further results for enhanced strain methods with isoparametric elements abstract in this contribution the enhanced strain finite element method is investigated further with particular attention given to the analysis of the method for isoparametric elements it is shown that the results established earlier b d reddy and j c simo stability and convergence of a class of enhanced strain methods siam j numer anal 32 1995 in press for affine equivalent meshes carry over to the case of isoparametric elements that is the method is stable and convergent provided that a set of three criteria is satisfied and for plane elements at least convergence is at the same rate as in the standard method a procedure for recovering the stress is shown to lead to an approximate stress which converges at the optimal rate to the actual stress with regard to computations a new basis for enhanced strains is introduced and numerical results are presented for this basis as well as for existing bases the results for enhanced strain methods are distinguished by the fact that the constant appearing in asymptotic error estimates is much smaller for these methods than for standard approaches

quadrilateral mesh revisited several quadrilateral shape regular mesh conditions commonly used in the finite element method are proven to be equivalent the effect of the bi section condition on the degenerate mesh conditions is also checked

variational and projection methods for the volume constraint in finite deformation elasto plasticity this paper focuses on the treatment of volume constraints which in the context of elasto plasticity typically arise as a result of assuming volume preserving plastic flow projection methods based on the modification of the discrete gradient operator b often proposed on an ad hoc basis are systematically obtained in the variational context furnished by a three field hu washizu principle the fully nonlinear formulation proposed here is based on a local multiplicative split of the deformation gradient into volume preserving and dilatational parts without relying on rate forms of the weak form of momentum balance this approach fits naturally in a formulation of plasticity based on the multiplicative decomposition of the deformation gradient and enables one to exactly enforce the condition of volume preserving plastic flow within the framework proposed in this paper rate forms and incrementally objective algorithms are entirely bypassed

well posedness and numerical performances of the strain gap method a mixed method of approximation is discussed starting from a suitably modified expression of the hu washizu variational principle in which the independent fields are displacements stresses and strain gaps defined as the difference between compatible strains and strain fields the well posedness of the discrete problem is discussed and necessary and sufficient conditions are provided the analysis of the mixed method reveals that the discrete problem can be split into a reduced problem and in a stress recovery accordingly the discrete stress solution is univocally determined once an interpolating stress subspace is chosen the enhanced assumed strain method by simo and rifai is based on an orthogonality condition between stresses and enhanced strains and coincides with the reduced problem it is shown that the mixed method is stable and converges computational issues in the context of the finite element method are discussed in detail and numerical performances and comparisons are carried out copyright 2001 john wiley sons ltd

stability and convergence of a class of enhanced strain methods a stability and convergence analysis is presented of a recently proposed variational formulation and finite element method for elasticity which incorporates an enhanced strain field the analysis is carried out for problems posed on polygonal domains in r n the finite element meshes of which are generated by affine maps from a master element the formulation incorporates as a special case the classical method of incompatible modes the problem initially has three variables viz displacement stress and enhanced strain but the stress is later eliminated by imposing a condition of orthogonality with respect to the enhanced strains two other conditions on the choice of finite element spaces ensure that the approximations are stable and convergent some features of nearly incompressible and incompressible problems are also investigated for these cases it is possible to argue that locking will not occur and that the only spurious pressures present are the so called checkerboard modes it is shown th

efficient modeling of localized material failure by means of a variationally consistent embedded strong discontinuity approach this paper is concerned with a novel embedded strong discontinuity approach suitable for the analysis of material failure at finite strains focus is on localized plastic deformation particularly relevant for slip bands in contrast to already existing models the proposed implementation allows to consider several interacting discontinuities in each finite element based on a proper re formulation of the kinematics an efficient parameterization of the deformation gradient is derived it permits to compute the strains explicitly that improves the performance significantly however the most important novel contribution of the present paper is the advocated variational constitutive update within this framework every aspect is naturally driven by energy minimization i e all unknown variables are jointly computed by minimizing the stress power the proposed update relies strongly on an extended principle of maximum dissipation this framework provides enough flexibility for different failure types and for a broad class of non associative evolution equations by discretizing the aforementioned continuous variational principle an efficient numerical implementation is obtained it shows in addition to its physical and mathematical elegance several practical advantages for instance the physical minimization principle itself specifies automatically and naturally the set of active strong discontinuities copyright 2011 john wiley sons ltd

implicit high order accurate in space algorithms for the navier stokes equations high order accurate alternating direction implicit schemes have been developed these schemes can be used to obtain efe ciently high resolution numerical solutions of the compressible euler and navier stokes equations implicit solvers compatible with both centered and upwind schemes for the discretization of the convective terms arediscussed forcenteredspacediscretizationoftheconvectivee uxes fourth orderspatialaccuracyoftheimplicit operators is obtained at no additional computing cost by performing compact space differentiation this implicit compact scheme which requires block tridiagonal matrix inversions is used to obtain viscous and inviscid e ow solutions in curvilinear coordinates in addition high order accurate in space implicit operators are obtained for diagonalized schemes which require scalar matrix inversions both high order algorithms improve convergence characteristics for subsonic and transonic e ow compared to second order accurate in space implicit schemes high order accurate in space implicit algorithms compatible with upwind high resolution shock capturing total variation diminishing schemes are also developed third order accurate upwind biased diagonalized algorithms were found to be as accurate and more efe cient than the standard block tridiagonal implicit solvers

a strain gradient isotropic elastoplastic damage model with j3 dependence abstract a plastic strain gradient version of an isotropic elastoplastic damage model that depends on the third invariant j3 of the stress deviator is developed the model is based on the non local equivalent plastic strain ep defined by peerlings et al 2001 and engelen et al 2003 and introduces a material length l to the constitutive equations it is shown that the non local equivalent plastic strain ep at a material point p can be identified with the average value of the local von mises equivalent plastic strain e p over a sphere centered at p and of radius approximately equal to 3 l a methodology for the numerical integration of the constitutive equations is presented the algorithm is appropriate for rate independent as well as rate dependent viscoplastic models the model is implemented in the abaqus general purpose finite element program and both quasi static and dynamic problems are solved two possible abaqus implementations are discussed first user elements are developed which can be used for the solution of both quasi static and dynamic problems reduced 1 point gauss integration is discussed in 8 node hexahedral elements and the physical stabilization method of puso 2000 is used to remove the resulting numerical singularities hourglass control second the implementation of the model via user material subroutines is discussed quasi static problems can be solved with abaqus standard using a coupled temperature displacement steady state analysis together with user subroutine umat in which temperature is identified with the non local equivalent plastic strain ep the solution of dynamic problems requires use of abaqus explicit together with a dynamic temperature displacement analysis option and user subroutines vumat and dflux several example problems are solved

coadjoint orbits and reductive dual pairs let g g be a reductive dual pair of subgroups of the metaplectic group s 2m r where g is compact then the restriction of the oscillator representation o of sp 2m r to g decomposes as x 5 t t where the correspondence zj r is a bijection 7 the modules t are unitary highest weight modules and all such representations are obtained this way 5 on the other hand the unitary highest weight modules of g have been constructed in 3 via derived functors in particular each such representation is associated to is the quantization of a coadjoint orbit for g the purpose of this paper is to establish the connection between these two realizations via the orbit structure of the symplectic manifold r co these results have been known in principle for some time the main problem being an understanding of how to quantize nilpotent and degenerate elliptic coadjoint orbits let 8 lie g 0 lie c let respectively ic be projection from gp 2m r to s respectively a here hom r then and i restriced to the minimal coadjoint orbit i of gp 2m r define the graph of a correspondence between coadjoint gand orbits note that 0 in z r o via the moment map for the action of sp 2m r on r 0 generically this is a bijection nilpotent orbits for c do arise suppose a c orbit 0 corresponds to a orbit c in 111 it was observed that in some cases if we associate representations x o and x p to 0 and 0 via geometric quantization then x o x 0 occurs in wjgg i e x 6 corresponds to x 0 in 2 the derived functor construction was used to quantize some elliptic orbits and this was done in greater generality that is for 0 g i elliptic 8 is cohomologically induced from a one dimensional representation of l stab i and similarly for g if 0 and n 0 have regular infinitesimal character then n o corresponds to 6 at the time 2 was written the modules n o with singular infinitesimal character were not understood furthermore it was not known how 138 oool 8708 87 7 50

high order semi implicit schemes for unsteady compressible flow simulations direct numerical simulation of stability and transition of compressible boundary layers requires high orderaccurate and computationally efe cient numerical methods to resolve a wide range of time and length scales associated with wave e elds in the boundary layers explicit methods have been used mainly in such simulations to advance the compressible navier stokes equations in time however the small wall normal grid sizes for viscous e ow simulations impose a severe stability restriction on the allowable time steps in simulations using the explicit method this requires implicit treatment to our numerical method although fully implicit methods are often used in steady e ow calculations to remove the stability restriction on time steps they are seldom used in transient e ow simulations because the time steps used in time accurate calculations are often not large enough to offset high computational cost of using fully implicit methods a high order accurate semi implicit scheme is presented for the direct numerical simulation of the stability and transition of compressible wall bounded e ows the efe ciency and accuracy of the semi implicit scheme are evaluated by applying the method to transient e ow simulations of several supersonic and hypersonic wall bounded e ow stability problems

a formulation for the 4 node quadrilateral element a formulation for the plane 4 node quadrilateral finite element is developed based on the principle of virtual displacements for a deformable body incompatible modes are added to the standard displacement field then expressions for gradient operators are obtained from an expansion of the basis functions into a second order taylor series in the physical co ordinates the internal degrees of freedom of the incompatible modes are eliminated on the element level a modified change of variables is used to integrate the element matrices for a linear elastic material the element stiffness matrix can be separated into two parts these are equivalent to a stiffness matrix obtained from underintegration and a stabilization matrix the formulation includes the cases of plane stress and plane strain as well as the analysis of incompressible materials further the approach is suitable for non linear analysis there an application is given for the calculation of inelastic problems in physically non linear elasticity the element is efficient to implement and it is frame invariant locking effects and zero energy modes are avoided as well as singularities of the stiffness matrix due to geometric distortion a high accuracy is obtained for numerical solutions in displacements and stresses

geometrically non linear enhanced strain mixed methods and the method of incompatible modes a class of assumed strain mixed finite element methods for fully non linear problems in solid mechanics is presented which when restricted to geometrically linear problems encompasses the classical method of incompatible modes as a particular case the method relies crucially on a local multiplicative decomposition of the deformation gradient into a conforming and an enhanced part formulated in the context of a three field variational formulation the resulting class of mixed methods provides a possible extension to the non linear regime of well known incompatible mode formulations in addition this class of methods includes non linear generalizations of recently proposed enhanced strain interpolations for axisymmetric problems which cannot be interpreted as incompatible modes elements the good performance of the proposed methodology is illustrated in a number of simulations including 2 d 3 d and axisymmetric finite deformation problems in elasticity and elastoplasticity remarkably these methods appear to be specially well suited for problems involving localization of the deformation as illustrated in several numerical examples

enhanced assumed strain elements and locking in membrane problems abstract the assumptions which guarantee convergence of eas elements first introduced by simo and rifai can be reduced to two postulates specifically the stability condition refers to a relaxed stability of an associated hu washizu principle we investigate the problem of volume locking of membrane problems estimates of a certain type which for instance imply volume locking of the q1 element are fortunately not present with eas elements finally we verify an equivalence of the eas concept with a hellinger reissner method which was observed in numerical computations by andelfinger and ramm

nonlinearly stable compact schemes for shock calculations in this paper the authors discuss the applications of high order compact finite difference methods for shock calculations the main idea is the definition of a local mean that serves as a reference for introducing a local nonlinear limiting to control spurious numerical oscillations while keeping the formal accuracy of the scheme for scalar conservation laws the resulting schemes can be proven total variation stable in one space dimension and maximum norm stable in multispace dimensions numerical examples are shown to verify accuracy and stability of such schemes for problems containing shocks the idea in this paper can also be applied to other implicit schemes such as the continuous galerkin finite element methods

non smooth multisurface plasticity and viscoplasticity loading unloading conditions and numerical algorithms rate independent plasticity and viscoplasticity in which the boundary of the elastic domain is defined by an arbitrary number of yield surfaces intersecting in a non smooth fashion are considered in detail it is shown that the standard kuhn tucker optimality conditions lead to the only computationally useful characterization of plastic loading on the computational side an unconditionally convergent return mapping algorithm is developed which places no restrictions aside from convexity on the functional forms of the yield condition flow rule and hardening law the proposed general purpose procedure is amenable to exact linearization leading to a closed form expression of the so called consistent algorithmic tangent moduli for viscoplasticity a closed form algorithm is developed based on the rate independent solution the methodology is applied to structural elements in which the elastic domain possesses a non smooth boundary numerical simulations are presented that illustrate the excellent performance of the algorithm

consistent tangent operators for rate independent elastoplasticity abstract it is shown that for problems involving rate constitutive equations such as rate independent elastoplasticity the notion of consistency between the tangent stiffness operator and the integration algorithm employed in the solution of the incremental problem plays a crucial role in preserving the quadratic rate of asymptotic convergence of iterative solution schemes based upon newton s method within the framework of closest point projection algorithms a methodology is presented whereby tangent operators consistent with this class of algorithms may be systematically developed to wit associative j 2 flow rules with general nonlinear kinematic and isotropic hardening rules as well as a class of non associative flow rules are considered the resulting iterative solution scheme preserves the asymptotic quadratic convergence characteristic of newton s method whereas use of the socalled elastoplastic tangent in conjunction with a radial return integration algorithm a procedure often employed results in newton type of algorithms with suboptimal rate of convergence application is made to a set of numerical examples which include saturation hardening laws of exponential type

relations between enhanced strain methods and the hr method abstract the three field hu washizu functional is the starting point to develop a comparative analysis of approximate linear elastostatic problems in particular we will analyse the limitation phenomena concerning two mixed methods respectively denoted the strain gap method and the mixed enhanced strain method and the two field hellinger reissner hr finite element formulation accordingly two original limitation principles are contributed we provide the theoretical motivation of the numerical observations provided in computational literature on the coincidence of the displacement and stress solutions between the enhanced assumed strain method and the hr method if different choices of shape functions are made it is further shown that the hr method provides the exact stress solution and the exact nodal displacements with one element the related analytical motivation are thus given the theoretical analyses presented in the paper are supported by numerical examples on tipical benchmarks

spurious waves in discrete computation of wave phenomena and flow problems in the present work we focus on spurious propagating disturbances q waves to establish the existence of q waves in computations we compare properties of different numerical methods drawn from finite difference finite volume and finite element methods existence and properties of q waves are demonstrated with propagation of wave packets following one dimensional 1d convection equation skewed wave propagation and by solution of linearized rotating shallow water wave equation lrswe specific numerical experiments are performed with parameters that convert a wave packet into a q wave we also show the case where q waves are created additionally to physical disturbances those propagate downstream formation of q waves are shown in the case of a discrete shielded vortex in the uniform flow and incompressible transitional flow past an aerofoil by solving the navier stokes equation in performing this exercise we establish critical wavenumber range beyond which q waves are created relevance of this information for dns and les is discussed we have further discussed the case of spurious caustics in discrete computing

theta lifting of unitary lowest weight modules and their associated cycles we consider a reductive dual pair g g in the stable range with g the smaller member and of hermitian symmetric type we study theta lifting of holomorphic nilpotent k c orbits in relation to theta lifting of unitary lowest weight modules of g we determine the associated cycles of all such representations in particular we prove that the multiplicity in the associated cycle is preserved under theta lifting

four node semi eas element in six field nonlinear theory of shells we propose a new four node c finite element for shell structures undergoing unlimited translations and rotations the considerations concern the general six field theory of shells with asymmetric strain measures in geometrically nonlinear static problems the shell kinematics is of the two dimensional cosserat continuum type and is described by two independent fields the vector field for translations and the proper orthogonal tensor field for rotations all three rotational parameters are treated here as independent hence as a consequence of the shell theory the proposed element has naturally six engineering degrees of freedom at each node with the so called drilling rotation this property makes the element suitable for analysis of shell structures containing folds branches or intersections to avoid locking phenomena we use the enhanced assumed strain eas concept we derive and linearize the modified hu washizu principle for six field theory of shells what makes the present approach original is the combination of eas method with asymmetric membrane strain measures based on literature we propose new enhancing field and specify the transformation matrix that accounts for the lack of symmetry to gain knowledge about the suitability of this field for asymmetric strain measures and to assess the performance of the element we solve typical benchmark examples with smooth geometry and examples involving orthogonal intersections of shell branches

conditions for equivalence between the hu washizu and related formulations and computational behavior in the incompressible limit the relationship of the hu washizu mixed formulation to other mixed and enhanced formulations is examined in detail in the context of linear elasticity with a view to presenting a unified framework for such formulations the hu washizu formulation is considered in both its classical form and in a modified form that is suited to establishing well posedness in the incompressible limit recently established theoretical results on uniform well posedness are studied computationally by considering a range of numerical examples which illustrate where appropriate the good behavior predicted by the theory as well as the locking behavior that is evident in those problems in which the conditions for stability and convergence are not satisfied 2005 elsevier b v all rights reserved

a stable affine approximate finite element method the notion of the affine figure closest to a given quadrilateral can be given a precise mathematical definition the resulting figure is referred to as the equivalent parallelogram associated with a quadrilateral equipped with such a concept it is then feasible to consider finite element approximations in which the original quadrilateral elements are replaced by their equivalent parallelograms the idea is appealing not least because of the resulting economy arising from computations performed on an element generated by an affine map furthermore numerical experiments reported recently indicate that highly efficient and accurate schemes result when such a concept is combined with the enhanced strain method or the method of incompatible modes the purpose of this work is to analyze finite element schemes resulting from approximation of quadrilaterals by their equivalent parallelograms the focus is on low order bilinear elements and the analysis is carried out in the context of linear elasticity for standard approximations as well as for those which use enhanced strains the affine approximation applies only to the element map and the primary unknown the displacement vector in the context of elasticity is approximated by conventional piecewise bilinear functions the analysis confirms convergence at the optimal rate provided that the deviations of the quadrilaterals from their equivalent parallelograms are at most o h

a meshfree enriched finite element method for compressible and near incompressible elasticity summary in this paper a two dimensional displacement based meshfree enriched fem me fem is presented for the linear analysis of compressible and near incompressible planar elasticity the me fem element is established by injecting a first order convex meshfree approximation into a low order finite element with an additional node the convex meshfree approximation is constructed using the generalized meshfree approximation method and it possesses the kronecker delta property on the element boundaries the gradient matrix of me fem element satisfies the integration constraint for nodal integration and the resultant me fem formulation is shown to pass the constant stress test for the compressible media the me fem interpolation is an element wise meshfree interpolation and is proven to be discrete divergence free in the incompressible limit to prevent possible pressure oscillation in the near incompressible problems an area weighted strain smoothing scheme incorporated with the divergence free me fem interpolation is introduced to provide the smoothing on strains and pressure with this smoothed strain field the discrete equations are derived based on a modified hu washizu variational principle several numerical examples are presented to demonstrate the effectiveness of the proposed method for the compressible and near incompressible problems copyright 2012 john wiley sons ltd

optimized compact difference based finite volume schemes for linear wave phenomena high order compact difference based finite volume schemes are developed analyzed and implemented for linear wave propagation phenomena with particular emphasis on computational electromagnetics in the time domain the formulation combines the primitive function approach with five point spatially sixth and fourth order methods optimization in the semi discrete case is achieved by minimizing dispersion and isotropy error the fully discrete scheme is examined by adopting the classical fourth order runge kutta technique stability bounds are established and the coefficients for the spatial discretization are readjusted for optimum performance the scheme is then formally extended to multiple dimensions consistent boundary conditions are presented for the reconstruction operator as well as flux specification several calculations in one and three dimensions confirm the properties of the method

on howe s duality theorem abstract we adopt the langlands classification to the context of real reductive dual pairs and prove that howe s duality correspondence maps hermitian representations to hermitian representations

singular unitary representations of classical groups on presente une description de la partie relativement singuliere du dual unitaire d un groupe classique de type i sur un corps local f de caracteristique autre que 2

a return mapping algorithm for plane stress elastoplasticity an unconditionally stable algorithm for plane stress elastoplasticity is developed based upon the notion of elastic predictor return mapping plastic corrector enforcement of the consistency condition is shown to reduce to the solution of a simple nonlinear equation consistent elastoplastic tangent moduli are obtained by exact linearization of the algorithm use of these moduli is essential in order to preserve the asymptotic rate of quadratic convergence of newton methods the accuracy of the algorithm is assessed by means of iso error maps the excellent performance of the algorithm for large time steps is illustrated in numerical experiments

the equivalent parallelogram and parallelepiped and their application to stabilized finite elements in two and three dimensions a new class of quadrilateral and hexahedral elements four and eight noded in two and three dimensions respectively is presented these elements are obtained by combining the concept of the equivalent parallelogram for plane problems and the equivalent parallelepiped for three dimensional problems with the notion of incompatible modes a key feature of the new elements is that integration of the element stiffness matrices is carried out using one point integration the use of affine equivalent elements parallelograms and parallelepipeds permits a closed form eigenvalue analysis which includes the incompatible modes and a stabilization procedure based on the eigenvalue analysis ensures the full rank of the stiffness matrix numerical results for problems in elasticity and plasticity indicate equivalent or superior performance of the new elements when compared with various elements based on enhanced strains or incompatible modes

large elasto plastic finite element analysis of solids and shells with the enhanced assumed strain concept abstract a finite element simulation of arbitrarily large elasto plastic deformations of three dimensional and shell structures is described two numerical aspects originally developed by j c simo have been combined i e the multiplicative large strain plasticity and the enhanced assumed strain finite element concept the constitutive model is worked out in its algorithmic version applying projection methods and consistent linearization the enhanced strain field is added to the conventional hexahedral displacement elements avoiding volumetric locking in the plastic range in addition to solid structures the three dimensional material model without any modifications is also applied to thin walled shell structures here an extended shell formulation a so called seven parameter model is used in which the thickness strain is augmented by a linear term the applicability of the entire formulation is demonstrated by several numerical examples

treatment of internal constraints by mixed finite element methods unification of concepts a general method to generate assumed stress and strain fields within the context of mixed finite element methods is presented the assumed fields are constructed in such a way that internal constraints are satisfied a priori consequently the locking behaviour commonly observed in finite element solutions of problems with internal constraints is avoided to this end the assumed stress and strain fields are constructed to satisfy a priori the homogeneous part of the equilibrium equations thus avoiding fraeijs de veubeke s limitation principle results obtained using the proposed methodology on a nearly incompressible plane strain problem and thin plate application using a shear deformable theory are indicated

variationally consistent state determination algorithms for nonlinear mixed beam finite elements abstract this paper presents and evaluates several variationally consistent state determination algorithms for geometric and material nonlinear beam finite elements based on the hellinger reissner hr assumed stress variational principle the specifically targeted element type is derived from the two field displacement and generalized stress form of this principle momentum balance and strain compatibility are expressed in a weak form and the constitutive equations are satisfied directly at each integration point i e section along the element length a specific formulation of one element of this type is presented in a companion paper interelement compatibility is not enforced in the dual stress resultant variables for this element and thus various state determination algorithms can be formulated at the local i e element and section levels four state determination algorithms referred to as the l l l n n l and n n procedures are considered the first symbol in these names indicates the element level and the second denotes the section level furthermore the symbol n indicates that local nonlinear iteration is performed prior to returning to the higher level whereas the symbol l indicates that only the linearized equations are satisfied at the corresponding local level the l l algorithm corresponds to conventional newton iteration on both the element and section levels whereas the n n algorithm entails the iterative satisfaction of the nonlinear element compatibility and section constitutive equations for each global iteration the performance of these algorithms is evaluated and compared it is found that the algorithms in which the local nonlinear strain displacement compatibility conditions are solved iteratively at the element level for every global iteration lead to fewer global iterations at the expense of iterations at the element level in particular the n n algorithm is overall the most efficient of the four algorithms for the problems tested also the n n algorithm has substantially smaller element storage requirements the n n algorithm is expected to be particularly advantageous for cases in which a large number of elements remain elastic and inelasticity is concentrated in a few elements

a variational multiscale approach to strain localization formulation for multidimensional problems abstract the multiscale approach to strain localization problems developed earlier is generalized to higher dimensions the key idea is the identification of the fine scale field with a component of the displacement that has a large gradient the difference between the total displacement and the fine scale is the coarse scale field the formulation is variationally based with the weak form as the point of departure with suitable assumptions on the space of fine scale fields the weak form is separable into coarse and fine scale parts the weak form of the fine scale problem is used to eliminate the fine scales from the formulation this is achieved by way of a projection onto the fine scale space and allows a reformulation of the full problem in terms of coarse scale components alone in this framework fine scale interpolations are identified that ensure sharp resolution of localized displacement irrespective of the underlying finite element mesh it is demonstrated that by correctly accounting for the microstructural fine scale behavior the formulation results in solutions devoid of pathological mesh sensitivity for problems wherein the detailed structure of the localized displacement is of interest recovery of the fine scale components can be performed to reconstruct the entire displacement field several numerical examples are presented that demonstrate the robustness of the formulation

on an equivalence between a discontinuous galerkin method and reduced integration with hourglass stabilization for finite elasticity abstract discontinuous galerkin methods and methods of reduced integration with hourglass stabilization have different points of origin whereas the discontinuous galerkin idea was developed to investigate a wide range of applications among them problems of electrodynamics fluid and solid mechanics the reduced integration technology started out from the observation of the so called locking problem in linear elasticity today the two methodologies are still considered separately from each other although it has already been recognized that discontinuous galerkin methods can be also used to circumvent locking phenomena in elasticity the idea of the present contribution is to find a direct equivalence between a discontinuous galerkin method and a finite element technology based on reduced integration with hourglass stabilization the transfer between the two methods is carried out in the context of finite elasticity thus the derivation is valid for arbitrarily large deformations the main advantage of this analysis is that the choice of the free parameter in nitsche s method often also called stabilization parameter is no longer unclear but prescribed by the connection to the hourglass stabilization further important in this context is the replacement of the scalar parameter by a symmetric 2 2 matrix if two dimensional problems are considered which is here the case the result of the derivation is a discontinuous galerkin formulation which shows very good convergence behaviour not only in the limit of incompressibility but also for bending of thin structures

development and testing of stable invariant isoparametric curvilinear 2 and 3 d hybrid stress elements abstract linear and quadratic serendipity hybrid stress elements are examined in respect of stability coordinate invariance and optimality a formulation based upon symmetry group theory successfully addresses these issues in undistorted geometries and is fully detailed for plane elements the resulting least order stable invariant stress polynomials can be applied as astute approximations in distorted cases through a variety of tensor components and variational principles a distortion sensitivity study for two and three dimensional elements provides favourable numerical comparisons with the assumed displacement method

analysis of central and upwind compact schemes central and upwind compact schemes for spatial discretization have been analyzed with respect to accuracy in spectral space numerical stability and dispersion relation preservation a von neumann matrix spectral analysis is developed here to analyze spatial discretization schemes for any explicit and implicit schemes to investigate the full domain simultaneously this allows one to evaluate various boundary closures and their effects on the domain interior the same method can be used for stability analysis performed for the semi discrete initial boundary value problems ibvp this analysis tells one about the stability for every resolved length scale some well known compact schemes that were found to be g k s and time stable are shown here to be unstable for selective length scales by this analysis this is attributed to boundary closure and we suggest special boundary treatment to remove this shortcoming to demonstrate the asymptotic stability of the resultant schemes numerical solution of the wave equation is compared with analytical solution furthermore some of these schemes are used to solve two dimensional navier stokes equation and a computational acoustic problem to check their ability to solve problems for long time it is found that those schemes that were found unstable for the wave equation are unsuitable for solving incompressible navier stokes equation in contrast the proposed compact schemes with improved boundary closure and an explicit higher order upwind scheme produced correct results the numerical solution for the acoustic problem is compared with the exact solution and the quality of the match shows that the used compact scheme has the requisite drp property

compact finite volume schemes on boundary fitted grids the paper focuses on the development of a framework for high order compact finite volume discretization of the three dimensional scalar advection diffusion equation in order to deal with irregular domains a coordinate transformation is applied between a curvilinear non orthogonal grid in the physical space and the computational space advective fluxes are computed by the fifth order upwind scheme introduced by pirozzoli s pirozzoli conservative hybrid compact weno schemes for shock turbulence interaction j comp phys 178 2002 81 while the coupled derivative scheme m h kobayashi on a class of pade finite volume methods j comp phys 156 1999 137 is used for the discretization of the diffusive fluxes numerical tests include unsteady diffusion over a distorted grid linear free surface gravity waves in a irregular domain and the advection of a scalar field the proposed methodology attains high order formal accuracy and shows very favorable resolution characteristics for the simulation of problems with a wide range of length scales

analysis of some quadrilateral nonconforming elements for incompressible elasticity in this work some nonconforming elements on arbitrary quadrilateral meshes in solving incompressible elastic equations are analyzed a uniform optimal convergence rate is established at the incompressible limit nu 0 5 for both displacement and stresses or pressure in the case of incompressible flow

geometric realization of discrete series for semisimple symmetric spaces let g be a connected semisimple lie group a an involution of g and h the connected component of the fixed point set of a containing the identity then g h is a semisimple symmetric space we assume g is a real form of a complex lie group and rank g h rank k k c h where k is a a stable maximal compact subgroup of g flensted jensen using his duality principle and poisson transform constructed countably many discrete series in u g h f j i then using deep results of hyperfunction theory and microlocal analysis oshima and matsuki gave a detailed characterization of these discrete series including a proof of flensted jensen s conjecture c 0 om based on these results we give the discrete series a geometric interpretation in locally symmetric spaces f c where g k and f cg is a cocompact discrete group such that f c h c h is cocompact our geometric interpretation is the following first of all to a flensted jensen function which is the generating function of a discrete series v we associate a harmonic form cb z on g with values in a finite dimensional g module v right g translates of coefficients of 5z realizes the contragredient t of r and tba is left invariant under h and under right k action it transforms according to the minimal k type with highest weight of 3 is the pull back of a v valued from coz on and v determines a locally constant bundle e on f so that if convergence holds

on the discrete series of generalized stiefel manifolds a study of the discrete series of generalized stiefel manifolds is made using the oscillator representation new infinite families of such discrete series are constructed

some geometrical results and estimates for quadrilateral finite elements abstract the concept of the equivalent parallelogram associated with a quadrilateral is introduced the quadrilateral may be regarded as a perturbation of this parallelogram which is most conveniently described by making use of properties of the isoparametric map which defines the quadrilateral the equivalent parallelogram generates a natural means of defining a regular family of quadrilaterals this definition is used together with other properties to obtain in a relatively simple manner estimates in appropriate seminorms or norms of the isoparametric map and its jacobian for use in the determination of finite element interpolation error estimates

a finite volume formulation of compact central schemes on arbitrary structured grids in the present paper a formulation allowing the use of compact schemes in the finite volume context on arbitrary meshes is presented the proposed formulation is based on the use of an implicit formula to evaluate the fluxes on the cell faces a series of numerical experiments for a 2d model convection equation a flat plate a subsonic vortical problem as well as the les simulation of channel flow has been carried out the results indicate an important improvement in obtained accuracy compared to a standard central finite volume formulation

numerical integration with taylor truncations for the quadrilateral and hexahedral finite elements for general quadrilateral or hexahedral meshes the finite element methods require evaluation of integrals of rational functions instead of traditional polynomials it remains as a challenge in mathematics to show the traditional gauss quadratures would ensure the correct order of approximation for the numerical integration in general however in the case of nested refinement the refined quadrilaterals and hexahedra converge to parallelograms and parallelepipeds respectively based on this observation the rational functions of inverse jacobians can be approximated by the taylor expansion with truncation then the gauss quadrature of exact order can be adopted for the resulting integrals of polynomials retaining the optimal order approximation of the finite element methods a theoretic justification and some numerical verification are provided in the paper

a fourth order accurate finite volume compact method for the incompressible navier stokes solutions abstract this paper presents a finite volume fourth order accurate compact scheme for discretization of the incompressible navier stokes equations in primitive variable formulation the numerical method of integrating the navier stokes equations comprises a compact finite volume formulation of the average convective and diffusive fluxes the pressure velocity coupling is achieved via the coupled solution of the resulting system of equations the solution of the coupled set of equations is performed with an implicit newton krylov matrix free method for stationary problems for simulation of unsteady flows a standard fourth order runge kutta method was used for temporal discretization and the velocity pressure coupling was ensured at each stage also using the matrix free method several incompressible viscous steady and unsteady flow problems have been computed to assess the robustness and accuracy of the proposed method

higher order kfvs algorithms using compact upwind difference operators a family of high order accurate compact upwind difference operators have been used together with the split fluxes of the kfvs kinetic flux vector splitting scheme to obtain high order semidiscretizations of the 2d euler equations of inviscid gas dynamics in general coordinates a tvd multistage runge kutta time stepping scheme is used to compute steady states for selected transonic supersonic flow problems which indicate the higher accuracy and low diffusion realizable in such schemes

cycles with local coefficients for orthogonal groups and vector valued siegel modular forms the purpose of this paper is to generalize the relation between intersection numbers of cycles in locally symmetric spaces of orthogonal type and fourier coefficients of siegel modular forms to the case where the cycles have local coefficients now the correspondence will involve vector valued siegel modular forms

improved versions of assumed enhanced strain tri linear elements for 3d finite deformation problems abstract improved three dimensional tri linear elements for finite deformation problems are developed based on an assumed enhanced strain methodology which in the linear regime incorporates the classical method of incompatible modes as a particular case three crucial modifications of a recently proposed element which reduces to wilson s brick in the linear regime are introduced to prevent locking response in distorted configurations and to maintain proper rank while preserving excellent performance in bending dominated and localization problems i a modified quadrature rule ii an additional enhancement of the divergence term and iii a modification of the isoparametric shape function derivatives for the three dimensional problem moreover these modified shape function derivatives are shown to improve the performance of the standard tri linear brick in distorted configurations in addition a strategy is described to circumvent the memory storage requirements in the static condensation procedure of the enhanced strain parameters the excellent performance of the improved methodology is illustrated in representative numerical simulations

extended embedded finite elements with continuous displacement jumps for the modeling of localized failure in solids abstract this paper addresses novel extended embedded finite elements with continuous displacement jumps for the modeling of localized failure in solids on one hand based upon the unified multiscale kinematics of strong discontinuities standard finite elements at the coarse scale are enriched with fine scale kinematics in which non uniform discontinuity modes are incorporated on the other hand the traction continuity condition across the discontinuity is enforced in the statically optimal form as the fine scale statics the admissible discontinuity modes satisfying a priori the traction continuity condition are derived in addition to the relative rigid body motions translations and rotations more general relative stretching modes that induce discontinuous strain stress fields in the bulk are obtained with no limit of a vanishing poisson s ratio the proposed model then particularizes to 2d quadrilateral elements the displacement jumps at the discontinuity nodes are selected as the enrichment parameters and regarded as global variables shared by neighboring elements the resulting model not only is intrinsically stress locking free for a fully softened discontinuity but also automatically guarantees global continuity of the displacement jumps another benefit is that the numerical instability suffered under the unfavorable element discontinuity configuration can be easily circumvented furthermore the vanishing displacement jumps at the discontinuity tip can be enforced trivially as conventional essential boundary conditions and those complex strategies introduced in existing models are avoided together with the failure criterion related to the element average stress and the propagation orientation based on a simplified nonlocal stress a local crack tracking algorithm is adopted to guarantee global continuity of the discontinuity path representative numerical simulations of element and structure benchmark tests are presented to verify the performance of the proposed approach in the modeling of arbitrary discontinuity propagation in solids

unitary highest weight modules the unitary highest weight modules of a semisimple lie group g have been classified s 93 unfortunately this classification does not fit well with a more general picture of the unitary dual of g we give such a classification for g a classical group using derived functors and the philosophy of unipotent representations in particular these representations are associated to coadjoint orbits of g let 8 lie g 0 a cartan involution of 6 8 c a derived functor module is defined by the data q i u a o stable parabolic subalgebra of 0 and 17 an irreducible unitary representation of l the stabilizer of l in g considering z7 as a representation of i write z7 a rc where a e c c center of i denotes dual and rt z7l r we define a rc i rc cf definition 6 1 now fix n and vary 1 under certain restrictions on i which amount to a positivity condition on the corresponding bundle over g l a i rr is known to be irreducible and unitary as ii varies within this range the langlands parameters of a a rr vary smoothly however one cannot obtain all unitary highest weight modules under these restrictions the orbit method suggests how to obtain the remaining unitary highest weight modules the modules a rr are associated to coadjoint orbits as follows if rc is trivial we say a rr is associated to the elliptic orbit 0 g ii not all unitary highest weight modules may be obtained with rc trivial an example of which is the oscillator representation of 2n r the metapletic group we define 2n irreducible unitary highest weight modules rc 1 2 n k r is 113 oool 8708 87 7 50

unified analysis of enriched finite elements for modeling cohesive cracks abstract aiming to provide a justified theoretical ground based on which different enriched finite elements can be systematically compared we developed in this work a unified framework for modeling cohesive cracks using the variational multiscale method the kinematics i e coarse and fine scale displacement and strain fields and statics i e coarse and fine scale equilibrium equations are thoroughly investigated in both continuum and discrete settings with respect to the fine scale kinematics and statics adopted in the embedded finite element method efem and the extended finite element method xfem we mainly discuss four groups of enriched finite elements with non uniform discontinuity modes i e the kinematically optimal symmetric efem and xfem as well as the kinematically and statically optimal non symmetric efem and xfem in all these methods the enrichment parameters can be regarded either as element wise local or continuous global variables the enriched finite elements with material element node enrichments are then exemplified in an increasing order of their respective capabilities in representing the fine scale kinematics and the interrelations between them are also discussed owing to this unified framework we are able to clarify some existing points of view related to efem and xfem it is found that if the same fine scale statics is used and the same local global property is assumed for the involved enrichment parameters xfem can be regarded as a kinematically enhanced efem since it accounts for a more general fine scale kinematics than that i e relative rigid body motions and self stretching considered in efem finally several simple but sufficiently representative numerical examples are presented to show the significance in appropriately reflecting the fine scale kinematics and statics in an enriched finite element for modeling cohesive cracks

discrete decomposability of the restriction of aq λ with respect to reductive subgroupsiii restriction of harish chandra modules and associated varieties let h g be real reductive lie groups and an irreducible unitary representation of g we introduce an algebraic formulation discretely decomposable restriction to single out the nice class of the branching problem breaking symmetry in physics in the sense that there is no continuous spectrum in the irreducible decomposition of the restriction h this paper offers basic algebraic properties of discretely decomposable restrictions especially for a reductive symmetric pair g h and for the zuckerman vogan derived functor module and proves that the sufficient condition invent math 94 is in fact necessary a finite multiplicity theorem is established for discretely decomposable modules which is in sharp contrast to known examples of the continuous spectrum an application to the restriction h of discrete series for a symmetric space g h is also given

on the nested refinement of quadrilateral and hexahedral finite elements and the affine approximation it is shown in this paper that the optimal approximation property of bilinear or trilinear finite elements would be retained when the affine mapping is used to replace the q1 mapping on each element if the grids are refined nestedly the new method truncates the quadratic and cubic terms in reference mappings and produces constant jacobians and jacobian matrices this would avoid a shortcoming of the quadrilateral and hexahedral elements where the integrals of rational functions have to be computed or approximated numerical tests verify the analysis

discrete decomposability of the restriction of a q λ with respect to reductive subgroups and its applications letg g be real reductive lie groups and q a stable parabolic subalgebra of lie g this paper offers a sufficient condition on g g q that the irreducible unitary representation mathop a q limits ofg with non zero continuous cohomology splits into a discrete sum of irreducible unitary representations of a subgroupg each of finite multiplicity as an application to purely analytic problems new results on discrete series are also obtained for some pseudo riemannian non symmetric spherical homogeneous spaces which fit nicely into this framework some explicit examples of a decomposition formula are also found in the cases wherea q is not necessarily a highest weight module

finite volume compact schemes on staggered grids compact finite difference schemes have been recently used in several direct numerical simulations of turbulent flows since they can achieve high order accuracy and high resolution without exceedingly increasing the size of the computational stencil the development of compact finite volume schemes is more revolved due to the appearance of surface and volume integrals while pereira et al j comput phys 167 2001 and smirnov et al aiaa paper 2546 2001 focused on collocated grids in this paper we use the staggered grid arrangement compact schemes can be tuned to achieve very high resolution for a given formal order of accuracy we develop and test high resolution schemes by following a procedure proposed by lele j comput phys 103 1992 which to the best of our knowledge has not yet been applied to compact finite volume methods on staggered grids results from several one and two dimensional simulations for the scalar transport and navier stokes equations are presented showing that the proposed method is capable to accurately reproduce complex steady and unsteady flows

the patch test a condition for assessing fem convergence this paper discusses various forms of the irons patch test and shows again that its satisfaction is a necessary convergence condition being equivalent to consistency further it is shown that the test can be applied for verification of stability requirements thus providing also a sufficient condition of convergence the patch test is useful in testing the order of asymptotic convergence and the satisfaction of the test gives a guide for development of certain incompatible element forms

a stabilized formulation for incompressible elasticity using linear displacement and pressure interpolations in this paper a stabilized finite element method to deal with incompressibility in solid mechanics is presented a mixed formulation involving pressure and displacement fields is used and a continuous linear interpolation is considered for both fields to overcome the babuska brezzi condition a stabilization technique based on the orthogonal sub scale method is introduced the main advantage of the method is the possibility of using linear triangular or tetrahedral finite elements which are easy to generate for real industrial applications results are compared with standard galerkin and q1p0 mixed formulations for nearly incompressible problems in the context of linear elasticity

a new flux vector splitting compact finite volume scheme a new high resolution finite volume method is proposed here that uses flux vector splitting as the building block to represent the physical processes the high accuracy projection in space is obtained here inter alia by using some compact schemes of sengupta et al 1 and lele 2 that have extremely high accuracy in spectral plane this produces a new class of finite volume fv scheme for spatial discretization that has been analyzed for spectral accuracy numerical stability and dispersion relation preservation drp property following the full domain analysis method of 1 using two different time integration strategies these combination of spatial and temporal methods have been tested for two linear wave problems reported in 1 3 and the solution of burgers equation is compared with the analytical results presented in adams and shariff 4 the shock capturing method is based on the proposed technique in 5 that does not require the usage of any nonlinear differencing techniques or limiters to show that the proposed method can also handle irregular grids the burgers equation is solved using non uniform grids also to demonstrate the utility of the proposed scheme to solve practical problems the benchmark problem of nonlinear wave propagation in a one dimensional shock tube has been solved with the initial data as given in 23 by solving the euler equation the analysis and comparison of this flux vector splitting scheme with other well known methods clearly demonstrate the superior scale resolution of the proposed method at the same time providing a neutrally stable scheme when used with four stage runge kutta scheme also the same scheme displays extended ranges of wave numbers and circular frequencies over which drp property is valid the computed results of three test cases and their comparison with analytical results clearly reveal that the presented method can be used for practical problems

rational approach for assumed stress finite elements a new method for the formulation of hybrid elements by the hellinger reissner principle is established by expanding the essential terms of the assumed stresses as complete polynomials in the natural coordinates of the element the equilibrium conditions are imposed in a variational sense through the internal displacements which are also expanded in the natural co ordinates the resulting element possesses all the ideal qualities i e it is invariant it is less sensitive to geometric distortion it contains a minimum number of stress parameters and it provides accurate stress calculations for the formulation of a 4 node plane stress element a small perturbation method is used to determine the equilibrium constraint equations the element has been proved to be always rank sufficient

a class of mixed assumed strain methods and the method of incompatible modes a three field mixed formulation in terms of displacements stresses and an enhanced strain field is presented which encompasses as a particular case the classical method of incompatible modes within this frame work incompatible elements arise as particular compatible mixed approximations of the enhanced strain field the conditions that the stress interpolation contain piece wise constant functions and be l2 ortho gonal to the enhanced strain interpolation ensure satisfaction of the patch test and allow the elimination of the stress field from the formulation the preceding conditions are formulated in a form particularly convenient for element design as an illustration of the methodology three new elements are developed and shown to exhibit good performance a plane 3d elastic plastic quad an axisymmetric element and a thick plate bending quad the formulation described herein is suitable for non linear analysis

new strategy for assumed stresses for 4 node hybrid stress membrane element an oblique skew co ordinate system defined at the origin of the isoparametric co ordinates is introduced as the reference co ordinate system for assumed stresses in the formulation of a 4 node hybrid membrane element the initially uncoupled stresses in these reference co ordinates can be constrained to satisfy the equilibrium conditions pointwise by using the procedure of pian and wu7 when suitable incompatible displacements are introduced such strategy allows the element stiffness to be formulated by using either the hellinger reissner or the complementary energy functional numerical results show that the performances of three elements constructed by using different sets of incompatible displacements in this paper are practically identical and are all of slightly higher accuracy than that of the pian sumihara element6

a note on enhanced strain methods for large deformations abstract enhanced strain elements have been applied to simulate geometrically and materially non linear problems their main advantage is due to the fact that they perform very good in the incompressible limit as well as in bending situations however in compressive deformation states these elements depict stability modes which are associated with hour glass forms and thus denote a rank deficiency for such deformations in this paper the appearance of these modes will be investigated analytically by means of a simple representative example

on strong discontinuities in anelastic solids a finite element approach taking a frame indifferent gradient of the discontinuous displacements this paper presents a two dimensional 2d large deformation analysis of strong discontinuities in anelastic solids and its numerical implementation we assume associative and ideal plasticity until localization occurs in the post localization phase discontinuous displacements develop and their material gradient is set up in a proper way one leg in the current configuration the other leg in the reference configuration to provide a frame indifferent objective description the numerical implementation via displacement based six node triangular finite elements enriched by a single displacement jump parameter t2 0 in the post localization phase te locte is described in detail the solution procedure is similar to that using assumed enhanced displacement gradient elements with the only but crucial difference that on the discontinuity surface the traction is linked to the displacement jump via a proper constitutive law finally numerical results of the shear test and of the tension test are presented copyright 2000 john wiley sons ltd