fora a fuzzy set based framework for online reputation management the social web offers increasingly simple ways to publish and disseminate personal or opinionated information which can rapidly exhibit a disastrous influence on the online reputation of organizations based on social web data this study describes the building of an ontology based on fuzzy sets at the end of a recurring harvesting of folksonomies by web agents the aggregated tags are purified linked and transformed to a so called fuzzy grassroots ontology by means of a fuzzy clustering algorithm this self updating ontology is used for online reputation analysis a crucial task of reputation management with the goal to follow the online conversation going on around an organization to discover and monitor its reputation in addition an application of the fuzzy online reputation analysis fora framework lessons learned and potential extensions are discussed in this article

a block equation solver for large unsymmetric matrices arising in the boundary integral equation method an equation solver for the large unsymmetric systems of linear equations arising in the application of the boundary integral equation method to problems of linear elasticity in homogeneous or piecewise homogeneous solids is presented the solver uses gaussian elimination the advantages of the solver over many existing eliminational or iterational methods are that it ignores many of the large groups of zeros that occur in piecewise homogeneous work and also restrains growth of the number of non zero matrix entries memory requirements and computation times therefore are reduced for many piecewise homogeneous problems

numerical implementation of the symmetric galerkin boundary element method in 2d elastodynamics the symmetric galerkin boundary element method sgbem employs both the displacement integral equation and the traction integral equation which lead to a symmetric system of equations a two dimensional sgbem is implemented in this paper with emphasis on the special treatments of singular integrals the integrals in the time domain are carried out by an analytical method in order to evaluate the strong singular double integrals and the hypersingular double integrals in the space domain which are associated with the fundamental solutions gpu and gpp artificial body forces are introduced which can be used to indirectly derive the singular terms thus those singular integrals which behave like 1 r and 1 r2 are all avoided in the proposed sgebm implementation an artificial body force scheme is proposed to evaluate the body force term effectively two numerical examples are presented to assess the accuracy of the numerical implementation and show similar accuracy when compared with the fem and the analytical solutions copyright 2003 john wiley sons ltd

integration of singular galerkin type boundary element integrals for 3d elasticity problems a galerkin approximation of both strongly and hypersingular boundary integral equation bie is considered for the solution of a mixed boundary value problem in 3d elasticity leading to a symmetric system of linear equations the evaluation of cauchy principal values v p and finite parts p f of double integrals is one of the most difficult parts within the implementation of such boundary element methods bems a new integration method which is strictly derived for the cases of coincident elements as well as edge adjacent and vertex adjacent elements leads to explicitly given regular integrand functions which can be integrated by the standard gauss legendre and gauss jacobi quadrature rules problems of a wide range of integral kernels on curved surfaces can be treated by this integration method we give estimates of the quadrature errors of the singular four dimensional integrals

on the use of quarter point boundary elements for stress intensity factor computations this communication studies a procedure for stress intensity factor computations using traction singular quarter point boundary elements opening mode stress intensity factors are computed from the tractions nodal values at the crack tip a comparison is made between the factors calculated using this procedure and those obtained by previously recommended methods which made use of the nodal values of the displacements the proposed procedure was seen to be less discretization sensitive than any other of the considered methods accurate results were obtained even in the case of coarse meshes

elastodynamics by bem a new direct formulation a new direct be formulation is proposed for the solution of elastodynamic problems an analytical regularization procedure is devised via an integration by parts technique without introducing any hypothesis about either the discretization of the boundary geometry or the space time interpolation of the elastic elds involved the only requirement is for continuity in the displacement eld the regularization of the integral equations for static elasticity using the same approach already available in the literature is presented as a particular case of the general procedure introduced herein the numerical implementation of this technique is discussed and two dimensional examples are presented copyright 1999 john wiley sons ltd

the effect of structural elasticity on the efficiency of noise barriers the efficiency of noise barriers is usually estimated neglecting their elastic behaviour in this paper the total vibro acoustical response of simple barriers is considered a variational approach with a boundary element technique is used it is a generalization of an existing formalism developed for the study of two dimensional acoustical problems the case of straight and thin barriers is studied it is found that at low frequencies their vibrations can modify their insertion losses by several decibels

elastoplastic analysis by active macro zones with linear kinematic hardening and von mises materials in this paper a strategy to perform elastoplastic analysis with linear kinematic hardening for von mises materials under plane strain conditions is shown the proposed approach works with the symmetric galerkin boundary element method applied to multidomain problems using a mixed variables approach to obtain a more stringent solution the elastoplastic analysis is carried out as the response to the loads and the plastic strains the latter evaluated through the self equilibrium stress matrix this matrix is used both in the predictor phase for trial stress evaluation and in the corrector phase for solving a nonlinear global system which provides the elastoplastic solution of the active macro zones i e those zones collecting bem elements where the plastic consistency condition has been violated the simultaneous use of active macro zones gives rise to a nonlocal approach which is characterized by a large decrease in the plastic iteration number although the proposed strategy requires the inversion and updating of jacobian operators generally of big dimensions a strategy developed in order to reduce the computational efforts due to the use of this matrix in a recursive process is shown

solution of fluid structure interaction problems using a coupled finite element and variational boundary element technique this work is concerned with the numerical modeling of elasto acoustic problems applied to thin shells and specifically curved plates a finite element formulation of the elastic problem is coupled to a variational boundary element solution of the acoustic problem this solution to the acoustic problem proposed by mariem and hamdi j b mariem and m a hamdi int j num methods eng 24 1251 1267 1987 is implemented using high order isoparametric elements and attention is given to techniques of accelerating the numerical implementation for solutions at multiple frequencies these techniques include a reduction in the problem size through the use of symmetry and more importantly the interpolation of the fluid impedance matrix within the frequency regime the advantages in using this variational formulation are first the manner in which a highly singular integral operator is made amenable to numerical approximation second its application to nonclosed thin shells and third its numerical im

a symmetric formulation of coupled bem fem in solving responses of submerged elastic structures for large degrees of freedom this work presents a symmetric formulation for the coupling of boundary element method bem with finite element method fem to compute responses of submerged elastic structures in a heavy acoustic medium the acoustic loading derived from bem is formulated in a symmetric complex matrix the symmetry of the acoustic loading matrix is proven by an acoustic reciprocal principle which relate two sets of arbitrary surface normal velocities and surface pressures in terms of surface integrals the structural equation is represented by fem the fact that the acoustic loading and the structural equation are symmetric allows us to take the storage and computational advantages of the banded matrix which has been widely used in conventional finite element methods consequently the computational efficiency of the proposed coupled fem bem is significantly increased the proposed method involving 20 000 degrees of freedom can be implemented on a personal computer numerical results are verified by analytical solutions of a constant thickness spherical shell subject to a point alternating force as well as the previously published variational solution of a constant thickness spheroidal shell excited by a concentrated force

multi domain bem for two dimensional problems of elastodynamics an advanced implementation of the boundary element technique for the periodic and transient dynamic analyses of two dimensional elastic or visco elastic solids of arbitrary shape and connectivity is presented for transient dynamic analysis the problem is first solved in the laplace transform space and then the time domain solutions are obtained by numerical inversion of transformed domain solutions the present analysis is capable of treating very large multi domain problems by substructuring and satisfying the equilibrium and compatibilities at the interfaces with the help of this substructuring capability problems related to the layered media and soil structure interaction can all be analysed this paper also introduces a new type of element called enclosing element which has been developed and used to model the infinitely extending boundaries of a half space or a layered medium a number of numerical examples are presented and through comparisons with available analytical and numerical results the accuracy stability and efficiency of the present analysis are established

generic domain decomposition and iterative solvers for 3d bem problems summary in the past two decades considerable improvements concerning integration algorithms and solvers involved in boundary element formulations have been obtained first a great deal of efficient techniques for evaluating singular and quasi singular boundary element integrals have been definitely established and second iterative krylov solvers have proven to be advantageous when compared to direct ones also including non hermitian matrices the former fact has implied in cpu time reduction during the assembling of the system of equations and the latter fact in its faster solution in this paper a triangle polar co ordinate transformation and the telles co ordinate transformation applied in previous works independently for evaluating singular and quasi singular integrals are combined to increase the efficiency of the integration algorithms and so to improve the performance of the matrixassembly routines in addition the jacobi preconditioned biconjugate gradient j bicg solver is used to develop a generic substructuring boundary element algorithm in this way it is not only the system solution accelerated but also the computer memory optimized discontinuous boundary elements are implemented to simplify the coupling algorithm for a generic number of subregions several numerical experiments are carried out to show the performance of the computer code with regard to matrix assembly and the system solving in the discussion of results expressed in terms of accuracy and cpu time advantages and potential applications of the be code developed are highlighted copyright 2006 john wiley sons ltd

integral evaluation in the bem solution of hyper singular integral equations 2d problems on polygonal domains abstract the formulation of certain classes of boundary value problems in terms of hypersingular integral equations is currently gaining increasing interest in this paper we consider such type of equations on 2d polygonal domains and assume we have to solve them by a collocation or a galerkin bem in particular given any polynomial local basis we show how to compute efficiently using a very low number of points all integrals required by these methods these integrals have kernels of the type log r r 1 and r 2 the quadrature rules we propose to compute the above mentioned integrals require the user to specify only the local polynomial degrees therefore they are quite suitable for the construction of a p or h p version of the bem

symmetric galerkin boundary integral formulation for interface and multi zone problems domains containing an internal boundary such as a bi material interface arise in many applications e g composite materials and geophysical simulations this paper presents a symmetric galerkin boundary integral method for this important class of problems in this situation the physical quantities are known to satisfy continuity conditions across the interface but no boundary conditions are specied the algorithm described herein achieves a symmetric matrix of reduced size moreover the symmetry can also be invoked to lessen the numerical work involved in constructing the system of equations and thus the method is computationally very ecient a prototype numerical example with several variations in the boundary conditions and material properties is employed to validate the formulation and corresponding numerical procedure the boundary element results are compared with analytical solutions and with numerical results obtained with the nite element method 1997 by john wiley sons ltd

implementation of a symmetric boundary element method in transient heat conduction with semi analytical integrations a time convolutive variational hypersingular integral formulation of transient heat conduction over a 2 d homogeneous domain is considered the adopted discretization leads to a linear equation system whose coefficient matrix is symmetric and is generated by double integrations in space and time assuming polynomial shape functions for the boundary unknowns a set of compact formulae for the analytical time integrations is established the spatial integrations are performed numerically using very efficient formulae just recently proposed the competitiveness from the computational point of view of the symmetric boundary integral equation approach proposed herein is investigated on the basis of an original computer implementation copyright 1999 john wiley sons ltd

on the numerical stability of time domain elastodynamic analyses by bem abstract in this paper the issue of the numerical stability of time domain be solution procedures in elastodynamics is discussed with reference to a simple benchmark problem which is apt to be analyzed in different contexts as a 1 d problem an antiplane shear and a plane strain problem the simplicity of the problems considered allows to pinpoint the causes of instability and to explain how the choice of the time step and or of the be mesh affects the numerical solution

a general regularization of the hypersingular integrals in the symmetric galerkin boundary element method the symmetric galerkin boundary element method is used to solve boundary value problems by keeping the symmetric nature of the matrix obtained after discretization the matrix elements are obtained from a double integral involving the double derivative of green s operator which is highly singular the paper presents a regularization of the hypersingular integrals which depend only on the properties of green s tensor the method is presented in the case of laplace s operator with an example of application the case of elasticity is finally addressed theoretically showing an easy extension to any case of anisotropy

examples counterexamples and measuring fuzzy associations this paper examines the measurement of the degree to which tuples in a database support a relation among attributes based on a comparison of the number of examples and counterexamples of the relation in particular we are concerned with associations that represent imprecise constraints placed upon the value of one attribute by those of other attributes associations of this form may be described by fuzzy rules and the analysis requires an assessment of the degree to which a tuple satisfies the imprecise constraint specified by the rule standard measures of rule validity are extended to fuzzy associations based on the degree that the tuples are examples counterexamples or irrelevant to imprecise relations a scaling of the relevance of a tuple is proposed to minimize the impact of the accumulation of small membership values on the confidence based validity measures

discovering fuzzy exception and anomalous rules nowadays searching for specific kind of knowledge that deviates from the usual standards is very useful in several domains such as network traffic anomalies fraud detection economic analysis or medical diagnosis fuzzy association rules have been developed as a powerful tool for dealing with imprecision in databases that may come from the source i e imprecise measures taken by the machine or from the human understanding of a concept and offering a comprehensive representation of found knowledge in this paper we introduce the notion of fuzzy exception and fuzzy anomalous rule for the recognition of these types of deviations the deviations are associated with the common patterns which usually are hidden in data affected by some kind of fuzziness we present a new approach for mining such rules based on a recently proposed model for representing and evaluating fuzzy rules important advantages are to obtain more understandable results and that the mining process can be parallelized an algorithm following the proposed model is developed and some experiments are performed in data where some numerical attributes have been fuzzified and also in some real fuzzy transactional datasets for testing the proposed algorithm from experimentation we have seen that the proposed fuzzy rules give some insights on the exception and anomaly detection in credit payments

transient analysis of the dynamic stress intensity factors using sgbem for frequency domain elastodynamics in this paper a two dimensional symmetric galerkin boundary integral formulation for elastodynamic fracture analysis in the frequency domain is described the numerical implementation is carried out with quadratic elements allowing the use of an improved quarter point element for accurately determining frequency responses of the dynamic stress intensity factors dsifs to deal with singular and hypersingular integrals the formulation is decomposed into two parts the first part is identical to that for elastostatics while the second part contains at most logarithmic singularities the treatment of the elastostatic singular and hypersingular singular integrals employs an exterior limit to the boundary while the weakly singular integrals in the second part are handled by gauss quadrature time histories transient responses of the dsifs can be obtained in a post processing step by applying the standard fast fourier transform fft and algorithm to the frequency responses of these dsifs several test examples are presented for the calculation of the dsifs due to two types of impact loading heaviside step loading and blast loading the results suggest that the combination of the symmetric galerkin boundary element method and standard fft algorithms in determining transient responses of the dsifs is a robust and effective technique

analytical integrations and sifs computation in 2d fracture mechanics analytical integrations in the framework of linear elastic problems modelled by means of boundary integral equations have been considered in a previous publication int j numer methods eng 2002 53 7 1695 1719 the present note aims at extending the subject to linear elastic fracture mechanics in such a context special shape functions have been recently proposed siam j appl math 1998 58 428 455 in order to increase accuracy in stress intensity factors approximation the closed form solution for integrals that arise from the boundary element method is a goal of the present work exploiting the analytical integrations asymptotical analysis around the crack tip are made possible with the purpose of formulating a coherent and accurate correlation between approximated stress intensity factors and crack opening displacements over the crack tip straight special elements copyright 2006 john wiley sons ltd

fuzzy association rules general model and applications the theory of fuzzy sets has been recognized as a suitable tool to model several kinds of patterns that can hold in data in this paper we are concerned with the development of a general model to discover association rules among items in a crisp set of fuzzy transactions this general model can be particularized in several ways each particular instance corresponds to a certain kind of pattern and or repository of data we describe some applications of this scheme paying special attention to the discovery of fuzzy association rules in relational databases

boundary discretization based on the residual energy using the sgbem abstract the paper has as objective the estimation of the error in the structural analysis performed by using the displacement approach of the symmetric galerkin boundary element method sgbem and suggests a strategy able to reduce this error through an appropriate change of the boundary discretization the body characterized by a domain and a boundary is embedded inside a complementary unlimited domain bounded by a boundary in such new condition it is possible to perform a separate valuation of the strain energies in the two subdomains through the computation of the work defined generalized obtained as the product among nodal and weighted quantities on the actual boundary and on the complementary boundary in order to reduce the error in the analysis phases the scattered energy has been computed as generalized work in each boundary element of and an adequate node number has been introduced inside the boundary elements where this generalized work is higher this strategy made in a recursive way has shown effectiveness whether in the convergence proofs of some mechanical and kinematical quantities or in computing the percentage error obtained as ratio between the scattered work in and the total work both expressed in terms of generalized quantities

coupling bem with fem by a direct computation of the boundary stiffness matrix the boundary stiffness matrix characterizing in a discretized form the response of the boundary to given dirichlet boundary conditions allows the coupling between bem and fem the paper presents an approach based on the direct computation of the stiffness matrix from the potential function related to a given dirichlet boundary condition the method produces a symmetric stiffness matrix as for the singular galerkin boundary element method but does not need to compute hypersingular integrals in addition the method uses only the nodal values of the boundary potential but does not need discretized values of the normal gradient at the boundary as for usual boundary element methods which reduces the number of matrices to be constructed the regularization of the integrals is achieved by means used for simply singular integrals introduced for the collocation boundary element method an example of application is produced in the case of the solution of laplace equation within a plane domain

efficient analytical integration of symmetric galerkin boundary integrals over curved elements thermal conduction formulation abstract substantial improvements are reported in the computational efficiency of galerkin boundary element analysis bea employing curved continuous boundary elements a direct analytical treatment of the singular double integrations involved in galerkin bea adapting a limit to the boundary concept used successfully in collocation bea is used to obviate significant computation in the determination of the galerkin coefficient matrices symbolic manipulation has been strategically employed to aid in the analytical evaluation of the singular contributions to these double integrals the analytical regularization procedure separates the potentially singular galerkin integrands into an essentially singular but simple part plus a regular remainder that can be integrated numerically the finite contribution from the simplified singular term is then computed analytically it is shown that the key to containing the explosive growth in the length of the formulae associated with such a hybrid analytical numerical integration scheme is the strategic timing of when to take the limit to the boundary this regularization also isolates the contribution from the curvature of the boundary element thus facilitating enhanced computational efficiency in problems with many straight elements example problems are presented to quantify the performance of this approach it is concluded that with these techniques galerkin symmetric bea can be more efficient than its collocation based counterpart

direct evaluation of hypersingular galerkin surface integrals a direct algorithm for evaluating hypersingular integrals arising in a three dimensional galerkin boundary integral analysis is presented the singular integrals are defined as limits to the boundary and by integrating two of the four dimensions analytically the coincident integral is shown to be divergent however the divergent terms can be explicitly calculated and shown to cancel with corresponding singularities in the adjacent edge integrals a single analytic integration is employed for the edge and vertex singular integrals this is sufficient to display the divergent term in the edge adjacent integral and to show that the vertex integral is finite by explicitly identifying the divergent quantities we can compute the hypersingular integral without recourse to stokes s theorem or the hadamard finite part the algorithms are developed in the context of a linear element approximation for the laplace equation but are expected to be generally applicable as an example the algorithms are applied to solve a thermal problem in an exponentially graded material

boundary element solution of heat convection diffusion problems abstract a boundary element method is described in detail for the solution of two dimensional steady state convective heat diffusion problems in homogeneous and isotropic media with both linear and nonlinear boundary conditions through an exponential variable transformation the introduction of fundamental solutions and the use of green s theorem the problem is reduced to one involving values of temperature and or heat flux in the form of an integral only along the boundary the integral is solved numerically for three examples two of them have linear boundary conditions and their numerical results are compared with the corresponding analytical solutions the other has a nonlinear boundary condition due to heat radiation and an iterative procedure is applied to obtain the numerical solution the fictitious source formulation leading to the boundary element solution of the same problems is discussed as an alternative the extension of the method to formulate transient and or three dimensional convective heat diffusion problems is also described and the relevant fundamental solutions are given finally the exponential variable transformation is applied to construct a functional of variational principle which leads to developing a finite element formulation of the problems with a banded symmetric stiffness matrix

a new boundary element technique without domain integrals for elastoplastic solids summary a simple idea is proposed to solve boundary value problems for elastoplastic solids via boundary elements namely to use the green s functions corresponding to both the loading and unloading branches of the tangent constitutive operator to solve for plastic and elastic regions respectively in this way domain integrals are completely avoided in the boundary integral equations though a discretization of the region where plastic flow occurs still remains necessary to account for the inhomogeneity of plastic deformation the elastoplastic analysis reduces in essence to a straightforward adaptation of techniques valid for anisotropic linear elastic constitutive equations the loading branch of the elastoplastic constitutive operator may be viewed formally as a type of anisotropic elastic law numerical examples using j2 flow theory with linear hardening demonstrate that the proposed method retains all the advantages related to boundary element formulations is stable and performs well the method presented is for simplicity developed for the associative flow rule however a full derivation of green s function and boundary integral equations is also given for the general case of non associative flow rule it is shown that in the non associative case a domain integral unavoidably arises in the formulation copyright 2005 john wiley sons ltd

fuzzy confirmation measures this paper proposes a number of measures for assessing the quality of fuzzy association rules the focus is on a particular class of measures which are fuzzy counterparts of probabilistic confirmation measures the distinguishing feature of such measures is that they are based on probabilistic in dependence and so a corresponding definition of fuzzy in dependence is proposed this forms the basis for the definition of a fuzzy confirmation measure and for proposing a number of such measures based on a well known fuzzy confidence measure various properties are considered to narrow the field of viable fuzzy confirmation measures with one particular measure being found to have a number of advantages

extremum convergence and stability properties of the finite increment problem in elastic plastic boundary element analysis abstract the boundary element be analysis is formulated by a symmetric galerkin weightedresidual double integration approach rather than by a traditional collocation or by a nonsymmetric galerkin approach the internal variable associative elastoplastic material model is discretized in time by a stepwise holonomic backward difference integration scheme it is then enforced in a weighted average sense over cells and reformulated in terms of cell generalized variables in the above context the following results are established under suitable constitutive hypotheses a a minimum characterization of the solution to the discretized step problem in finite increments b a convergence theorem concerning a conventional iterative algorithm for solving this problem c a proof of the stability of the marching solution method in the sense of non amplification of errors along a finite step sequence an illustrative example corroborates the theoretical results

a high order discontinuous galerkin approach to the elasto acoustic problem abstract we address the spatial discretization of an evolution problem arising from the coupling of elastic and acoustic wave propagation phenomena by employing a discontinuous galerkin scheme on polygonal and polyhedral meshes the coupled nature of the problem is ascribed to suitable transmission conditions imposed at the interface between the solid elastic and fluid acoustic domains we state and prove a well posedness result for the strong formulation of the problem present a stability analysis for the semi discrete formulation and finally prove an a priori h p version error estimate for the resulting formulation in a suitable mesh dependent energy norm we also discuss the time integration scheme employed to obtain the fully discrete system the convergence results are validated by numerical experiments carried out in a two dimensional setting

solution of bem systems of equations via iterative techniques the present paper is concerned with the application of iterative techniques to solve boundary element method bem systems of equations initially a brief description of some algorithms which have been employed for symmetric positive definite matrices is given finite element method matrices for instance subsequently non symmetric versions of these algorithms are described and their performance is checked for bem matrices through various numerical experiments preconditioned algorithms were found to work quite well

a coupled fe and boundary integral equation method based on exterior domain decomposition for fluid structure interface problems abstract a coupled finite element and exterior domain decomposition based boundary integral formulations for the solutions of two or three dimensional time harmonic fluid structure interaction problems is described in this paper it is known that the memory limitation of computers has been one of the major obstacles for solving large scale high frequency fluid structure interface systems using various existing nonlocal finite element and boundary integral equation coupling techniques due to the fully populated resultant matrix generated from the boundary integral equation representation the essence of this study is to decompose through domain decomposition of the exterior region the original exterior problem into arbitrary subproblems with data sharing only at the interfaces by decomposing the exterior infinite domain into an appropriate number of infinite subdomains this method not only ensures the validity of the formulation for all frequencies but also leads to a diagonalized blockwise banded system of discretized equations the size of an individual submatrix i e a block that is associated with an exterior subdomain may be decided by the user and may be selected such that the restriction due to the memory limitation of a given computer may be accommodated in addition the method is suited for parallel processing since the data associated with each subdomain impedance matrices load vectors etc may be generated in parallel and the communication needed will be only for the interface values most significantly unlike the existing coupled finite element and boundary integral equation techniques that are valid for all frequencies our method avoids the use of both the hypersingular operator and the double integrals therefore reducing the computational complexity numerical experiments have been performed for elastic cylindrical shells subjected to a plane incident wave the results have demonstrated the accuracy of the method for wavenumbers ranging from 0 to 30 both directly on the shell and in the far field and have confirmed that the procedure is valid for all frequencies

dynamic stress concentration studies by boundary integrals and laplace transform the dynamic stress field and its concentrations around holes of arbitrary shape in infinitely extended bodies under plane stress or plane strain conditions are numerically determined the material may be linear elastic or viscoelastic while the dynamic load consists of plane compressional waves of harmonic or general transient nature the method consists of applying the laplace transform with respect to time to the governing equations of motion and formulating and solving the problem numerically in the transfomed domain by the boundary integral equation method the stress field can then be obtaind by a numerical inversion of the trasformed solution the correspondence principle is invoked for the case of viscoelastic material behavious the method is simplified for the case of harmonic waves where no numerical inversion is involved

mining axiomatic fuzzy set association rules for classification problems abstract in this paper we propose a novel method to mine association rules for classification problems namely afsrc afs association rules for classification realized in the framework of the axiomatic fuzzy set afs theory this model provides a simple and efficient rule generation mechanism it can also retain meaningful rules for imbalanced classes by fuzzifying the concept of the class support of a rule in addition afsrc can handle different data types occurring simultaneously furthermore the new model can produce membership functions automatically by processing available data an extensive suite of experiments are reported which offer a comprehensive comparison of the performance of the method with the performance of some other methods available in the literature the experimental result shows that afsrc outperforms most of other methods when being quantified in terms of accuracy and interpretability afsrc forms a classifier with high accuracy and more interpretable rule base of smaller size while retaining a sound balance between these two characteristics

out of core solver for large multi zone boundary element matrices in this paper an out of core solver is developed for a three dimensional elastostatic boundary element program this program includes multi regions which enables a large model to be divided into a number of homogeneous sub models each with their own material properties the system matrix produced by multi regions is sparse blocked and unsymmetric in character and so reduces disc space and solution time the solver presented in this paper utilizes efficiently the structure of this matrix by holding only non zero parts of this matrix in a sequential unformatted direct access file reading in as much of the file as possible into the working space performing gauss elimination then writing part of the matrix back to file the maximum utilization of working space is particularly important on vector machines as vector activity is maximized whilst record read write is minimized the effect of multi regions on cpu is demonstrated on both the convex and cray machines

on hypersingular surface integrals in the symmetric galerkin boundary element method application to heat conduction in exponentially graded materials a symmetric galerkin formulation and implementation for heat conduction in a three dimensional functionally graded material is presented the green s function of the graded problem in which the thermal conductivity varies exponentially in one co ordinate is used to develop a boundary only formulation without any domain discretization the main task is the evaluation of hypersingular and singular integrals which is carried out using a direct limit to the boundary approach however due to complexity of the green s function for graded materials the usual direct limit procedures have to be modified incorporating taylor expansions to obtain expressions that can be integrated analytically several test examples are provided to verify the numerical implementation the results of test calculations are in good agreement with exact solutions and corresponding finite element method simulations copyright 2004 john wiley sons ltd

symmetric galerkin boundary formulations employing curved elements accounts of the symmetric galerkin approach to boundary element analysis bea have recently been published this paper attempts to add to the understanding of this method by addressing a series of fundamental issues associated with its potential computational efficiency a new symmetric galerkin theoretical formulation for both the harmonic heat conduction and the biharmonic elasticity problem that employs regularized singular and hypersingular boundary integral equations bies is presented the novel use of regularized bies in the galerkin context is shown to allow straightforward incorporation of curved isoparametric elements a symmetric reusable intrinsic sample point risp numerical integration algorithm is shown to produce a galerkin i e double integration strategy that is competitive with its counterpart i e singular integration procedure in the collocation bea approach when the time saved in the symmetric equation solution phase is also taken into account this new formulation is shown to be capable of employing hypersingular bies while obviating the requirement of c 1 continuity a fact that allows the employment of the popular continuous element technology the behavior of the symmetric galerkin bea method with regard to both direct and iterative equation solution operations is also addressed a series of example problems are presented to quantify the performance of this symmetric approach relative to the more conventional unsymmetric bea in terms of both accuracy and efficiency it is concluded that appropriate implementations of the symmetric galerkin approach to bea indeed have the potential to be competitive with if not superior to collocation based bea for large scale problems

a p extension of the symmetric boundary element method abstract this paper describes an implementation of the symmetric galerkin boundary element method for plane potential and elasticity problems on domains with polygonal boundaries the method makes use of the hyper singular boundary integral equations for the normal derivatives of the unknown function we discuss an integration technique which is sufficiently robust to handle p extensions on geometrically graded meshes computer times required compare favorably with corresponding finite element methods we present numerical results obtained by a uniform p extension for various mixed boundary value problems we demonstrate that the same convergence rates can be obtained by the symmetric variational boundary element method as with p extensions of the finite element method on the basis of the p extension process a reliable error estimate based on extrapolation from a sequence of p levels can be obtained this is a unique feature of the variational methods as compared to the classical collocation approach the error estimate remains valid even for boundary element analysis employing substructures and mixed discretizations with boundary elements and finite elements

analysis of problems in elasto plasticity via an adaptive fem bem coupling method abstract the purpose of this paper is to present an adaptive finite element boundary element coupling method for elasto plastic analysis the finite element method is utilized in regions where plastic material behavior is expected to develop whereas substantial parts of the bounded unbounded linear elastic body are approximated using the boundary element method in order to obtain a computationally efficient coupling method considerable attention is devoted to the generation and adaption of the finite element and boundary element discretizations according to the state of computation the proposed method is computationally efficient since it employs smaller finite element regions unlike available coupling approaches the adaptive finite element boundary element coupling method has the potential advantage that it does not demand predefinition and manual localization of the finite element and boundary element sub domains

a new space time energetic formulation for wave propagation analysis in layered media by bems in this paper considering a dirichlet neumann problem for 1d wave propagation analysis in layered media reformulated in terms of boundary integral equations we compare two classical weak formulations for the boundary element method with a new space time energetic formulation continuity and coerciveness of the bilinear form corresponding to this last formulation are proved several numerical results will be presented pointing out the numerical properties of the derived linear systems instability phenomena arising using one of the classical techniques can be prevented choosing suitable time steps in the discretization phase of course with a higher computational cost with respect to the new procedure which appears to be unconditionally stable copyright 2008 john wiley sons ltd

a formal model for mining fuzzy rules using the rl representation theory data mining techniques managing imprecision are very useful to obtain meaningful and interesting information for the user among some other techniques fuzzy association rules have been developed as a powerful tool for dealing with imprecision in databases and offering a good representation of found knowledge in this paper we introduce a formal model for managing the imprecision in fuzzy transactional databases using the restriction level representation theory a recent representation of imprecision that extends that of fuzzy sets this theory introduces some new operators keeping the usual crisp properties even when negation is involved the model allows us to mine fuzzy association rules in a straightforward way extending the accuracy measures from the crisp case in addition we introduce several ways of representing and summarizing the obtained results in order to offer new and very interesting semantics as an application we present how to extract fuzzy association rules involving both the presence and the absence of items using the proposed model and we also perform some experiments with real fuzzy transactional datasets

symmetric boundary element method versus finite element method the paper examines the effectiveness of the symmetric boundary element formulation when the continuum body is subdivided into large elements called macro elements the approach proposed combines a strong reduction of variables with an elastic solution close to the real response indeed if the displacement method is used this approach permits one to determine for every macro element a relationship connecting the weighted traction vector defined on the sides of the interface boundary with the node displacement vector of the same boundary and with the external action vector such a strategy is very similar to that followed through the finite element method but with the advantages of having the punctual satisfaction of the equilibrium and compatibility by using the fundamental solution and of employing large elements whose discretization is performed on the boundary only some examples are shown using a general computing programme developed by the present authors

stability assessment of a unified variational boundary integral method applicable to thin scatterers and scatterers with corners abstract the objective of this study is to assess the stability especially at and near critical frequencies of a new unified stable symmetric domain finite element and boundary integral methodology for solving time harmonic interface problems for scatterers of arbitrary shape the validity of this energy based variational procedure for rigid and penetrable smooth scatterers including the existence uniqueness and optimal convergence of the corresponding numerical approximations has been proved rigorously in the context of fluid structure interaction problems the emphasis here is on investigating the applicability of this procedure to the case of scatterers with corners using square and thin rectangular two dimensional rigid obstacles as prototypes we also establish that the apparently distinct direct boundary integral formulation due to burton and miller and the combined single and double layer indirect formulation due to leis brakhage and werner and panich introduced to insure that boundary integral equations for scattering problems are uniquely solvable for all wavenumbers are entirely equivalent within our variational setting by examining the condition number of the matrix of coefficients of the discretized equations as well as the resulting solutions both directly on the surface of the scatterers and in the far field it is demonstrated that the new methodology is robust and completely insensitive to critical frequencies even for thin objects most significantly the precise singular behaviour of the pressure field at corners is also predicted quite accurately by using standard finite elements along the boundary of the scatterer without having to introduce special singularity functions which for general interface problems may not be known in advance

responses of partially immersed elastic structures using a symmetric formulation for coupled boundary element and finite element methods using a coupled bem fem this work describes a numerical method to compute the response and acoustic radiation for structures partially immersed in fluid the structures and their responses are assumed to be symmetric about a symmetric plane a symmetric complex matrix derived from the bem and a reciprocal principle for surface acoustics is also used to represent the acoustic loading against the structures in addition selecting a proper green s function based on image source method satisfies the boundary conditions of pressure release on the fluid surface and null normal velocity on the symmetric plane moreover a boundary integral equation emerges when the field point approaches the structural surface where the normal derivative of the green s function over partial infinitesimal spheres is evaluated these limiting values depend on locations of the field point on the surface owing to the symmetry of the acoustic loading matrix the matrix for the coupled bem fem is a banded symmetric one thereby allowing us to employ a variable banded storage method and invert of the matrix doing so markedly increases computational efficiency furthermore an analytical solution of a spherical thin shell with the lower semi sphere immersed in water is carried out by characteristic function expansions for shell equation and acoustic loading these analytical solutions compare with the results obtained from the proposed numerical method a good correlation for low frequencies is obtained and minor discrepancies are observed with an increasing frequency

deformations of dihedral 2 group extensions of fields given a g galois extension of number fields l k we ask whether it is a specialization of a regular g galois cover of pk this is the inverse of the usual use of the hilbert irreducibility theorem in the inverse galois problem we show that for many groups such arithmetic liftings exist by observing that the existence of generic extensions implies the arithmetic lifting property we explicitly construct generic extensions for dihedral 2 groups under certain assumptions on the base field k we also show that dihedral groups of order 8 and 16 have generic extensions over any base field k with characteristic different from 2

a galerkin symmetric and direct bie method for kirchhoff elastic plates formulation and implementation a variational boundary element formulation is proposed for the solution of the elastic kirchhoff plate bending problem the stationarity conditions of an augmented potential energy functional are first discussed after addressing the topic of the choice of the test functions a regularization process based on integrations by parts is developed which allows to express the formulation in terms of double integrals the inner being at most weakly singular and the outer regular standard integration procedures may then be applied for their numerical evaluation in the presence of both straight and curved boundaries the normal slope and the vertical displacement must be c0 and c1 continuous respectively numerical examples show through comparisons with analytical solutions that a high accuracy is achieved

analytical integration of singular kernels in symmetric boundary element analysis of kirchhoff plates summary an analytical integration method for evaluating the singular integrals arising in the construction of symmetric boundary element models is proposed referring to the analysis of kirchhoff plates kernels involved in the symmetric boundary formulation of kirchhoff plates exhibit singularities up to o 1 r 4 the proposed technique temporarily deactivates the singularities by using a limit approach and carries out the integration on contiguous boundary elements in order to smooth the singularities of the kernels through sufficiently continuous shape functions the paper contains a brief presentation of the boundary integral formulation of the kirchhoff plate with the explicit expressions of the fundamental solutions involved and the derivation of the symmetric boundary element model a detailed description of the proposed integration technique is presented which discusses the main steps of the analytical procedure and provides the final results the technique is illustrated through the discussion of a series of relevant cases including high singularities and referring to both collinear and corner supports copyright q 2008 john wiley sons ltd

sgbem fem coupling for analysis of cracks in 3d anisotropic media a weakly singular symmetric galerkin boundary element method sgbem is coupled with the standard finite element method fem in order to establish an accurate and efficient numerical technique for analysis of fractures in three dimensional anisotropic linearly elastic media in the strategy the weakly singular sgbem developed by rungamornrat and mear textitint j solids struct 2008 45 1283 1301 comput methods appl mech engrg 2008 197 4319 4332 is utilized to model a small scale region containing the crack while the possibly large and complex compliment region is treated by the fem the coupled technique exploits the positive features of both methods the sgbem proves to be a convenient and highly accurate method for obtaining mixed mode stress intensity factors along the crack front whereas the fem is very efficient for modeling large scale problems in the absence of cracks an important aspect of the formulation and implementation of the technique is that continuity of displacement and traction across the interface between the sgbem and fem regions is enforced in a weak sense this allows the two regions one modeled by the sgbem and the other by the fem to be discretized independently without the need for the resulting meshes to conform on the interface separating the regions and this flexibility in the discretization process leads to a significant reduction in the modeling effort to demonstrate the utility and accuracy of the technique several boundary value problems involving both embedded and surface breaking cracks are treated and it is shown that the coupled technique yields highly accurate stress intensity factors that exhibit only a slight dependence upon mesh refinement copyright 2010 john wiley sons ltd

on a family of connectives for fuzzy sets abstract in this paper we find the general solution of the functional equation s t x y t x n y x where s is a t conorm t is a t norm and n is a strong negation on the unit interval in particular the result yields a family of connectives for fuzzy sets

a galerkin symmetric boundary element method in elasticity formulation and implementation a symmetric boundary element method based on a weighted residual galerkin approach for elastoplastic analysis is revisited and its computer implementation for two dimensional homogeneous problems is described

an acoustic boundary integral formulation for open shells allowing different impedance conditions top and bottom surfaces abstract in the automotive aerospace industries as well as the underwater acoustics defense applications the addition of coatings to modify the response of the vibrating structure is commonplace the formulation developed is an extension of the existing thin body formulation currently found in commercial noise prediction codes such as sysnoise in order to allow problems requiring different boundary condition on both sides of the thin shell to be solved for instance a generalised thin body acoustic formulation would allow for a local impedance boundary condition to be specified on the top surface and a hard neumann boundary condition to be specified on the bottom surface such a formulation would allow for different local impedance coatings to be specified on the top and bottom surfaces due to the lack of analytical solutions for such problems even for the simplest geometries it is difficult to validate such a formulation however three test cases are presented two flat plate examples and a open cylinder with a point monopole source excitation at its centre

fuzzy rule base ensemble generated from data by linguistic associations mining as there are many various methods for time series prediction developed but none of them generally outperforms all the others there always exists a danger of choosing a method that is inappropriate for a given time series to overcome such a problem distinct ensemble techniques that combine several individual forecasts are being proposed in this contribution we employ the so called fuzzy rule based ensemble this method is constructed as a linear combination of a small number of forecasting methods where the weights of the combination are determined by fuzzy rule bases based on time series features such as trend seasonality or stationarity for identification of fuzzy rule bases we use the linguistic association mining a huge experimental justification is provided

analytical integrations in 3d bem for elliptic problems evaluation and implementation the present publication deals with 3d elliptic boundary value problems potential stokes elasticity in the framework of linear isotropic and homogeneous materials numerical approximation of the unique solution is achieved by 3d boundary element methods bems adopting polynomial test and shape functions of arbitrary degree on flat triangular discretizations the closed form of integrals that are involved in the 3d bems is proposed and discussed analyses are performed for all operators single layer double layer hypersingular the lebesgue integrals are solved working in a local coordinate system for singular integrals both a limit to the boundary as well as the finite part of hadamard lectures on cauchy s problem in linear partial differential equations yale university press new haven ct u s a 1923 approach have been considered copyright 2010 john wiley sons ltd

an accurate and efficient scheme for acoustic structure interaction problems based on unstructured mesh abstract this paper focuses on the accurate and efficient numerical implementation of acoustic structure coupling formulations using the edge based smoothed finite element method for the flexible shell and the gradient weighted finite element method for the acoustic fluid field namely the es gw fem the shell is discretized using the simplest linear triangular elements and the edge based smoothing domain is then constructed by introducing an edge local coordinate system the edge based smoothing operation is performed on the smoothing domain as for the acoustic fluid domain the tetrahedron elements are adopted a compacted support domain is then constructed and the gradient weighted operation is performed on the support domain to model the exterior acoustic domain an artificial boundary is introduced and the dirichlet to neumann dtn boundary condition is imposed based on the appropriate compatibility and equilibrium conditions on the interface boundaries the coupled es gw fem formulation is finally obtained both the interior acoustic structure coupled problems and exterior acoustic structure coupled problems are available as the dtn boundary is considered numerical examples demonstrate that the coupled es gw fem achieves much higher accuracy and works more reliably compared with the coupled fem fem in solving practical engineering problems

direct evaluation of double singular integrals and new free terms in 2d symmetric galerkin bem in this paper a new general algorithm is developed for the direct evaluation of all singular double integrals arising in the 2d galerkin bem including those with hypersingular kernels a distinguishing feature of the proposed method is that double singular integrals are treated as a whole that is not as inner integrals followed by outer ones therefore when applied to the symmetric galerkin bem the proposed technique is strictly symmetry preserving moreover a careful analysis of the limiting process is performed which shows that some new free terms may arise

finite element solution of a boundary integral equation for mode i embedded three dimensional fractures the singular integral equation governing the opening of a mode i embedded three dimensional fracture in an infinite solid was solved by applying the finite element method the strategy is to formulate the equation into weak form and to transfer the differentiation from the singular term 1 r in the equation to the test function a numerical algorithm was thus developed the numerical solutions for circular and elliptical fractures under the action of polynomial pressure distributions were compared with the analytical solutions by green and sneddon 12 irwin 13 shah and kobayashi14 and nishioka and atluri 16 the results have demonstrated that the numerical method reported is accurate and efficient

fundamental solutions for linear viscoelastic continua abstract the full set of fundamental solutions for the linear viscoelastic problem is derived from the relevant elastic fundamental solutions using the well known so called correspondence principle the fundamental solutions are given for the 3d continuum the 2d plane strain and the 2d plane stress problem using a wide range of linear viscoelastic constitutive law models finally the possible fields of application of the determined fundamental solutions are given using symmetric bie formulations in space and time

an energy approach to space time galerkin bem for wave propagation problems in this paper we consider dirichlet or neumann wave propagation problems reformulated in terms of boundary integral equations with retarded potential starting from a natural energy identity a space time weak formulation for 1d integral problems is briefly introduced and continuity and coerciveness properties of the related bilinear form are proved then a theoretical analysis of an extension of the introduced formulation for 2d problems is proposed pointing out the novelty with respect to existing literature results at last various numerical simulations will be presented and discussed showing unconditional stability of the space time galerkin boundary element method applied to the energetic weak problem copyright 2009 john wiley sons ltd

hypersingular integrals in boundary element fracture analysis a new general purpose boundary element method for domains with cracks has been recently developed this technique avoids the use of a multi domain decomposition by including an additional integral equation expressing the boundary condition on the crack the principal requirement of this technique is the analytic determination of certain hypersingular integrals of the green s function which arise from this equation in order to establish the applicability of this method for fracture these integrals are evaluated herein for the kelvin solution of the three dimensional navier equations of linear elasticity numerical results for fracture problems using the single domain boundary element analysis are also presented

learning the membership function contexts for mining fuzzy association rules by using genetic algorithms different studies have proposed methods for mining fuzzy association rules from quantitative data where the membership functions were assumed to be known in advance however it is not an easy task to know a priori the most appropriate fuzzy sets that cover the domains of quantitative attributes for mining fuzzy association rules this paper thus presents a new fuzzy data mining algorithm for extracting both fuzzy association rules and membership functions by means of a genetic learning of the membership functions and a basic method for mining fuzzy association rules it is based on the 2 tuples linguistic representation model allowing us to adjust the context associated to the linguistic term membership functions experimental results show the effectiveness of the framework

hypersingular kernel integration in 3d galerkin boundary element method we consider cauchy singular and hypersingular boundary integral equations associated with 3d potential problems defined on polygonal domains whose solutions are approximated with a galerkin boundary element method related to a given triangulation of the boundary in particular for constant and linear shape functions the most frequently used basis functions we give explicit results of the analytical inner integrations and suggest suitable quadrature schemes to evaluate the outer integrals required to form the galerkin matrix elements these numerical indications are given after an analysis of the singularities arising in the whole integration process which is valid also for shape functions of higher degrees

efficient analytical integration of symmetric galerkin boundary integrals over curved elements elasticity formulation abstract substantial improvements are reported in the computational efficiency of galerkin boundary element analysis bea 1employing curved continuous boundary elements for elasticity problems a direct analytical treatment of the singular and hypersingular double integrations employing a limit to the boundary definition is adapted to gain computational economy symbolic manipulation has been employed to derive the analytical expressions for the singular contributions to these double integrals the analytical regularization procedure separates the potentially singular galerkin integrands into an essentially singular but simple part plus a regular remainder that can be integrated numerically the exact finite contributions from the simplified singular terms are then computed analytically it is shown that the key to containing the explosive growth in the length of the formulae associated with such a hybrid analytical numerical integration scheme is the strategic timing of when to take the limit to the boundary this regularization also isolates the contribution from the curvature of the boundary element thus facilitating enhanced computational efficiency in problems with many straight elements although the evaluation of the integrals of the kelvin fundamental solution essentially follows the procedures described earlier for the scalar laplace equation the analytical treatment is now more involved in terms of the complexity and number of terms present in each of these second rank tensor kernel functions the complete analytical formulation is explicitly provided in a series of tables example problems indicate that with these techniques galerkin symmetric bea can be more efficient than collocation for moderate or large scale problems

interface relaxation algorithms for bem bem coupling and fem bem coupling this paper presents several interface relaxation algorithms for boundary element boundary element coupling bem bem and for finite element boundary element coupling fem bem the domain of the original problem is sub divided into sub domains which are modeled by the finite element or boundary element methods the multi domain system is coupled using smoothing operators on the inter domain boundaries separate computations for the bem and fem sub domains and successive update of the boundary conditions at the interfaces are performed until convergence is achieved the interface relaxation coupling algorithms preserve the nature of the fem and bem further they do not require any access to the matrices generated by the fem or bem and make it easier to utilize different software in different sub domains

on the removal of rigid body motions in the solution of elastostatic problems by direct bem a theoretical and numerical study of the removal of rigid body motions in the solution of the boundary form of somigliana identity and of the corresponding discretized linear system of the direct bem is presented this study is based on the fredholm theory of linear operators and mechanical aspects of the problem various methods suitable for implementation in bem codes are analyzed and relations between apparently different methods are shown the relation between global equilibrium conditions and solvability of the discretized linear system of the direct bem is discussed

stability of crack fronts under griffith criterion a computational approach using integral equations and domain derivatives of potential energy abstract this paper deals with the numerical study of stability and instantaneous extension of cracks under griffith criterion within the classical linear fracture mechanics framework first and second order domain derivatives of the potential energy w in crack extensions play a central role in the mathematical formulation of such situations the proposed solution strategy called the integral method by reference to the fem based method possesses the following main characteristics i it is based on a symmetric galerkin boundary integral formulations and ii explicit expressions for the domain derivatives of w are established using lagrangian formulas so that the derivations do not increase crack front singularities the numerical solution procedure for the extension velocity problem including all domain derivative evaluations is entirely supported by the boundary element mesh of the current crack configuration numerical differentiation is avoided numerical examples for an isolated crack in a 3 d unbounded elastic body show that in practice an excellent accuracy can be achieved for the energy release rate the second order domain derivatives of w and the prediction of stability or instability of crack growth

a variational approach to boundary element elastodynamic analysis and extension to multidomain problems abstract time dependent discontinuities of both tractions and displacements are considered on the boundary of a homogeneous linear elastic solid conceived as embedded in the elastic space the analysis of the dynamic response of the solid to external actions is formulated in the time domain by means of suitable integral representations of boundary displacements and of boundary tractions using time dependent fundamental solutions the integral operator generated is proven to be symmetric in both space and time with respect to a time convolutive bilinear form as a consequence the history of boundary tractions and displacements along any assigned time interval 0 is shown to be characterized by a variational theorem the variational formulation developed is generalized to zonewise homogeneous systems and to elastically constrained bodies the linear algebraic equations generated by boundary element modelling in space and time turn out to exhibit symmetry of the coefficient matrix

sgbem with lagrange multipliers applied to elastic domain decomposition problems with curved interfaces using non matching meshes an original approach to the solution of linear elastic domain decomposition problems by the symmetric galerkin boundary element method is developed the approach is based on searching for the saddle point of a new potential energy functional with lagrange multipliers the interfaces can be either straight or curved open or closed the two coupling conditions equilibrium and compatibility along an interface are fulfilled in a weak sense by means of lagrange multipliers interface displacements and tractions which enables non matching meshes to be used at both sides of interfaces between subdomains the accuracy and robustness of the method is tested by several numerical examples where the numerical results are compared with the analytical solution of the solved problems and the convergence rates of two error norms are evaluated for h refinements of matching and non matching boundary element meshes copyright 2010 john wiley sons ltd

a coupling of multi zone curved galerkin bem with finite elements for independently modelled sub domains with non matching nodes in elasticity when the different parts of a structure are modelled independently by bem or fem methods it is sometimes necessary to put the parts together without remeshing of the nodes along the part interfaces frequently the nodes do not match along the interface in this work the symmetric galerkin multi zone curved boundary element is a fully symmetric formulation and is the method used for the boundary element part for bem fem coupling it is then necessary to interpolate the tractions in between the non matching nodes for the fem part finally the coupling is achieved by transforming the finite element domains to equivalent boundary element domains in a block symmetric formulation this system is then coupled with a boundary element domain with non matching nodes in between copyright 2004 john wiley sons ltd

dynamic elastic plastic analysis by a symmetric galerkin boundary element method with time independent kernels abstract boundary integral equations formulated by the combined use of single layer and double layer sources in such a way that the integral operator is symmetric with respect to a suitable bilinear form and their discretization by a galerkin weighted residual procedure are the basic features of the symmetric galerkin boundary element method sgbem this approach which has been applied to various mechanical problems in the last few years is proposed and developed herein for elastic plastic dynamic analysis using elastostatic kernels i e time independent green functions for unbounded spaces for displacements and tractions on the boundary and for stresses and displacements on the domain thus only double integrations are required instead of quadruple required by elastodynamic kernels at the price of domain integrals regularization procedures for singular integrals are developed assuming material behaviours as elastic plastic stable in drucker sense and suitable multifield modelling in space basic results for a computational theory are established extremum property and uniqueness of time step solution convergence of an iterative solution algorithm algorithmic stability along the step sequence finally the sgbem developed is corroborated by two numerical comparative tests

elastoplastic bie analysis of cracked plates and related problems part 1 formulation the boundary integral equation formulation for two dimensional planar fracture mechanics based on the use of a special green s function forms the basis of this analytical paper the green s function method is extended to problems of anelastic strain distributions e g elastoplasticity thermal gradients residual strains through a volume area integral the role of the elastic green s function for the crack problem on the distribution of elastoplastic strains is reviewed further new analytical results for elastic stress intensity factor models for the residual strain and thermal gradient problems are presented part 2 of this paper outlines the numerical solution strategy and results for several test problems