fuzzy measures on metric spaces abstract the aim of the present paper is to study the regularity and tightness properties of fuzzy measures on metric spaces among other results we shall give lusin s theorem and egoroff s theorem we shall also prove the singleton characterization of atom of fuzzy measure and an algorithm to evaluate the fuzzy integrals of non negative measurable functions over an atom and a union of finite disjoint atoms

regular non additive measure and choquet integral the regular non additive measure is defined it is shown that the choquet integral of a choquet integrable function can be approximated by the integral of a continuous function with compact support

on the equality of integrals considering a finite space x several necessary conditions and one rather general sufficient condition describing when the choquet integral coincides with the pan integral with respect to the standard arithmetic operations are shown these conditions are characterized by using the minimal atoms of monotone measure under the introduced constraints the calculation of these coinciding two integrals is also given

regularity aspects of non additive set multifunctions abstract in this paper continuity properties of set multifunctions such as regularity and continuity from above and below as well as others are introduced by way of a wijsman topology some of the relationships between them are established different examples counterexamples and applications are provided

the alexandroff theorem for riesz space valued non additive measures the alexandroff theorem for a compact non additive measure with values in a riesz space is still valid for the following two cases one is the case that the measure is autocontinuous and the riesz space has the weak asymptotic egoroff property and the other is the case that the measure is uniformly autocontinuous and the riesz space is weakly distributive a close connection between regularity and continuity of non additive measures is also given

the range of null additive fuzzy and non fuzzy measures abstract in this paper a wide class of non additive set functions is investigated for finite null additive fuzzy and non fuzzy measures saks decomposition type theorem theorem on darboux property and lyapunov s type theorems are proved

the curved beam deep arch finite ring element revisited an attempt is made to understand the errors arising in curved finite elements which undergo both flexural and membrane deformation it is shown that with elements of finite size i e a practical level of discretization at which reasonably accurate results can be expected there can be errors of a special nature that arise because the membrane strain fields are not consistently interpolated with terms from the two independent field functions that characterize such a problem these lead to errors described here as of the second kind and a physical phenomenon called membrane locking it seems possible to determine optimal integration rules that will allow the extensional deformation of a curved beam deep arch finite ring element to be modelled by independently chosen low order polynomial functions and which will recover the inextensional case in the penalty limit of extreme thinness without spurious locking constraints what is emphasized is that the choice of shape functions or subsequent operations to determine the discretized functionals must consistently model the physical requirements the problem imposes on the field variables

lebesgue and saks decompositions of σ finite fuzzy measures two kinds of absolute continuity of fuzzy measures are distinguished and relations between them are established the scope of fuzzy measures under our consideration is limited in a family of those that are finite and absolute continuous with respect to a finite autocontinuous fuzzy measure under this restriction lebesgue decomposition and saks decomposition are proved

continuity and compactness of the indirect product of two non additive measures let x and y be non empty sets e a field of subsets of x and f a field of subsets of y then every uniformly autocontinuous indirect product of two non additive measures m on e and n on f is continuous on the product field generated by e and f whenever m is continuous and n is compact a similar result holds for the compactness of indirect product measures

some sufficient optimality conditions in nonsmooth analysis in this paper we study some second order conditions that may be added to the first order nessessary optimality condition 0 in partial p f bar x with partial p f denoting the proximal subdifferential in order to obtain a sufficient condition for a strict local minimum for extended real valued nonsmooth functions three different types of second order conditions are investigated all based on a different second order subdifferential namely the subhessian the graphical derivative and the contingent coderivative to the proximal subdifferential

user s guide to viscosity solutions of second order partial differential equations the notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems existence theorems and theorems about continuous dependence may now be proved by very efficient and striking arguments the range of important applications of these results is enormous this article is a self contained exposition of the basic theory of viscosity solutions

order continuous of monotone set function and convergence of measurable functions sequence in this paper we introduce the concept of strongly order continuity of a set function and use it to investigate the convergence of measurable functions sequence and of integral sequence on fuzzy measure space several equivalent conditions of strongly order continuity are presented it is shown that a necessary and sufficient condition that lebesgue s theorem remains valid for a monotone set function is that the set function possesses strongly order continuity

lusin s theorem on monotone measure spaces in this paper a kind of regularity of monotone measures is shown by using the pseudometric generating property of set function for short p g p and an equivalence condition for egoroff s theorem lusin s theorem which is well known in classical measure theory is generalized to monotone measure spaces the continuity from above and below of set functions is not required in the discussions therefore the previous results obtained by jiang et al are generalized an approximation of measurable functions by continuous functions on monotone measure spaces is presented

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

on finite element implementation of geometrically nonlinear reissner s beam theory three dimensional curved beam elements abstract finite element implementation of the three dimensional finite strain beam theory of reissner is considered in this work in contrast with some earlier works on the subject discussed here are the beam elements whose reference axes are arbitrary space curved lines we have shown that an improved representation of curved reference geometry significantly increases the accuracy of the results however it also makes the choice of non locking finite element interpolations somewhat more delicate a hierarchical displacement interpolation proposed here is proved to be capable of eliminating both shear and membrane locking phenomena a very satisfying non locking performance is demonstrated for a set of problems in nonlinear elasto statics

reduced integration and the shear flexible beam element the timoshenko beam element is studied in an investigation of shear locking in the development of c 0 continuous elements using shear flexible or penalty function type formulations a penalty type argument is used to degenerate thick elements to thin elements and the various approximations of the shear related energy terms act as different types of constraints depending on the formulation two types of constraints may emerge which are classified as true or spurious formulations that ensure only true constraints in the extreme penalty limit cases display superior performance in the thick element situation the argument is extended to a shallow curved timoshenko beam and another mechanism inplane locking arises if all energy terms corresponding to the membrane energy are exactly integrated

a three node mindlin plate element with improved transverse shear abstract a displacement methodology for mindlin elements recently employed in the development of an efficient four node quadrilateral min4 is the basis for a three node explicitly integrated triangular element min3 the approach herein referred to as anisoparametric is founded upon two kinematic requirements that are auxiliary to the standard convergence criteria the initial complete quadratic deflection field is constrained by continuous shear edge constraints to achieve an isoparametric like three node configuration much success of the element is due to an innovative shear correction factor concept several numerical experiments are performed in the linear elasto static regime to ascertain the element performance

atoms of weakly null additive monotone measures and integrals in this paper we prove some properties of atoms of weakly null additive monotone measures by using the regularity and weak null additivity a sin gleton characterization of atoms of monotone measures on a metric space is shown it is a generalization of previous results obtained by pap the calculation of the sugeno integral and the choquet integral over an atom is also presented respectively similar results for recently introduced universal integral are also given following these results it is shown that the sugeno integral and the choquet integral over an atom of monotone measure is maxitive linear and standard linear respectively convergence theorems for the sugeno integral and the choquet integral over an atom of a monotone measure are also shown

finite element analysis of linear and non linear planar deformations of elastic initially curved beams reference epfl article 102719view record in web of science record created on 2007 04 23 modified on 2016 08 08

stress resultant geometrically non linear shell theory with drilling rotations part iii linearized kinematics a consistent formulation of the geometrically linear shell theory with drilling rotations is obtained by the consistent linearization of the geometrically non linear shell theory considered in parts i and ii of this work it was also shown that the same formulation can be recovered by linearizing the governing variational principle for the three dimensional geometrically non linear continuum with independent rotation field in the finite element implementation of the presented shell theory relying on the modified method of incompatible modes we were able to construct a four node shell element which delivers a very high level performance in order to simplify finite element implementation a shallow reference configuration is assumed over each shell finite element this approach does not impair the element performance for the present four node element the results obtained herein match those obtained with the state of the art implementations based on the classical shell theory over the complete set of standard benchmark problems

a special class of fuzzy measures choquet integral and applications abstract we model a space of agents as a product space x x 0 1 and discuss the choquet integral with respect to a fuzzy measure on this space we introduce a fubini like and a lyapunov like theorems and based on these results core of economy and walras equilibria are studied

invariant hermitian finite elements for thin kirchhoff rods i the linear plane case abstract the objective of this work is to develop finite elements for the simulation of thin kirchhoff rods that is rods where the influence of transverse shear strain can be neglected leading to governing equations that require c 1 continuous finite element interpolations we start in this paper with the formulation of new finite elements for the infinitesimal plane deformations of otherwise generally curved rods addressing in particular the lack of invariance observed in related traditional treatments of plane arches by non invariance we mean that the classical rigid body modes of translations and infinitesimal rotations of the underlying structural theory lead to non zero strains in the element an effect sometimes referred to as self straining this phenomenon occurs in curved configurations of the elements and in the infinitesimal setting of interest in this paper it results in the elements stiffness matrix not to exhibit the correct zero energy modes associated with these physical rigid body motions as a consequence the basic equilibrium relations of balance of forces and moments are not satisfied for the associated nodal forces and moments in non invariant finite elements in this context we propose a new framework for the formulation of c 1 continuous finite elements based on hermitian shape functions that do lead to the satisfaction of this fundamental invariance property accounting fully for the rod s curvature and associated kirchhoff s kinematics in contrast to common straight framework element approximations based on the simplified euler bernoulli beam kinematics the formulation relies crucially on a consistent treatment of the kinematics and the assumed interpolation of the rods geometry an additional assumed strain treatment is considered to avoid limitations of membrane locking complete rigorous analyses and several numerical simulations are presented to prove and illustrate the properties and performance of the newly proposed finite element methods

a two node beam element including transverse shear and transverse normal deformations a variational higher order theory for bending and stretching of linearly elastic orthotropic beams including the deformations due to transverse shearing and stretching of the transverse normal fibre is presented the theory assumes a linear distribution for the longitudinal displacement and a parabolic variation of the transverse displacement across the thickness additionally independent expansions are introduced for the through thickness displacement gradients with the requirement of a least square compatibility for the transverse strains and the satisfaction of exact stress boundary conditions at the top bottom beam surfaces the theory is shown to be well suited for finite element development requiring simple c0 and c 1 continuous displacement interpolation fields to demonstrate the computational utility of the theory a simple two node stretching bending finite element is formulated the analytic and finite element results are obtained for a simple bending problem for which an exact elasticity solution is available it is shown that the inclusion of the transverse normal deformation in the present theory enables improved displacement strain and stress predictions particularly in the analysis of deep beams

analytical and numerical results for vibration analysis of multi stepped and multi damaged circular arches this paper investigates the in plane linear dynamic behaviour of multi stepped and multi damaged circular arches under different boundary conditions cracked cross sections are modelled as massless elastic rotational hinges in damaged configuration cracks can be located both at the interface between two adjacent portions as well as inside the portion itself for each arch portion bounded by two cracks the differential equations of motion have been established considering axial extension transverse shear effects and rotatory inertia the equilibrium equations of arch portions are combined in the coupled fundamental system in terms of radial displacement tangential displacement and rotation analytical and numerical solutions for multi stepped arches in undamaged as well as in damaged configurations are proposed the analytical solution is based on the euler characteristic exponent procedure involving the roots of characteristic polynomials while the numerical method is focused on the generalized differential quadrature gdq method and the generalized differential quadrature element gdqe technique numerical results are shown in terms of the first 10 analytical and numerical frequencies of multi stepped and multi damaged arches with different boundary conditions finally convergence and stability characteristics of the gdqe procedure are investigated the convergence rate of the natural frequencies is shown to be very fast and the stability of the numerical procedure is very good

atoms of fuzzy measures and fuzzy integrals abstract some analytical properties of sugeno s fuzzy measures especially of atoms of fuzzy measures are investigated a fuzzy integral of riemann type is defined through atoms and it is proved that a continuous function is fuzzy integrable in the sense of riemann and has the same integral as that of sugeno

on the regularity of the fuzzy measure on metric fuzzy measure spaces abstract in this paper the concept of the regular fuzzy measure on metric spaces is introduced some of its properties are discussed and lusin s theorem is shown in addition a condition for which a uniformly autocontinuous set function is a fuzzy measure is given

a universal integral as common frame for choquet and sugeno integral the choquet and the sugeno integral provide a useful tool in many problems in engineering and social choice where the aggregation of data is required however their applicability is restricted because of the special operations used in the construction of these integrals therefore we provide a concept of integrals generalizing both the choquet and the sugeno case for functions with values in the nonnegative real numbers universal integrals are introduced and investigated which can be defined on arbitrary measurable spaces and for arbitrary monotone measures for a fixed pseudo multiplication on the nonnegative real numbers the smallest and the greatest universal integrals are given finally another construction method for obtaining universal integrals is introduced and the restriction to the unit interval i e to fuzzy integrals is considered

locking free curved beam element based on curvature the formulation of a curved beam element with 3 nodes for curvature to eliminate the shear membrane locking phenomenon is presented the element is based on curvature so that it may represent the bending energy fully and the shear membrane strain energy is incorporated into the formulation by the equilibrium equations to deal with general boundary conditions a transformation matrix between nodal curvature and nodal displacement vector is introduced several examples are presented in order to verify the element formulation and its analytical capability the solutions obtained reveal that the element describes the curved beam behaviour quite correctly and efficiently showing no locking phenomena and that it is also applicable to the analysis of both thin and thick curved beams

super quantum measures on effect algebras with the riesz decomposition properties we give one basis of the space of super quantum measures on finite effect algebras with the riesz decomposition properties rdp for short then we prove that the super quantum measures and quantum interference functions on finite effect algebras with the rdp are determined each other at last we investigate the relationships between the super quantum measures and the diagonally positive signed measures on finite effect algebras with the rdp in detail

a study of tilt stable optimality and sufficient conditions abstract recent results by eberhard et al 2006 4 and eberhard and wenczel 2009 3 on the interaction of single and double envelope operations of nonsmooth functions and their interaction with second order derivations have been used to study tilt stability of local minima this continues the study begun by poliquin and rockafellar 1998 1 but now armed with new tools we are able to make some new observations we observe that tilt stability entails a local density within the graph of the proximal subderivative of strict local minima order two of the tilted function indeed it also entails the strict local minimality order two of the tilt stable local minimum itself for prox regular subdifferentially continuous functions this density property characterises tilt stability

an improved treatment of transverse shear in the mindlin type four node quadrilateral element abstract an improved displacement methodology based on mindlin theory is developed and applied to a four node twelve degrees of freedom quadrilateral element special attention is directed toward enhancement of the transverse shear energy representation particularly a non uniform order kinematic interpolation scheme is accompanied by what is termed element appropriate shear correction factors the element matrices are consistently derived from hamilton s variational principle using exact numerical integration throughout the element stiffness matrix possesses correct rank and is well conditioned over the entire mindlin theory range of thickness to length ratios exceptionally good element performance is demonstrated by solutions to a set of static and vibrational problems

choquet like integrals abstract integrals based on a pseudo addition and a pseudo multiplication with properties similar to those of the choquet and the sugeno integral respectively are introduced the structure of convenient pseudo arithmetical operations leading to a choquet like integral is studied

mixed models and reduced selective integration displacement models for nonlinear analysis of curved beams simple mixed models are developed for the geometrically nonlinear analysis of deep arches a total lagrangian description of the arch deformation is used and the analytical formulation is based on a form of the nonlinear deep arch theory with the effects of transverse shear deformation included the fundamental unknowns consist of the six internal forces and generalized displacements of the arch and the element characteristic arrays are obtained by using hellinger reissner mixed variational principle the polynomial interpolation functions used in approximating the forces are one degree lower than those used for approximating the displacements and the forces are discontinuous at the interelement boundaries the equivalence between the mixed models developed herein and displacement models based on reduced integration of both the transverse shear and extensional energy terms is discussed the advantages of mixed models over equivalent displacement models are outlined numerical results are presented to demonstrate the high accuracy and effectiveness of the mixed models developed and compare their performance with other mixed models reported in the literature

necessary and sufficient conditions for isolated local minima of nonsmooth functions we consider the mathematical programming problem find inf f x mid x in c where f is an arbitrary extended real valued function and c a subset of a finite dimensional space we give necessary and sufficient optimality conditions for this problem generalizing previous results of a auslendex this journal 22 1984 pp 239 254

relationship among continuity conditions and null additivity conditions in non additive measure theory the paper shows all the implication relationship among six continuity conditions and two null additivity conditions with respect to non additive measures the six continuity conditions are continuity from above order continuity strong order continuity exhaustivity continuity from below and null continuity and the two null additivity conditions are null additivity and weak null additivity the implication relationship is summarized in a diagram

pseudo atoms of fuzzy and non fuzzy measures in this paper we introduce the concept of pseudo atoms of set functions and establish some fundamental conclusions about pseudo atoms on the assumption of null null additivity we give the necessary and sufficient conditions which insure that the set of non null measure contains no pseudo atoms further we obtain several decomposition theorems about pseudo atoms and atoms of set functions

regularities of riesz space valued non additive measures with applications to convergence theorems for choquet integrals a deeper investigation of radonness and t smoothness properties of riesz space valued borel non additive measures is carried out to this end due to a lack of e argument in a riesz space the multiple egoroff property is introduced and enforced on the involved riesz space the established regularity properties of borel non additive measures are instrumental when formulating certain types of monotone convergence theorems for choquet integrals

on partial smoothness tilt stability and the mathcal vu decomposition under the assumption of prox regularity and the presence of a tilt stable local minimum we are able to show that a mathcal vu like decomposition gives rise to the existence of a smooth manifold on which the function in question coincides locally with a smooth function