an analysis of a new class of integration algorithms for elastoplastic constitutive relations an accuracy analysis of a new class of integration algorithms for finite deformation elastoplastic constitutive relations recently proposed by the authors is carried out in this paper for simplicity attention is confined to infinitesimal deformations the integration rules under consideration fall within the category of return mapping algorithms and follow in a straightforward manner from the theory of operator splitting applied to elastoplastic constitutive relations general rate independent and rate dependent behaviour with plastic hardening or softening associated or non associated flow rules and nonlinear elastic response can be efficiently treated within the present framework isoerror maps are presented which demonstrate the good accuracy properties of the algorithm even for strain increments much larger than the characteristic strains at yielding

group decision making with a fuzzy linguistic majority abstract the determination of solutions in group decision making is considered the point of departure is a collection of individual fuzzy preference relations a solution is derived either directly from the individual fuzzy preference relations or by constructing first a social fuzzy preference relation as opposed to conventional approaches in which a crisp threshold type majority rule is used we employ a fuzzy majority rule specified by a fuzzy linguistic quantifier e g most much more than 50 etc a calculus of linguistically quantified propositions is applied using the fuzzy majority various solution concepts are derived mainly of the type of core minimax opposition set and consensus winner

numerical simulation of martensitic phase transitions in shape memory alloys using an improved integration algorithm the numerical simulation of structures made of shape memory materials is of increasing interest in different fields among others the computation of pipe connectors or medical devices like endoscopic instruments and stents is a challenge in such practical applications the pseudoelastic effect as well as the one way and two way shape memory effects are utilized these material properties are caused by martensitic phase transitions between austenite and martensite in the present contribution a recently proposed constitutive theory is numerically treated in the context of the finite element method this constitutive theory is formulated in the framework of continuum thermomechanics for geometrically linear problems and is able to represent the occurring martensitic phase transitions in shape memory alloys for the numerical integration of the evolution equations the backward euler method is applied in spite of the complexity of the constitutive theory it is shown that an improved integration procedure can be formulated which merely involves the solution of three non linear equations for three scalar valued unknown variables numerical examples show the capability of the proposed model and the improved integration algorithm copyright 2006 john wiley sons ltd

discrete decomposability of the restriction of a_q λ with respect to reductive subgroups ii micro local analysis and asymptotic k support let g c g be real reductive lie groups this paper offers a criterion on the triplet g g ir that the irreducible unitary representation ir of g splits into a discrete sum of irreducible unitary representations of a subgroup g when restricted to g each of finite multiplicity furthermore we shall give an upper estimate of the multiplicity of an irreducible unitary representation of g occurring in wrig

consistent tangent operator for cutting plane algorithm of elasto plasticity abstract the paper presents a derivation of the consistent tangent operator cto for the cutting plane algorithm cpa for a class of plasticity models that are suitable to be integrated using cpa an explicit recursive expression is analytically derived and is updated in each iteration of the cpa integration procedure to yield the final value of the cto when the cpa is converged

numerical implementation of a shape memory alloy thermomechanical constitutive model using return mapping algorithms previous studies by the authors and their co workers show that the structure of equations representing shape memory alloy sma constitutive behaviour can be very similar to those of rate independent plasticity models for example the boyd lagoudas polynomial hardening model has a stress elastic strain constitutive relation that includes the transformation strain as an internal state variable a transformation function determining the onset of phase transformation and an evolution equation for the transformation strain such a structure allows techniques used in rate independent elastoplastic behaviour to be directly applicable to smas in this paper a comprehensive study on the numerical implementation of sma thermomechanical constitutive response using return mapping elastic predictor transformation corrector algorithms is presented the closest point projection return mapping algorithm which is an implicit scheme is given special attention together with the convex cutting plane return mapping algorithm an explicit scheme already presented in an earlier work the closest point algorithm involves relatively large number of tensorial operations than the cutting plane algorithm besides the evaluation of the gradient of the transformation tensor in the flow rule and the inversion of the algorithmic tangent tensor a unified thermomechanical constitutive model which does not take into account reorientation of martensitic variants but unifies several of the existing sma constitutive models is used for implementation remarks on numerical accuracy of both algorithms are given and it is concluded that both algorithms are applicable for this class of sma constitutive models and preference can only be given based on the computational cost copyright 2000 john wiley sons ltd

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

a fuzzy extension of saaty s priority theory we present a fuzzy method for choosing among a number of alternatives under conflicting decision criteria a fuzzy version of saaty s pairwise comparison method 1980 extended by de graan 1980 and lootsma 1981 each ratio expressing the relative significance of a pair of factors is displayed in a matrix from which suitable weights can be extracted since these ratios are essentially fuzzy they express the opinion of a decision maker on the importance of a pair of factors we have adapted the above mentioned method in such a way that decision makers are asked to express their opinions in fuzzy numbers with triangular membership functions we apply the method at two distinct levels first to find fuzzy weights for the decision criteria and second to find fuzzy weights for the alternatives under each of the decision criteria by a suitable combination of these results we obtain fuzzy scores for the alternatives as well as their sensitivities using these fuzzy scores the decision makers should be able to make a choice for one of the alternatives

numerical simulation of thermomechanical behaviours of shape memory alloys via a non linear mesh free galerkin formulation a new computational approach is developed based on the mesh free method for the numerical simulation of shape memory alloys a thermomechanical constitutive model is used to describe the complex material response the incremental displacement based mesh free formulation is constructed in a total lagrangian description by employing the moving least square shape function and rate form of the shape memory alloy constitutive model in the variational equations this mesh free formulation is not only applicable to large deformation problems but also accounts for both stress and thermally induced phase transformation moreover the newly developed mesh free codes can deal with complex loading paths and multiple temperature cycles in numerical simulation the performance of the proposed mesh free scheme for the simulation of shape memory alloys is demonstrated in several numerical examples copyright 2005 john wiley sons ltd

lyapunov exponents estimation for hysteretic systems abstract this article discusses the lyapunov exponent estimation of non linear hysteretic systems by adapting the classical algorithm by wolf and co workers wolf a swift j b swinney h l vastano j a 1985 determining lyapunov exponents from a times series physica d 16 285 317 this algorithm evaluates the divergence of nearby orbits by monitoring a reference trajectory evaluated from the equations of motion of the original hysteretic system and a perturbed trajectory resulting from the integration of the linearized equations of motion the main issue of using this algorithm for non linear rate independent hysteretic systems is related to the procedure of linearization of the equations of motion the present work establishes a procedure of linearization performing a state space split and assuming an equivalent viscous damping in order to represent hysteretic dissipation in the linearized system the dynamical response of a single degree of freedom pseudoelastic shape memory alloy sma oscillator is discussed as an application of the proposed algorithm the restitution force of the oscillator is provided by an sma element described by a rate independent hysteretic thermomechanical constitutive model two different modeling cases are considered for isothermal and non isothermal heat transfer conditions and numerical simulations are performed for both cases the evaluation of the lyapunov exponents shows that the proposed procedure is capable of quantifying chaos capturing the non linear dissipation of hysteretic systems

finite multiplicity theorems for induction and restriction abstract we find upper and lower bounds of the multiplicities of irreducible admissible representations of a semisimple lie group g occurring in the induced representations ind h g from irreducible representations of a closed subgroup h as corollaries we establish geometric criteria for finiteness of the dimension of hom g ind h g induction and of hom h h restriction by means of the real flag variety g p and discover that uniform boundedness property of these multiplicities is independent of real forms and characterized by means of the complex flag variety

fuzzy multi attribute selection among transportation companies using axiomatic design and analytic hierarchy process the basic concept in axiomatic design ad is the existence of design axioms first of these axioms is the independence axiom and the second one is the information axiom information axiom proposes the selection of the best alternative that has minimum information analytic hierarchy process ahp is another multi attribute method which is a decision making method for selecting the best among a set of alternatives given some criteria the method has been extensively applied especially in large scale problems where many criteria must be considered and where the evaluation of alternatives is mostly subjective multi attribute transportation company selection is a very important activity for effective supply chain selection of the best company under determined criteria such as cost time damage loss flexibility and documentation ability using both multi attribute ad and ahp will be realized in this study the fuzzy multiattribute ad approach is also developed and it is compared by one of fuzzy ahp methods in the literature the selection process has been accomplished by aiding a software that includes crisp ad and fuzzy ad

orbital symmetric spaces and finite multiplicity abstract it is proven that any algebraic symmetric space has finite multiplicity the multiplicity is then shown to be bounded provided that is the case for reductive symmetric spaces a widely believed but as yet unproven fact the method of proof involves an amalgamation of the mackey machine and the orbit method a necessary and sufficient orbital condition is also derived for the quasi regular representation of a symmetric space to be irreducible

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

multiplicity one theorems in the local characteristic 0 non archimedean case we consider distributions on gl n 1 which are invariant under the adjoint action of gl n we prove that such distributions are invariant by transposition this implies multiplicity at most one for restrictions from gl n 1 to gl n similar theorems are obtained for orthogonal or unitary groups

matching demanders and suppliers in knowledge service the advancement of knowledge service has enabled the demanders and suppliers to find satisfied cooperation results an optimal match between demanders and suppliers can facilitate continuous improvement and efficiency in knowledge services while selecting suitable matching knowledge demander and supplier pairs is of significance for effective knowledge services an area that has been generally neglected in previous studies this paper reports on a method for effectively matching suitable knowledge service demanders and suppliers in which the expectation levels of attributes given by demanders and suppliers are considered linguistic information is used to describe the demanders and suppliers expectation levels and their actual levels a new matching degree calculation method is proposed which takes account of the fuzzy linguistic information first the matching relationship between the demanders and suppliers is defined then from the principle of axiomatic design ad a method based on fuzzy axiomatic design fad is developed to identify the matching degree between the knowledge demanders and suppliers further a multi objective optimization model is formulated to maximize the overall matching degree of the pairs and to select the optimal matching pairs finally an example illustrates the potential applications of the proposed method the obtained computational process and results clearly demonstrate how optimal matching pairs can be identified for knowledge services demanders and suppliers

a method for group decision making with multi granularity linguistic assessment information this paper proposes a method to solve the group decision making gdm problems with multi granularity linguistic assessment information in the method the multi granularity linguistic information provided by experts is firstly expressed in the form of fuzzy numbers in order to make the collective opinion close to each expert s opinion a linear goal programming model is constructed to integrate the fuzzy assessment information and to directly compute the collective ranking values of alternatives without the need of information transformation then a fuzzy preference relation on the pairwise comparisons of the collective ranking values of alternatives is constructed using the dominance possibility degree of the comparison between the fuzzy numbers by applying a non dominance choice degree to this fuzzy preference relation the ranking of alternatives is determined and the most desirable alternative s is selected an example is used to illustrate the applicability of the proposed method and its advantages

a variational multiscale method for inelasticity application to superelasticity in shape memory alloys this paper presents a variational multiscale method for developing stabilized finite element formulations for small strain inelasticity the multiscale method arises from a decomposition of the displacement field into coarse resolved and fine unresolved scales the resulting finite element formulation allows arbitrary combinations of interpolation functions for the displacement and the pressure fields and thus yields a family of stable and convergent elements specifically equal order interpolations that are easy to implement but violate the celebrated babuska brezzi condition become stable and convergent an important feature of the present method is that it does not lock in the incompressible limit a nonlinear constitutive model for the superelastic behavior of shape memory alloys is integrated in the multiscale formulation numerical tests of the performance of the elements are presented and representative simulations of the superelastic behavior of shape memory alloys are shown 2005 elsevier b v all rights reserved

on the computational significance of the strain space formulation of plasticity theory the strain space and traditional stress space formulations of plasticity theory are compared we show how plasticity theory has been implemented numerically to solve static and dynamic problems and conclude that the numerical loading criteria that have been used for two decades are identical to the strain space loading criteria proposed by naghdi and co workers

efficient algorithms for generalized stable marriage and roommates problems we consider a generalization of the stable roommates problem sr in which preference lists may be partially ordered and forbidden pairs may be present denoted by srpf this includes as a special case a corresponding generalization of the classical stable marriage problem sm denoted by smpf by extending previous work of feder we give a two step reduction from srpf to 2 sat this has many consequences including fast algorithms for a range of problems associated with finding optimal stable matchings and listing all solutions given variants of sr and sm for example given an smpf instance i we show that there exists an o m succinct certificate for the unsolvability of i an o m algorithm for finding all the super stable pairs in i an o m kn algorithm for listing all the super stable matchings in i an o m 1 5 algorithm for finding an egalitarian super stable matching in i and an o m algorithm for finding a minimum regret super stable matching in i where n is the number of men m is the total length of the preference lists and k is the number of super stable matchings in i analogous results apply in the case of srpf

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

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

a sequential selection process in group decision making with a linguistic assessment approach in this paper a sequential selection process in group decision making under linguistic assessments is presented where a set of linguistic preference relations represents individuals preferences a collective linguistic preference is obtained by means of a defined linguistic ordered weighted averaging operator whose weights are chosen according to the concept of fuzzy majority specified by a fuzzy linguistic quantifier then we define the concepts of linguistic non dominance linguistic dominance and strict dominance degrees as parts of the sequential selection process the solution alternative s is obtained by applying these concepts

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 element analysis of the behavior of shape memory alloys and their applications abstract a nonlinear finite element procedure is developed which incorporates a thermodynamically derived constitutive law for shape memory alloy material behavior the constitutive equations include the necessary internal variables to account for the material transformations and are utilized in a one dimensional finite element procedure that captures the unique shape memory alloy responses of pseudoelasticity and of the shape memory effect at all temperatures stress levels and loading conditions detailed material properties for the alloy used are necessary for the analysis the solution of the geometrically and physically nonlinear problem is achieved by application of a newton s method in which a sequence of linear problems is numerically solved due to consistent linearization a quadratic rate of convergence is obtained several test cases are presented to illustrate the potential of the finite element procedure cases simulating the stress strain behavior of a bar of shape memory alloy under simple uniaxial loading as well as restrained recovery responses at different temperatures compare well with experimental and analytical results two further generalized applications are examined the use of a shape memory alloy ring as a pipe connector and eigenfrequency tuning of a composite beam with embedded shape memory wires the results of these analyses correlate well with analytical results and the methodology for use of the finite element procedure in general cases is demonstrated the finite element procedure is thus shown to be a powerful tool for studying various applications of shape memory alloys

a multi variant martensitic phase transformation model formulation and numerical implementation the development of models for shape memory alloys and other materials that undergo martensitic phase transformations has been moving towards a common generalized thermodynamic framework several promising models utilizing single martensitic variants and some with multiple variants have appeared recently in this work we develop a model in a general multi variant framework for single crystals that is based upon lattice correspondence variants and the use of dissipation arguments for the generation of specialized evolution equations the evolution equations that appear are of a unique nature in that not only are the thermodynamic forces restricted in range but so are their kinematic conjugates this unusual situation complicates the discrete time integration of the evolution equations we show that the trial elastic state method that is popular in metal plasticity is inadequate in the present situation and needs to be replaced by a non linear programming problem with a simple geometric interpretation the developed integration methodology is robust and leads to symmetric tangent moduli example computations show the behavior of the model in the pseudoelastic range of particular interest is the fact that the model can predict the generation of habit plane like variants solely from the lattice correspondence variants this is demonstrated through a comparison to the experimental work of shield j mech phys solids 43 1995 869