a computationally viable higher order theory for laminated composite plates abstract a variational higher order theory involving all transverse strain and stress components is proposed for the analysis of laminated composites plates derived from three dimensional elasticity with emphasis on developing a viable computational methodology the theory is well studied for finite element approximations as it incorporates both c0 and c 1 continuous kinematic fields and poisson boundary conditions from the theory a simple three node stretching bending finite element is developed and applied to the problem of cylindrical bending of a symmetric carbon epoxy laminate for which an exact solution is available both the analytic and finite element result were found to be in excellent agreement with the exact solution for a wide range of the length to thickness ratio the proposed higher order theory has the same computational advantages as first order shear deformable theories the present methodology however provides greater predictive capability especially for thick section composites

finite element multiple mode approach to nonlinear free vibrations of shallow shells two finite element fe modal formulations for large amplitude free vibration of isotropic and arbitrary laminated composite shallow shells are presented the system equation of motion is formulated first in the physical structural node degrees of freedom dof then the system is transformed into two distinctly different sets of general duffing type modal equations based on 1 modal amplitudes of coupled linear bending and in plane modes where in plane inertia is included in the formulation and 2 modal amplitudes of linear bending modes only where the in plane inertia is neglected multiple modes and the first order transverse shear deformation are considered in the formulations a shallow shell finite element is developed as an extension from the triangular mindlin min3 plate element with the improved shear correction factor by tessler time numerical integration is employed to determine the nonlinear periodic frequency characteristics the inaccuracy in characterizing a shallow shell response with coupled linear bending and in plane modes is demonstrated and discussed by comparing with the fe solution in structural node dof study cases include isotropic and composite panels of different shallow shell geometries

on stabilized finite element methods for linear systems of convection diffusion reaction equations abstract a stabilized finite element method for solving systems of convection diffusion reaction equations is studied in this paper the method is based on the subgrid scale approach and an algebraic approximation to the subscales after presenting the formulation of the method it is analyzed how it behaves under changes of variables showing that it relies on the law of change of the matrix of stabilization parameters associated to the method an expression for this matrix is proposed for the case of general coupled systems of equations that is an extension of the expression proposed for a one dimensional 1d model problem applications of the stabilization technique to the stokes problem with convection and to the bending of reissner mindlin plates are discussed next the design of the matrix of stabilization parameters is based on the identification of the stability deficiencies of the standard galerkin method applied to these two problems

q schur algebras asymptotic forms and quantum sln abstract we studied asymptotic methods for q schur algebras and related quantum groups and constructed a kind of asymptotic form for q schur algebras and quantum special linear groups the structure and representations for these forms were also discussed

an improved variational method for finite element stress recovery and a posteriori error estimation abstract a new variational formulation is presented which serves as a foundation for an improved finite element stress recovery and a posteriori error estimation in the case of stress predictions interelement discontinuous stress fields from finite element solutions are transformed into a c 1 continuous stress field with c 0 continuous stress gradients these enhanced results are ideally suited for error estimation since the stress gradients can be used to assess equilibrium satisfaction the approach is employed as a post processing step in finite element analysis the variational statement used herein combines discrete least squares penalty constraint and curvature control functionals thus enabling automated recovery of smooth stresses and stress gradients the paper describes the mathematical foundation of the method and presents numerical examples including stress recovery in two dimensional structures and built up aircraft components and error estimation for adaptive mesh refinement procedures

constructing quantized enveloping algebras via inverse limits of finite dimensional algebras abstract it is known that a generalized q schur algebra may be constructed as a quotient of a quantized enveloping algebra u or its modified form u on the other hand we show here that both u and u may be constructed within an inverse limit of a certain inverse system of generalized q schur algebras working within the inverse limit u clarifies the relation between u and u this inverse limit is a q analogue of the linear dual r g of the coordinate algebra of a corresponding linear algebraic group g

a posteriori error analysis of the linked interpolation technique for plate bending problems we develop a posteriori error estimates for the so called linked interpolation technique to approximate the solution of plate bending problems we show that the proposed residual based estimator is both reliable and efficient

presenting generalized schur algebras in types b c d abstract we give explicit presentations by generators and relations of certain generalized schur algebras associated with tensor powers of the natural representation in types b c d this extends previous results in type a obtained by two of the authors the presentation is compatible with the serre presentation of the corresponding universal enveloping algebra in types c d this gives a presentation of the corresponding classical schur algebra the image of the representation on a tensor power since the classical schur algebra coincides with the generalized schur algebra in those types this coincidence between the generalized and classical schur algebra fails in type b in general

a generic algebra associated to certain hecke algebras abstract we initiate the systematic study of endomorphism algebras of permutation modules and show they are obtainable by a descent from a certain generic algebra infinite dimensional in general coming from the universal enveloping algebra of sl n or gl n the endomorphism algebras and the generic algebras are cellular in the latter case of profinite type in the sense of r m green we give several equivalent descriptions of these algebras find a number of explicit bases for them and describe indexing sets for their irreducible representations moreover we show that the generic algebra embeds densely in an endomorphism algebra of a certain infinite dimensional induced module

assumed strain formulation for triangular c0 plate elements based on a weak form of the kirchhoff constraints application of a weak form of the kirchhoff constraints in the formulation of triangular assumed shear strain c0 plate element is described it is shown that compared to a similar formulation of the quadrilateral elements formulation of the triangles requires some additional considerations which lead to additional terms in the energy expression with those terms performance of the assumed shear strain triangular elements is comparable to that of the quadrilateral elements

a free formulation based flat shell element for non linear analysis of thin composite structures a flat shell element based on the free formulation finite element concept is developed for analysing geometrically non linear thin composite shells a corotational form of the updated lagrangian formulation is utilized numerical results for typical validation problems are presented in order to demonstrate the accuracy and validity of this element these results are obtained by solving the incremental equilibrium equations through the cylindrical arc length method

harmonic maps into lie groups classical solutions of the chiral model on considere deux aspects de la structure algebrique de 7b m l espace des applications harmoniques d un domaine a 2 dimensions simplement connexe dans un groupe de lie reel g r la forme reelle d un groupe complexe g on construit une representation du groupe boucle 7b a s 1 g r sur 7b m correspondant a l algebre de lie de kacmoody des deformations infinitesimales on decrit l action sur 7b m et l action d un sous groupe sur l espace des applications harmoniques dans des gaussmanniens dans une seconde partie on se restreint a une theorie qui s applique seulement quand est un domaine riemannien a 2 dimensions simplement connexe et le groupe est g r u n

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

schur weyl duality for orthogonal groups we prove schur weyl duality between the brauer algebra bn m and the orthogonal group om k over an arbitrary infinite field k of odd characteristic if m is even we show that each connected component of the orthogonal monoid is a normal variety this implies that the orthogonal schur algebra associated to the identity component is a generalized schur algebra as an application of the main result an explicit and characteristic free description of the annihilator of n tensor space v n in the brauer algebra bn m is also given

schur algebras of classical groups abstract throughout this paper the base field will be c by doty s definition s doty polynomial representations algebraic monoids and schur algebras of classical type j pure appl algebra 123 1998 165 199 a schur algebra of a classical group g is the image of the representation map c g end c c n r where c n is the natural representation and r any natural number these schur algebras are semisimple over c firstly we determine when the schur algebras are generalized schur algebras in donkin s sense see s donkin on schur algebras and related algebras i j algebra 104 1986 310 328 the main step is to decompose the tensor space c n r using path model by littelmann p littelmann a littlewood richardson rule for symmetrizable kac moody algebras invent math 116 1994 329 346 secondly we relate schur algebras with different parameters and form inverse systems from schur algebras in the same type we find the inverse limit naturally contains the universal enveloping algebra of the corresponding lie algebra

a note on decomposition numbers for reductive algebraic groups in a recent paper 7 james proves two theorems on the decomposition numbers for the general linear groups and working within the context of green s monograph 5 derives properties of the decomposition numbers for the symmetric groups this note grew out of an attempt to formulate for arbitrary reductive groups these theorems of james we prove a natural result on decomposition numbers for reductive groups from which james s theorems are deduced the result the theorem of section 2 is the analogue of jantzen s satz 1 18 of 8 on decomposition numbers for representations of complex semisimple lie algebras also proved independently by deodhar very little direct use of 5 is made though some of the ideas are cribbed from that source as one may see by comparing the properties of the functor fa in section 2 with green s treatment see section 6 2 of s of ese theory s a ring e an idempotent

robust bddc preconditioners for reissner mindlin plate bending problems and mitc elements a balancing domain decomposition method by constraints bddc is constructed and analyzed for the reissner mindlin plate bending problem discretized with mixed interpolation of tensorial components mitc finite elements this bddc algorithm is based on selecting the plate rotations and deflection degrees of freedom at the subdomain vertices as primal continuity constraints after the implicit elimination of the interior degrees of freedom in each subdomain the resulting plate schur complement is solved by the preconditioned conjugate gradient method the preconditioner is based on the solution of local reissner mindlin plate problems on each subdomain with clamping conditions at the primal degrees of freedom and on the solution of a coarse reissner mindlin plate problem for the primal degrees of freedom the main results of the paper are the proof and numerical verification that the proposed bddc plate algorithm is scalable quasi optimal and most important robust with respect to the plate thickness while this result is due to an underlying mixed formulation of the problem both the interface plate problem and the preconditioner are positive definite the numerical results also show that the proposed algorithm is robust with respect to discontinuities of the material properties

a three node mindlin plate element with improved transverse shear abstract a displacement methodology for mindlin elements recently employed in the development of an efficient four node quadrilateral min4 is the basis for a three node explicitly integrated triangular element min3 the approach herein referred to as anisoparametric is founded upon two kinematic requirements that are auxiliary to the standard convergence criteria the initial complete quadratic deflection field is constrained by continuous shear edge constraints to achieve an isoparametric like three node configuration much success of the element is due to an innovative shear correction factor concept several numerical experiments are performed in the linear elasto static regime to ascertain the element performance

non linear finite element modal approach for the large amplitude free vibration of symmetric and unsymmetric composite plates a theoretical analysis is presented for the large amplitude vibration of symmetric and unsymmetric composite plates using the non linear finite element modal reduction method the problem is first reduced to a set of duffing type modal equations using the finite element modal reduction method the main advantage of the proposed approach is that no updating of the non linear stiffness matrices is needed without loss of generality accurate frequency ratios for the fundamental mode and the higher modes of a composite plate at various values of maximum deflection are then determined by using the runge kutta numerical integration scheme the procedure for obtaining proper initial conditions for the periodic plate motions is very time consuming thus an alternative scheme the harmonic balance method is adopted and assessed as it was employed to formulate the large amplitude free vibration of beams in a previous study and the results agreed well with the elliptic solution the numerical results that are obtained with the harmonic balance method agree reasonably well with those obtained with the runge kutta method the contribution of each linear mode to the maximum deflection of a plate can also be obtained the frequency ratios for isotropic and composite plates at various maximum deflections are presented and convergence of frequencies with the number of finite elements number of linear modes and number of harmonic terms is also studied copyright 2005 john wiley sons ltd

on schur algebras and related algebras ii this paper is a continuation of 7 the purpose of 7 was to set up in the context of reductive algebraic groups a theory of generalized schur algebras a special case of our construction gives the schur algebras s n r studied extensively in lo we concentrate here on the schur algebras themselves and show that our construction yields new results in their representation theory by means of the schur functor see 10 chap 6 we obtain new results in the representation theory of the symmetric groups the main results are as follows the schur algebras s n r defined over a principal ideal domain r have finite global dimension see also 1 i over a field or complete valuation ring r every finitely generated projective s n r module has a weyl module filtration we prove the irreducibility of the socle of certain weyl modules see also 15 we describe a connection between weights of projective indecomposable modules for the schur algebras in terms of the involution on irreducible representations of symmetric groups given by tensoring with the sign representation we show that over a complete valuation ring or a field every young module for a symmetric group has a specht series in particular the projective indecomposables have specht series finally we show that for r n and a complete valuation ring or field r the blocks of the schur algebra s n r are given by the rule embodied in nakayama s conjecture the notations and conventions are as in the first part of this work 7

a two node beam element including transverse shear and transverse normal deformations a variational higher order theory for bending and stretching of linearly elastic orthotropic beams including the deformations due to transverse shearing and stretching of the transverse normal fibre is presented the theory assumes a linear distribution for the longitudinal displacement and a parabolic variation of the transverse displacement across the thickness additionally independent expansions are introduced for the through thickness displacement gradients with the requirement of a least square compatibility for the transverse strains and the satisfaction of exact stress boundary conditions at the top bottom beam surfaces the theory is shown to be well suited for finite element development requiring simple c0 and c 1 continuous displacement interpolation fields to demonstrate the computational utility of the theory a simple two node stretching bending finite element is formulated the analytic and finite element results are obtained for a simple bending problem for which an exact elasticity solution is available it is shown that the inclusion of the transverse normal deformation in the present theory enables improved displacement strain and stress predictions particularly in the analysis of deep beams

first order shear deformation p version finite element for laminated plate nonlinear vibrations a p version hierarchical finite element for moderately thick composite laminated plates is presented where the effects of the rotary inertia transverse shear and geometrical nonlinearity are taken into account the time domain free vibration equations of motion are obtained by applying the principle of virtual work those equations are mapped into the frequency domain by the harmonic balance method and solved by a predictor corrector procedure the linear natural frequencies of vibration of several plates are determined and the convergence properties of the element are investigated it is shown that the element is not prone to shear locking and that a moderate number of degrees of freedom is sufficient for accuracy the influences of the plate s thickness of the width to length ratio and of the fiber orientation on nonlinear free vibrations are investigated

nonlinear flutter of composite panels under yawed supersonic flow using finite elements a finite element formulation is presented for the effects of arbitrary flow direction on the large amplitude supersonic flutter of composite panels the von karman large deflection plate theory is used to account for large amplitude limit cyde oscillations quasisteady first order piston theory aerodynamics is employed for aerodynamic loading and first order shear deformation theory is used for laminated composite panels an efficient solution procedure is presented by using the modal transformation to reduce the number of nonlinear panel flutter equations and then applying the linearized updated mode with nonlinear time function approximation to the reduced nonlinear panel flutter modal equations a modal participation is defined and the minimum number of linear modes for accurate and converged limit cycle response can be ensured examples are given for isotropic and composite panels at yawed supersonic flow

c0 finite element discretization of kirchhoff s equations of thin plate bending an alternative formulation of kirchhoff s equations is given which is amenable to a standard c 0 finite element discretization in this formulation the potential energy of the plate is formulated entirely in terms of rotations whereas the deflections are the outcome of a subsidiary problem the nature of the resulting equations is such that c 0 interpolation can be used on both rotations and deflections in particular general classes of triangular and quadrilateral isoparametric elements can be used in conjunction with the method unlike other finite element methods which are based on three dimensional or mindlin formulations the present approach deals directly with kirchhoff s equations of thin plate bending excellent accuracy is observed in standard numerical tests using both distorted and undistorted mesh patterns

a mixed formulation of c0 linear triangular plate shell element the role of edge shear constraints a simple and effective linear c0 triangular element for plates and shells is developed on the basis of the hellinger reissner mixed variational principle with independently assumed stress and displacement fields two main features are emphasized in this development concerning the assumed transverse shear stress field firstly this assumption results in edge type penalty constraints in the thin plate shell regimes secondly the element is used in the form of a four triangle cross diagonal macroelement mesh as a result the element is shown to be free from shear locking in thin plate shell applications and it satisfied all the appropriate patch tests required for kirchhoff plate models in addition the element exhibits good overall convergence properties in a variety of test problems for plates and shells finally from the computational standpoint the element is very efficient since all stiffness component matrices are derived in explicit forms

global anti self dual yang mills fields in split signature and their scattering this article concerns solutions to the anti self dual yang mills asdym equations in split signature that are global on the double cover of the appropriate conformally compactified minkowski space e m s 2 s 2 ward s asdym twistor construction is adapted to this geometry using a correspondence between points of e m and holomorphic discs in cp 3 twistor space with boundary on the real slice rp 3 smooth global u n solutions to the asdym equations on e m are shown to be in 1 1 correspondence with pairs consisting of an arbitrary holomorphic vector bundle e over cp 3 together with a positive definite hermitian metric h on e rp 3 there are no topological or other restrictions on the bundle e in ultrahyperbolic signature solutions are generically non analytic or only finitely differentiable and such solutions arise from a corresponding choice of regularity for h when e is trivial the twistor data consists of the hermitian matrix function h on rp 3 up to constants and the correspondence provides a nonlinear generalisation of the x ray transform in general it provides a higher dimensional analogue of the inverse scattering transform in which h plays the role of the reflection coefficient ande the algebraic data explicit examples are constructed for different choices of the topology of e a scattering problem for asdym fields on affine minkowski spacein split signature is set up and it is shown that sufficiently small data at past null infinity uniquely determines data at future null infinity by taking a family of holonomies associated to the initial data followed by a sequence of two birkhoff factorizations the scattering map is simple at the level of the holonomies but non trivial at the level of the connection in the non abelian case

schur algebras of brauer algebras i a classical problem of invariant theory and of lie theory is to determine endomorphism rings of representations of classical groups for instance of tensor powers of the natural module schur weyl duality or of full direct sums of tensor products of exterior powers ringel duality in this article the endomorphism rings of full direct sums of tensor products of symmetric powers over symplectic and orthogonal groups are determined these are shown to be isomorphic to schur algebras of brauer algebras as defined in henke and koenig math z 272 3 4 729 759 2012 this implies structural properties of the endomorphism rings such as double centraliser properties quasi hereditary and a universal property as well as a classification of simple modules

an improved treatment of transverse shear in the mindlin type four node quadrilateral element abstract an improved displacement methodology based on mindlin theory is developed and applied to a four node twelve degrees of freedom quadrilateral element special attention is directed toward enhancement of the transverse shear energy representation particularly a non uniform order kinematic interpolation scheme is accompanied by what is termed element appropriate shear correction factors the element matrices are consistently derived from hamilton s variational principle using exact numerical integration throughout the element stiffness matrix possesses correct rank and is well conditioned over the entire mindlin theory range of thickness to length ratios exceptionally good element performance is demonstrated by solutions to a set of static and vibrational problems

a higher order plate theory with ideal finite element suitability abstract a variational tenth order theory for stretching and bending of orthotropic elastic plates is proposed which lends itself perfectly to finite element formulations based upon c 0 and c 1 continuous displacement approximations the deformations due to all strain and stress components are accounted the theory is derived from three dimensional elasticity via a modified virtual work statement based upon independent displacement and transverse strain expansions through the thickness the transverse displacement employs a special parabolic form while the in plane displacements are taken to be linear the issues of thickness expansion related inconsistencies in the transverse shear strains and the transverse normal stress are resolved by the enforcement of physical stress boundary conditions and variationally consistent weak transverse strain compatibility the resulting transverse shear strains are parabolic while the transverse normal strain varies cubically across the plate thickness the variational principle yields seven equations of motion and exclusively poisson type edge boundary conditions a qualitative assessment of the theory is carried out for the problem of static equilibrium involving an infinite plate under a sinusoidal normal pressure a simple three node plate element is then developed comparable in computational efficiency to its mindlin theory counterpart but which enables accurate computation of all displacement strain and stress components for a wide range of the plate span to thickness ratio

a c0 triangular plate element with one point quadrature on developpe un element de plaque triangulaire du type de mindlin qui utilise des champs lineaires pour les rotations et les deflexions transversales l element ne necessite qu un seul point de quadrature ce qui est tres interessant pour l analyse non lineaire