geometrically exact beam elements and smooth contact schemes for the modeling of fiber based materials and structures abstract this work focuses on finite element formulations for the accurate modeling and efficient simulation of the implicit dynamics of slender fiber or rod like components and their contact interaction when being embedded in complex systems of fiber based materials and structures recently the authors have proposed a novel all angle beam contact abc formulation that combines the advantages of existing point and line contact models in a variationally consistent manner however the abc formulation has so far only been applied in combination with a special torsion free beam model which yields a very simple and efficient finite element formulation but which is restricted to initially straight beams with isotropic cross sections in order to abstain from these restrictions the current work combines the abc formulation with a geometrically exact kirchhoff love beam element formulation that is capable of treating even the most general cases of slender beam problems in terms of initial geometry and external loads while the neglect of shear deformation that is inherent to this formulation has been shown to provide considerable numerical advantages in the range of high beam slenderness ratios alternative shear deformable beam models are required for examples with thick beams for that reason the current contribution additionally proposes a novel geometrically exact beam element based on the simo reissner theory similar to the torsion free and the kirchhoff love beam elements also this simo reissner element is based on a c1 continuous hermite interpolation of the beam centerline which will allow for smooth contact kinematics for this hermitian simo reissner element a consistent spatial convergence behavior as well as the successful avoidance of membrane and shear locking will be demonstrated numerically all in all the combination of the abc formulation with these different beam element variants i e the torsion free element the kirchhoff love element and the simo reissner element results in a very flexible and modular simulation framework that allows to choose the optimal element formulation for any given application in terms of accuracy efficiency and robustness based on several practically relevant examples the different variants are compared numerically and eventually a general recommendation concerning the optimal choice of beam elements is made

objective energy momentum conserving integration for the constrained dynamics of geometrically exact beams in this paper the results in s leyendecker p betsch p steinmann energy conserving integration of constrained hamiltonian systems a comparison of approaches comput mech 33 2004 174 185 are extended to geometrically exact beams the finite element formulation for nonlinear beams in terms of directors providing a framework for the objective description of their dynamics is considered geometrically exact beams are analysed as hamiltonian systems subject to holonomic constraints with a hamiltonian being invariant under the action of so 3 the reparametrisation of the hamiltonian in terms of the invariants of so 3 is perfectly suited for a temporal discretisation which leads to energy momentum conserving integration in this connection the influence of alternative procedures the lagrange multiplier method the penalty method and the augmented lagrange method for the treatment of the constraints is investigated for the example of a beam with concentrated masses 2005 elsevier b v all rights reserved

a generalization of the discrete choquet and sugeno integrals based on a fusion function abstract in this paper we present an approach to generalization of the discrete choquet and sugeno integrals for the choquet integral we replace the product operator joining the values of a capacity m of criteria sets and values of a score vector by a fusion function f satisfying some constraints similarly as was already done for another form of the discrete choquet integral by mesiar et al in 15 for the sugeno integral we use an analogous method of generalization replacing the minimum operator by a fusion function the properties of the obtained functionals c f m and s f m are studied and some examples for particular capacity m and particular fusion function f are given

nonlinearity of the fuzzy integral we prove that the fuzzy integral has some linearity properties only for small classes of fuzzy measures we also show that an extension of this concept to bounded functions as proposed by kandel 2 5 is not well defined in general

on medical diagnosis using possibility measures this paper presents a model of clinical diagnosis in the context of possibility distributions by using b optimal membership functions an expression for automatic diagnosis is formulated for a concrete fuzzy set of symptoms their properties and relation with the composition of fuzzy relations are analyzed by means of a new formulation of fuzzy integrals for additive fuzzy measures a practical case is also analyzed

two integrals and some modified versions critical remarks the aim of this paper is to discuss different constructions of integrals sections 3 and 4 based on decomposable measures section 1 according to the classification of the continuous t conorms in essentially two types namely v and archimedean t conorms there exist mainly two types of integrals namely the constructions of sugeno section 3 and of weber section 4 further constructions corresponding to the archimedean case result to be special cases or not well defined section 4 in all cases a crucial property is some restricted distribution law for the pair with an appropriate operation section 2 some applications shall illustrate the use of the two integrals section 5

frame indifferent beam finite elements based upon the geometrically exact beam theory this paper describes a new beam finite element formulation based upon the geometrically exact beam theory in contrast to many previously proposed beam finite element formulations the present discretization approach retains the frame indifference or objectivity of the underlying beam theory the space interpolation of rotational degrees of freedom is circumvented by the introduction of a reparameterization of the weak form corresponding to the equations of motion of the geometrically exact beam theory copyright 2002 john wiley sons ltd

stochastic convergence uniform integrability and convergence in mean on fuzzy measure spaces the paper deals with the convergence of sequences of measurable functions on fuzzy measure spaces a classical result that relates the uniform integrability plus stochastic convergence with convergence in mean is extended to this case where the additivity property of measures is not required we also investigate the sufficient and necessary conditions that fuzzy measures must satisfy in the dominated convergence theorem

decision theoretic foundations of qualitative possibility theory abstract this paper presents a justification of two qualitative counterparts of the expected utility criterion for decision under uncertainty which only require bounded linearly ordered valuation sets for expressing uncertainty and preferences this is carried out in the style of savage starting with a set of acts equipped with a complete preordering relation conditions on acts are given that imply a possibilistic representation of the decision maker uncertainty in this framework pessimistic i e uncertainty averse as well as optimistic attitudes can be explicitly captured the approach thus proposes an operationally testable description of possibility theory

lower integrals and upper integrals with respect to nonadditive set functions nonadditive set functions have been used as a proper mathematical model for describing the contribution rates as well as their interaction from predictive attributes toward some target in information fusion and data mining a mathematical tool is needed to aggregate contributions from each predictive attribute to the target essentially it is a mapping from a higher dimensional space sample space to a lower dimensional space decision space the mapping of course depends on the nonadditive set function such a tool is generally called an integral due to the nonadditivity of the set function the integral is a nonlinear functional defined on the set of the so called nonnegative measurable functions where each function is a point in the sample space the upper integral the lower integral and the choquet integral are some special types of nonlinear integrals when the set of attributes is finite all nonlinear integrals are generally called indeterminate integrals in this case the upper integral and the lower integral are two extreme specified indeterminate integrals a way for calculating the newly defined integrals is shown in this paper when the universal set the set of attributes is finite recalling the concept of indeterminate integral the value of any specified indeterminate integral of a given function can be expressed as a convex combination of the values of its upper integral and lower integral in such a point of view the inverse problem of the indeterminate integral with respect to a given nonadditive set function is rather easy to be solved

a new type of nonlinear integrals and the computational algorithm in information fusion aggregations with various backgrounds require a variety of integrals to handle these integrals are generally nonlinear since the set functions used are nonadditive in many real problems in this study the set functions considered are nonnegative and vanishing at the empty set they are a class of set functions including fuzzy measures and even imprecise probabilities a new type of nonlinear integrals with respect to such a set function for nonnegative functions is introduced and its primary properties are detailed these type of integrals has a natural explanation and therefore has wide applicability we also show a comparison between the newly introduced nonlinear integral and other nonlinear integrals such as the choquet integral the natural extension in the theory of imprecise probabilities and the common pan integral with a flowchart the algorithm for calculating the integral is given in this paper when the universe of discourse the set of all information sources is finite

human motion tracking with a kinematic parameterization of extremal contours this paper addresses the problem of human motion tracking from multiple image sequences the human body is described by five articulated mechanical chains and human body parts are described by volumetric primitives with curved surfaces if such a surface is observed with a camera an extremal contour appears in the image whenever the surface turns smoothly away from the viewer we describe a method that recovers human motion through a kinematic parameterization of these extremal contours the method exploits the fact that the observed image motion of these contours is a function of both the rigid displacement of the surface and of the relative position and orientation between the viewer and the curved surface first we describe a parameterization of an extremal contour point velocity for the case of developable surfaces second we use the zero reference kinematic representation and we derive an explicit formula that links extremal contour velocities to the angular velocities associated with the kinematic model third we show how the chamfer distance may be used to measure the discrepancy between predicted extremal contours and observed image contours moreover we show how the chamfer distance can be used as a differentiable multi valued function and how the tracker based on this distance can be cast into a continuous non linear optimization framework fourth we describe implementation issues associated with a practical human body tracker that may use an arbitrary number of cameras one great methodological and practical advantage of our method is that it relies neither on model to image nor on image to image point matches in practice we model people with 5 kinematic chains 19 volumetric primitives and 54 degrees of freedom we observe silhouettes in images gathered with several synchronized and calibrated cameras the tracker has been successfully applied to several complex motions gathered at 30 frames second

snakes active contour models a snake is an energy minimizing spline guided by external constraint forces and influenced by image forces that pull it toward features such as lines and edges snakes are active contour models they lock onto nearby edges localizing them accurately scale space continuation can be used to enlarge the capture region surrounding a feature snakes provide a unified account of a number of visual problems including detection of edges lines and subjective contours motion tracking and stereo matching we have used snakes successfully for interactive interpretation in which user imposed constraint forces guide the snake near features of interest

non monotonic fuzzy measures and the choquet integral abstract this paper discusses non monotonic fuzzy measures which are set functions without monotonicity and the choquet integral with respect to non monotonic fuzzy measures a concrete example shows that the choquet integral is meaningful in the case of non monotonic fuzzy measures as well as in the case of ordinary fuzzy measures every comonotonically additive positively homogeneous functional of bounded variation can be represented as a choquet integral with respect to a non monotonic fuzzy measure of bounded variation the space of such functionals is a real banach space isometrically isomorphic to the space of non monotonic fuzzy measures of bounded variation

toward a general theory of fuzzy variables abstract a general framework for a theory is presented that encompasses both statistical uncertainty which falls within the province of probability theory and nonstatistical uncertainty which relates to the concept of a fuzzy set and possibility theory l a zadeh j fuzzy sets 1 1978 3 28 the concept of a fuzzy integral is used to define the expected value of a random variable properties of the fuzzy expectation are stated and a mean value theorem for the fuzzy integral is proved comparisons between the fuzzy and the lebesgue integral are presented after a new concept of dependence is formulated various convergence concepts are defined and their relationships are studied by using a chebyshev like inequality for the fuzzy integral the possibility of using this theory in bayesian estimation with fuzzy prior information is explored

fully measurable grand lebesgue spaces abstract using variable exponents we build a new class of rearrangement invariant banach function spaces independent of the variable lebesgue spaces whose function norm is f ess sup x 0 1 p x x f where p x denotes the norm of the lebesgue space of exponent p x assumed measurable and possibly infinite and is measurable too such class contains some known banach spaces of functions among which are the classical and the grand lebesgue spaces and the exp spaces 0 we analyze the function norm and we prove a boundedness result for the hardy littlewood maximal operator via a hardy type inequality

set valued choquet integrals revisited this paper performs a further investigation on the set valued choquet integral given by jang and kwon fuzzy sets and systems 112 2000 233 some incorrect properties are revised it is pointed out that the definition for convergence of sequence of sets or set valued functions is unreasonable by using the usual kuratowski s convergence some new convergence theorems for the set valued choquet integral are shown meanwhile some other properties are obtained

a finite element approach for the line to line contact interaction of thin beams with arbitrary orientation abstract the objective of this work is the development of a novel finite element formulation describing the contact interaction of slender beams in complex 3d configurations involving arbitrary beam to beam orientations it is shown in a mathematically concise manner that standard beam contact models based on a point wise contact force fail to describe a considerable range of configurations which are however likely to occur in practical applications on the contrary the formulation proposed here models beam to beam contact by means of distributed line forces a procedure that is shown to be applicable for arbitrary geometrical configurations the proposed formulation is based on a gauss point to segment type contact discretization and a penalty regularization of the contact constraint by means of detailed theoretical and numerical investigations it is shown that this approach is more suitable for beam contact than possible alternatives based on mortar type contact discretizations or constraint enforcement by means of lagrange multipliers the proposed formulation is enhanced by a consistently linearized integration interval segmentation avoiding numerical integration across strong discontinuities in combination with a smoothed contact force law and the employed c 1 continuous beam elements this procedure drastically reduces the numerical integration error an essential prerequisite for optimal spatial convergence rates the resulting line to line contact algorithm is supplemented by contact contributions of the beam endpoints which represent boundary minima of the underlying minimal distance problem finally a series of numerical test cases is analyzed in order to investigate the accuracy and consistency of the proposed formulation regarding integration error spatial convergence behavior and resulting contact force distributions for one of these test cases an analytical solution based on the kirchhoff theory of thin rods is derived which can serve as valuable benchmark for the proposed model but also for future beam to beam contact formulations

on the representation of choquet integrals of set valued functions and null sets in this paper we consider the definition of set valued choquet integrals we obtain some properties and the representation of set valued choquet integrals and also we discuss some fundamental relations between null sets and set valued choquet integrals

determining nonnegative monotone set functions based on sugeno s integral an application of genetic algorithms abstract regarding the set of all information sources as the universe of discourse we used a nonnegative monotone set function defined on its power set to describe the importance of each individual information source and their varied combinations such a set function is called an importance measure or a fuzzy measure the sugeno integral with respect to the nonnegative monotone set function possesses many desired properties such as the fuzzy linearity when the set function is fuzzy additive and can be adopted as an aggregation means in information fusion in real problems viewing the sugeno integral as a multi input single output system we use a genetic algorithm to determine the values of the importance measure from the input output data of the system

coherent lower previsions and choquet integrals walley statistical reasoning with imprecise probabilities chapman hall london 1991 has given a helpful general framework of uncertain reasoning which is grounded on a behavioural foundation and extends de finetti s work for some important applications like the expected utility theory it might be a tool alternatively to the techniques of choquet integration therefore this paper tries to clarify the relation between walley s central concept of coherent lower prevision and the choquet integration theory in one direction we deal with the problem to represent coherent lower previsions by choquet integrals and obtain general results using greco s representation theorem another aspect of investigation is to compare walley s concept to define integrals of coherent fuzzy measures the so called natural extensions with choquet integrals we succeed in exploring completely the relationship

on the geometrically exact beam model a consistent effective and simple derivation from three dimensional finite elasticity the goal of the present work is to emphasize some intrinsic features of the three dimensional beam model originally proposed by simo simo j c 1985 a finite strain beam formulation the three dimensional dynamic problem part i comput methods appl mech eng 49 55 70 and to derive the model equations for the general finite deformation case as well as for the finite deformation small strain case in a consistent but simpler way with respect to what it is generally done in the literature

a locking free finite element formulation and reduced models for geometrically exact kirchhoff rods in this work we suggest a locking free geometrically exact finite element formulation incorporating the modes of axial tension torsion and bending of thin kirchhoff beams with arbitrary initial curvatures and cross section shapes the proposed formulation has been designed in order to represent general load cases and three dimensional problem settings in the geometrically nonlinear regime of large deformations from this comprehensive theory we not only derive a general beam model but also several reduced formulations which deliver accurate solutions for special problem classes concerning the beam geometry and the external loads the advantages of these reduced models arise for example in terms of simplified finite element formulations less degrees of freedom per element and consequently a higher computational efficiency of the corresponding numerical models a second core topic of this publication is the treatment of membrane locking which is a locking phenomenon predominantly occurring in highly slender curved structures thus exactly in the prime field of application for kirchhoff theories in order to address the membrane locking effect we will propose a new interpolation strategy for the axial strain field and compare this method with common approaches such as assumed natural strains ans or reduced integration the effectiveness of this method as well as the consistency and accuracy of the general finite element formulation and the reduced beam models will be illustrated with selected numerical examples

studentized dynamical system for robust object tracking this paper describes a studentized dynamical system sds for robust target tracking using a subspace representation dynamical systems ds provide a powerful framework for the probabilistic modeling of temporal sequences visual tracking problems are often cast as a sequential inference problem within the ds framework and a compact way to model the observation distributions i e object appearances is through probabilistic principal component analysis ppca ppca is a classic gaussian based subspace representation method and a popular tool for appearance modeling although gaussian density has theoretically nice properties resulting in models that are always tractable they are also severely limited in practical settings one of the central issues in the use of ppca for target appearance modeling is that it is very sensitive to outliers the gaussian density has a very light tail while real world data with outliers exhibit heavy tails recently more heavy tailed distributions e g student s t distribution have been introduced to increase the robustness of the original ppca we propose to augment the traditional target tracking ds by adding a set of auxiliary latent variables to adjust the shape of the observation distribution we show that by carefully choosing the probability density of these auxiliary latent variables a more robust observation distribution can be obtained with tails heavier than gaussian numerical experiments verify that the proposed sds has a better capability to handle considerable amount of outlier noise and an improved tracking performance over ds with a gaussian based observation model

on a multiplication and a theory of integration for belief and plausibility functions abstract belief and plausibility functions have been introduced as generalizations of probability measures which abandon the axiom of additivity it turns out that elementwise multiplication is a binary operation on the set of belief functions if the set functions of the type considered here are defined on a locally compact and separable space x a theorem by choquet ensures that they can be represented by a probability measure on the space containing the closed subsets of x the so called basic probability assignment this is basic for defining two new types of integrals one of them may be used to measure the degree of non additivity of the belief or plausibility function the other one is a generalization of the lebesgue integral the latter is compared with choquet s and sugeno s integrals for non additive set functions

some applications of the study of the image of a fuzzy number in this paper we present a characterization of the image of a fuzzy number in terms of the extremes of its level sets then we deduce some consequences we show some relationships between the image of two fuzzy numbers and the images of their usual operations and it is proved that the continuity of some fuzzy numbers is preserved under the usual operations as applications we introduce a fuzzy regression model involving a parametric family of fuzzy semidistances between fuzzy numbers with finite image and an ordering process of fuzzy numbers with compact support that satisfies specificity type properties

optimal approach for fast object template matching this paper proposes a novel algorithm for an optimal reduction of object description for object matching purposes our aim is to decrease the computation needs by considering simplified objects thus reducing the number of pixels involved in the matching process we develop the appropriate theoretical background based on centroidal voronoi tessellations its use within the chamfer matching framework is also discussed we present experimental results regarding the performance of this approach for 2 d contour and region like object matching as a special case we investigate how the snake based representation of target objects can be employed in chamfer matching the experimental results concern the use of object part matching for recognizing humans and show how the proposed simplification leads to valid replacements of the original templates

a bayesian exemplar based approach to hierarchical shape matching this paper presents a novel probabilistic approach to hierarchical exemplar based shape matching no feature correspondence is needed among exemplars just a suitable pairwise similarity measure the approach uses a template tree to efficiently represent and match the variety of shape exemplars the tree is generated offline by a bottom up clustering approach using stochastic optimization online matching involves a simultaneous coarse to fine approach over the template tree and over the transformation parameters the main contribution of this paper is a bayesian model to estimate the a posteriori probability of the object class after a certain match at a node of the tree this model takes into account object scale and saliency and allows for a principled setting of the matching thresholds such that unpromising paths in the tree traversal process are eliminated early on the proposed approach was tested in a variety of application domains here results are presented on one of the more challenging domains real time pedestrian detection from a moving vehicle a significant speed up is obtained when comparing the proposed probabilistic matching approach with a manually tuned nonprobabilistic variant both utilizing the same template tree structure

probabilistic tracking with exemplars in a metric space a new exemplar based probabilistic paradigm for visual tracking is presented probabilistic mechanisms are attractive because they handle fusion of information especially temporal fusion in a principled manner exemplars are selected representatives of raw training data used here to represent probabilistic mixture distributions of object configurations their use avoids tedious hand construction of object models and problems with changes of topology using exemplars in place of a parameterized model poses several challenges addressed here with what we call the metric mixture m2 approach which has a number of attractions principally it provides alternatives to standard learning algorithms by allowing the use of metrics that are not embedded in a vector space secondly it uses a noise model that is learned from training data lastly it eliminates any need for an assumption of probabilistic pixelwise independence experiments demonstrate the effectiveness of the m2 model in two domains tracking walking people using chamfer distances on binary edge images and tracking mouth movements by means of a shuffle distance

fuzzy sets as a basis for a theory of possibility the theory of possibility described in this paper is related to the theory of fuzzy sets by defining the concept of a possibility distribution as a fuzzy restriction which acts as an elastic constraint on the values that may be assigned to a variable more specifically if f is a fuzzy subset of a universe of discourse u u which is characterized by its membership function f then a proposition of the form x is f where x is a variable taking values in u induces a possibility distribution tx which equates the possibility of x taking the value u to f u the compatibility of u with f in this way x becomes a fuzzy variable which is associated with the possibility distribution tx in much the same way as a random variable is associated with a probability distribution in general a variable may be associated both with a possibility distribution and a probability distribution with the weak connection between the two expressed as the possibility probability consistency principle a thesis advanced in this paper is that the imprecision that is intrinsic in natural languages is in the main possibilistic rather than probabilistic in nature thus by employing the concept of a possibility distribution a proposition p in a natural language may be translated into a procedure which computes the probability distribution of a set of attributes which are implied by p several types of conditional translation rules are discussed and in particular a translation rule for propositions of the form x is f is possible where is a number in the interval 0 1 is formulated and illustrated by examples

some properties of choquet integrals of set valued functions abstract in this paper we will define choquet integrals of set valued functions then we show some properties of choquet integrals of set valued functions

active appearance models we describe a new method of matching statistical models of appearance to images a set of model parameters control modes of shape and gray level variation learned from a training set we construct an efficient iterative matching algorithm by learning the relationship between perturbations in the model parameters and the induced image errors

new axiomatisations of discrete quantitative and qualitative possibilistic integrals necessity resp possibility measures are very simple min decomposable resp max decomposable representations of epistemic uncertainty due to incomplete knowledge they can be used in both quantitative and qualitative settings in the present work we revisit choquet and sugeno integrals as criteria for decision under uncertainty and propose new axioms when uncertainty is representable in possibility theory first a characterization of choquet integral with respect to a possibility or a necessity measure is proposed we respectively add an optimism or a pessimism axiom to the axioms of the choquet integral with respect to a general capacity this new axiom enforces the maxitivity or the minitivity of the capacity without requiring the same property for the functional it essentially assumes that the decision maker preferences only reflect the plausibility ordering between states of nature the obtained pessimistic resp optimistic criterion is an average maximin resp maximax criterion of wald across cuts of a possibility distribution on the state space the additional axiom can be also used in the axiomatic approach to sugeno integral and generalized forms thereof to justify possibility and necessity measures the axiomatization of these criteria for decision under uncertainty in the setting of preference relations among acts is also discussed we show that the new axiom justifying possibilistic choquet integrals can be expressed in this setting in the case of sugeno integral we correct a characterization proof for an existing set of axioms on acts and study an alternative set of axioms based on the idea of non compensation

fuzzy integrals and conditional fuzzy measures we introduce a fuzzy integral for fuzzy events with respect to l additive fuzzy measures this integral is the canonical generalization of the lehesgue integral a radon nikodym like theorem is used to give the definition of the conditional fuzziness

theory and numerics of three dimensional beams with elastoplastic material behaviour a theory of space curved beams with arbitrary cross sections and an associated finite element formulation is presented within the present beam theory the reference point the centroid the centre of shear and the loading point are arbitrary points of the cross section the beam strains are based on a kinematic assumption where torsion warping deformation is included each node of the derived finite element possesses seven degrees of freedom the update of the rotational parameters at the finite element nodes is achieved in an additive way applying the isoparametric concept the kinematic quantities are approximated using lagrangian interpolation functions since the reference curve lies arbitrarily with respect to the centroid the developed element can be used to discretize eccentric stiffener of shells due to the implemented constitutive equations for elastoplastic material behaviour the element can be used to evaluate the load carrying capacity of beam structures copyright 2000 john wiley sons ltd

characterization and comparison of sugeno and choquet integrals abstract starting from the concept of equiordered functions we characterize two types of fuzzy integrals that can be defined on any kind of fuzzy measure sugeno and choquet integrals the characterization theorems that we obtain allow us to carry out a comparative study of these two fuzzy integrals pointing out their formal similarities and their conceptual differences

monotone set functions defined by choquet integral abstract given a nonnegative monotone set function and a nonnegative measurable function on a measurable space the choquet integral determines a new nonnegative monotone set function that is absolutely continuous with respect to the original one in a generalized sense for monotone set functions this new set function preserves almost all desirable structural characteristics of the original monotone set function such as continuity subadditivity superadditivity null additivity converse null additivity autocontinuity converse autocontinuity uniform autocontinuity uniform converse autocontinuity and fuzzy multiplicativity such a construction is a useful method to define sound fuzzy measures in various applications

director based beam finite elements relying on the geometrically exact beam theory formulated in skew coordinates summary in the present work a new director based finite element formulation for geometrically exact beams is proposed the new beam finite element exhibits drastically improved numerical performance when compared with the previously developed director based formulations this improvement is accomplished by adjusting the underlying variational beam formulation to the specific features of the director interpolation in particular the present approach does not rely on the assumption of an orthonormal director frame the excellent performance of the new approach is illustrated with representative numerical examples copyright 2013 john wiley sons ltd

a unified approach for beam to beam contact abstract existing beam contact formulations can be categorized in point to point contact models that consider a discrete contact force at the closest point of the beams and line to line contact models that assume distributed contact forces in this work it will be shown that line contact formulations applied to slender beams provide accurate and robust mechanical models in the range of small contact angles whereas the computational efficiency considerably decreases with increasing contact angles on the other hand point contact formulations serve as sufficiently accurate and very efficient models in the regime of large contact angles while they are not applicable for small contact angles as a consequence of non unique closest point projections in order to combine the advantages of these basic formulations a novel all angle beam contact abc formulation is developed that applies a point contact formulation in the range of large contact angles and a recently developed line contact formulation in the range of small contact angles the two being smoothly connected by means of a variationally consistent model transition based on a stringent analysis two different transition laws are investigated optimal algorithmic parameters are suggested and conservation of linear momentum angular momentum and total energy is shown all configuration dependent quantities within the point the line and the transition contact regime are consistently linearized thus allowing for their application within implicit time integration schemes furthermore a step size control of the nonlinear solution scheme is proposed that allows for displacement increments per time step that exceed the order of magnitude of the beam cross section radius for many standard beam to beam contact algorithms this is the typical limitation concerning possible time step sizes especially when considering high beam slenderness ratios finally an efficient two stage contact search based on dynamically adapted search segments is proposed this algorithm yields in a tight set of potential contact pairs and enables a subdivision into potential point and potential line contact pairs which is essential in order to fully exploit the efficiency potential of the proposed contact formulation a series of numerical test cases is analyzed in order to verify the accuracy and consistency of the proposed contact model transition regarding contact force distributions and conservation properties but also for quantifying the efficiency gains as compared to standard beam contact formulations

representation of fuzzy measures through probabilities abstract in this paper we develop a method to study fuzzy measures associating certain sets of probabilities to them this development is based on the consideration of one property of a fuzzy integral called monotone expectation some results about the monotone expectation in relation to associated probabilities are also obtained

axiomatizations of lovasz extensions of pseudo boolean functions three important properties in aggregation theory are investigated namely horizontal min additivity horizontal max additivity and comonotonic additivity which are defined by certain relaxations of the cauchy functional equation in several variables we show that these properties are equivalent and we completely describe the functions characterized by them by adding some regularity conditions these functions coincide with the lovasz extensions vanishing at the origin which subsume the discrete choquet integrals we also propose a simultaneous generalization of horizontal min additivity and horizontal max additivity called horizontal median additivity and we describe the corresponding function class additional conditions then reduce this class to that of symmetric lovasz extensions which includes the discrete symmetric choquet integrals

two families of fuzzy integrals abstract in this paper we present two definitions of fuzzy integrals arising from the t seminorm and the t semiconorm concepts we show that sugeno s fuzzy integral is a particular case of them and we study their principal properties finally we suggest some applications of these results

aggregation functions means this two part state of the art overview on aggregation theory summarizes the essential information concerning aggregation issues an overview of aggregation properties is given including the basic classification on aggregation functions in this first part the stress is put on means i e averaging aggregation functions both with fixed arity n ary means and with multiple arities extended means

a bayesian approach to dynamic contours through stochastic sampling and simulated annealing in many applications of image analysis simply connected objects are to be located in noisy images during the last 5 6 years active contour models have become popular for finding the contours of such objects connected to these models are iterative algorithms for finding the minimizing energy curves making the curves behave dynamically through the iterations these approaches do however have several disadvantages the numerical algorithms that are in use constrain the models that can be used furthermore in many cases only local minima can be achieved in this paper the author discusses a method for curve detection based on a fully bayesian approach a model for image contours which allows the number of nodes on the contours to vary is introduced iterative algorithms based on stochastic sampling is constructed which make it possible to simulate samples from the posterior distribution making estimates and uncertainty measures of specific quantities available further simulated annealing schemes making the curve move dynamically towards the global minimum energy configuration are presented in theory no restrictions on the models are made in practice however computational aspects must be taken into consideration when choosing the models much more general models than the one used for active contours may however be applied the approach is applied to ultrasound images of the left ventricle and to magnetic resonance images of the human brain and show promising results

indeterminate integrals with respect to nonadditive measures recently nonadditive set functions have been used in information fusion and data mining to describe the interaction among the predictive attributes in this case replacing the traditional weighted average or more generally the linear mapping from a higher dimensional space to a one dimensional space relevant nonlinear integrals should be used as the aggregation tool to express how the objective attribute depends on predictive attributes several different types of nonlinear integral such as the choquet integral and the wang integral have been discussed in literature in these models the objective attribute is the integral while the predictive attributes are the integrand in this paper a new concept of indeterminate integral is introduced when the universe of discourse is finite it is a family of integrals including nonlinear integrals mentioned above and therefore possesses a large adaptability as a new aggregation tool each specified type of indeterminate integral can be obtained from the family of indeterminate integrals by specifying a decomposition of the integrand such a new aggregation tool can be used in information fusion and data mining as well as in expert systems

on the use of geometrically exact shells in a conserving framework for flexible multibody dynamics abstract the present work deals with the design of energy momentum conserving schemes for flexible multibody dynamics the proposed approach is based on nonlinear finite element methods for the space discretization of flexible bodies in particular the focus is on geometrically exact shells relying on reissner mindlin kinematics it is shown that the equations of motion pertaining to the semi discrete shell formulation can be written in the form of differential algebraic equations daes the daes provide a uniform framework for a rotationless description of flexible multibody dynamics the use of rotational parameters is circumvented throughout the discretization process in space and time the rotationless description facilitates the straightforward incorporation of geometrically exact shells and beams into a multibody framework in addition to that the advocated approach makes possible the design of a uniform energy momentum conserving time stepping scheme for general multibody systems numerical examples demonstrate the excellent numerical stability properties of the present scheme moreover comparison is made with more traditional formulations based on rotational parameters

an objective finite element approximation of the kinematics of geometrically exact rods and its use in the formulation of an energy momentum conserving scheme in dynamics we present in this paper a new finite element formulation of geometrically exact rod models in the three dimensional dynamic elastic range the proposed formulation leads to an objective or frame indifferent under superposed rigid body motions approximation of the strain measures of the rod involving finite rotations of the director frame in contrast with some existing formulations this goal is accomplished through a direct finite element interpolation of the director fields defining the motion of the rod s cross section furthermore the proposed framework allows the development of time stepping algorithms that preserve the conservation laws of the underlying continuum hamiltonian system the conservation laws of linear and angular momenta are inherited by construction leading to an improved approximation of the rod s dynamics several numerical simulations are presented illustrating these properties copyright 2002 john wiley sons ltd

an interpretation of fuzzy measures and the choquet integral as an integral with respect to a fuzzy measure abstract in this paper the non additivity of sugeno s fuzzy measures is interpreted in terms of addition and the rationality of the choquet integral is discussed it is pointed out that a fuzzy measure on a set x expresses the interaction between the subsets of x and can be represented by an additive measure it is shown through concrete examples that the choquet integral is reasonable as an integral with respect to a fuzzy measure it is also found that the choquet integral is closely related with the representation of a fuzzy measure

fuzzy measures and measures of fuzziness abstract in this paper the fuzzy integral defined by z x wang fuzzy math wuhan china in press which is different from that defined by m sugeno theory of fuzzy integrals and its applications ph d tokyo inst of technology 1974 is further considered and it is shown that the fuzzy measures of ordinary sets and fuzzy sets can be determined by each other summing up the results on the measure of fuzziness by a deluca and s a termini inform and control 20 1972 301 312 z x wang op cit and r r yager internat j gen systems 5 1979 221 229 inform and control 44 1980 236 260 the axioms for measures of fuzziness are given furthermore as an application of the furry integrals a measure of fuzziness is defined inversely it is proven that a measure of fuzziness satisfying some conditions can surely be expressed as a fuzzy integral with respect to some fuzzy measure

convergence properties of the monotone expectation and its application to the extension of fuzzy measures we define a functional on fuzzy measures called monotone expectation based on choquet s integral operator and we study its convergence properties the monotone expectation is used to extend fuzzy measures to fuzzy subsets also sugeno s bound for the difference between his integral and the mathematical expectation is generalized