nonlinear panel flutter by finite element method les equations non lineaires sont calculees a partir de considerations energetiques et la force d etirement non lineaire est formulee en termes de deplacement transversal seul

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

a mixed variational formulation based on exact intrinsic equations for dynamics of moving beams abstract a nonlinear intrinsic formulation for the dynamics of initially curved and twisted beams in a moving frame is presented the equations are written in a compact matrix form without any approximations to the geometry of the deformed beam reference line or to the orientation of the intrinsic cross section frame in accordance with previously published work when effects of warping on the dynamics and local constraints on the cross sectional deformation are ignorable the in and out of plane st venant warping displacements which are fully coupled for nonhomogeneous anisotropic beams need only be included explicitly in the determination of a suitable elastic law a two dimensional problem and need not be considered explicitly in the one dimensional equations governing global deformation in this paper it is presupposed that such an elastic law is given as a one dimensional strain energy function thus the present equations which are based on only six generalized strain variables are valid for beams with closed cross sections and for which warping is unrestrained when simplified for various special cases they agree with similar intrinsic equations in the literature although the resulting equations are newtonian in structure closely resembling euler s dynamical equations for a rigid body the formulation adheres to a variational approach throughout thus providing a link between newtonian and energy based methods in particular the present development provides substantial insight into the relationships among variational formulations in which different displacement and rotational variables are used as well as between these formulations and newtonian ones for computational purposes a compact and complete mixed variational formulation is presented that is ideally suited for development of finite element analyses finally a specialized version of the intrinsic equations is developed in which shear deformations is suppressed

interpretability of linguistic fuzzy rule based systems an overview of interpretability measures linguistic fuzzy modelling developed by linguistic fuzzy rule based systems allows us to deal with the modelling of systems by building a linguistic model which could become interpretable by human beings linguistic fuzzy modelling comes with two contradictory requirements interpretability and accuracy in recent years the interest of researchers in obtaining more interpretable linguistic fuzzy models has grown whereas the measures of accuracy are straightforward and well known interpretability measures are difficult to define since interpretability depends on several factors mainly the model structure the number of rules the number of features the number of linguistic terms the shape of the fuzzy sets etc moreover due to the subjectivity of the concept the choice of appropriate interpretability measures is still an open problem in this paper we present an overview of the proposed interpretability measures and techniques for obtaining more interpretable linguistic fuzzy rule based systems to this end we will propose a taxonomy based on a double axis complexity versus semantic interpretability considering the two main kinds of measures and rule base versus fuzzy partitions considering the different components of the knowledge base to which both kinds of measures can be applied the main aim is to provide a well established framework in order to facilitate a better understanding of the topic and well founded future works

a higher order beam finite element for bending and vibration problems abstract the finite element equations for a variationally consistent higher order beam theory are presented for the static and dynamic behavior of rectangular beams the higher order theory correctly accounts for the stress free conditions on the upper and lower surfaces of the beam while retaining the parabolic shear strain distribution the need for a shear correction coefficient is therefore eliminated full integration of the shear stiffness terms is shown to result in the recovery of the kirchhoff constraint for thin beams without introducing spurious locking constraints the accuracy of this formulation is demonstrated by using several numerical examples for the cases of small and large displacements for a hinged hinged beam the linear thickness shear mode frequency can be matched with the timoshenko frequency to yield a shear coefficient of 0 824 matching the bending frequencies between the two theories indicates a shear coefficient for the timoshenko theory that changes with mode number and slenderness ratio the influence of in plane inertia and slenderness ratio on the non linear frequency is examined for beams with a number of different support conditions

genetic training instance selection in multiobjective evolutionary fuzzy systems a coevolutionary approach when dealing with datasets that are characterized by a large number of instances multiobjective evolutionary learning moel of fuzzy rule based systems frbss suffers from high computational costs mainly because of the fitness evaluation the use of a reduced set of representative instances in place of the overall training set ts would considerably lessen the computational effort even though a large number of papers have proposed instance selection approaches mainly in classification problems how this selection should be performed especially in the context of regression is still an open issue in this paper we tackle the instance selection problem in the framework of moel of frbss through a coevolutionary approach in the execution of the moel periodically a single objective genetic algorithm soga evolves a population of reduced tss the soga aims to maximize a purposely defined index which measures how much the pareto fronts computed by using respectively the reduced ts and the overall ts are close to each other the closer the fronts the more the reduced ts is representative of the overall ts during the execution of the moel the rule base and the membership function parameters of the fuzzy sets are concurrently learned by maximizing the accuracy and minimizing the complexity we tested our approach on 12 large datasets we adopted reduced tss composed of 5 10 and 20 of the overall ts using nonparametric statistical tests we verified that with 10 and 20 of the overall ts the pareto front approximations that are generated by our coevolutionary approach are comparable with the ones generated by applying the moel with the overall ts although the coevolution allows us to save up to 86 36 of the execution time in addition the analysis of the behavior of three representative solutions on the test set highlights that the use of the reduced tss does not affect the generalization capabilities of the generated frbss

explicit free floating beam element summary a two node free floating beam element capable of undergoing arbitrary large displacements and finite rotations is presented in explicit form the configuration of the beam in three dimensional space is represented by the global components of the position of the beam nodes and an associated set of convected base vectors directors the local constitutive stiffness is derived from the complementary energy of a set of six independent deformation modes each corresponding to an equilibrium state of constant internal force or moment the deformation modes are characterized by generalized strains formed via scalar products of the element related vectors this leads to a homogeneous quadratic strain definition in terms of the generalized displacements whereby the elastic energy becomes at most bi quadratic additionally the use of independent equilibrium modes to set up the element stiffness avoids interpolation of kinematic variables resulting in a locking free formulation in terms of three explicit matrices a set of classic benchmark examples illustrates excellent performance of the explicit beam element copyright 2014 john wiley sons ltd

a finite element method for non linear forced vibrations of beams geometric non linearities for large amplitude free and forced vibrations of beam are investigated longitudinal displacement and inertia are included in the formulation the finite element method is used the harmonic force matrix is introduced and derived various out of plane and inplane boundary conditions are considered results showing the dependence of the amplitude on the frequency ratio and on the strain are presented for different boundary conditions and loads it is concluded that the effects of longitudinal deformation and inertia are to reduce the non linearity

bifurcations and internal resonances in space curved rods abstract the paper discusses a geometrically non linear model of space curved beams the timoshenko type model is used which includes the shear effects and rotatory inertia the motion of the system is described by a non linear matrix equation which accounts for non linearities up to the second order to solve the non linear problem discretization methods based on the galerkin method are used and the resulting non linear eigenvalue problem is then solved by the continuation methods the analysis of the discretized problem allows the study of the bifurcations of solutions the post bifurcation analysis is used to explain the phenomenon of internal resonance which is of much importance in the prediction of the dynamic response of the analyzed systems the approach is illustrated by numerical examples which consider the free vibration of beams and circular arches with different boundary conditions

on a non linear formulation for curved timoshenko beam elements considering large displacement rotation increments summary an incremental total lagrangian formulation for curved beam elements that includes the effect of large rotation increments is developed a complete and symmetric tangent stiffness matrix is obtained and the numerical results show in general an improvement over the standard formulation where the assumption of infinitesimal rotation increments is made in the derivation of the tangent stiffness matrix

fuzzy modeling of high dimensional systems complexity reduction and interpretability improvement fuzzy modeling of high dimensional systems is a challenging topic this paper proposes an effective approach to data based fuzzy modeling of high dimensional systems an initial fuzzy rule system is generated based on the conclusion that optimal fuzzy rules cover extrema redundant rules are removed based on a fuzzy similarity measure then the structure and parameters of the fuzzy system are optimized using a genetic algorithm and the gradient method during optimization rules that have a very low firing strength are deleted finally interpretability of the fuzzy system is improved by fine training the fuzzy rules with regularization the resulting fuzzy system generated by this method has the following distinct features 1 the fuzzy system is quite simplified 2 the fuzzy system is interpretable and 3 the dependencies between the inputs and the output are clearly shown this method has successfully been applied to a system that has 11 inputs and one output with 20 000 training data and 80 000 test data

vibration analysis of non linear beams subjected to a moving load using the finite element method this paper is concerned with the non linear vibration of immovably supported variable beams in which the geometric non linearity due to the axial force generated by stretching the middle surface is taken into account when the beam is subjected to a moving load the dynamic deflections of the beam are computed by using a galerkin finite element formulation and the time differential terms are integrated by using the implicit direct integration method three types of approximations for solving the non linear problem are considered in the first of which both the longitudinal deflections and inertia are considered with only the longitudinal deflections being considered and in the second neither the longitudinal deflections nor inertia in the third the results obtained by using these non linear models are numerically compared with that obtained by the linear model

explicit isogeometric collocation for the dynamics of three dimensional beams undergoing finite motions abstract we initiate the study of three dimensional shear deformable geometrically exact beam dynamics through explicit isogeometric collocation methods the formulation we propose is based on a natural combination of the chosen finite rotations representation with an explicit geometrically consistent lie group time integrator we focus on extending the integration scheme originally proposed for rigid body dynamics to our nonlinear initial boundary value problem where special attention is required by neumann boundary conditions the overall formulation is simple and only relies on a geometrically consistent procedure to compute the internal forces once control angular and linear accelerations of the beam cross sections are obtained from the previous time step the capabilities of the method are shown through numerical applications involving very large displacements and rotations and different boundary conditions

solving linearly constrained matrix least squares problem by lsqr abstract matrix iterative algorithm lsqr is proposed for solving the linearly constrained matrix least squares ls problem with the special properties of constraint matrix kronecker product and the coordinate mapping from the constrained space to its independent parameter space we transform the constrained matrix ls problem to the unconstrained long vector least squares problem and rewrite the corresponding vector form algorithm back to the matrix one the resulting matrix form iteration only consists of matrix matrix product and does not involve the kronecker product numerical results are reported to show the feasibility of the proposed method

iterative algorithms for solving the matrix equation axb cx td e in this paper we propose two iterative algorithms to solve the matrix equation axb cx td e the first algorithm is applied when the matrix equation is consistent in this case for any special initial matrix x 1 a solution the minimal frobenius norm solution can be obtained within finite iteration steps in the absence of roundoff errors the second algorithm is applied when the matrix equation is inconsistent in this case for any special initial matrix x 1 a least squares solution the minimal frobenius norm least squares solution can be obtained within finite iteration steps in the absence of roundoff errors some examples verify the efficiency of these algorithms

an iterative method for the least squares symmetric solution of the linear matrix equation axb c abstract this paper an iterative method is presented to solve the minimum frobenius norm residual problem min axb c with unknown symmetric matrix x by this iterative method for any initial symmetric matrix x0 a solution x can be obtained within finite iteration steps in the absence of roundoff errors and the solution x with least norm can be obtained by choosing a special kind of initial symmetric matrix in addition the unique optimal approximation solution x to a given matrix x in frobenius norm can be obtained by first finding the least norm solution x of the new minimum residual problem min a x b c with unknown symmetric matrix x where c c a x x t 2 b given numerical examples are show that the iterative method is quite efficient

closed form solutions to the nonhomogeneous yakubovich transpose matrix equation abstract the nonhomogeneous yakubovich transpose matrix equation x a x t b c y r which contains the well known kalman yakubovich transpose matrix equation and general discrete lyapunov transpose matrix equation as special cases has many important applications in control system theory this study presents two methods to obtain the closed form solutions of the nonhomogeneous yakubovich transpose matrix equation moreover the equivalent forms of the solutions are provided and one of the solutions is established with the controllability matrix the observability matrix and symmetric operator matrix

nonlinear dynamic analysis of an eccentrically prestressed damped beam under a concentrated moving harmonic load this paper focuses on the geometrically nonlinear dynamic analysis of an eccentrically prestressed simply supported damped beam subjected to a concentrated moving harmonic load the nonlinear dynamic deflections of the beam are obtained by polynomial functions the kelvin voigt model for the material of the beam is used two coupled nonlinear systems of equations of motion are derived using lagrange s equations under the assumptions of the euler bernoulli beam theory with the von karman s nonlinear strain displacement relationships the rotary inertia axial displacement and axial inertia are included in the formulation the nonlinear equations of motion are solved by using the implicit time integration method of newmark in conjunction with the newton raphson iteration method in this study the effects of large deflections the internal damping of the beam the velocity of the moving harmonic load the prestress load the eccentricity of the prestress load and the excitation frequency on the dynamic response of the beam are discussed the obtained results are compared with the results based on the linear beam theory convergence studies are performed numerical results show that the above mentioned effects play a very important role in the deflections of the beam

bcr method for solving generalized coupled sylvester equations over centrosymmetric or anti centrosymmetric matrix abstract this paper introduces another version of biconjugate residual method bcr for solving the generalized coupled sylvester matrix equations over centrosymmetric or anti centrosymmetric matrix we prove this version of bcr algorithm can find the centrosymmetric solution group of the generalized coupled matrix equations for any initial matrix group within finite steps in the absence of round off errors furthermore a method is provided for choosing the initial matrices to obtain the least norm solution of the problem at last some numerical examples are provided to illustrate the efficiency and validity of methods we have proposed

vibration analysis of a non linear beam subjected to moving loads by using the galerkin method abstract this paper presents the analysis of dynamic deflections of a beam including the effects of geometric non linearity subjected to moving vehicle loads the beam is assumed to be elastic and simply supported with immovable ends and the vehicles are assumed to be single degree of freedom spring mass damper with the vehicles moving on the beam from one end to the other the dynamic reflections of the beam and vehicles are computed by using the galerkin method thus the dynamic deflections are assumed to be a set of time functions multiplied by approximate functions respectively and the time functions are numerically computed by solving the non linear differential equations by the newmark method

vibration and buckling analysis of rectangular plates with nonlinear elastic end restraints against rotation abstract the fundamental natural frequencies and buckling loads of a rectangular plate with nonlinearly rotational restraints are obtained by using the finite element technique if the rotational springs are unsymmetric the iterative scheme must be employed to acquire the solutions of the nonlinear problem the values which describe the free vibration and stability behaviour of the plate will increase when either the parameters of rotational spring or the initial rotational angles increase incidentally it can be concluded that these results grown nonlinearly with respect to either the linear or nonlinear rotational spring constants finally both the frequency and stability parameters are evaluated for several boundary conditions which are quite useful in engineering analysis and design

an iterative algorithm for the least frobenius norm least squares solution of a class of generalized coupled sylvester transpose linear matrix equations abstract the iterative algorithm of a class of generalized coupled sylvester transpose matrix equations is presented we prove that if the system is consistent a solution can be obtained within finite iterative steps in the absence of round off errors for any initial matrices if the system is inconsistent the least squares solution can be obtained within finite iterative steps in the absence of round off errors furthermore we provide a method for choosing the initial matrices to obtain the least frobenius norm least squares solution of the problem finally numerical examples are presented to demonstrate that the algorithm is efficient

lagrange type formulation for finite element analysis of non linear beam vibrations abstract a lagrange type formulation for finite element analysis of non linear vibrations of immovably supported beams is presented two equations of motion coupled in axial and transverse displacements are derived by using lagrange s equations by neglecting the in plane inertial effects these equations are written in terms of the transverse displacement alone upon defining certain properties for the non linear oscillatory behaviour of the transverse displacement the governing equation is reduced to an equation in space alone from which the eigenvalue like quantity is computed the governing equation is solved in two ways a direct iteration technique is used in the first method to compute a numerically exact mode shape and the corresponding frequency a rayleigh quotient type of formulation similar to linear vibration analysis is used in the second approach to evaluate the frequency of vibration for a fundamental mode which is determined from a linear fem model and is maintained constant at all amplitudes numerical results are compared with available results and they corroborate the observations of earlier research workers

on the sylvester equation ax x b c abstract we consider the solution of the sylvester equations ax x b c for t h and a b c n n and the related linear matrix equations axb x c axb cx d e and ax x a c solvability conditions and numerical methods are considered in terms of the generalized and periodic schur and qr decompositions we emphasize the square cases where m n but the rectangular cases will be considered

a matrix crs iterative method for solving a class of coupled sylvester transpose matrix equations abstract in this paper we apply kronecker product and vectorization operator to extend the conjugate residual squared crs method for solving a class of coupled sylvester transpose matrix equations some numerical examples are given to compare the accuracy and efficiency of the new matrix iterative method with other methods presented in the literature numerical results validate that the proposed method can be much more efficient than some existing methods

application of the ritz method to the analysis of non linear free vibrations of beams this paper presents an analytical solution for geometrically non linear free vibrations of beams with elastically supported ends in the horizontal direction the equation of motion is obtained by employing hamilton s principle and assuming that horizontal inertia forces can be neglected the ritz method with a continuum solution and an iterative procedure are used for determining the frequencies and non linear modes of vibrations the orthogonality conditions for these modes are also discussed numerical results for various beam boundary conditions are presented and compared with available results

on the robustness of type 1 and interval type 2 fuzzy logic systems in modeling research on the robustness of fuzzy logic systems flss an imperative factor in the design process is very limited in the literature specifically when a system is subjected to small deviations of the sampling points operating points it is of great interest to find the maximum tolerance of the system which we refer to as the system s robustness in this paper we present a methodology for the robustness analysis of interval type 2 flss it2 flss that also holds for t1 flss hence making it more general a procedure for the design of robust it2 flss with a guaranteed performance better than or equal to their t1 counterparts is then proposed several examples are performed to demonstrate the effectiveness of the proposed methodologies it was concluded that both t1 and it2 flss can be designed to achieve robust behavior in various applications and preference one or the other in general is application dependant it2 flss having a more flexible structure than t1 flss exhibited relatively small approximation errors in the several examples investigated the methodologies presented in this paper lay the foundation for the design of flss with robust properties that will be very useful in many practical modeling and control applications

dynamics of a flexible beam and a system of rigid rods with fully inverse one sided boundary conditions the problem of the fully inverse time dependent boundary value of a flexible beam where all six boundary conditions on one side of the beam are known is discussed a linear problem of a euler beam and a nonlinear problem of a system of rigid rods with connecting rotational springs are solved analytically and restrictions associated with the transfer of boundary conditions from one side of the beam to the other are analyzed it is shown that if the boundary conditions are analytic then both linear and the nonlinear solutions exist and they depend solely on these boundary constraints a case study shows that a limited number of rod elements and time derivatives of the boundary conditions is sufficient in such cases for close simulation of a flexible beam possible applications of the fully inverse solution in the areas of robotics and measurement are discussed

a proposal for the genetic lateral tuning of linguistic fuzzy systems and its interaction with rule selection linguistic fuzzy modeling allows us to deal with the modeling of systems by building a linguistic model which is clearly interpretable by human beings however since the accuracy and the interpretability of the obtained model are contradictory properties the necessity of improving the accuracy of the linguistic model arises when complex systems are modeled to solve this problem one of the research lines in recent years has led to the objective of giving more accuracy to linguistic fuzzy modeling without losing the interpretability to a high level in this paper a new postprocessing approach is proposed to perform an evolutionary lateral tuning of membership functions with the main aim of obtaining linguistic models with higher levels of accuracy while maintaining good interpretability to do so we consider a new rule representation scheme base on the linguistic 2 tuples representation model which allows the lateral variation of the involved labels furthermore the cooperation of the lateral tuning together with fuzzy rule reduction mechanisms is studied in this paper presenting results on different real applications the obtained results show the good performance of the proposed approach in high dimensional problems and its ability to cooperate with methods to remove unnecessary rules

a strategy to identify exciting forces acting on structures the strategy for identifying the external forces acting on structures sketched by turco comput method appl mech eng 1998 165 291 306 is extended to the dynamic case starting from the measurement of the stress or strain history in a suitable number of points of the structure the exciting forces are reconstructed this inverse problem is tackled in the frequency domain by using the standard tools of computational mechanics along with a classical approach to treat ill conditioned problems some numerical results relating to pin jointed trusses are discussed in order to validate the proposed strategy copyright 2005 john wiley sons ltd

free vibrations of a certain geometrically nonlinear system with initial imperfection the equations of motion of a beam are assumed within the framework of the moderately large bending theory the effects of an initial imperfection and amplitude on the nonlinear vibration frequency and value of axial internal force in a beam are presented for solving the problem the lindstedt poincare method is used

an iteration method for the symmetric solutions and the optimal approximation solution of the matrix equation axb c an iteration method is constructed to solve the linear matrix equation axb c over symmetric x by this iteration method the solvability of the equation axb c over symmetric x can be determined automatically when the equation axb c is consistent over symmetric x its solution can be obtained within finite iteration steps and its least norm symmetric solution can be obtained by choosing a special kind of initial iteration matrix furthermore its optimal approximation solution to a given matrix can be derived by finding the least norm symmetric solution of a new matrix equation axb c finally numerical examples are given for finding the symmetric solution and the optimal approximation symmetric solution of the matrix equation axb c

direct computation of critical equilibrium states for spatial beams and frames summary in this paper explicit formulas for second order derivatives of the residual vector with respect to the state variables for a geometrically exact 3d beam element based on the reissner s model are presented these derivatives are required when a direct non linear stability eigenvalue problem is solved by the newton s method if the external load is parametrized by a single parameter such an eigenvalue problem consists of solving the critical state variables the eigenmode and the critical load parameter from the equation system consisting of the equilibrium equations the criticality condition and some auxiliary conditions depending on the type of a critical point copyright 2011 john wiley sons ltd

toward solution of matrix equation x af x b c abstract this paper studies the solvability existence of unique solution closed form solution and numerical solution of matrix equation x af x b c with f x x t f x x and f x x h where x is the unknown it is proven that the solvability of these equations is equivalent to the solvability of some auxiliary standard stein equations in the form of w a w b c where the dimensions of the coefficient matrices a b and c are the same as those of the original equation closed form solutions of equation x af x b c can then be obtained by utilizing standard results on the standard stein equation on the other hand some generalized stein iterations and accelerated stein iterations are proposed to obtain numerical solutions of equation x af x b c necessary and sufficient conditions are established to guarantee the convergence of the iterations

dynamic finite element analysis of a nonlinear beam subjected to a moving load abstract in this paper the deterministic and random vibration analysis of a nonlinear beam on an elastic foundation subjected to a moving load which may simulate railway track runway etc has been performed the effects of longitudinal deflection and inertia have been considered so that the coupled equations of longitudinal and transverse deflections can be derived based on bernoulli euler hypothesis the randomness of the beam profile has been considered in such a way that the mean line of the beam is variable with respect to position in the vertical plane and is superimposed by stochastic uncertainty and the moving load travels along the beam with constant velocity or acceleration the deterministic and statistical dynamic responses of the beam have been calculated by using the galerkin s method in conjunction with the finite element method and the derived nonlinear system differential equation has been solved by using the implicit direct integration method in particular the standard deviation of the transverse deflection of the nonlinear beam has been calculated and presented by using the monte carlo simulation technique also the distribution of the midpoint deflection of the beam has been investigated by using the probability paper plot

genetic generation of fuzzy systems with rule extraction using formal concept analysis fuzzy classification systems have been widely researched with many approaches proposed in the literature several methods are available for the automatic definition of fuzzy classification systems which basically comprehend two tasks i the definition of the attributes in terms of fuzzy sets and ii the generation of a rule set containing the domain knowledge named fuzzy rule base genetic fuzzy systems are used to learn or tune in fuzzy classification systems some genetic approaches for learning the fuzzy rule base require the previous extraction of a set of rules to be used as the genetic search space in this paper we present the fca based method a proposal for the automatic generation of fuzzy rule bases which extracts a set of rules using the formal concept analysis theory directly from data after extracting the rules forming the genetic search space fca based uses a genetic algorithm to select the final rule base the last step of the fca based method is a rule pruning step in order to improve the interpretability of the fuzzy rule bases the extraction of rules proposed for the fca based algorithm presents polynomial complexity and does not require the predefinition of the number of rules to be extracted as it extracts rules directly from data the proposed method avoids the random extraction of rules it also presents the advantage of automatically extracting rules with variable number of conditions in their antecedents a feature subset selection method specifically designed for fuzzy classification systems is integrated into the fca based method in order to reduce the search space of solutions the fca based method is detailed and compared to eight different rule based fuzzy systems experimental results using 27 benchmark datasets and a 10 fold cross validation strategy show that fca based presents higher accuracy and statistically significant difference with seven of the eight compared methods

the symmetric solution of the matrix equations ax ya c axat bybt c and atxa btxb c d abstract the necessary and sufficient conditions for the existence of and the expressions for the symmetric solutions of matrix equations i ax ya c ii axa t byb t c and iii a t xa b t xb c d are derived in addition the minimum 2 norm least squares symmetric solution of equation i the minimum 2 norm symmetric solution of equation ii and the least squares solution of equation iii are obtained

structure identification of fuzzy model abstract the problems of structure identification of a fuzzy model are formulated a criterion for the verification of a structure is discussed using the criterion an algorithm for identifying a structure is suggested further a successive identification algorithm of the parameters is suggested the proposed methods are applied to an example

numerical solution procedures for nonlinear elastic rods using the theory of a cosserat point the theory of a cosserat point is developed as a continuum model which is inherently nonlinear and is valid for arbitrary constitutive equations here attention is confined to nonlinear elastic response which is hyperelastic with a strain energy function but large displacements deformations and rotations are allowed it is shown that the theory of a cosserat point can be used to formulate a numerical solution procedure for the dynamic three dimensional motion of nonlinear curved rods by modeling the rod as a set of n connected cosserat points like finite elements specifically the cosserat model allows for axial extension tangential shear deformation normal cross sectional extension normal cross sectional shear deformation and rotary inertia the cosserat approach ensures that the global forms of the balances of linear and angular momentum are satisfied and the hyperelastic nature of the constitutive equations is preserved since the response functions are determined by derivatives of a strain energy function a number of static example problems have been considered which examine the influence of shear deformation by comparing cosserat solutions with nonlinear solutions of an elastica

a semi analytical approach to the non linear dynamic response problem of beams at large vibration amplitudes part ii multimode approach to the steady state forced periodic response abstract the semi analytical approach to the non linear dynamic response of beams based on multimode analysis has been presented in part i of this series of papers azrar et al 1999 journal of sound and vibration 224 183 207 1 the mathematical formulation of the problem and single mode analysis have been studied the objective of this paper is to take advantage of applying this semi analytical approach to the large amplitude forced vibrations of beams various types of excitation forces such as harmonic distributed and concentrated loads are considered the governing equation of motion is obtained and can be considered as a multi dimensional form of the duffing equation using the harmonic balance method the equation of motion is converted into non linear algebraic form techniques of solution based on iterative incremental procedures are presented the non linear frequency and the non linear modes are determined at large amplitudes of vibration the basic function contribution coefficients to the displacement response for various beam boundary conditions are calculated the percentage of participation for each mode in the response is presented in order to appraise the relation to higher modes contributing to the solution also the percentage contributions of the higher modes to the bending moment near to the clamps are given in order to determine accurately the error introduced in the non linear bending stress estimated by different approximations solutions obtained in the jump phenomena region have been determined by a careful selection of the initial iteration at each frequency the non linear deflection shapes in various regions of the solution the corresponding axial force ratios and the bending moments are presented in order to follow the behaviour of the beam at large vibration amplitudes the numerical results obtained here for the non linear forced response are compared with those from the linear theory with available non linear results based on various approaches and with the single mode analysis

a simplified structure evolving method for mamdani fuzzy system identification and its application to high dimensional problems this paper proposes the simplified structure evolving method ssem for fuzzy system identification which improves our earlier work on the structure evolving learning method for fuzzy systems selm the improvement is that ssem applies a scheme that starts with the simplest fuzzy rule set with only one fuzzy rule instead of 2 n fuzzy rules as in selm where n is the number of input variables whilst retaining all the advantages of selm selm is able to solve the problem of the exponential increase of fuzzy rules however it requires a basic fuzzy rule set which is exponential to the number of input variables 2 n fuzzy rules as a starting point the improvement offered by ssem enables automatic feature selection and system structure identification and avoids inefficient rules and inefficient variable involvement for system identification this improvement enables fuzzy systems to be applicable to problems of any input dimension three benchmark examples with high dimension inputs are given to illustrate the advantages of the proposed algorithm

nonlinear finite element analysis of elastic systems under nonconservative loading natural formulation part ii dynamic problems abstract the paper presents a nonlinear finite element analysis of elastic structures subject to nonconservative forces attention is focused on the stability behaviour of such systems this leads mathematically to non self adjoint boundary value problems which are of great theoretical and practical interest in particular in connection with alternative modes of instability like divergence of flutter only quasistatic effects are however considered in the present part the methodology of our theory is general but the specific thrust of the present research is directed towards the analysis of structures acted upon by displacement dependent nonconservative follower forces in a finite element formulation the analysis of geometrically nonlinear elastic systems subject to such forces gives in general rise to a contributory nonsymmetric stiffness matrix known as the load correction matrix as a result the total tangent stiffness matrix becomes unsymmetric an indication of the non self adjoint character of the problem our theory is based on the natural mode technique 1 2 3 and permits i a a simple but elegant derivation of the load correction matrix the application of the general theory as evolved in this paper is demonstrated on the beam element in space a number of numerical examples are considered including divergence and flutter types of instability for which exact analytic solutions are known the problems demonstrate the efficiency of the present finite element formulation the paper furnishes also a novel and concise formulation of finite rotations in space which may be considered as a conceptual generalization of the theory presented in 2 3

on solutions of matrix equation axb cyd f in this paper the matrix equation with two unknown matrices x y of form axb cyd f is discussed by applying the canonical correlation decomposition ccd of matrix pairs we obtain expressions of the least squares solutions of the matrix equation and sufficient and necessary conditions for the existence and uniqueness of the solutions we also derive a general form of the solutions we also study the least squares hermitian skew hermitian solutions of equation axah cych f

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

a review of the application of multiobjective evolutionary fuzzy systems current status and further directions over the past few decades fuzzy systems have been widely used in several application fields thanks to their ability to model complex systems the design of fuzzy systems has been successfully performed by applying evolutionary and in particular genetic algorithms and recently this approach has been extended by using multiobjective evolutionary algorithms which can consider multiple conflicting objectives instead of a single one the hybridization between multiobjective evolutionary algorithms and fuzzy systems is currently known as multiobjective evolutionary fuzzy systems this paper presents an overview of multiobjective evolutionary fuzzy systems describing the main contributions on this field and providing a two level taxonomy of the existing proposals in order to outline a well established framework that could help researchers who work on significant further developments finally some considerations of recent trends and potential research directions are presented

isogeometric configuration design sensitivity analysis of finite deformation curved beam structures using jaumann strain formulation abstract using an isogeometric approach a continuum based configuration design sensitivity analysis dsa method is developed for curved kirchhoff beams with multi patch junctions under the total lagrangian formulation large deformations considering the initial curvature of curved beams are described by geometrically exact beam theory gebt and jaumann strain formulation in the isogeometric approach the higher order continuity and the exact description of initial geometry are naturally embedded using nurbs basis functions in multi patch models c 0 continuity of physical displacement or c 1 continuity of displacement component at junction is weakly imposed using the lagrange multiplier method the superior accuracy of isogeometric analysis iga is verified through the comparison with the results of finite element analysis fea using cubic hermite interpolation in the dsa a material derivative is utilized and the kinematical description of gebt is consistently employed to express orientation design variations contrary to the iga based dsa the hermite basis function explicitly depends on design in the fea based dsa due to its element length parameter moreover since the design velocity field is approximated using the nodal velocity imposed at nodal tangential vector the amount of design perturbations should be very small to obtain precise design sensitivity

iterative algorithms for the minimum norm solution and the least squares solution of the linear matrix equations abstract in this paper two iterative algorithms are proposed to solve the linear matrix equations a 1 xb 1 c 1 x t d 1 m 1 a 2 xb 2 c 2 x t d 2 m 2 when the matrix equations are consistent by the first algorithm a solution x can be obtained within finite iterative steps in the absence of roundoff error for any initial value furthermore the minimum norm solution can be got by choosing a special kind of initial matrix additionally the unique optimal approximation solution to a given matrix x 0 can be derived by finding the minimum norm solution of a new matrix equations a 1 x b 1 c 1 x t d 1 m 1 a 2 x b 2 c 2 x t d 2 m 2 when the matrix equations are inconsistent we present the second algorithm to find the least squares solution with the minimum norm finally two numerical examples are tested by matlab the results show that these iterative algorithms are efficient

a timoshenko beam reduced order model for shape tracking with a slender mechanism abstract we consider a flexible bio inspired slender mechanism modeled as a timoshenko beam it is coupled to the environment by a continuous distribution of compliant elements we derive a reduced order model by projecting the governing partial differential equations along the linear modal basis of the timoshenko beam the coupling with the substrate allows us to formulate the problem in a control framework and eventually to treat the system as a sensor to reconstruct the profile of the substrate through the deformation of the body the coupling is modeled in the framework of two parameters elastic foundations the convergence of the reduced order model with increasing number of basis functions is addressed in a suitable h1 error norm a closed loop force control is simulated for shape morphing when the system is coupled with a smooth substrate

direct and inverse dynamics of a very flexible beam abstract the problem of direct and inverse dynamics of a very flexible plane beam was discussed and analyzed direct dynamics is referred to as an ordinary dynamics problem where initial conditions are known and where three conditions either forces or motion are prescribed at each end of the beam as boundary conditions partially or fully inverse dynamics are defined to be the case when some or all of the conditions are moved from one end to the other so that one end is overprescribed including both forces and motion and the constraints at the other end of the beam are partially or fully unspecified a new model for direct and inverse dynamics of a straight or curved planar beam at small strains and large deflections has been derived lagrange equations in a local frame of reference and a finite element method were utilized for the formulation the direct dynamics problems were solved by a fast and relatively simple linear iteration method and verified by results of existing programs for specific cases this formulation is particularly useful for more complicated constitutive relations on the other hand inverse dynamics solutions were stable for only short periods of time this result demonstrates the need for further research in the area of inverse dynamics practical application of the study may be considered in the field of robotics where very flexible beams may be used in order to reduce the number of arms and actuators in a robotics system

hierarchical finite element analyses of geometrically non linear vibration of beams and plane frames geometrically non linear vibrations of beams and plane frameworks are analyzed by the hierarchical finite element method hfem two main points are of interest the first is to compare polynomials trigonometric functions and beam eigenfunctions as displacement shape functions for beam hierarchical finite elements the second is to examine the suitability of the hfem for time domain non linear analyses

vibrational control of a flexible beam the effect of vibrations applied to a flexible beam is investigated a thorough analysis of an n l link approximation to the flexible beam is presented with bounds on the vibrations guaranteeing stability amplitude and frequency calculated the main conclusion which is quantified as well in our analysis is that the vibrations act to rigidify the flexible beam this conclusion brings very interesting potential applications some very preliminary laboratory experiments are also presented

calculation of eigenvalue and eigenvector derivatives for nonlinear beam vibrations a beam with immovable ends under large amplitude oscillations is axially subjected to an amplitudedependent stretching force which is induced by the geometrical nonlinearity the design sensitivity analysis for such a beam is investigated in this study two variational formulations pertaining to nonlinear beam vibration based on two different approximations of nonlinear stretching force are presented the analytical equations of design sensitivity analysis for these nonlinear equations are then derived finally a computational scheme using the finite element method is developed to calculate the design sensitivity derivatives of the eigenvalue and eigenvector numerically the numerical results show that the proposed algorithm for calculating design derivatives of nonlinear eigenvalues and eigenvectors is valid and compared with the direct finite difference method the proprosed algorithm is efficient

numerical formulations of elasto viscoplastic response of beams accounting for the effect of shear the finite deformation elasto viscoplastic response of beams is considered from a numerical point of view in this paper formulations in terms of stress resultants are discussed and extended to include viscoplastic material response by introducing rate equations for the evolution of the finite inelastic deformations special attention is given to the objectivity of the rates and to the form of the plastic flow potential an alternative one dimensional formulation obtained by introducing a kinematic constraint and numerically integrating over the cross section of the beam is also presented both formulations account for the effect of warping which arises as a result of shear deformation a numerical algorithm for the time dependent problem is presented in which the numerically integrated nonlinear rate equations are exactly satisfied at each iteration of the newton raphson scheme the implications of the formulations discussed in this paper are illustrated through a set of numerical examples

uniqueness of solution of a generalized sylvester matrix equation abstract we present necessary and sufficient conditions for the existence of a unique solution of the generalized sylvester matrix equation a x b c x d e where a b c d e are square matrices of the same size with real or complex entries and where stands for either the transpose or the conjugate transpose this generalizes several previous uniqueness results for specific equations like the sylvester or the stein equations

shape optimal design of elastic space frames with non linear response this paper describes an approach to shape optimal design of elastic planar frames with non linear response the foundation of the proposed approach forms an appropriate strategy of shape representation of the structure based on the design element technique a frame structure is treated as to be assembled from several frame design elements which in turn may consist of several appropriately joined beam finite elements the shape of each frame design element is defined by convenient functions involving bezier blending polynomials the original formulation of the beam finite element proposed by saje is modified in order to fit nicely into the context of the frame design element technique the formulation of the shape optimal design problem in a form of a problem of non linear mathematical programming and its solution by employing gradient based methods of mathematical programming are discussed briefly the theory is illustrated with two numerical examples

a homotopy method applied to elastica problems abstract the inverse problem in nonlinear incompressible elastica theory where the end positions and inclinations rather than the forces and moment are specified is considered based on the globally convergent chow yorke algorithm a new homotopy method which is simple accurate stable and efficient is developed for comparison numerical results of some other simple approaches e g newton s method based on shooting or finite differences standard embedding are presented the new homotopy method does not require a good initial estimate and is guaranteed to have no singular points the homotopy method is applied to the problem of a circular elastica ring subjected to n symmetrical point loads and numerical results are given for n 2 3 4

iterative method to solve the generalized coupled sylvester transpose linear matrix equations over reflexive or anti reflexive matrix abstract the iterative method of generalized coupled sylvester transpose linear matrix equations a x b c y t d s 1 e x t f g y h s 2 over reflexive or anti reflexive matrix pair x y is presented on the condition that the coupled matrix equations are consistent we show that the solution pair x y proposed by the iterative method can be obtained within finite iterative steps in the absence of roundoff error for any initial value given a reflexive or anti reflexive matrix moreover the optimal approximation reflexive or anti reflexive matrix solution pair to an arbitrary given reflexive or anti reflexive matrix pair can be derived by searching the least frobenius norm solution pair of the new generalized coupled sylvester transpose linear matrix equations finally some numerical examples are given which illustrate that the introduced iterative algorithm is quite efficient

a discrete model for geometrically nonlinear transverse free constrained vibrations of beams with various end conditions abstract the purpose of the present paper was the development of a physically discrete model for geometrically nonlinear free transverse constrained vibrations of beams which may replace if sufficient degrees of freedom are used the previously developed continuous nonlinear beam constrained vibration models the discrete model proposed is an n degrees of freedom n dof system made of n masses placed at the ends of solid bars connected by torsional springs presenting the beam flexural rigidity the large transverse displacements of the bar ends induce a variation in their lengths giving rise to axial forces modelled by longitudinal springs the calculations made allowed application of the semi analytical model developed previously for nonlinear structural vibration involving three tensors namely the mass tensor m ij the linear rigidity tensor k ij and the nonlinearity tensor b ijkl by application of hamilton s principle and spectral analysis the nonlinear vibration problem is reduced to a nonlinear algebraic system examined for increasing numbers of dof the results obtained by the physically discrete model showed a good agreement and a quick convergence to the equivalent continuous beam model for various fixed boundary conditions for both the linear frequencies and the nonlinear backbone curves and also for the corresponding mode shapes the model validated here for the simply supported and clamped ends may be used in further works to present the flexural linear and nonlinear constrained vibrations of beams with various types of discontinuities in the mass or in the elasticity distributions

boundary control of a timoshenko beam attached to a rigid body planar motion a flexible spacecraft modelled as a rigid body which rotates in an inertial space is considered a light flexible beam is clamped to the rigid body at one end and free at the other end the equations of motion are obtained by using the geometrically exact beam model for the flexible beam and it is then shown that under planar motion assumption linearization of this model yields the timoshenko beam model it is shown that suitable boundary controls applied to the free end of the beam and a control torque applied to the rigid body stabilize the system the proof is obtained by using a lyapunov functional based on the energy of the system

the modified conjugate gradient methods for solving a class of generalized coupled sylvester transpose matrix equations in this paper we consider the iteration solutions of generalized coupled sylvester transpose matrix equations a1xb1 c1ytd1 f1 a2yb2 c2xtd2 f2 when the coupled matrix equations are consistent we propose a modified conjugate gradient method to solve the equations and prove that a solution x y can be obtained within finite iterative steps in the absence of roundoff error for any initial value furthermore we show that the minimum norm solution can be got by choosing a special kind of initial matrices when the coupled matrix equations are inconsistent we present another modified conjugate gradient method to find the least squares solution with the minimum norm finally some numerical examples are given to show the behavior of the considered algorithms

metsk hde in this contribution we propose a two stage method for accurate fuzzy modeling in high dimensional regression problems using approximate takagi sugeno kang fuzzy rule based systems in the first stage an evolutionary data base learning is performed involving variables granularities and slight fuzzy partition displacements together with an inductive rule base learning within the same process the second stage is a post processing process to perform a rule selection and a scatter based tuning of the membership functions for further refinement of the learned solutions moreover the second stage incorporates an efficient kalman filter to learn the coefficients of the consequent polynomial function in the takagi sugeno kang rules both stages include mechanisms that significantly improve the accuracy of the model and ensure a fast convergence in high dimensional and large scale regression datasets we tested our approach on 28 real world datasets with different numbers of variables and instances five well known methods have been executed as references we compared the different approaches by applying non parametric statistical tests for pair wise and multiple comparisons the results confirm the effectiveness of the proposed method showing better results in accuracy within a reasonable computing time

vibration of multi span non uniform bridges under moving vehicles and trains by using modified beam vibration functions abstract based on the lagrangian approach the vibration of a multi span non uniform bridge subjected to a moving vehicle is analyzed by using modified beam vibration functions as the assumed modes the vehicle is modelled as a two degree of freedom system the method is extended to the action of a moving train by modelling it as a series of two degree of freedom systems all the derived formulae are expressed in matrix form and therefore programming is quite straightforward the total number of unknowns for this method is very small compared with that of the finite element method convergence is very quick and in almost all cases 12 16 terms are sufficient to give satisfactory results

free vibration of structures with cubic non linearity remarks on amplitude equation and rayleigh quotient in the paper several aspects concerning the formulation of and solution to amplitude equations for free vibration of systems with cubic non linearity are discussed in detail the use of several possible constraint equations to achieve the non trivial solution to the amplitude equation is also presented the well known concept of the rayleigh quotient is extended to the non linear case of interest some general remarks on the formulation of the non linear amplitude equation and the non linear rayleigh quotient are also presented moreover the introduced rayleigh quotient is used to develop a new and suitably efficient method to solve amplitude equations the accuracy of solutions obtained by means of some widely used methods of analysis of free vibration problems is also presented it is found that the galerkin method gives the most accurate results

an excursion into large rotations the present discourse develops an enlarged exploration of the matrix formulation of finite rotations in space initiated in 1 it is shown how a consistent but subtle matrix calculus inevitably leads to a number of elegant expressions for the transformation or rotation matrix t appertaining to a rotation about an arbitrary axis also analysed is the case of multiple rotations about fixed or follower axes particular attention is paid to an explicit derivation of a single compound rotation vector equivalent to two consecutive arbitrary rotations this theme is discussed in some detail for a number of cases semitangential rotations for which commutativity holds first proposed in 2 3 are also considered furthermore an elementary geometrical analysis of large rotations is also given finally we deduce in an appendix using a judicious reformulation of quarternions the compound pseudovector representing the combined effect of n rotations in the author s opinion the present approach appears preferable to a pure vectorial scheme and even more so to an indicial formulation and is computationally more convenient

formulation and solution of inverse spaghetti problem application to beam deployment dynamics a finite element model of the dynamics of axially moving highly flexible beams is presented the model is based on a geometrically nonlinear beam formulation that allows for large overall motions to account for the varying length of a deploying beam a moving finite element reference grid is incorporated within the nonlinear beam formulation such that the number of finite element nodes remains fixed and the finite element length is allowed to vary hamilton s law is used to formulate the equations of motion and a transient integration solution procedure is derived from a space time finite element discretization of the hamiltonian variational principle computational results of the methodology are presented for a planar inverse spaghetti problem he dynamics of axially moving beamlike structures are becoming increasingly important for the analysis of spacecraft and large space structures that deploy flexible appendages such as antenna stabilizing booms solar arrays and long trusslike structures as well as for other applications such as magnetic tape drives printing machines traveling cables and band saws an extensive amount of research has focused on the modeling of axially moving continua to analyze the dynamic behavior of such structures one of the most common models of axially moving continua that has received the most attention is the traveling string problem in what he termed the spaghetti problem carrier1 analyzed the motion of a string being accelerated upward into a fixed orifice in other works since then analytical expressions representing both linear and nonlinear vibrations of axially moving strings subject to various support conditions have been derived 2 9 the dynamics of beamlike structures traveling between or over fixed supports have also been studied to address industrial applications such as high speed tape drives and band saws 10 13 to address spacecraft applications in which antenna or other long flexible structures are deployed from a host satellite the dynamics of a cantilever beam that is ejected from a single fixed guide are modeled using bernoulli euler beam theory in ref 14 in a quite different approach the extrusion of a beam from a rotating base is modeled using a series of elastically connected rigid links in which the number of rigid links are continuously increased decreased to account for deployment retrieval of the beam 15 general formulations of axially moving bernoulli euler beam models cantilevered to a rotating rigid host body have also been developed to study the effect of appendage deployment on the attitude dynamics of orbiting spacecraft 16 20 all of these given analyses are based on an assumption of small elastic deformations with the exception of the discrete spring mass model of ref 15 all of the other models that have been referenced thus far use linear combinations of space depende nt admissible functions of a time varying length weighted by time dependen t generalized coordi

an iterative algorithm for discrete periodic lyapunov matrix equations abstract in this paper a novel iterative algorithm with a tuning parameter is developed to solve the forward discrete periodic lyapunov matrix equation associated with discrete time linear periodic systems an important feature of the proposed algorithm is that the information in the current and the last steps is used to update the iterative sequence the convergence rate of the algorithm can be significantly improved by choosing a proper tuning parameter it is shown that the sequence generated by this algorithm with zero initial conditions monotonically converges to the unique positive definite solution of the periodic lyapunov matrix equation if the tuning parameter is within the interval 0 1 in addition a necessary and sufficient convergence condition is given for the proposed algorithm in terms of the roots of a set of polynomial equations also a method to choose the optimal parameter is developed such that the algorithm has the fastest convergence rate finally numerical examples are provided to illustrate the effectiveness of the proposed algorithm

finite element formulation of geometrically exact three dimensional beam theories based on interpolation of strain measures this paper presents a new finite element formulation of the geometrically exact finite strain beam theory the governing equations of the beam element are derived in which the strain vectors are the only unknown functions the consistency condition that the equilibrium and the constitutive internal force and moment vectors are equal is enforced to be satisfied at chosen points the solution is found by a collocation algorithm the linearity of the strain space not only simplifies the application of newton s method on the non linear configuration space but also leads to the strain objectivity of the proposed method the accuracy and the efficiency of the derived numerical algorithm are demonstrated by several examples c 2003 elsevier b v all rights reserved

least squares solution with the minimum norm to general matrix equations via iteration two iterative algorithms are presented in this paper to solve the minimal norm least squares solution to a general linear matrix equations including the well known sylvester matrix equation and lyapunov matrix equation as special cases the first algorithm is based on the gradient based searching principle and the other one can be viewed as its dual form necessary and sufficient conditions for the step sizes in these two algorithms are proposed to guarantee the convergence of the algorithms for arbitrary initial conditions sufficient condition that is easy to compute is also given moreover two methods are proposed to choose the optimal step sizes such that the convergence speeds of the algorithms are maximized between these two methods the first one is to minimize the spectral radius of the iteration matrix and explicit expression for the optimal step size is obtained the second method is to minimize the square sum of the f norm of the error matrices produced by the algorithm and it is shown that the optimal step size exits uniquely and lies in an interval several numerical examples are given to illustrate the efficiency of the proposed approach

an extension on statistical comparisons of classifiers over multiple data sets for all pairwise comparisons in a recently published paper in jmlr dem sar 2006 recommends a set of non parametric statistical tests and procedures which can be safely used for comparing the performance of classifiers over multiple data sets after studying the paper we realize that the paper correctly introduces the basic procedures and some of the most advanced ones when comparing a control method however it does not deal with some advanced topics in depth regarding these topics we focus on more powerful proposals of statistical procedures for comparing n n classifiers moreover we illustrate an easy way of obtaining adjusted and comparable p values in multiple comparison procedures

on solutions of the matrix equations x axb c and x axb c this paper studies the solutions of complex matrix equations x axb c and x axb c and obtains explicit solutions of the equations by the method of characteristic polynomial and a method of real representation of a complex matrix respectively

on the correct representation of bending and axial deformation in the absolute nodal coordinate formulation with an elastic line approach abstract in finite element methods that are based on position and slope coordinates a representation of axial and bending deformation by means of an elastic line approach has become popular such beam and plate formulations based on the so called absolute nodal coordinate formulation have not yet been verified sufficiently enough with respect to analytical results or classical nonlinear rod theories examining the existing planar absolute nodal coordinate element which uses a curvature proportional bending strain expression it turns out that the deformation does not fully agree with the solution of the geometrically exact theory and even more serious the normal force is incorrect a correction based on the classical ideas of the extensible elastica and geometrically exact theories is applied and a consistent strain energy and bending moment relations are derived the strain energy of the solid finite element formulation of the absolute nodal coordinate beam is based on the st venant kirchhoff material therefore the strain energy is derived for the latter case and compared to classical nonlinear rod theories the error in the original absolute nodal coordinate formulation is documented by numerical examples the numerical example of a large deformation cantilever beam shows that the normal force is incorrect when using the previous approach while a perfect agreement between the absolute nodal coordinate formulation and the extensible elastica can be gained when applying the proposed modifications the numerical examples show a very good agreement of reference analytical and numerical solutions with the solutions of the proposed beam formulation for the case of large deformation pre curved static and dynamic problems including buckling and eigenvalue analysis the resulting beam formulation does not employ rotational degrees of freedom and therefore has advantages compared to classical beam elements regarding energy momentum conservation

the natural frequencies and mode shapes of a uniform cantilever beam with multiple two dof spring mass systems abstract because of the complexity of the mathematical expressions the literature concerning the free vibration analysis of a uniform beam carrying a single two degrees of freedom d o f spring mass system is rare and the publications relating to that carrying multiple two d o f spring mass systems have not yet appeared hence the purpose of this paper is to present some information in this area first of all the closed form solution for the natural frequencies and the corresponding normal mode shapes of the uniform beam alone or the bare beam with the prescribed boundary conditions are determined analytically next a method is presented to replace each two d o f spring mass system by two massless equivalent springs with spring constants k v eq iandk v eq k and then the foregoing natural frequencies and normal mode shapes for the bare beam are in turn used to derive the equation of motion of the loading beam i e the bare beam carrying any number of two d o f spring mass systems by using the expansion theorem finally the natural frequencies and the associated mode shapes of the loading beam are obtained from the last equation by using the numerical method to confirm the reliability of the present method all the numerical results obtained in this paper are compared with the corresponding ones obtained from the conventional finite element method fem and good agreement is achieved because the order of the property matrices for the equation of motion of the loading beam derived from the present method is much lower than that derived from the fem the computer time required by the former is much less than that required by the latter besides the equation of motion derived from the present method may always run on the cheaper personal computers but that from the fem may run only on the more expensive larger computers if the degree of freedom of the loading beam exceeds a certain limit

steady state response of an infinite string on a non linear visco elastic foundation to moving point loads the steady state response of a long string on a non linear visco elastic foundation to uniformly moving constant point loads is studied the phase plane is employed to construct a phase portrait that determines the string response this portrait consists of trajectories of the autonomous system that represent the string displacement everywhere except at the loading points and vertical segments that satisfy the boundary conditions in these points it is shown that the string response depends crucially on the ratio between the load velocity and the wave speed in the string if the load moves slower than the waves in the string then the response is nearly symmetric with respect to the load and decays exponentially with the distance form the load if the load velocity exceeds the wave speed then the string exhibits a wave pattern which extends well behind the load in front of the load in this case the string is not disturbed

an iterative algorithm for solving a pair of matrix equations ayb e cyd f over generalized centro symmetric matrices a matrix email protected r n x n is said to be a symmetric orthogonal matrix if p p t p 1 a matrix email protected r n x n is said to be generalized centro symmetric generalized central anti symmetric with respect to p if a pap a pap the generalized centro symmetric matrices have wide applications in information theory linear estimate theory and numerical analysis in this paper we propose a new iterative algorithm to compute a generalized centro symmetric solution of the linear matrix equations ayb e cyd f we show when the matrix equations are consistent over generalized centro symmetric matrix y for any initial generalized centro symmetric matrix y 1 the sequence y k generated by the introduced algorithm converges to a generalized centro symmetric solution of matrix equations ayb e cyd f the least frobenius norm generalized centro symmetric solution can be derived when a special initial generalized centro symmetric matrix is chosen furthermore the optimal approximation generalized centro symmetric solution to a given generalized centro symmetric matrix can be derived several numerical examples are given to show the efficiency of the presented method

a fuzzy genetic programming based algorithm for subgroup discovery and the application to one problem of pathogenesis of acute sore throat conditions in humans this paper proposes a novel algorithm for subgroup discovery task based on genetic programming and fuzzy logic called fuzzy genetic programming based for subgroup discovery fugepsd the genetic programming allows to learn compact expressions with the main objective to obtain rules for describing simple interesting and interpretable subgroups this algorithm incorporates specific operators in the search process to promote the diversity between the individuals the evolutionary scheme of fugepsd is codified through the genetic cooperative competitive approach promoting the competition and cooperation between the individuals of the population in order to find out the optimal solutions for the sd task fugepsd displays its potential with high quality results in a wide experimental study performed with respect to others evolutionary algorithms for subgroup discovery moreover the quality of this proposal is applied to a case study related to acute sore throat problems