on plastic incompressibility within time adaptive finite elements combined with projection techniques abstract this article treats the interpretation of quasi static finite elements applied to constitutive equations of evolutionary type as a solution scheme to solve globally differential algebraic equations this concept is applied to finite strain viscoplasticity based on a model with non linear kinematic hardening under the assumption of plastic incompressibility the model is based on multiple multiplicative decomposition both for the deformation gradient into an elastic and an inelastic part as well as for the inelastic part into a kinematic hardening energy storage and a dissipative part both intermediate configurations are described by inelastic right cauchy green tensors satisfying inelastic incompressibility in the theoretical context the attention in view of the numerical treatment within finite elements is focused on diagonally implicit runge kutta methods which destroy the assumption of plastic incompressibility during the time integration due to an additive structure of the integration step in combination with a multilevel newton algorithm these algorithms embed the classical strain driven radial return method to this end a concept of geometric numerical integration is applied where the plastic incompressibility condition is taken into account as an additional side condition since the literature states large integration errors if the side condition is not taken into account a particular focus lies on the application of a time adaptive procedure accordingly the article investigates i the algorithmic treatment of kinematic hardening within time adaptive finite elements ii the influence of the perzyna type viscoplasticity approach in view of an order reduction phenomenon and iii the influence of taking into account the exact fulfillment of plastic incompressibility using a projection method having the advantage of simple implementation

stress computation and consistent tangent operator using non linear kinematic hardening models one possibility of formulating the tinite element method is founded on the principle of virtual displacement in which we want to include a rate independent elastoplastic constitutive model based on the assumption of a yield surface the constitutive equations result from the assumptions of small deformations hooke s law for the elastic domain the normality rule for the evolution of plastic strains the von mises yield condition and a special kind of kinematic hardening due to armstrong and frederick 1 in which linear kinematic hardening is generalized with a saturation term we show that it is not generally recommendable to propose large load steps to this end we investigate the influences of the non linear kinematic hardening model on the stress computation and the resulting consistent elastoplastic tangent operator the main topics of this paper are 1 development of a problem optimized backward euler method with regard to the kinematic hardening model 2 study of the influence of the saturation term on the numerical accuracy through isoerror maps and 3 computation of the consistent elastoplastic tangent operator

tilting modules and tilting torsion theories abstract we generalize basic results about classical tilting modules and partial tilting modules to the infinite dimensional case over an arbitrary ring r the methods employed combine classical techniques of representation theory of finite dimensional algebras with new techniques of the theory of modules using a generalization of the bongartz lemma we characterize tilting torsion theories in mod r i e torsion theories induced by infinitely generated tilting modules we investigate lattices gen p p of torsion classes induced by partial tilting modules p applying our results to tilting torsion classes we prove a version of the brenner butler theorem and a generalization of the assem smalo theorem to the case when r is artinian

a return mapping algorithm for isotropic elastoplasticity a return mapping algorithm is presented for the numerical time integration of the constitutive equations for elastoplasticity with isotropic yield surfaces constructed from all three invariants of the stress tensor based on the first order backward euler difference formula bdf the governing equations for the stresses are solved in the space of the invariants and the discretized persistence parameter the stresses are recovered afterwards the solution concept is applied to a pressure independent yield function expressed in terms of the second and third invariant of the stress tensor the numerical performance of the method is demonstrated with two examples

on fuzzy spaces and fuzzy group theory abstract the concept of fuzzy space is introduced this concept corresponds to the concept of the universal set in the ordinary case the algebra of fuzzy spaces and fuzzy subspaces is studied using the concept of fuzzy space and fuzzy binary operation a new approach to study fuzzy group theory is given this approach can be considered as a generalization and reformulation of the rosenfeld theory of fuzzy subgroups therefore it is an active tool to develop the theory of fuzzy groups

consistent tangent operator for plasticity models based on the plastic strain rate potential a stress updating integration algorithm is derived for use with plastic strain rate potentials and with the backward implicit euler method an explicit expression is also deduced for the consistent tangent modulus this analysis extends an earlier treatment developed for elastic perfectly plastic materials in that it applies to materials which harden isotropically the method is intended for use in finite element calculations that employ plasticity models based on the plastic strain rate potential it is particularly suitable for cases where the form of the plastic dual potential has been obtained from texture measurements or from crystallographic models that describe texture evolution during metal forming

an efficient stress algorithm with applications in viscoplasticity and plasticity this paper deals with two main topics the first one concerns the equivalence of stress algorithms based on a backward euler step applied on viscoplastic models of chaboche type and their elastoplastic counterpart generally the stress algorithm yields a system of non linear algebraic equations and the corresponding consistent tangent operator occurring in the principle of virtual displacements leads to a system of linear equations this procedure can be obtained utilizing only numerical methods the second topic concerns a special constitutive relation based on a kinematic hardening model using a sum of armstrong frederick terms which is equivalent to a multi surface plasticity model applying this model a so called problem adapted stress algorithm is derived where only one non linear equation must be solved this result is independent of the number of terms in the hardening model furthermore only the viscoplastic algorithm must be implemented since it includes the elastoplastic constitutive model as a special case 1997 by john wiley sons ltd

a general approach to the evaluation of consistent tangent operators for rate independent elastoplasticity abstract we present a general approach to the derivation of the explicit expression of tangent operators consistent with the finite step integration schemes of the flow rule for rate independent elastoplastic models with mixed hardening by exploiting the model of generalized standard material we show that the algorithmic tangent operator can be obtained by inverting a suitable positive definite matrix use of the sherman morrison woodbury formula allows us to reduce to a half the burden associated with such inversion and to derive an expression of the consistent tangent operator prone to computer implementation the application of the proposed approach to the von mises yield criterion with linear kinematic and isotropic hardening shows that the closed form expression of the operator can be obtained by a straightforward procedure

inference of fuzzy relational tableaux from fuzzy exemplifications the paper describes a method for deriving fuzzy relational tableaux from fuzzy exemplifications in particular the work by thole zimmerman and zysno 4 is cited as they derive an operator for and using data derived from human subjects the method results in an operator or operators which is a maximal restriction of the operators implied by the data results showing the process are described and a value of and is derived using data presented in 4

some properties of fuzzy groups on definit des sous groupes flous normaux des sous groupes flous normaux de niveau et leurs homomorphismes et on donne certaines de leurs proprietes

exceptional components of wild hereditary algebras this paper studies regular components of wild hereditary algebras it is clear that the existence of extremely many maps in the infinite radical of the module category causes algebras to be wild whereas the dimension of the horn spaces of maps from indecomposable preprojective modules or to indecomposable preinjective modules can be calculated by linear methods via the euler bilinearform these methods give only poor information if we pass to regular modules so it is natural to study as a first step maps between regular modules which are in the same regular component v and we see in 4 7 that this is a way to get information about the maps between arbitrary regular modules there is another less obvious reason for the study of single components if a and b are connected wild hereditary algebras then by 9 via tilting modules there can be constructed bijections between the regular components of the auslander reiten quivers t a and t b in order to find finally properties of these bijections we have to study properties of components proposition 6 3 points in that direction if g is a regular component in t a with a wild hereditary we denote by the quasi rank rk of v the smallest integer n such that rad x r x 0 for all n 2 n and all xe we call a component v exceptional if there is an indecomposable quasi simple module xe such that hom x yx 0 but hom x z r 1 0 for some r 0 in section 4 we show that there are only finitely many exceptional components in t a and that the existence of those components has strict consequences for the algebra a that is for its ordinary quiver 9 a in section 5 we present the numerical invariants of the most important exceptional components in the last section we give applications to tilting theory the applications are chosen under the aspect that the notion of the quasi rank of a regular component might be a pendant to the period of a tube in the tame case 184 0021 8693 92 5 00

tilting for regular rings of krull dimension two we classify tilting classes over regular rings r of krull dimension two they are parametrized by the set of all pairs x y such that assrr x spec r y consists of maximal ideals of height 2 and y contains all the maximal ideals of height 2 that contain some element of x assrr for r local we also classify the corresponding infinitely generated tilting modules

on the implementation of inelastic constitutive equations with special reference to large deformation problems abstract methods for finite element analysis of inelastic problems are reviewed problems with currently popular methods based on rate principles of virtual work are pointed out a formulation is presented based on the exact incremental virtual work equation the procedure for integration of the constitutive rate equations to obtain incremental constitutive equations is based on the assumption of a constant strain rate or straight strain path during the increment full newton raphson iteration is used to solve the resulting set of nonlinear equations the treatment of the constitutive equations in this newton raphson scheme leads to a linearized form which is substantially different from the classical rate equations the procedure is implemented in a finite element program and its effectiveness is shown in a number of examples

a semi analytical integration method for j2 flow theory of plasticity with linear isotropic hardening abstract in this paper an exact time integration scheme is presented for von mises elastoplasticity with linear isotropic hardening at small deformations the method is based on the constant strain rate assumption which is widely accepted in displacement based finite element applications the deviatoric form of the rate equation using the method proposed by krieg and krieg in r d krieg d b krieg accuracies of numerical solution methods for the elastic perfectly plastic model j press vess technol trans asme 99 1977 510 515 is rewritten to a system of nonlinear odes with two scalar functions the radius of the mises circle and an angle obtained by using the scalar product of the stress deviator and the strain rate the time integration of these functions gives an exact solution in implicit form using the incomplete beta function in addition by the exact linearization of this new semi analytical solution a stress updating algorithm and the consistent tangent operator are derived the numerical performance and accuracy of the proposed method are illustrated on numerical examples moreover a comparison of the proposed method with the well known radial return method is included

whitehead test modules a right r module n is said to be a whitehead test module for projectivity shortly a p test module provided for each module m extr m n 0 implies m is projective dually i test modules are defined for example z is a p test abelian group iff each whitehead group is free our first main result says that if r is a right hereditary non right perfect ring then the existence of p test modules is independent of zfc gch on the other hand for any ring r there is a proper class of i test modules dually there is a proper class of p test modules over any right perfect ring a non semisimple ring r is said to be fully saturated saturated provided that all non projective generated non projective modules are i test we show that classification of saturated rings can be reduced to the indecomposable ones indecomposable 1 saturated rings fall into two classes type i where all simple modules are isomorphic and type ii the others our second main result gives a complete characterization of rings of type ii as certain generalized upper triangular matrix rings gt 1 n p s t the four parameters involved here are skew fields s and t and natural numbers n p for rings of type i we have several partial results e g using a generalization of bongartz lemma we show that it is consistent that each fully saturated ring of type i is a full matrix ring over a local quasi frobenius ring in several recent papers our results have been applied to tilting theory and to the theory of modules in modern algebra the structure of rings r is studied by means of properties of corresponding module categories mod r in most cases it is not possible to characterize mod r fully nevertheless there are important subclasses of mod r that can be treated in detail and that shed light on the whole of mod r among the prominent ones are the classes of all projective and all injective modules recall that a module m is said to be projective injective provided that the functorhomr m homr m preserves short exact sequences there is also a universal algebraic aspect each module is a factor module of a projective module and a submodule of an injective module so a possible strategy to investigate modr consists in describing all injective modules and for each injective module i all its submodules the first step is usually relatively easy but the second may be quite hard for example using this strategy for abelian groups one meets serious difficulties already for i q q see e g e theorem 2 received by the editors march 17 1995 1991 mathematics subject classification primary 16e30 secondary 03e35 20k35

a hybrid mixed model for non linear shell analysis and its applications to large rotation problems adopting an updated lagrange approach the general framework for the fully non linear analysis of curved shells is developed using a simple quadrilateral c0 model hmsh5 the governing equations are derived based on a consistent linearization of an incremental mixed variational principle of the modified hellinger reissner type with independent assumptions for displacement and strain fields emphasis is placed on devising effective solution procedures to deal with large rotations in space finite stretches and generalized rate type material models in particular a geometrically exact scheme for configuration update is developed by making use of the so called exponential mapping algorithm and the resulting element was shown to exhibit a quadratic rate of asymptotic convergence in solving practical shell problems with newton raphson type iterative schemes for the purpose of updating the spatial stress field of the element an objective generalized midpoint integration rule is utilized which relies crucially on the concept of polar decomposition for the deformation gradient and is in keeping with the underlying mixed method finally the effectiveness and practical usefulness of the hmsh5 element are demonstrated through a number of test cases involving beams plates and shells undergoing very large displacements and rotations

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

on the numerical treatment of finite deformations in elastoviscoplasticity abstract this paper deals with the generalization of a geometric linear viscoplastic model to finite strains and its numerical application we owe the original formulation of the applied model to perzyna and chaboche it includes nonlinear isotropic and kinematic hardening as well as a nonlinear rate dependence the constitutive equations are integrated numerically in the context of a finite element formulation from theoretical considerations it is known that in the case of vanishing viscosity or slow processes rate independent plasticity arises as an asymptotic limit accordingly the numerical formulation includes this property in fact the stress algorithm corresponding to viscoplasticity is reduced to the asymptotic limit in a most simple way namely by setting the viscosity parameter equal to zero furthermore it is shown that the numerical integration of the constitutive model involves the solution of only one nonlinear equation for one scalar unknown this even applies to a sum of armstrong frederick terms the algorithm incorporates the inelastic incompressibility on the level of the gau points numerical computations of examples taken from metal forming technology show the physical significance of the model and the reliability of the numerical algorithm these calculations have been carried out by means of the finite element program psu

implementation of cyclic plasticity models based on a general form of kinematic hardening this paper deals with implementation of cyclic plastic constitutive models in which a general form of strain hardening and dynamic recovery is employed to represent the multilinear as well as non linear evolution of back stress first in order to incorporate such a general form of kinematic hardening in finite element methods successive substitution and its convergence are discussed for implicitly integrating stress moreover a new expression of consistent tangent modulus is derived by introducing a set of fourth rank constitutive parameters into discretized kinematic hardening then the constitutive parameters introduced are specified in three cases of the general form of kinematic hardening the three cases have distinct capabilities of simulating ratcheting and cyclic stress relaxation numerical examples are given to verify the convergence in successive substitution and the new expression of consistent tangent stiffness error maps for implicitly integrating stress under non proportional as well as proportional loading are also given to show that the multilinear case of the general form provides high accuracy even if strain increment is very large copyright 2002 john wiley sons ltd

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

fuzzy ideals and fuzzy bi ideals in fuzzy semigroups abstract the purpose of this paper is to introduce some basic concepts of fuzzy algebra such as fuzzy left right ideal and fuzzy bi ideal in fuzzy semigroup through the new approach of fuzzy space and fuzzy group introduced by dib 1994 our notion of fuzzy ideal and fuzzy bi ideal includes the classical concepts of fuzzy ideal and fuzzy bi ideal of ordinary semigroup many counterexamples are also given

the effective stress function algorithm for thermo elasto plasticity and creep an algorithm for stable and accurate computations of stresses in finite element thermo elastic plastic and creep analysis of metals is presented the effective stress function algorithm solves the governing equations of the inelastic constitutive behaviour by calculating the zero of the appropriate effective stress function a functional relationship which involves as unknown only the effective stress the derivation of the effective stress function for thermo elasto plasticity conditions including creep for 2 d and 3 d analysis is presented and the algorithmic steps of the stress solution are discussed for use in the stiffness matrix a tangent material stress strain relationship is evaluated consistent with the effective stress function algorithm the solution of some demonstrative problems shows the effectiveness of the solution procedure

the fuzzy normal subgroup using the concept of fuzzy spaces we define the fuzzy normal subgroup in a fuzzy group its relation with the classical fuzzy normal subgroup is studied

accuracy and stability of integration algorithms for elastoplastic constitutive relations an analysis of accuracy and stability of algorithms for the integration of elastoplastic constitutive relations is carried out in this paper reference is made to a very general internal variable formulation of plasticity and to two families of algorithms that generalize the well known trapezoidal and midpoint rules to fit the present context other integration schemes such as the radial return mean normal and closest point procedures are particular cases of this general formulation the meaning of first and second order accuracy in the presence of the plastic consistency condition is examined in detail and the criteria derived are used to identify two second order accurate members of the proposed algorithms a general methodology is also derived whereby the numerical stability properties of integration schemes can be systematically assessed with the aid of this methodology the generalized midpoint rule is seen to have far better stability properties than the generalized trapezoidal rule finally numerical examples are presented that illustrate the performance of the algorithms

numerical computation of algorithmic consistent tangent moduli in large strain computational inelasticity abstract an algorithm for the numerical computation of so called algorithmic or consistent tangent moduli in finite inelasticity is presented these moduli determine the sensitivity of algorithmic expressions for stresses with respect to the change in total deformation they serve as iteration operators by application of newton type solvers for the iterative solution of non linear initial boundary value problems in finite inelasticity the underlying concept of the numerical computation is a perturbation technique based on a forward difference approximation which reduces the computation of the tangent moduli to a multiple stress computation the algorithmic procedure is material independent and surprisingly simple it is outlined for a lagrangian as well as an eulerian geometric setting and applied to model problems of finite elasticity and finite elastoplasticity

an implicit time integration scheme for inelastic constitutive equations with internal state variables in a broad class of inelastic constitutive models for the deformation of metals the inelastic strain rates are functions of the current state of stress and internal state variables only all known models are in some regions of application mathematically stiff and therefore difficult to integrate the unconditionally stable implicit euler rule is used for integration it leads to a system of highly nonlinear algebraic equations which have to be solved by an iterative process the general newton raphson method which converges under very broad conditions requires repeated solution of the finite element system and is infeasible for large inelastic problems but for the inelastic strains and internal state variables the jacobian can be computed analytically and therefore the nri can be used for the stresses the jacobian cannot be computed analytically and therefore the accelerated jacobi iteration is used a new method for computing the relaxation parameter is introduced which increases the rate of convergence significantly the new algorithm is applied on hart s model a comparison with prior computations using an approximation is made

on nonisothermal elastoplastic analysis of shell components employing realistic hardening responses abstract in the present paper efficient numerical algorithms for elastoplastic analysis of shell like structural components will be proposed employing nonisothermal realistic highly nonlinear hardening responses the closest point projection integration algorithm is presented using a reissner mindlin type kinematic shell model completely formulated in tensor notation further a consistent elastoplastic tangent modulus is derived which ensures high convergence rates in the global iteration approach the integration algorithm has been implemented into a layered assumed strain isoparametric finite element which also enables geometrical nonlinearities including finite rotations the nonisothermal elastoplastic response of a circular cylindrical shell and a box column under axial compression is analysed under the assumption of an adiabatic process the increase in temperature is computed during elastoplastic deformation robustness and numerical stability of the proposed algorithms are demonstrated

integration methods for complex plastic constitutive equations abstract this paper shows new results concerning the finite element computations with complex plastic and viscoplastic constitutive equations the integration procedure then needs special numerical treatments when a large number of internal variables are present or for stiff non linearities implicit and explicit integration methods are compared the general solution proposed can be applied either in plasticity or in viscoplasticity for isotropic or anisotropic materials several options are proposed in the numerical scheme and for the completion step for the semi implicit scheme numerical tests are performed in order to compare the relative performances of the various approaches

symmetry preserving return mapping algorithms and incrementally extremal paths a unification of concepts in this work we seek to characterize the conditions under which an elastic plastic stress update algorithm preserves the symmetries inherent to the material response from a numerical standpoint the aim is to determine under what conditions a stress update algorithm produces symmetric consistent tangents when applied to materials obeying normality for the ideally plastic solid we show that only the fully implicit or closest point return mapping algorithm is symmetry preserving for hardening plasticity symmetry cannot be preserved in general unless suitable restrictions are imposed on the constitutive equations we show that these restrictions amount to the existence of a pseudo internal energy function acting as a joint potential for both the direction of plastic flow and the hardening moduli in view of the fact that holonomic methods based on incrementally extremal paths also result in update rules possessing a potential structure and hence in symmetric tangents we address the question of whether any connections exist between the two approaches we show that holonomic methods and the fully implicit algorithm may indeed be brought into correspondence

a characterization of fuzzy subgroups abstract an ordinary subgroup of a group g is 1 a subset of g 2 closed under the group operation in a fuzzy subgroup it is precisely these two notions that lose their deterministic character a fuzzy subgroup of a group g associates with each group element a number the larger the number the more certainly that element belongs to the fuzzy subgroup the closure property is captured by the inequality x y t x y in a rosenfeld s original definition t was the function minimum however any t norm t provides a meaningful generalization of the closure property two classes of fuzzy subgroups are investigated the fuzzy subgroups in one class are subgroup generated those in the other are function generated each fuzzy subgroup in these classes satisfies the above inequality with t given by t a b max a b 1 0 while the two classes look different each fuzzy subgroup in either is isomorphic to one in the other it is shown that a fuzzy subgroup satisfies the above inequality with t minimum if and only if it is subgroup generated of a very special type finally these notions are applied to some abstract pattern recognition problems

on fuzzy subgroups and fuzzy ideals under triangular norms abstract in this communication we explicitly point out that the principal results of liu 1982 basically deduced from the definition of binary operation on the set f x of all fuzzy subsets of x also hold if one uses the weaker definition of product under triangular norm t fuzzy ideals with respect to the triangular norms are also defined

lie symmetries of finite strain elastic perfectly plastic models and exactly consistent schemes for numerical integrations abstract for finite strain elastic perfectly plastic models the use of non spinning objective stress rates leads to cubic degree non linear differential equations as well as the coupling of deviatoric and volumetric constitutive equations the governing equations reduce to quadratic non linearity and the coupling disappears when spinning objective stress rates are used in order to effectively deal with these non linearities we first convert the non linear constitutive equations into a lie type system x ax a so 5 1 for x in the minkowski spacetime m 5 1 which has an indefinite metric g of signature 5 1 however for spinning objective stress rates a merely depends on t through deformation history and the above equation reduces to a time varying linear system the new representation admits a lie symmetry of the proper orthochronous lorentz group soo 5 1 in the plastic phase in terms of x the yield condition is transformed to a null cone condition x t gx 0 in m 5 1 due to this nullity we thus assign a quaternionic hermitian matrix to represent x and convert the six dimensional system to a more economic lower dimensional quaternionic two component spinor system q q sl 2 h in the two dimensional spinor space the lie symmetry is found to be sl 2 h the mapping of which onto soo 5 1 is derived in addition to the mapping between so 5 1 and sl 2 h an isomorphic mapping between sl 2 h and su 4 is also established the latter of which generates the group su 4 finally according to these lie symmetries the numerical schemes preserving the group properties are developed which satisfy the consistency condition 1 exactly for every time step without iterations at all

stress evaluation algorithms for rate constitutive equations in finite deformation analysis the stress integration algorithm for hypoelastic constitutive equations proposed by pinsky et al 3 is extended for the treatment of finite deformation elastoplastic constitutive relations another approach based on the polar decomposition of the deformation gradient tensor f r u is also introduced numerical examples and a discussion on these two approaches are given

linearization and return mapping algorithms for elastoplasticity models the return mapping algorithm is one of the most efficient procedures to solve elasto plastic problems however a criticism that may be lodged against this method is the difficulty of the practical computation of the consistent tangent matrix when the return is non radial much research has been done to handle this matrix in this paper a unified approach is presented in such a way that a simple closed form expression gives the consistent tangent matrix for the classical constitutive relations von mises tresca mohr coulomb drucker prager the basic ideas are in the properties of eikonal equations appearing in several fields as image treatment short time computation in elastic waves and others the same kinds of ideas can be extended to non classical models copyright 2003 john wiley sons ltd

fuzzy invariant subgroups and fuzzy ideals abstract the purpose of this paper is to introduce some basic concepts of fuzzy algebra as fuzzy invariant subgroups fuzzy ideals and to prove some fundamental properties in particular it will give a characteristic of a field by a fuzzy ideal

tilting and cotilting modules over concealed canonical algebras we study infinite dimensional tilting modules over a concealed canonical algebra of domestic or tubular type in the domestic case such tilting modules are constructed by using the technique of universal localization and they can be interpreted in terms of gabriel localizations of the corresponding category of quasi coherent sheaves over a noncommutative curve of genus zero in the tubular case we have to distinguish between tilting modules of rational and irrational slope for rational slope the situation is analogous to the domestic case in contrast for any irrational slope there is just one tilting module of that slope up to equivalence we also provide a dual result for infinite dimensional cotilting modules and a description of the indecomposable pure injective modules

adaptive return mapping algorithms for j2 elasto viscoplastic flow in this paper a new class of integration algorithms for elasto viscoplastic constitutive equations is proposed it is based on the generalized trapezoidal rule which is a weighted combination of the start and end of the increment but instead of taking constant weights the weights are a function of the plastic multiplier in this way the magnitude of the plastic strain increment determines the way the integration is performed the stress update and consistent tangent are derived for the case of j2 flow several candidates within the class of adaptive return mapping algorithms are investigated it is shown numerically that some of the proposed algorithms are more accurate than commonly used algorithms such as mean normal and radial return

fully implicit integration and consistent tangent modulus in elasto plasticity this paper deals with the numerical integration of a class of rate independent elasto plastic models the backward euler scheme is used to integrate the rate constitutive relations the non linear equations obtained are solved by the newton method the consistent tangent modulus is obtained by exact linearization of the algorithm in the case of j 2 elastoplasticity with non linear isotropic hardening and non linear kinematic hardening chaboche marquis model explicit formulas are derived without any approximations

a new approach to fuzzy groupoids abstract we establish a new approach to fuzzy groupoids a concept of fuzzy binary operation is introduced in terms of the concepts of fuzzy cartesian product and fuzzy function introduced by the authors in a foregoing paper having defined a fuzzy binary operation the concepts of fuzzy groupoid subgroupoid homomorphism etc are introduced and investigated a theory of fuzzy groupoids is built up this approach is both intrinsic and more general than the well known current approach

tilting classes over wild hereditary algebras in this paper we investigate tilting classes over connected hereditary algebras of in nite representation type and in particular over connected wild hereditary algebras thecase when the generating tilting module is nitely generated was studied in 13 in 17 lukas proved several facts important for our general setting in the present terminology heshowed that given a wild hereditary algebra

baer and mittag leffler modules over tame hereditary algebras we develop a structure theory for two classes of infinite dimensional modules over tame hereditary algebras the baer modules and the mittag leffler ones a right r module m is called baer if rm ext 1 r m t 0 for all torsion modules t and m is mittag leffler in case the canonical map m otimes r prod i in i q i to prod i in i m otimes rq i is injective where q i i in i are arbitrary left r modules we show that a module m is baer iff m is p filtered where p is the preprojective component of the tame hereditary algebra r we apply this to prove that the universal localization of a baer module is projective in case we localize with respect to a complete tube using infinite dimensional tilting theory we then obtain a structure result showing that baer modules are more complex then the infinite dimensional preprojective modules in the final section we give a complete classification of the mittag leffler modules

constructing tilting modules we investigate the structure of infinite dimensional tilting modules over hereditary artin algebras for connected algebras of infinite representation type with grothendieck group of rank n we prove that for each 0 i n 1 there is an infinite dimensional tilting module t i with exactly i pairwise non isomorphic indecomposable finite dimensional direct summands we also show that any stone is a direct summand in a tilting module in the final section we give explicit constructions of infinite dimensional tilting modules over iterated one point extensions

non linear b stability and symmetry preserving return mapping algorithms for plasticity and viscoplasticity a class of second order accurate return mapping algorithms is presented which lead to symmetric algorithmic tangent moduli and contain the classical backward euler return maps as a particular case more importantly it is shown that this class of return maps is contractive relative to the natural norm defined by the complementary helmholz free energy function b stability since the equations of classical plasticity and viscoplasticity are shown to be contractive relative to this natural norm the requirement of b stability furnishes the appropriate notion of unconditionally stable algorithms for plasticity and viscoplasticity the analysis that follows depends critically on the assumption of convexity in particular the models of plasticity and viscoplasticity considered obey the principle of maximum plastic dissipation the proposed algorithms obey the discrete counterpart of this classical principle

products of fuzzy subgroups fuzzy subgroups are different from ordinary subgroups in that one cannot tell with certainty which group elements belong and which do not of course this requires an appropriate modification of the closure property which takes the form of an inequality in this paper a study of products of fuzzy subgroups is begun some results are expected the product of fuzzy subgroups is a fuzzy subgroup products with the same but permuted factors are isomorphic and there is a natural isomorphism from any factor into the product functions called t norms are used to construct products of fuzzy subgroups different t norms yielding different products since a fuzzy subgroup must satisfy an inequality generalizing closure and the strength of that inequality is important some results relate the t norm used in forming the product to the strength of the ensuing inequality when can complicated fuzzy subgroups be expressed as products of simple ones this question is addressed for fuzzy subgroups of finite abelian groups

a canonical form return mapping algorithm for rate independent plasticity a canonical form for the representation of elastic predictor radial return plasticity algorithms is presented which is deceptive in its simplicity iterative application of the corrector is in a form used universally in the solution of ordinary differential equations and substitution of different yield functions and state variable evolution equations is trivial the consistency condition is maintained by an additional constraint equation via what is in effect a lagrange multiplier a consistent material jacobian may be obtained automatically by applying partial elimination to the same set of equations the process is numerical and requires no additional algebraic manipulation to demonstrate the validity of such a simple technique existing apparently more complex formulations are derived through the simple expedient of static condensation as a practical example of the application of the method a standard von mises plasticity model is implemented and results are presented for two standard benchmarks that test quadratic convergence for large increments copyright 2001 john wiley sons ltd

fuzzy cartesian product fuzzy relations and fuzzy functions abstract a new approach to cartesian product relations and functions in fuzzy set theory is established a concept of fuzzy cartesian product is introduced using a suitable lattice a fuzzy relation is then defined as a subset of the fuzzy cartesian product analogously to the crisp case fuzzy equivalence relations are introduced and investigated results corresponding to those on ordinary equivalence relations are proved for fuzzy equivalence relations finally the notion of a fuzzy function is introduced as a special type of fuzzy relations and is then investigated this fuzzy function generalizes zadeh s definition of functions in the fuzzy context

a return mapping algorithm for cyclic viscoplastic constitutive models abstract this paper presents a return mapping algorithm for cyclic viscoplastic constitutive models that include material memory effects the constitutive model is based on multi component forms of kinematic and isotropic hardening variables in conjunction with von mises yield criterion armstrong frederick a f type rules are used to describe the nonlinear evolution of each of the multi component kinematic hardening variables a saturation type exponential rule is used to describe the nonlinear evolution of each of the isotropic hardening variables the concept of memory surface is used to describe the strain range dependent material memory effects that are induced by the prior strain histories in this paper the above class of cyclic viscoplastic constitutive models is formulated within a consistent thermodynamic framework that encompasses the standard generalized materials framework furthermore a complete algorithmic treatment of the above rate dependent constitutive model is also presented for any desired stress or strain constrained configuration subspace a generalized midpoint algorithm is used to integrate the rate constitutive equations the consistent tangent operator is obtained by linearizing the return mapping algorithm and is found to be unsymmetric due to the presence of nonlinear evolution rules for the kinematic hardening variables several numerical examples representing the cyclic hardening and softening behavior transient and stabilized hysteresis behavior and the non fading memory effects of the material are presented these examples demonstrate the accuracy and robustness of the present algorithmic framework for modeling the cyclic viscoplastic behavior of the material

second order accurate integration algorithms for von mises plasticity with a nonlinear kinematic hardening mechanism abstract two second order numerical schemes for von mises plasticity with a combination of linear isotropic and nonlinear kinematic hardening are presented the first scheme is the generalized midpoint integration procedure originally introduced by ortiz and popov in 1985 detailed and applied here to the case of armstrong frederick nonlinear kinematic hardening the second algorithm is based on the constitutive model exponential based reformulation and on the integration procedure previously introduced by the authors in the context of linearly hardening materials there are two main targets to the work firstly we wish to extensively test the generalized midpoint procedure since in the scientific literature no thorough numerical testing campaign has been carried out on this second order algorithm secondly we wish to extend the exponential based integration technique also to nonlinear hardening materials a wide numerical investigation is carried out in order to compare the performance of the two methods

shape design sensitivity analysis of viscoplastic structures abstract design sensitivity analysis of nonlinear viscoplastic structures is developed in the continuum form starting from hamilton s principle constitutive models based on internal variable theory are incorporated in response analysis such models are described by a set of first order nonlinear differential equations with respect to time and some of them allow development of the yield surface the direct variation method is employed to obtain the sensitivity of the response discretization of the analysis and sensitivity equations and computer implementation aspects are discussed the discretized equations are implemented into a computer program and two numerical examples are solved to demonstrate the theory in the numerical examples only material nonlinearity under quasi static loading history is considered and the explicit integration method is employed to integrate the constitutive equations and their design variations the accuracy and efficiency of the developed sensitivity analysis are compared with the central finite difference method cyclic loading and loading rate effects are studied and discussed to show the general applicability of the developed sensitivity formulation

fuzzy hyperrings hv rings based on fuzzy universal sets the aim of this paper is to define and study the concept of a fuzzy hyperring which depends on the concept of a fuzzy universal set a correspondence relation between a fuzzy hyperring based on a fuzzy universal set and both ordinary and fuzzy hyperideal in the sense of davvaz is obtained