a 3d brick element based on hu washizu variational principle for mesh distortion in order to improve the accuracy of the mixed element for irregular meshes a penalty equilibrating 3d mixed element based on the hu washizu variational principle has been proposed in this paper the key idea in this work is to introduce a penalty term into the hu washizu three field functional which can enforce the stress components to satisfy the equilibrium equations in a weak form compared with the classical hybrid and mixed elements this technique can efficiently reduce the sensitivity of the element to mesh distortion the reason for the better results of this penalty technique has been investigated by considering a simple 2d problem from this investigation it has been found that the penalty parameter here plays the role of a scaling factor to reduce the influence of the parasitic strain or stress which is similar to the devised selective scaling factor proposed by sze furthermore compared with the hybrid stress element the proposed element based on the three field variational principle is more suitable for material non linear analysis numerical examples have demonstrated the improved performance of the present element especially in stress computation when fem meshes are irregular copyright 2002 john wiley sons ltd

a unified theory for formulation of hybrid stress membrane elements a theory is proposed in this paper to explain in a unified manner the three rational approaches using the incompatible displacements u in the hybrid element formulation limited to the plane stress case the theory suggests that the introduction of u is to constrain the total value of the invariant i2 x y of the assumed stresses over the element to zero in the plane stress case this is the well known condition for the stress distributions to be independent of the elastic constants of the material the theory proposed is also used to explain the closeness of the performances of the four 4 node hybrid stress membrane elements 5 i 5 ii 5 a and 5 c that have been developed previously the differences among them are shown to be of the second degree in the distortion measures of the element shape when they are compared on the basis of the non vanishing total value of i2 of their respectively adopted assumed stress field several numerical examples are used to verify and to illustrate the proposed theory

new stress assumption for hybrid stress elements and refined four node plane and eight node brick elements a new stress assumption for hybrid stress elements is presented generalized incompatible modes are proposed and incorporated into the constraint equations for assumed stresses the physical meaning of the resulting constraint equations is discussed the present stress assumption which can consider the mesh distortion more rigorously is based on the physical interpretation of the role of the generalized incompatible modes and substantiated with simple mesh distortion measures defined in this paper the stress assumption is adapted to the previous four node hybrid stress element 5 i and the eight node hybrid stress brick element 18 which results in a new four node plane element m5 and an new eight node brick element m18 numerical results show that the refined elements are noticeable in low sensitivity to mesh distortion and in high accuracy of stresses 1997 john wiley sons ltd

nonassociative tori and applications to t duality in this paper we initiate the study of c algebras open image in new window endowed with a twisted action of a locally compact abelian lie group open image in new window and we construct a twisted crossed product open image in new window which is in general a nonassociative noncommutative algebra the duality properties of this twisted crossed product algebra are studied in detail and are applied to t duality in type ii string theory to obtain the t dual of a general principal torus bundle with general h flux which we will argue to be a bundle of noncommutative nonassociative tori nonassociativity is interpreted in the context of monoidal categories of modules we also show that this construction of the t dual includes the other special cases already analysed in a series of papers

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

a consistent approach for mixed stress finite element formulations in linear elastodynamics abstract in this paper a mixed stress formulation for linear elastodynamic analysis based on a modified hellinger reissner functional and a consistent approach for selecting finite element approximations are presented the key idea in this new approach is to choose stress approximations by taking into account for suitable modes to equilibrate inertia forces feasibility and effectiveness of the proposed approach are numerically verified through three benchmark tests

homology and k theory methods for classes of branes wrapping nontrivial cycles we apply some methods of homology and k theory to special classes of branes wrapping homologically nontrivial cycles we treat the classification of four geometries in terms of compact stabilizers by analogy with thurston s classification of three geometries and derive the k amenability of lie groups associated with locally symmetric spaces listed in this case more complicated examples of t duality and topology change from fluxes are also considered we analyse d branes and fluxes in type ii string theory on with torsion h flux and demonstrate in detail the conjectured t duality to with no flux in the simple case of t dualizing the circles reduces to the duality between with h flux and with no flux

quantization by cochain twists and nonassociative differentials we show that several standard associative quantizations in mathematical physics can be expressed as cochain module algebra twists in the spirit of moyal products at least to o 3 but to achieve this we twist not by a 2 cocycle but by a 2 cochain this implies a hidden nonassociativity not visible in the algebra itself but present in its deeper noncommutative differential geometry a phenomenon first seen in our previous work on semiclassicalization of differential structures the quantizations are induced by a classical group covariance and include enveloping algebras u g as quantizations of g a fedosov type quantization of the sphere s2 under a lorentz group covariance the mackey quantization of homogeneous spaces and the standard quantum groups cq g we also consider the differential quantization of rn for a given symplectic connection as part of our semiclassical analysis and we outline a proposal for the dirac operator

alternative ways for formulation of hybrid stress elements an element stiffness matrix can be derived by the conventional potential energy principle and indirectly also by generalized variational principles such as the hu washizu principle and the hellinger reissner principle the present investigation has the objective to show an approach which is concerned with the formulation of incompatible elements for solid continuum and for plate bending problems by the hellinger reissner principle it is found that the resulting scheme is equivalent to that considered by tong 1982 for the construction of hybrid stress elements in tong s scheme the inversion of a large flexibility matrix can be avoided it is concluded that the introduction of additional internal displacement modes in mixed finite element formulations by the hellinger reissner principle and the hu washizu principle can lead to element stiffness matrices which are equivalent to the assumed stress hybrid method

t duality for torus bundles with h fluxes via noncommutative topology it is known that the t dual of a circle bundle with h flux given by a neveu schwarz 3 form is the t dual circle bundle with dual h flux however it is also known that torus bundles with h flux do not necessarily have a t dual which is a torus bundle a big puzzle has been to explain these mysterious missing t duals here we show that this problem is resolved using noncommutative topology it turns out that every principal t2 bundle with h flux does indeed have a t dual but in the missing cases which we characterize the t dual is non classical and is a bundle of noncommutative tori the duality comes with an isomorphism of twisted k theories just as in the classical case the isomorphism of twisted cohomology which one gets in the classical case is replaced by an isomorphism of twisted cyclic homology

extension of mitc to higher order beam models and shear locking analysis for compact thin walled and composite structures summary a class of mixed interpolated beam elements is introduced in this paper under the framework of the carrera unified formulation cuf to eliminate the detrimental effects due to shear locking the mixed interpolation of tensorial components mitc method is adopted to generate locking free displacement based beam models using general 1d finite elements an assumed distribution of the transverse shear strains is employed for the derivation of the virtual work and the full gauss legendre quadrature is used for the numerical computation of all the components of the stiffness matrix linear quadratic and cubic beam elements are developed using the unified formulation and applied to linear static problems including compact laminated and thin walled structures a comprehensive study of how shear locking affects general beam elements when different classical integration schemes are employed is presented evidencing the outstanding capabilities of the mitc method to overcome this numerical issue refined beam theories based on the expansion of pure and generalized displacement variables are implemented making use of lagrange and legendre polynomials over the cross sectional domain allowing one to capture complex states of stress with a 3d like accuracy the numerical examples are compared to analytic numerical solutions from the literature and commercial software solutions whenever it is possible the efficiency and robustness of the proposed method is demonstrated throughout all the assessments illustrating that mitc elements are the natural choice to avoid shear locking and showing an unprecedent accuracy in the computation of transverse shear stresses for beam formulations this article is protected by copyright all rights reserved

a review on singularly perturbed differential equations with turning points and interior layers singular perturbation problems with turning points arise as mathematical models for various physical phenomena the problem with interior turning point represent one dimensional version of stationary convection diffusion problems with a dominant convective term and a speed field that changes its sign in the catch basin boundary turning point problems on the other hand arise in geophysics and in modeling thermal boundary layers in laminar flow in this paper we review some existing literature on asymptotic and numerical analysis of singularly perturbed turning point and interior layer problems the purpose is to find out what problems are treated and what numerical asymptotic methods are employed with an eye towards the goal of developing general methods to solve such problems since major work in this area started after 1970 so this paper limits its coverage to the work done by numerous researchers between 1970 and 2011

variational principles for non conforming finite element methods variational principles with relaxed inter element continuity requirement for non conforming element methods in linear and non linear analyses are developed based on the principles any non conforming element displacement can be used directly to derive the explicit expressions of non conforming displacement function which can ensure the passage of the patch test c for the requirement of convergence copyright 2001 john wiley sons ltd

a rational approach for choosing stress terms for hybrid finite element formulations a new approach for choosing the stress terms for hybrid stress elements is based on the condition of vanishing of the virtual work along the element boundary due to the stress terms higher than constant and the additional incompatible displacements examples using 4 node plane stress elements have shown that when the incompatible displacements also satisfy the constant strain patch test the resulting element will provide the most accurate solutions

on the incompressible constraint of the 4 node quadrilateral element the standard plane 4 node element is written as the summation of a constant gradient matrix usually obtained from underintegration and a stabilization matrix the split is based on a taylor series expansion of element basis functions in the incompressible limit the locking effect of the quadrilateral is traced back to the stabilization matrix which reflects the incomplete higher order term in the taylor series the incompressibility condition is formulated in a weak sense so that the element displacement field is divergence free when integrated over the element volume the resulting algebraic constraint is shown to coincide with a particular eigenvector of the constant gradient matrix which is obtained from the first order terms of the taylor series the corresponding eigenvalue enforces incompressibility implicitly by means of a penalty constraint analytical expressions for that constant dilatation eigenpair are derived for arbitrary element geometries it is shown how the incompressible constraint carries over to the element stiffness matrix if the element stabilization is performed in a particular manner for several classical and recent elements the eigensystems are analysed numerically it is shown that most of the formulations reflect the incompressible constraint identically in the incompressible limit the numerical accuracies of the elements are compared

extension of field consistence approach into developing plane stress elements in this research paper the possibilities for extending the field consistence approach l yunhua on shear locking in finite elements licentiate thesis stockholm 1997 l yunhua explanation and elimination of shear locking and membrane locking with field consistence approach comput methods appl mech engrg in press starting from different variational principles to plane stress elements are investigated in the extension two main difficulties are explicitly solving a set of coupled partial differential equations and satisfying inter element compatibility the first one is alleviated by constructing element interpolations from a set of quasi general solutions rather than the real general solutions to the euler lagrangian equations the second one is solved by combining the field consistence approach with the iso parametric interpolation technique the traditional assumed stress method is improved and an efficient plane stress element is obtained it seems that the relations between the three commonly used variational principles can be more reasonably established in the framework of the field consistence approach

a dixmier douady theorem for fell algebras abstract we generalise the dixmier douady classification of continuous trace c algebras to fell algebras to do so we show that c diagonals in fell algebras are precisely abelian subalgebras with the extension property and use this to prove that every fell algebra is morita equivalent to one containing a diagonal subalgebra we then use the machinery of twisted groupoid c algebras and equivariant sheaf cohomology to define an analogue of the dixmier douady invariant for fell algebras and to prove our classification theorem

a higher order method for stationary shock problems an equidistant finite difference method is proposed for quasilinear singularly perturbed boundary value problems the method uses a combination of one sided schemes and a third order three point scheme it is easy to implement and produces third order accuracy away from shocks

finite difference schemes for quasilinear singular perturbation problems finite difference schemes for singularly perturbed quasilinear boundary value problems are considered the schemes have fitting factors which guarantee their uniform stability with respect to the perturbation parameter besides the usual stability in the discrete l1 norm we consider the maximum norm stability as well various schemes are compared numerically

a groupoid approach to noncommutative t duality topological t duality is a transformation taking a gerbe on a principal torus bundle to a gerbe on a principal dual torus bundle we give a new geometric construction of t dualization which allows the duality to be extended in the following two directions first bundles of groups other than tori even bundles of some nonabelian groups can be dualized second bundles whose duals are families of noncommutative groups in the sense of noncommutative geometry can be treated though in this case the base space of the bundles is best viewed as a topological stack some methods developed for the construction may be of independent interest these are a pontryagin type duality that interchanges commutative principal bundles with gerbes a nonabelian takai type duality for groupoids and the computation of certain equivariant brauer groups

an incompatible element for axisymmetric structure and its modification by hybrid method this paper introduces three four node quadrilateral axisymmetric elements the first one is an incompatible element while the second one is a modification of the first element by an extended hellinger reissner principle the second element is then simplified by incorporating the conceptual idea of free formulation and thus forms the third element all of the three elements are found to be invariant insensitive to nodal point numbering free of locking for nearly incompressible material able to pass the patch test and do not exhibit the false shear phenomenon numerical examples are given and satisfactory predictions are achieved

three cocycle in mathematics and physics it is shown that the three cocycle arises when a representation of a transformation group is nonassociative so that the jacobi identity fails a physical setting is given when the translation group in the presence of a magnetic monopole is represented by gauge invariant operators a trivial three cocycle occurs insisting that finite translations be associative leads to dirac s monopole quantization condition attention is called to the possible relevance of three cocycles in the quark model s u 6 ensuremath bigotimes u 6 algebra

stability of a streamline diffusion finite element method for turning point problems a one dimensional singularly perturbed problem with a boundary turning point is considered in this paper let v h be the linear finite element space on a suitable grid t h a variant of streamline diffusion finite element method is proved to be almost uniform stable in the sense that the numerical approximation u h satisfies u u email protected

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

a systematic construction of b bar functions for linear and non linear mixed enhanced finite elements for plane elasticity problems in a previous paper a modified hu washizu variational formulation has been used to derive an accurate four node plane strain stress finite element denoted qe2 for the mixed element qe2 two enhanced strain terms are used and the assumed stresses satisfy the equilibrium equations a priori for the linear elastic case in this paper an alternative approach is discussed the new formulation leads to the same accuracy for linear elastic problems as the qe2 element however it turns out to be more efficient in numerical simulations especially for large deformation problems using orthogonal stress and strain functions we derive b functions which avoid numerical inversion of matrices the b strain matrix is sparse and has the same structure as the strain matrix b obtained from a compatible displacement field the implementation of the derived mixed element is basically the same as the one for a compatible displacement element the only difference is that we have to compute a b strain matrix instead of the standard b matrix accordingly existing subroutines for a compatible displacement element can be easily changed to obtain the mixed enhanced finite element which yields a higher accuracy than the q4 and qm6 elements copyright 1999 john wiley sons ltd

a brief survey on numerical methods for solving singularly perturbed problems in the present paper a brief survey on computational techniques for the different classes of singularly perturbed problems is given this survey is a continuation of work performed earlier by the first author and contains the literature of the work done by the researchers during the years 2000 2009 however some older important relevant papers are also included in this survey we also mentioned those papers which are not surveyed in the previous survey papers by the first author of this paper see appl math comput 30 1989 223 259 130 2002 457 510 134 2003 371 429 for details thus this survey paper contains a surprisingly large amount of literature on singularly perturbed problems and indeed can serve as an introduction to some of the ideas and methods for the singular perturbation problems

a quadrilateral mixed finite element with two enhanced strain modes summary an improved plane strain stress element is derived using a hu washizu variational formulation with bilinear displacement interpolation seven strain and stress terms and two enhanced strain modes the number of unknowns of the four node element is increased from eight to ten degrees of freedom for linear and non linear applications the two unknowns associated with the enhanced strain terms can be eliminated by static condensation so that eight displacement degrees of freedom remain for the proposed element which is denoted by qe2 the excellent performance of the proposed element is demonstrated using several linear and non linear examples

quantum hall effect on the hyperbolic plane in this paper we study both the continuous model and the discrete model of the quantum hall effect qhe on the hyperbolic plane the hall conductivity is identified as a geometric invariant associated to an imprimitivity algebra of observables we define a twisted analogue of the kasparov map which enables us to use the pairing between k theory and cyclic cohomology theory to identify this geometric invariant with a topological index thereby proving the integrality of the hall conductivity in this case

an equivariant brauer group and actions of groups onc algebras suppose that g t is a second countable locally compact trans formation group given by a homomorphism l g homeo t and that a is a separable continuous trace c algebra with spectrum t an action g aut a is said to cover l if the induced action of g on t coincides with the original one we prove that the set brg t of morita equivalence classes of such systems forms a group with multiplication given by the balanced tensor product a b a c0 t b and we refer to brg t as the equivariant brauer group we give a detailed analysis of the structure of brg t in terms of the moore cohomology of the group g and the integral cohomology of the space t using this we can characterize the stable continuous trace c algebras with spectrum t which admit actions covering l in particular we prove that if g r then every stable continuous trace c algebra admits an essentially unique action covering l thereby substantially improving results of raeburn and rosenberg

braided cyclic cocycles and nonassociative geometry we use monoidal category methods to study the noncommutative geometry of nonassociative algebras obtained by a drinfeld type cochain twist these are the so called quasialgebras and include the octonions as braided commutative but nonassociative coordinate rings as well as quasialgebra versions cq g of the standard q deformation quantum groups we introduce the notion of ribbon algebras in the category which are algebras equipped with a suitable generalized automorphism and obtain the required generalization of cyclic cohomology we show that this braided cyclic cohomology is invariant under a cochain twist we also extend to our generalization the relation between cyclic cohomology and differential calculus on the ribbon quasialgebra the paper includes differential calculus and cyclic cocycles on the octonions as a finite nonassociative geometry as well as the algebraic noncommutative torus as an associative example

numerical solution of quasilinear attractive turning point problems abstract a quasilinear singularity perturbed boundary value problem with a turning point of the attractive type is considered analytic properties of its solution are established and used for the construction of a numerical method uniform in the perturbation parameter the paper is an extension of a result obtained previously for the semilinear case

the mode amplitude technique and hierarchical stress elements a simplified and natural approach this paper reviews the derivation procedure of conventional stress based elements and then shows how the procedure can be simplified by using degrees of freedom which are amplitudes of the boundary loading modes mode amplitude technique this gives one class of element based on stress assumptions and uses only one virtual principle the natural formulation of hierarchical stress elements is shown

d branes rr fields and duality on noncommutative manifolds we develop some of the ingredients needed for string theory on noncommutative spacetimes proposing an axiomatic formulation of t duality as well as establishing a very general formula for d brane charges this formula is closely related to a noncommutative grothendieck riemann roch theorem that is proved here our approach relies on a very general form of poincare duality which is studied here in detail among the technical tools employed are calculations with iterated products in bivariant mathsf k theory and cyclic theory which are simplified using a novel diagram calculus reminiscent of feynman diagrams

stress analysis around holes or notches by special finite elements in this paper three special elements for stress concentration analysis around holes or notches are presented one is based on a variational principle involving displacements unsymmetric stresses and rotations as independent variables the other two on the classical hellinger reissner principle the new elements are designed to be used in a single layer along the cavity rim where enhanced properties are needed to get a satisfactory level of accuracy special properties are obtained by enforcing the stress approximation to satisfy a priori the traction free boundary condition on the element side positioned along the cavity rim and by properly enriching the displacement interpolation the proposed elements are applicable to geometries of arbitrary shape easy to use low cost and readily implementable into existing finite element codes copyright 2005 john wiley sons ltd

a unified analysis for stress strain hybrid methods of high performance abstract several methods have been developed in the literatures of computational mechanics to improve the performance of the conventional lower order displacement finite elements which yield poor results for problems with bending and for nearly incompressible medium this paper is devoted to a unified analysis of convergence for pian sumihara s chen cheung s and piltner taylor s enhanced stress strain schemes by virtue of the energy compatibility and the rank condition error estimates for these typical finite elements of high performance are obtained in a unified framework and especially weakly locking free error estimates with respect to the poisson s ratio in energy norms are obtained uniformly for 1 ch 2 as h 0 where c is a constant independent of and the mesh size h very much the same about the three methods is pointed out

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

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

relations between incompatible displacement model and hybrid stress model an examination of the variational formulations confirms the similarity between the incompatible displacement model and the assumed stress hybrid model that was pointed out by irons in 1972 but the basic differences between the two are also identified for 8 node solid elements the assumed stress terms obtained through a rational procedure also agree with those deduced by irons purely from his physical insight