exponential codimension growth of pi algebras an exact estimate abstract letabe an associative pi algebra over a fieldfof characteristic zero by studying the exponential behavior of the sequence of codimensions cn a ofa we prove thatinv a limn c n a always exists and is an integer we also give an explicit way for computing such integer letbbe a finite dimensionalz2 graded algebra whose grassmann envelopeg b satisfies the same identities ofa theninv a inv g b dim c 0 dim c 1 wherec 0 c 1 is a suitablez2 graded semisimple subalgebra ofb

a coupled multipoint stress multipoint flux mixed finite element method for the biot system of poroelasticity abstract we present a mixed finite element method for a five field formulation of the biot system of poroelasticity that reduces to a cell centered pressure displacement system on simplicial and quadrilateral grids a mixed stress displacement rotation formulation for elasticity with weak stress symmetry is coupled with a mixed velocity pressure darcy formulation the spatial discretization is based on combining the multipoint stress mixed finite element msmfe method for elasticity and the multipoint flux mixed finite element mfmfe method for darcy flow it uses the lowest order brezzi douglas marini mixed finite element spaces for the poroelastic stress and darcy velocity piecewise constant displacement and pressure and continuous piecewise linear or bilinear rotation a vertex quadrature rule is applied to the velocity stress and stress rotation bilinear forms which block diagonalizes the corresponding matrices and allows for local velocity stress and rotation elimination this leads to a cell centered positive definite system for pressure and displacement at each time step we perform error analysis for the semidiscrete and fully discrete formulations establishing first order convergence for all variables in their natural norms the numerical tests confirm the theoretical convergence rates and illustrate the locking free property of the method

polynomial identities on superalgebras and exponential growth abstract let a be a finitely generated superalgebra over a field f of characteristic 0 to the graded polynomial identities of a one associates a numerical sequence cnsup a n 1 called the sequence of graded codimensions of a in case a satisfies an ordinary polynomial identity such sequence is exponentially bounded and we capture its exponential growth by proving that for any such algebra lim n c n sup a n exists and is a non negative integer we denote such integer by supexp a and we give an effective way for computing it as an application we construct eight superalgebras ai i 1 8 characterizing the identities of any finitely generated superalgebra a with supexp a 2 in the following way supexp a 2 if and only if idsup a idsup ai for some i 1 8 where idsup b is the ideal of graded identities of the algebra b we also compare the superexponent and the exponent see a giambruno m zaicev adv math 140 1998 145 155 of any finitely generated superalgebra

star polynomial identities computing the exponential growth of the codimensions abstract can one compute the exponential rate of growth of the codimensions of a pi algebra with involution over a field of characteristic zero it was shown in 2 that any such algebra a has the same identities as the grassmann envelope of a finite dimensional superalgebra with superinvolution b here by exploiting this result we are able to provide an exact estimate of the exponential rate of growth e x p a of any pi algebra a with involution it turns out that e x p a is an integer and in case the base field is algebraically closed it coincides with the dimension of an admissible subalgebra of maximal dimension of b

a mixed finite element method for nearly incompressible multiple network poroelasticity in this paper we present and analyze a new mixed finite element formulation of a general family of quasi static multiple network poroelasticity mpet equations the mpet equations describe flow a

a new efficient approach to the formulation of mixed finite element models for structural analysis abstract a new finite element formulation is developed based on the hellinger reissner principle with independent strain by dividing the assumed strain into the lower order part and the higher order part the new formulation can be made much more efficient than the standard mixed formulation in addition the present new approach provides a rational way of introducing stabilization matrix to suppress undesirable kinematic modes author

on the lie structure of the skew elements of a simple superalgebra with superinvolution abstract we investigate the lie structure of the lie superalgebra k of skew elements of a unital simple associative superalgebra a with superinvolution over a field of characteristic not 2 it is proved that if a is more than 16 dimensional over its center z then any lie ideal u of k satisfies either u z or u k k moreover any lie ideal u of k k satisfies either u z or u k k in particular k k z k k is a simple lie superalgebra

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 locking free solver for linear elasticity on quadrilateral and hexahedral meshes based on enrichment of lagrangian elements abstract this paper presents a new finite element solver for linear elasticity on quadrilateral and hexahedral meshes based on enrichment of the classical bilinear or trilinear lagrangian elements it solves the primal variable displacement in the strain div formulation and can handle both displacement and traction boundary conditions it is a locking free solver based on conforming finite elements the solver has second order accuracy in displacement and first order accuracy in stress and dilation divergence of displacement as validated by theoretical analysis and illustrated by numerical experiments on benchmarks deal ii implementation is also discussed

the exponent for superalgebras with superinvolution abstract let a be a superalgebra with superinvolution over a field of characteristic zero and let c n a n 1 2 be its sequence of codimensions in 6 it was proved that such a sequence is exponentially bounded in this paper we capture this exponential growth for finitely generated superalgebras with superinvolution a over an algebraically closed field of characteristic zero we shall prove that lim n c n a n exists and it is an integer denoted exp a and called exponent of a moreover we shall characterize finitely generated superalgebras with superinvolution according to their exponent

a new efficient mixed formulation for thin shell finite element models abstract a nine node shell element is developed by a new and more efficient mixed formulation the new shell element formulation is based on the hellinger reissner principle with independent strain and the concept of degenerate solid shell the new formulation is made more efficient in terms of computing time than the conventional mixed formulation by dividing the assumed strain fields into a lower part and a higher order part numerical results demonstrate that the present nine node element is free of locking even for very thin plates and shells and is also kinematically stable in fact the stiffness matrix associated with the higher order assumed strain plays the role of a stabilization matrix

a hybrid strain finite element for plates and shells this paper describes a new hybrid strain finite element for geometrically linear analysis of plates and shells the formulation for materially linear problems is based on a mixed variational principle having strain and displacement rates as independently varied fields to facilitate extension to materially non linear analysis the variational principle is used in rate form and the plane stress assumption is not imposed a priori in the formulation when desired the plane stress assumption is imposed in a manner similar to imposition of fixed boundary conditions the element geometry is based on a nine noded quadrilateral with biquadratic interpolation of the displacement field the strain field is based on a bilinear interpolation with additional non linear terms chosen on the basis of eigenvalue analysis the element passes the required patch tests does not display either membrane or shear locking effects and is free of communicable spurious modes numerical results are presented for elastic analyses of several standard plate and shell test problems

a posteriori error estimates for control problems governed by stokes equations in this paper we derive a posteriori error estimates for the finite element approximation of distributed optimal control problems governed by the stokes equations we obtain a posteriori error estimators for both the state and the control approximation in the l2 norm and the h1 norm these estimates can be used to construct reliable adaptive finite element approximation for the control problems

a functional for shells of arbitrary geometry and a mixed finite element method for parabolic and circular cylindrical shells in this study a higher order shell theory is proposed for arbitrary shell geometries which allows the cross section to rotate with respect to the middle surface and to warp into a non planar surface this new kinematic assumption satisfies the shear free surface boundary condition bc automatically a new internal force expression is obtained based on this kinematic assumption a new functional for arbitrary shell geometries is obtained employing g teaux differential method during this variational process the bc is constructed and introduced to the functional in a systematic way two different mixed elements prsh52 and crsh52 are derived for parabolic and circular cylindrical shells respectively using the new functional the element does not suffer from shear locking the excellent performance of the new elements is verified by applying the method to some test problems copyright 2000 john wiley sons ltd

a family of ans four node exact geometry shell elements in general convected curvilinear coordinates the non conventional exact geometry shell elements based on the timoshenko mindlin kinematics with five displacement degrees of freedom are proposed the term exact geometry exg reflects the fact that coefficients of the first and second fundamental forms of the reference surface and christoffel symbols are taken exactly at every gauss integration point the choice of only displacements as fundamental shell unknowns gives an opportunity to derive strain displacement relationships which are invariant under rigid body shell motions in a convected curvilinear coordinate system this paper presents a newly developed family consisting of three hybrid and one displacement based four node exg shell elements to avoid shear and membrane locking and have no spurious zero energy modes the ans concept is employed the ans interpolations satisfy exactly the plate compatibility equation for in plane strains as a result all exg shell elements developed pass membrane and bending plate patch tests and exhibit a superior performance in the case of distorted coarse mesh configurations copyright 2010 john wiley sons ltd

a finite element formulation with stabilization matrix for geometrically non linear shells an assumed strain finite element formulation with a stabilization matrix is developed for analysis of geometrically non linear problems of isotropic and laminated composite shells the present formulation utilizes the degenerate solid shell concept and assumes an independent strain as well as displacement the assumed independent strain field is divided into a lower order part and a higher order part subsequently the lower order part is set equal to the displacement dependent strain evaluated at the lower order integration points and the remaining higher order part leads to a stabilization matrix the strains and the determinant of the jacobian matrix are assumed to vary linearly in the thickness direction this assumption allows analytical integration through thickness independent of the number of plies a nine node element with a judiciously chosen set of higher order assumed strain field is developed numerical tests involving isotropic and composite shells undergoing large deflections demonstrate the validity of the present formulation

graded polynomial identities and codimensions computing the exponential growth abstract let g be a finite abelian group and a a g graded algebra over a field of characteristic zero this paper is devoted to a quantitative study of the graded polynomial identities satisfied by a we study the asymptotic behavior of c n g a n 1 2 the sequence of graded codimensions of a and we prove that if a satisfies an ordinary polynomial identity lim n c n g a n exists and is an integer we give an explicit way of computing such integer by proving that it equals the dimension of a suitable finite dimension semisimple g z 2 graded algebra related to a

on the strain assumption in a finite element model for plates and shells two different methods of assuming independent strain fields are examined for the nine node degenerate solid shell element in the first case the assumed strain field is chosen for the local orthogonal co ordinate systems defined at the gaussian integration points in the second case the independent strain is assumed for a local orthogonal co ordinate system defined at the origin of the parent co ordinates the results of numerical tests involving simple example problems demonstrate that the second method is capable of exactly representing constant stress or moment states even when element geometries are distorted in addition both methods lead to a finite element model which is free of locking

two higher order shell finite elements with stabilization matrix a 32 node three dimensional solid element and a 16 node degenerate solid element that are applicable to analysis of thin shell structural problems are presented in this paper both elements are formulated by using the hellinger reissner principle with independent strain the assumed independent strain field is divided into higherand lower order polynomial terms the element stiffness matrix associated with the higher order assumed strain plays the role of the stabilization matrix various types of the higher order assumed strain are tested for the present elements the resulting finite element models require much less time to compute the element stiffness matrix than the corresponding conventional mixed models or assumed displacement models with a full gaussian quadrature rule numerical results demonstrate that with a properly chosen set of higher order assumed strain the present elements produce reliable and very accurate solutions even for very thin plates and thin shells with deeply curved geometry

superalgebras and exponential growth abstract in this paper we study the exponential growth of graded identities of a finite dimensional superalgebra a over a field f of characteristic zero if a superalgebra a satisfies a non trivial identity then the sequence c n gri a n 1 of graded codimensions of a is exponentially bounded and so we study the graded exponent exp gri a lim n c n gri a n of a we show that exp gri a dim f a if and only if a is a simple superalgebra and f is the symmetric even center of a also we characterize the finite dimensional superalgebras such that exp gri a 1 by the exclusion of four superalgebras from var gri a and construct eleven superalgebras e i i 1 11 with the following property exp gri a 2 if and only if e i var gri a for some i 1 11 as a consequence we characterize the finite dimensional superalgebras a such that exp gri a 2

an explicit hybrid stabilized 9 node lagrangian shell element abstract this paper presents an explicit hybrid stabilized 9 node lagrangian shell element in the formulation the stress modes pertinent to the stabilization are contravariant in nature and their products with the displacement derived covariant strain are explicit linear functions of the nodal geometric parameters the element is particularly efficient because the leverage matrix or the stabilization vectors can be constructed without resorting to numerical integration or the gram schmidt orthogonalization accuracy of the element is promising and comparable to the state of the art stabilized and hybrid elements

group gradings on superinvolution simple superalgebras in this paper we describe all group gradings by an arbitrary finite group g on non simple finite dimensional superinvolution simple associative superalgebras over an algebraically closed field f of characteristic 0 or coprime to the order of g

primitive superalgebras with superinvolution abstract our main purpose is to provide for primitive associative superalgebras a structure theory analogous to that for algebras 5 6 10 and to classify primitive superrings with superinvolution having a minimal one sided superideal we were led to this problem by our work on finite dimensional central simple jordan superalgebras over fields of characteristic not 2 9 see also 7 of course just as symmetric elements give rise to jordan superalgebras skewsymmetric elements give rise to lie superalgebras 8 4 the results and methods are closely related to those of structure theory of associative rings and central simple associative algebras with involution 5 chap i 6 chaps ii iii 1 chap x 10 chap 2 some of the results have been announced in 13

analysis of some finite elements for the stokes problem we study some finite elements which are used in the approximation of the stokes problem so as to obtain error estimates of optimal order resume nous etudions deux elements finis utilises pour l approximation du probleme de stokes et obtenons des estimations d erreur d ordre optimal

polynomial codimension growth of algebras with involutions and superinvolutions abstract let a be an associative algebra over a field f of characteristic zero endowed with a graded involution or a superinvolution and let c n a be its sequence of codimensions in 4 12 it was proved that if a is finite dimensional such sequence is polynomially bounded if and only if a generates a variety not containing a finite number of algebras the group algebra of z 2 and a 4 dimensional subalgebra of the 4 4 upper triangular matrices with suitable graded involutions or superinvolutions in this paper we focus our attention on such algebras since they are the only finite dimensional algebras up to t 2 equivalence generating varieties of almost polynomial growth i e varieties of exponential growth such that any proper subvariety has polynomial growth we classify the subvarieties of such varieties by giving a complete list of generating finite dimensional algebras along the way we classify all minimal varieties of polynomial growth and surprisingly we show that their number is finite for any given growth finally we describe the algebras whose codimensions are bounded by a linear function

a high order hdg method for the biot s consolidation model abstract we propose a novel high order hdg method for the biot s consolidation model in poroelasticity we present optimal h version error analysis for both the semi discrete and full discrete combined with temporal backward differentiation formula schemes numerical tests are provided to demonstrate the performance of the method

standard polynomials and matrices with superinvolutions abstract let m n f be the algebra of n n matrices over a field f of characteristic zero the superinvolutions on m n f were classified by racine in 12 they are of two types the transpose and the orthosymplectic superinvolution this paper is devoted to the study of polynomial identities satisfied by m n f the goal is twofold on one hand we determine the minimal degree of a standard polynomial vanishing on suitable subsets of symmetric or skew symmetric matrices for both types of superinvolutions on the other in case of m 2 f we find generators of the ideal of identities and we compute the corresponding sequences of cocharacters and codimensions

the application of geometrically exact shell elements to b spline surfaces abstract in the present study we propose a framework that directly links a general tensor based geometrically exact shell finite element to b spline surface geometric modeling four node and 9 node assumed strain elements based on the partial mixed hellinger reissner variational functional and a 4 node assumed natural strain ans element are implemented in b spline surface representation bubble functions are included in the basis functions to improve the performance of the developed elements the bi cubic rectangular b spline tensor patch is employed to generate the general form of parameterized shell surfaces by using the b spline function the present general tensor based shell elements can handle the arbitrary geometry of the free form surfaces numerical results demonstrate the efficient linkage concept between surface modeling of computer aided geometric design cagd and finite element shell analysis in static and dynamic examples

finite element formulation by parametrized hybrid variational principles variable stiffness and removal of locking in this paper a new one parameter hybrid functional is obtained as a special case of felippa and militello s parametrized variational principles the functional contains stress strain and compatible displacement as the primary fields it will be proved that some of the existing variable stiffness formulations fall into the framework of the new functional novel applications of the functional are also suggested mainly for removal of locking solid element destabilized 8 node and stabilized 9 plate elements are designed all of them can handle thin plate shell analysis in particular a prominent method is devised for constructing stabilization vectors the vectors are explicit linear functions of the nodal coordinates and can be implemented without resorting to gram schmidt orthogonalization or numerical integration results of the new elements in popular benchmark tests are encouraging

a study of two modes of locking in poroelasticity in this paper we study two modes of locking phenomena in poroelasticity possion locking and pressure oscillations we first study the regularity of the solution of the biot model to gain some insight into the cause of poisson locking and show that the displacement gets into a divergence free state as the lame constant lambda to infty we also examine the cause of pressure oscillations from an algebraic point of view when a three field mixed finite element method is used based on the results of our study on the causes of the two modes of locking we propose a new family of mixed finite elements that are free of both pressure oscillations and poisson locking some numerical results are presented to validate our theoretical studies

on codimension growth of finitely generated associative algebras abstract letabe a pi algebra over a fieldf we study the asymptotic behavior of the sequence of codimensionscn a ofa we show that ifais finitely generated overftheninv a limn c n a always exists and is an integer we also obtain the following characterization of simple algebras ais finite dimensional central simple overfif and only ifinv a dim a

a consistent control of spurious singular modes in the 9 node lagrange element for the laplace and mindlin plate equations abstract when 2 2 quadrature is used with the 9 node lagrange element which is essential in c 0 plate elements to avoid locking spurious singular modes appear on the element level which can lead to singularity or near singularity of the global equations here these modes are controlled by a procedure that introduces additional generalized stresses and strains so that the spurious modes are eliminated and the consistency of the resulting finite difference equations is not impaired hence the procedure passes the patch test applications to the diffusion and mindlin plate equations are presented results show that h 3 convergence in the l 2 norm is almost retained

mixed finite element methods reduced and selective integration techniques a unification of concepts the equivalence of certain classes of mixed finite element methods with displacement methods which employ reduced and selective integration techniques is established this enables one to obtain the accuracy of the mixed formulation without incurring the additional computational expense engendered by the auxiliary field of the mixed method applications and numerical examples are presented for problems with constraints which can be difficult to enforce in finite element approximations and have often dictated the use of mixed principles these include thin beams and plates and linear and nonlinear incompressible and nearly incompressible continuum problems in solid and fluid mechanics

a new approach to the finite element modelling of beams with warping effect as a first step toward developing a finite element formulation that can model coupling among extensional bending and torsional behaviour of beams a new method is proposed to properly represent the warping of arbitrary cross sections the basic approach is to introduce a small warping displacement superimposed over flat cross sections of a shear flexible beam in a deformed configuration numerical tests involving simple isotropic beams undergoing a small elastic displacement demonstrate the validity of the new approach the present approach can be extended to composite beams as well as isotropic beams experiencing a large deflection or finite rotation