown to always include the infinite dimensional contragredient algebra k2 which is of infinite growth knowledge of faithful representations of this algebra would allow the determination of backlund transformations to evolve new solutions

a general methodology for deriving shear constrained reissner mindlin plate elements in this paper the necessary requirements for the good behaviour of shear constrained reissner mindlin plate elements for thick and thin plate situations are re interpreted and a simple explicit form of the substitute shear strain matrix is obtained this extends the previous work of the authors presented in references 18 and 31 the general methodology is applied to the re formulation of some well known quadrilateral plate elements and some new triangular and quadrilateral plate elements which show promising features some examples of the good behaviour of these elements are given

assumed strain finite element methods for conserving temporal integrations in non linear solid dynamics this paper presents a new class of assumed strain finite elements to use in combination with general energy momentum conserving time stepping algorithms so that these conservation properties in time are preserved by the fully discretized system in space and time the case of interest corresponds to nearly incompressible material responses in the fully non linear finite strain elastic and elastoplastic ranges the new elements consider the classical scaling of the deformation gradient with an assumed jacobian its determinant defined locally through a weighted averaging procedure at the element level the key aspect of the newly proposed formulation is the definition of the associated linearized strain operator or b bar operator the developments presented here start by identifying the conditions that this discrete operator must satisfy for the fully discrete system in time and space to inherit exactly the conservation laws of linear and angular momenta and the conservation dissipation law of energy for elastic and inelastic problems respectively care is also taken of the preservation of the relative equilibria and the corresponding group motions associated with the momentum conservation laws and characterized by purely rotational and translational motions superimposed to the equilibrium deformed configuration with these developments at hand a new general b bar operator is introduced that satisfies these conditions the new operator not only accounts for the spatial interpolations e g bilinear displacements with piece wise constant volume but also depends on the discrete structure of the equations in time the aforementioned conservation dissipation properties of energy and momenta are then proven to hold rigorously for the final numerical schemes unconditionally of the time step size and the material model elastic or elastoplastic different finite elements are considered in this framework including quadrilateral and triangular elements for plane problems and brick elements for three dimensional problems several representative numerical simulations are presented involving in particular the use of energy dissipating momentum conserving time stepping schemes recently developed by the author and co workers for general finite strain elastoplasticity in order to illustrate the properties of the new finite elements including these conservation dissipation properties in time and their locking free response in the quasi incompressible case copyright 2007 john wiley sons ltd

infinite dimensional estabrook wahlquist prolongations for the sine gordon equation we are looking for the universal covering algebra for all symmetries of a given partial differential equation pde using the sine gordon equation as a typical example for a nonevolution equation for nonevolution equations estabrook wahlquist prolongation structures for nonlocal symmetries depend on the choice of a specific subideal of the contact module to define the pde for each inequivalent such choice we determine the most general solution of the prolongation equations as subalgebras of the infinite dimensional algebra of all vector fields over the space of nonlocal variables associated with the pde in the style of vinogradov covering spaces we show explicitly how previously known prolongation structures known to lie within the kac moody algebra a 1 1 are special cases of these general solutions although we are unable to identify the most general solutions with previously studied algebras we show the existence of gauge transformations between prolongation structures viewed as determinin

analysis of some low order quadrilateral reissner mindlin plate elements four quadrilateral elements for the reissner mindlin plate model are considered the elements are the stabilized mitc4 element of lyly stenberg and vihinen 1933 the min4 element of tessler and hughes 1983 the q4bl element of zienkiewicz et al 1993 and the fmin4 element of kikuchi and ishii 1999 for all elements except the q4bl element a unifying variational formulation is introduced and optimal h 1 and l 2 error bounds uniform in the plate thickness are proven moreover we propose a modified q4bl element and show that it admits the optimal h 1 and l 2 error bounds uniform in the plate thickness in particular we study the convergence behavior of all elements regarding the mesh distortion

finite elements with displacement interpolated embedded localization lines insensitive to mesh size and distortions a new finite element formulation aimed at the solution of problems involving strain localization is presented the proposed formulation incorporates displacement interpolated embedded localization lines results are shown to converge to an exact solution when the mesh is refined and also to be quite insensitive to mesh distortions

on the limits of finite element perfectability it has been shown2 that a four noded membrane element of trapezoidal shape must either lock or fail constant strain patch tests that result is generalized here to establish similar limitations for all finite elements a modal analysis is used to show that essential coupling exists between low modes whose displacement states can be exactly represented by an element s basis functions and higher modes whose displacement states cannot be so represented such coupling can be avoided only when an element has particular shapes in all other cases the element designer is faced with the choice of patch test failure in a low mode or locking in a higher mode several examples are described

semiclassical quantization and spectral limits of ħ pseudodifferential and berezin toeplitz operators we introduce a minimalistic notion of semiclassical quantization and use it to prove that the convex hull of the semiclassical spectrum of a quantum system given by a collection of commuting operators converges to the convex hull of the spectrum of the associated classical system this gives a quick alternative solution to the isospectrality problem for quantum toric systems if the operators are uniformly bounded the convergence is uniform analogous results hold for non commuting operators

convexity properties of the moment mapping re examined abstract consider a hamiltonian action of a compact lie group on a compact symplectic manifold a theorem of kirwan s says that the image of the momentum mapping intersects the positive weyl chamber in a convex polytope i present a new proof of kirwan s theorem which gives explicit information on how the vertices of the polytope come about and on how the shape of the polytope near any point can be read off from infinitesimal data on the manifold it also applies to some interesting classes of noncompact or singular hamiltonian spaces such as cotangent bundles and complex affine varieties

a robust non linear mixed hybrid quadrilateral shell element in the paper a non linear quadrilateral shell element for the analysis of thin structures is presented the variational formulation is based on a hu washizu functional with independent displacement stress and strain fields the interpolation matrices for the mid surface displacements and rotations as well as for the stress resultants and strains are specified restrictions on the interpolation functions concerning fulfillment of the patch test and stability are derived the developed mixed hybrid shell element possesses the correct rank and fulfills the in plane and bending patch test using newton s method the finite element approximation of the stationary condition is iteratively solved our formulation can accommodate arbitrary non linear material models for finite deformations in the examples we present results for isotropic plasticity at finite rotations and small strains as well as bifurcation problems and post buckling response the essential feature of the new element is the robustness in the equilibrium iterations it allows very large load steps in comparison to other element formulations copyright 2005 john wiley sons ltd

inverse spectral theory for semiclassical jaynes cummings systems quantum semitoric systems form a large class of quantum hamiltonian integrable systems with circular symmetry which has received great attention in the past decade they include systems of high interest to physicists and mathematicians such as the jaynes cummings model 1963 which describes a two level atom interacting with a quantized mode of an optical cavity and more generally the so called systems of jaynes cummings type in this paper we consider the joint spectrum of a pair of commuting semiclassical operators forming a quantum integrable system of jaynes cummings type we prove assuming the bohr sommerfeld rules hold that if the joint spectrum of two of these systems coincide up to mathcal o hbar 2 then the systems are isomorphic

a finite element method with discontinuous rotations for the mindlin reissner plate model we present a continuous discontinuous finite element method for the mindlin reissner plate model based on continuous polynomials of degree k 2 for the transverse displacements and discontinuous polynomials of degree k 1 for the rotations we prove a priori convergence estimates uniformly in the thickness of the plate and thus show that locking is avoided we also derive a posteriori error estimates based on duality together with corresponding adaptive procedures for controlling linear functionals of the error finally we present some numerical results

a four node plate bending element based on mindlin reissner plate theory and a mixed interpolation this communication discusses a 4 node plate bending element for linear elastic analysis which is obtained as a special case from a general nonlinear continuum mechanics based 4 node shell element formulation the formulation of the plate element is presented and the results of various example solutions are given that yield insight into the predictive capability of the plate and shell element

convexity properties of the moment mapping ii be its associated momen t mapping see w for definitions the set x is the union of co adjoint orbits the main result of this paper is a description of the orbit structure of this set to describe this result we first note that the coadjoint orbits in q can be parametr ized as follows let t be a caf tan subalgebra of g and let b be a positive definite g invariant bilinear form on by means of b we get a g equivariant identification q let t be the subspace of q corresponding to t then every co adjoint orbit intersects i in a weyl group orbit so there is a one one correspondence between co adjoint orbits in q and weyl group orbits in t to get an even sharper parametrization let t be a weyl chamber in then every weyl group orbit intersects t in a single point so t is a modul i space for the co adjoint orbits two orbits in x are said to be of the same type if they are isomorphic as homogeneous g spaces since x is compact there are at most a finite number of different types of orbits see 1113 let h be a closed subgroup of t of codimension r and let cit be the set of all orbits in x of type g h

on the accuracy of p version elements for the reissner mindlin plate problem this paper addresses the question of accuracy of p version finite element formulations for reissner mindlin plate problems three model problems a circular arc a rhombic plate and a geometrically complex structure are investigated whereas displacements and bending moments turn out to be very accurate without any post processing even for very coarse meshes the quality of shear forces computed from constitutive equations is poor it is shown that significantly improved results can be obtained if shear forces are computed from equilibrium equations instead a consistent computation of second derivatives of the shape functions is derived 1998 john wiley sons ltd

a simple four node quadrilateral finite element for plates abstract a simple and accurate four node quadrilateral finite element based on the mindlin plate theory and kirchhoff constraints is presented for general thin plate bending applications the derivation of the element stiffness properties is straightforward starting with a specified eight node interpolation usual discrete kirchhoff dk constraints are employed to constrain out the four midside nodes of the element the present resulting dk element passes patch tests with elements of arbitrary and even highly distorted mesh types numerical studies of the element convergence behaviours are undertaken for various plate bending problems so far investigated it is indicated from comparative examples that fairly good convergence characteristics have been achieved

finite element concepts for finite elastoplastic strains and isotropic stress response in shells theoretical and computational analysis this paper presents appropriate finite element concepts accounting for finite elastoplastic strains and isotropic stress response in arbitrary shells three parameterization strategies for the calculation of thin and thick smooth shells as well as shell intersections are discussed in detail in this context the importance of the deformation gradient for an efficient implementation is especially emphasized according to the parameterizations the computational plasticity algorithms are derived in general three dimensional 3 d form for thick shell structures and a restricted 2 d form satisfying the plane stress state underlying thin shells in order to describe arbitrary shell geometries the isoparametric concept is applied to all proposed finite element formulations these are based on quadrilateral 4 node mixed finite shell elements the variational approaches of the enhanced assumed strain method the assumed natural strain concept and the reduced integration technique are accurately considered by means of representative numerical examples the performance of the three different finite element concepts is demonstrated furthermore their individual properties are addressed with respect to efficiency and numerical accuracy thus crucial consequences for an optimal modelling of finite plastic strains in shells can be outlined

a linear quadrilateral shell element with fast stiffness computation abstract a new quadrilateral shell element with 5 6 nodal degrees of freedom is presented assuming linear isotropic elasticity a hellinger reissner functional with independent displacements rotations and stress resultants is used within the mixed formulation the stress resultants are interpolated using five parameters for the membrane forces as well as for the bending moments and four parameters for the shear forces the hybrid element stiffness matrix resulting from the stationary condition is integrated analytically this leads to a part obtained by one point integration and a stabilization matrix the element possesses the correct rank is free of locking and is applicable within the whole range of thin and thick shells the in plane and bending patch tests are fulfilled and the computed numerical examples show that the convergence behaviour of the stress resultants is very good in comparison to comparable existing elements the essential advantage is the fast stiffness computation due to the analytically integrated matrices

a nilpotent prolongation of the robinson trautman equation a prolongation is constructed in the sense of wahlquist and estabrook for the nonlinear evolution equation determining robinson trautman space times the lie algebra so obtained is found to be naturally seven dimensional and nilpotent representations of the algebra are considered the simple relationship of such a prolongation to the conservation laws associated with the robinson trautman equation is discussed

application of the quadrilateral area co ordinate method a new element for mindlin reissner plate the quadrilateral area co ordinate method is used to formulate a new quadrilateral element for mindlin reissner plate bending problem firstly an independent shear field is assumed based on the locking free timoshenko s beam formulae secondly a fourth order deflection field is assumed by introducing some generalized conforming conditions thirdly the rotation field is determined by the strain displacement relations furthermore a hybrid post processing procedure is suggested to improve the stress internal force solutions following this procedure a new 4 node 12 dof quadrilateral element named ac mq4 is successfully constructed since all formulations are expressed by the area co ordinates element ac mq4 presents some different but beneficial characters when compared with other usual models numerical examples show the new element is free of shear locking insensitive to mesh distortion and possesses excellent accuracy in the analysis of both thick and thin plates it has also been demonstrated that the area co ordinate method the generalized conforming condition method and the hybrid post processing procedure are efficient tools for developing simple effective and reliable finite element models copyright 2005 john wiley sons ltd

moment polytopes for symplectic manifolds with monodromy abstract a natural way of generalising hamiltonian toric manifolds is to permit the presence of generic isolated singularities for the moment map for a class of such almost toric 4 manifolds which admits a hamiltonian s 1 action we show that one can associate a group of convex polygons that generalise the celebrated moment polytopes of atiyah guillemin sternberg as an application we derive a duistermaat heckman formula demonstrating a strong effect of the possible monodromy of the underlying integrable system