dimension of the orbit of marked subspaces given a nilpotent endomorphism we consider the manifold of invariant subspaces having a fixed segre characteristic in linear algebra appl 332 334 2001 569 the implicit form of a miniversal deformation of an invariant subspace with respect to the usual equivalence relation between subspaces is obtained here we obtain the explicit form of this deformation when the invariant subspace is marked and we use it to calculate the dimension of the orbit and in particular to characterize the stable marked subspaces those with open orbit moreover we study the rank of the endomorphisms in the quotient space by the subspaces in the miniversal deformation of the giving subspace

affine spaces of strong linearizations for rational matrices and the recovery of eigenvectors and minimal bases abstract the main aim of this paper is two fold first to define and analyze two affine spaces of matrix pencils associated with a realization of an n n rational matrix g and show that almost all of these pencils are strong linearizations of g second to describe the recovery of eigenvectors minimal bases and minimal indices of g from those of the strong linearizations of g the affine spaces of pencils are constructed from the vector spaces of linearizations of matrix polynomials defined and analyzed by mackey et al in siam j matrix anal appl 28 2006 pp 971 1004 we show that eigenvectors minimal bases and minimal indices of g can be easily recovered from those of the strong linearizations of g in particular we construct a symmetric strong linearization of g when g is regular and symmetric we also describe the recovery of pole zero structure of g at infinity from the pole zero structure at infinity of a strong linearization of g

vibration analysis of high speed rotating conical shell with arbitrary boundary conditions based on the energy method an analytical model for the vibration characteristics of high speed rotating conical shell with arbitrary boundary is constructed effects of centrifugal and coriolis accelerations as well as initial hoop tension due to rotating are all taken into account a set of translational and rotational artificial springs to simulate the elastic constraints imposed on the conical shell edges under the framework each of the displacement components of the conical shell is invariantly described by a modified fourier series which is composed of a standard fourier series and closed form auxiliary functions all the expansion coefficients are determined by using the familiar rayleigh ritz procedure as the generalized coordinates to validate the present analysis a series of comparisons between the present results and those available in the open literature are carried out and very good agreements are obtained on this basis some numerical results are given to illustrate the effects of rota

column reduction of polynomial matrices a few years ago beelen developed an algorithm to determine a minimal basis for the kernel of a polynomial matrix in this paper we use a modified version of this algorithm to find a column reduced polynomial matrix unimodularly equivalent to a given polynomial matrix

free vibration of rotating ring stiffened cylindrical shells with non uniform stiffener distribution in this research the free vibration analysis of simply supported rotating cylindrical shells with circumferential stiffeners i e rings with non uniform stiffeners eccentricity and non uniform stiffeners spacing distribution is investigated ritz method is applied while stiffeners are treated as discrete elements in strain energy formulation by adopting sander s theorem stretching and bending characteristics of shells are considered also stretching bending and wrapping effects of stiffeners are investigated the translational inertia in three directions for shell and stiffeners and rotary inertia for stiffeners are considered the effects of initial hoop tension centrifugal and coriolis forces due to the rotation of shell are studied the polynomial functions are used for ritz functions natural frequency results for rings with uniform spacing and constant eccentricity have been compared with analytical and experimental results of other researchers which showed good agreement fortunately the agreements of the presented analytical results with the experimental values are better than the analytical values at constant total mass of stiffeners the effects of non uniform eccentricity distribution and non uniform rings spacing distribution separately and simultaneously on natural frequencies are investigated moreover the influence of rotating speed on natural frequencies for the so called non uniform stiffeners distribution is studied

accurate solution of polynomial equations using macaulay resultant matrices we propose an algorithm for solving two polynomial equations in two variables our algorithm is based on the macaulay resultant approach combined with new techniques including randomization to make the algorithm accurate in the presence of roundoff error the ultimate computation is the solution of a generalized eigenvalue problem via the qz method we analyze the error due to roundoff of the method showing that with high probability the roots are computed accurately assuming that the input data that is the two polynomials are well conditioned our analysis requires a novel combination of algebraic and numerical techniques

solving time dependent engineering problems with multiquadrics abstract this paper deals with the solution of time dependent problems the multiquadric radial basis function method is formulated with a new approach for transient problems one and two dimensional problems are considered the forward difference and the crank nicolson time marching schemes for parabolic cases are considered the central difference integration method of the newmark family is considered for hyperbolic problems the method proves its accuracy in four numerical examples

free vibration analysis of functionally graded plates using the element free kp ritz method a free vibration analysis of metal and ceramic functionally graded plates that uses the element free kp ritz method is presented the material properties of the plates are assumed to vary continuously through their thickness according to a power law distribution of the volume fractions of the plate constituents the first order shear deformation plate theory is employed to account for the transverse shear strain and rotary inertia and mesh free kernel particle functions are used to approximate the two dimensional displacement fields the eigen equation is obtained by applying the ritz procedure to the energy functional of the system convergence studies are performed to examine the stability of the proposed method and comparisons of the solutions derived with those reported in the literature are provided to verify its accuracy four types of functionally graded rectangular and skew plates al al2o3 al zro2 ti 6al 4v aluminum oxide and sus304 si3n4 are included in the study and the effects of the volume fraction boundary conditions and length to thickness ratio on their frequency characteristics are discussed in detail

triangularizing matrix polynomials for an algebraically closed field f we show that any matrix polynomial p lambda in f lambda nbym n le m can be reduced to triangular form preserving the degree and the finite and infinite elementary divisors we also characterize the real matrix polynomials that are triangularizable over the real numbers and show that those that are not triangularizable are quasi triangularizable with diagonal blocks of sizes 1 times 1 and 2 times 2 the proofs we present solve the structured inverse problem of building up triangular matrix polynomials starting from lists of elementary divisors

matrix polynomials factorization via bisolvents abstract we reconsider the classification of all the factorizations of a matrix polynomial p as p q r with q a matrix polynomial and r t s a regular matrix pencil it is shown that the entire classification problem can be reduced to the simpler classification of factors r with commuting coefficients s t it is then shown that for these commuting factors s and t must satisfy a certain algebraic equation which we call the bisolvent equation this extends the generalized bezout theorem which associates monic factors i s with solutions s of a solvent equation in case p is regular the classification of commuting pairs s t of this type up to left equivalence is described in terms of enlarged standard pairs following a well known approach under a non derogatory generic condition on the roots of p the number of such pairs associated with degree minimal factorizations is finite and admits explicit description in terms of jordan chains

geometrically nonlinear analysis of functionally graded plates using the element free kp ritz method abstract the nonlinear response of functionally graded ceramic metal plates fgps under mechanical and thermal loads is investigated using the mesh free kp ritz method the nonlinear formulation is based on the first order shear deformation plate theory and the von karman strains which deal with small strains and moderate rotations the material properties of fgps are assumed to be graded through the thickness direction according to a power law distribution of the volume fraction of the constituents the approximation of the displacement field is expressed in terms of a set of mesh free kernel particle functions the bending stiffness of the plates is evaluated using a stabilized conforming nodal integration method and the membrane and shear stiffnesses are computed using direct nodal integration to eliminate shear locking the nonlinear behavior of the deflection and axial stress is studied for fgps under thermal and mechanical loading and the influences of the volume fraction exponent boundary condition and material properties on the nonlinear response of fgps are examined

computation of transfer function matrices of generalized state space models a reliable computational algorithm is proposed for the evaluation of the transfer function matrices of linear multivariable systems described by generalized state space models the algorithm is based on a new efficient and numerically stable procedure for computing irreducible state space realizations of generalized state space models for each input output channel the proposed algorithm computes an irreducible realization using this procedure then the parameters of the corresponding transfer function gain poles zeros are determined from the resulting irreducible model

stability of controlled invariant subspaces abstract let a b c n n c n m and m be an a b invariant subspace let c a b be the controllability subspace of the pair a b if m c a b m im b under additional hypotheses necessary and sufficient conditions for the stability of the subspace m are given

reproducing kernel particle methods for large deformation analysis of non linear structures abstract large deformation analysis of non linear elastic and inelastic structures based on reproducing kernel particle methods rkpm is presented the method requires no explicit mesh in computation and therefore avoids mesh distortion difficulties in large deformation analysis the current formulation considers hyperelastic and elasto plastic materials since they represent path independent and path dependent material behaviors respectively in this paper a material kernel function and an rkpm material shape function are introduced for large deformation analysis the support of the rkpm material shape function covers the same set of particles during material deformation and hence no tension instability is encountered in the large deformation computation the essential boundary conditions are introduced by the use of a transformation method the transformation matrix is formed only once at the initial stage if the rkpm material shape functions are employed the appropriate integration procedures for the moment matrix and its derivative are studied from the standpoint of reproducing conditions in transient problems with an explicit time integration method the lumped mass matrices are constructed at nodal coordinate so that masses are lumped at the particles several hyperelasticity and elasto plasticity problems are studied to demonstrate the effectiveness of the method the numerical results indicated that rkpm handles large material distortion more effectively than finite elements due to its smoother shape functions and consequently provides a higher solution accuracy under large deformation unlike the conventional finite element approach the nodal spacing irregularity in rkpm does not lead to irregular mesh shape that significantly deteriorates solution accuracy no volumetric locking is observed when applying non linear rkpm to nearly incompressible hyperelasticity and perfect plasticity problems further model adaptivity in rkpm can be accomplished simply by adding more points in the highly deformed areas without remeshing

geometric characterization and classification of marked subspaces abstract given an endomorphism of a finite dimensional c vector space we obtain geometric conditions in order to characterize and to classify the marked invariant subspaces w e that is to say the invariant subspaces having some jordan basis which can be extended to a jordan basis of e both conditions are expressed in terms of the double family of subspaces ker f h im f d the starting point is a new criterion for extensibility of jordan bases

postbuckling analysis of laminated composite plates using the mesh free kp ritz method abstract a ritz method based on kernel particle approximation for the field variables is proposed for the postbuckling analysis of laminated composite plates the first order shear deformation plate theory fsdt is employed to model the plate flexure the ritz method is used to obtain the discretized non linear equations a geometrically non linear analysis is used to trace the postbuckling paths of the plate typical numerical examples including isotropic plates and cross ply and angle ply laminated composite plates have been solved using the proposed method the results are in close agreement with the series solution as well as previous finite element results available in the literature

dynamic stability of rotating cylindrical shells subjected to periodic axial loads abstract in this paper the dynamic stability of rotating cylindrical shells under static and periodic axial forces is investigated using a combination of the ritz method and bolotin s first approximation the kernel particle estimate is employed in hybridized form with harmonic functions to approximate the 2 d transverse displacement field a system of mathieu hill equations is obtained through the application of the ritz energy minimization procedure the principal instability regions are then obtained via bolotin s first approximation in this formulation both the hoop tension and coriolis effects due to the rotation are accounted for various boundary conditions are considered and the present results represent the first instance in which the effects of boundary conditions for this class of problems have been reported in open literature effects of rotational speeds on the instability regions for different modes are also examined in detail

brief paper a class of marked invariant subspaces with an application to algebraic riccati equations invariant subspaces of a matrix a are considered which are obtained by truncation of a jordan basis of a generalized eigenspace of a we characterize those subspaces which are independent of the choice of the jordan basis an application to hamilton matrices and algebraic riccati equations is given

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

on a b t invariant subspaces having extendible brunovsky bases we consider a by invariant subspaces having a brunovsky basis which can be extended to a brunovsky basis of the whole space we obtain a geometrical characterization of this class of a by invariant subspaces and a complete family of numerical invariants to classify them 0 elsevier science inc 1997

the boundary value problem and the jensen inequality for an entropy functional of a markov diffusion process the paper introduces the recent results related to an entropy functional on trajectories of a controlled diffusion process expressed through an additive functional of the diffusion process with a lagrangian determined by the parameters of a controlled stochastic equation these results include a minimum condition for the entropy functional and the functional s jensen inequality which both are useful for the solution of important mathematical and applied problems

an improved toeplitz algorithm for polynomial matrix null space computation in this paper we present an improved algorithm to compute the minimal null space basis of polynomial matrices a problem which has many applications in control and systems theory this algorithm takes advantage of the block toeplitz structure of the sylvester matrix associated with the polynomial matrix the analysis of algorithmic complexity and numerical stability shows that the algorithm is reliable and can be considered as an efficient alternative to the well known pencil state space algorithms found in the literature

solution to the variation problem for information path functional of a controlled random process abstract the paper introduces a new approach to dynamic modeling using the variation principle applied to a functional on trajectories of a controlled random process and its connection to the process information functional in v s lerner dynamic approximation of a random information functional j math anal appl 327 1 2007 494 514 available online 5 24 06 we presented the information path functional with the lagrangian determined by the parameters of a controlled stochastic equation in this paper the solution to the path functional s variation problem provides both a dynamic model of a random process and the model s optimal control which allows us to build a two level information model with a random process at the microlevel and a dynamic process at the macrolevel a wide class of random objects modeled by the markov diffusion process and a common structure of the process information functional leads to a universal information structure of the dynamic model which is specified and identified on a particular object with the applied optimal control functions the developed mathematical formalism based on classical methods is aimed toward the solution of problems identification combined with an optimal control synthesis which is practically implemented and also demonstrated in the paper s example

first order spectral perturbation theory of square singular matrix pencils abstract let h a 0 a 1 be a square singular matrix pencil and let 0 c be an eventually multiple eigenvalue of h it is known that arbitrarily small perturbations of h can move the eigenvalues of h anywhere in the complex plane i e the eigenvalues are discontinuous functions of the entries of a 0 and a 1 therefore it is not possible to develop an eigenvalue perturbation theory for arbitrary perturbations of h however if the perturbations are restricted to lie in an appropriate set then the eigenvalues change continuously we prove that this set of perturbations is generic i e it contains almost all pencils and present sufficient conditions for a pencil to be in this set in addition for perturbations in this set explicit first order perturbation expansions of 0 are obtained in terms of the perturbation pencil and bases of the left and right null spaces of h 0 both for simple and multiple eigenvalues infinite eigenvalues are also considered finally information on the eigenvectors of the generically regular perturbed pencil is presented we obtain as corollaries results for regular pencils that are also new

fe meshfree quad4 element for free vibration analysis the fe lspim quad4 element which was recently introduced for the static analysis uses new shape functions that combine the meshfree and finite element shape functions so as to synergize the individual strengths of meshfree and finite element methods as a result the element inherits the completeness properties of meshfree shape functions and the compatibility properties of finite element shape functions in this paper the element is extended to free vibration analysis of two dimensional solids typical benchmark problems are solved to test the efficacy of the element the results show that the element gives more accurate solution than the peer elements particularly under distorted mesh

dynamic stability analysis of composite laminated cylindrical shells via the mesh free kp ritz method abstract in this paper a novel numerical technique is developed for the dynamic stability analysis of composite laminated cylindrical shells under static and periodic axial forces the mesh free kernel particle kp estimate is employed in hybridized form with harmonic functions to approximate the 2 d transverse displacement field a system of mathieu hill equations is obtained through the application of the ritz minimization procedure to the energy expressions the principal instability regions are then analyzed via bolotin s first approximation the mesh free kp ritz method is validated through comparison with existing available numerical data taken from open literature effects of boundary conditions and lamination schemes on the instability regions are also examined in detail

nonlinear analysis of corrugated plates using a fsdt and a meshfree method this paper presents a geometrically nonlinear analysis of stiffened and un stiffened corrugated plates using a meshfree galerkin method that is based on the first order shear deformation theory fsdt the strains are assumed to be small and the corrugated plates are modeled approximately as equivalent orthotropic plates the large deflection theory of von karman is adopted in the nonlinear analysis of the orthotropic plate and the equivalent flexure properties of the orthotropic plate are derived both the equivalent flexure and extensional properties are employed in the nonlinear analysis the stiffened corrugated plates are analyzed as stiffened orthotropic plates in which the stiffeners are modeled as beams and fitted to the equivalent orthotropic plate by implementing displacement compatibility conditions between the plate and the stiffeners because no mesh is required in the proposed method the stiffeners can be placed anywhere on the plate and changes to the positions of the stiffeners do not entail the remeshing of the plate to demonstrate the convergence and accuracy of the proposed method several numerical examples are employed the solutions that are computed by the proposed method are compared with precise solutions that are given by ansys using shell elements and with the results of other research work

the improved complex variable element free galerkin method for two dimensional schrodinger equation abstract a numerical study of two dimensional schrodinger equation is carried out using the improved complex variable element free galerkin icvefg method the icvefg method involves employment of the improved complex variable moving least squares icvmls in the element free galerkin efg procedure for numerical approximation the icvmls is used to construct trial functions for the two dimensional schrodinger equation in the form of one dimensional basis function that effectively reduces the number of unknown coefficients in this study the applicability of the icvefg method is examined through a number of numerical example problems convergence studies are carried out for these example problems by varying the number of nodes to ascertain convergent results are achieved as the number of nodes increases the stability and accuracy of the icvefg method are validated by comparing the computed results with the exact solutions

singular graph and extension of jordan chains of an m matrix abstract let s be a singular graph we study conditions on the vertices of s to extend jordan chains for the generalized nullspace of each minus m matrix a with singular graph s the conditions are the interlevel the strong interlevel and the strong predecessor properties

stable polefinding and rational least squares fitting via eigenvalues a common way of finding the poles of a meromorphic function f in a domain where an explicit expression of f is unknown but f can be evaluated at any given z is to interpolate f by a rational function pq such that r i f i at prescribed sample points i i 1l and then find the roots of q this is a two step process and the type of the rational interpolant needs to be specified by the user many other algorithms for polefinding and rational interpolation or least squares fitting have been proposed but their numerical stability has remained largely unexplored in this work we describe an algorithm with the following three features 1 it automatically finds an appropriate type for a rational approximant thereby allowing the user to input just the function f 2 it finds the poles via a generalized eigenvalue problem of matrices constructed directly from the sampled values f i in a one step fashion and 3 it computes rational approximants p q in a numerically stable manner in that p p q q f with small p q at the sample points making it the first rational interpolation or approximation algorithm with guaranteed numerical stability our algorithm executes an implicit change of polynomial basis by the qr factorization and allows for oversampling combined with least squares fitting through experiments we illustrate the resulting accuracy and stability which can significantly outperform existing algorithms

structure preserving stratification of skew symmetric matrix polynomials we study how elementary divisors and minimal indices of a skew symmetric matrix polynomial of odd degree may change under small perturbations of the matrix coefficients we investigate these change

buckling and free vibration analyses of stiffened plates using the fsdt mesh free method this paper presents a mesh free galerkin method for the free vibration and stability analyses of stiffened plates via the first order shear deformable theory fsdt the model of a stiffened plate is formed by 1 regarding the plate and the stiffener separately 2 imposing displacement compatible conditions between the plate and the stiffener so that displacement fields of the stiffener can be expressed in terms of the mid surface displacement of the plate and 3 superimposing the strain energy of plate and stiffener because there are no meshes used in this method the stiffeners can be placed anywhere on the plate and need not be placed along the mesh lines several numerical examples are computed by this method to show its accuracy and convergence the present results demonstrate good agreement with the existing solutions given by other researchers and the ansys influences of support size and order of the complete basis functions on the numerical accuracy are also investigated

free vibration analysis of circular cylindrical shells abstract a general analytical method is presented for evaluating the free vibration characteristics of a circular cylindrical shell with classical boundary conditions of any type the solution is obtained through a direct solution procedure in which sanders shell equations are used with the axial modal displacements represented as simple fourier series expressions stokes transformation is exploited to obtain correct series expressions for the derivatives of the fourier series an explicit expression of the exact frequency equation can be obtained for any kind of boundary conditions the accuracy of the method is checked against available data the method is used to find the modal characteristics of the thermal liner model of the u s fast test reactor ftp the numerical results obtained are compared with finite element method solutions

harmonic reproducing kernel particle method for free vibration analysis of rotating cylindrical shells abstract a meshfree approach the harmonic reproducing kernel particle method is proposed for the free vibration analysis of rotating cylindrical shells the reproducing kernel particle estimation is employed in hybridized form with harmonic functions to approximate the two dimensional displacement field this is the first instance in which a meshless technique has been adopted for rotating shell dynamics this technique provides ease of enforcing various types of boundary conditions and concurrently is able to capture the traveling modes the effects of centrifugal and coriolis forces as well as the initial hoop tension due to rotation are all taken into account in the present formulation this study examines in detail the effects of different boundary conditions on the frequency characteristics of rotating shells the present results wherever possible are verified by comparison against results available in the open literature in general close agreement between the authors results and those of others has been found further results presented here in selective parametric studies may be used as benchmarks for future related works

a simplified approach to fiedler like pencils via block minimal bases pencils abstract the standard way of solving the polynomial eigenvalue problem associated with a matrix polynomial is to embed the matrix coefficients of the polynomial into a matrix pencil transforming the problem into an equivalent generalized eigenvalue problem such pencils are known as linearizations many of the families of linearizations for matrix polynomials available in the literature are extensions of the so called family of fiedler pencils these families are known as generalized fiedler pencils fiedler pencils with repetition and generalized fiedler pencils with repetition or fiedler like pencils for simplicity the goal of this work is to unify the fiedler like pencils approach with the more recent one based on strong block minimal bases pencils introduced in f m dopico et al 2017 17 to this end we introduce a family of pencils that we have named extended block kronecker pencils whose members are under some generic nonsingularity conditions strong block minimal bases pencils and show that with the exception of the non proper generalized fiedler pencils all fiedler like pencils belong to this family modulo permutations as a consequence of this result we obtain a much simpler theory for fiedler like pencils than the one available so far moreover we expect this simplification to allow for further developments in the theory of fiedler like pencils such as global or local backward error analyses and eigenvalue conditioning analyses of polynomial eigenvalue problems solved via fiedler like linearizations

dynamic approximation of a random information functional abstract using the probabilistic evaluation of the marcovian diffusion process by a functional of action the paper introduces a dynamic approximation of a random information functional defined on the process trajectories and determined by the parameters of a controlled stochastic equation the developed mathematical formalism is aimed toward a dynamic modeling of a random object

a generalized state space for singular systems systems of the form e dot x ax bu y cx with e singular are studied of particular interest are the impulsive modes that may appear in the free response of such systems when arbitrary initial conditions are permitted modes that are associated with natural system frequencies at infinity a generalized definition of system order that incorporates these impulsive degrees of freedom is proposed and concepts of controllability and observability are defined for the impulsive modes allowable equivalence transformations of such singular systems are specified the present framework is shown to overcome several difficulties inherent in other treatments of singular systems and to extend in a natural and satisfying way many results previously known only for regular state space systems

an element free based solution for nonlinear schrodinger equations using the icvmls ritz method an improved complex variable moving least squares ritz icvmls ritz method is proposed for predicting numerical solution of the two dimensional nonlinear schrodinger equation in this element free solution procedure the icvmls approximation is employed to reduce the number of unknown coefficients in the trial function it follows by the ritz procedure to derive the final algebraic equation system through discretizing the constructed energy formulation of the nonlinear schrodinger equation the central differencing scheme and newton s algorithm are adopted to solve the nonlinear equation system numerical experiments are conducted on the final form of the governing equation system to demonstrate the accuracy and efficiency of the element free icvmls ritz method by comparing the computed results with the available analytical solutions

on stability of invariant subspaces of commuting matrices we study the stability of joint invariant subspaces of a finite set of commuting matrices we generalize some of the results of gohberg lancaster and rodman for the single matrix case for sets of two or more commuting matrices we exhibit some phenomena different from the single matrix case we show that each root subspace is a stable invariant subspace that each invariant subspace of a root subspace of a nonderogatory eigenvalue is stable and that even in the derogatory case the eigenspace is stable if it is one dimensional we prove that a pair of commuting matrices has only finitely many stable invariant subspaces at the end we discuss the stability of invariant subspaces of an algebraic multiparameter eigenvalue problem

buckling of rectangular mindlin plates subjected to partial in plane edge loads using the radial point interpolation method this paper considers the elastic buckling of rectangular mindlin plates that are subjected to partially distributed in plane edge loadings a numerical algorithm based on the radial point interpolation method rpim is proposed for the solution of such plates the pre buckling stresses are first determined using the rpim based on a two dimensional 2 d elastic plane stress problem the buckling load intensity factors for rectangular plates that incorporate these predetermined pre buckling stresses are then computed via the rpim based on the mindlin plate theory numerical examples of the plates with various boundaries and subjected to different partially distributed in plane edge loadings are presented shear locking of the buckling load is studied the results demonstrate the high accuracy of the proposed rpim

vibration characteristics of thin rotating cylindrical shells with various boundary conditions abstract an analysis is presented for the vibration characteristics of thin rotating cylindrical shells with various boundary conditions by use of fourier series expansion method based on sanders shell equations the governing equations of motion which take into account the effects of centrifugal and coriolis forces as well as the initial hoop tension due to rotating are derived the displacement field is expressed as a product of fourier series expressions which represents the axial modal displacements and trigonometric functions which represents the circumferential modal displacements stokes transformation is employed to derive the derivatives of the fourier series expressions then through the process of formula derivation an explicit expression of the exact frequency equation can be obtained for a thin rotating cylinder with classical boundary conditions of any type once the frequency equation has been determined the frequencies are calculated numerically to validate the present analysis comparisons between the results of the present method and previous studies are performed and very good agreement is achieved finally the method is applied to investigate the vibration characteristics of thin rotating cylindrical shells under various boundaries and the results are presented

elasto plasticity revisited numerical analysis via reproducing kernel particle method and parametric quadratic programming aiming to simplify the solution process of elasto plastic problems this paper proposes a reproducing kernel particle algorithm based on principles of parametric quadratic programming for elasto plasticity the parametric quadratic programming theory is useful and effective for the assessment of certain features of structural elasto plastic behaviour and can also be exploited for numerical iteration examples are presented to illustrate the essential aspects of the behaviour of the model proposed and the flexibility of the coupled parametric quadratic programming formulations with the reproducing kernel particle method copyright 2002 john wiley sons ltd

a meshfree method for transverse vibrations of anisotropic plates a meshfree approach called displacement boundary method for anisotropic kirchhoff plate dynamic analysis is presented this method is deduced from a variational principle which uses a modified hybrid functional involving the generalized displacements and generalized tractions on the boundary and the lateral deflection in the domain as independent variables the discretization process is based on the employment of the fundamental solutions of the static problem operator for the expression of the variables involved in the functional the stiffness and mass matrices obtained for the dynamic model are frequency independent symmetric and positive definite and their computation involves boundary integrals of regular kernels only due to its features the final resolving system can be solved with the classical approaches by using standard numerical procedures to assess the formulation the free vibrations of some anisotropic plates were calculated and the results compared with those obtained using other solution techniques the present results are in good agreement with those found in the literature showing the accuracy and effectiveness of the proposed approach

the generalized eigenstructure problem in linear system theory the algebraic theory of linear time invariant systems has been studied in large detail during the past few decades and numerous computational algorithms have been developed to solve problems arising in this context in this paper the numerical aspects of a certain class of such algorithms dealing with what the author calls generalized eigenstructure problems are discussed some new and or modified algorithms are presented both the nmnerical stability of the algorithms and the conditioning of the problems they solve are analyzed using numerical criteria

block minimal bases l ifications of matrix polynomials abstract the standard way of solving a polynomial eigenvalue problem associated with a matrix polynomial starts by embedding the matrix coefficients of the polynomial into a matrix pencil known as a strong linearization this process transforms the problem into an equivalent generalized eigenvalue problem however there are some situations in which is more convenient to replace linearizations by other low degree matrix polynomials this has motivated the idea of a strong l ification of a matrix polynomial which is a matrix polynomial of degree at most l having the same finite and infinite elementary divisors and the same numbers of left and right minimal indices as the original matrix polynomial we present in this work a novel method for constructing strong l ifications of matrix polynomials of size m n and grade d when l d and l divides nd or md this method is based on a family called strong block minimal bases matrix polynomials and relies heavily on properties of dual minimal bases we show how strong block minimal bases l ifications can be constructed from the coefficients of a given matrix polynomial p we also show that these l ifications satisfy many desirable properties for numerical applications they are strong l ifications regardless of whether p is regular or singular the minimal indices of the l ifications are related to those of p via constant uniform shifts and eigenvectors and minimal bases of p can be recovered from those of any of the strong block minimal bases l ifications in the special case where l divides d we introduce a subfamily of strong block minimal bases matrix polynomials named block kronecker matrix polynomials which is shown to be a fruitful source of companion l ifications

extensions of jordan bases for invariant subspaces of a matrix a characterization is obtained for the matrices a with the property that every some jordan basis of every a invariant subspace can be extended to a jordan basis of a these results are based on a criterion for a jordan basis of an invariant subspace to be extendable to a jordan basis of the whole space the criterion involves two concepts the constancy property and the depth property

analysis of thin shells by the element free galerkin method a meshless approach to the analysis of arbitrary kirchhoff shells by the element free galerkin efg method is presented the shell theory used is geometrically exact and can be applied to deep shells the method is based on moving least squares approximant the method is meshless which means that the discretization is independent of the geometric subdivision into finite elements the satisfaction of the c1 continuity requirements is easily met by efg since it requires only c1 weights therefore it is not necessary to resort to mindlin reissner theory or to devices such as discrete kirchhoff theory the requirements of consistency are met by the use of a polynomial basis of quadratic or higher order a subdivision similar to finite elements is used to provide a background mesh for numerical integration the essential boundary conditions are enforced by lagrange multipliers membrane locking which is due to different approximation order for transverse and membrane displacements is removed by using larger domains of influence with the quadratic basis and by using quartic polynomial basis which can prevent membrane locking completely it is shown on the obstacle course for shells that the present technique performs well

an algebraic theory for design of controllers for linear multivariable systems part i structure matrices and feedforward design in this two part paper a theory is presented in which several control problems can be solved the theory is applicable to a general class of linear multivariable systems where the measured output does not have to be equal to the controlled output or the state the system may be affected by nonmeasurable disturbances only controllers which stabilize the system and have proper transfer functions are allowed i e the controllers have to be physically realizable it is shown that the solutions to control problems of servo type e g problems of model matching decoupling and invertibility are special cases of the solution to a more general problem analogously the solutions to problems of regulator type e g disturbance decoupling output regulation and pole placement are also speclal cases of the solution to a more general problem it is shown that problems of servo type and regulator type can be solved independently of each other in part i generalized polynomials are introduced as a mathematical framework structue matrices which describe how well a system can be controlled are defined finally problems of servo type are solved part ii mainly deals with problems of regulator type

λ matrix formulation applied to the hertz contact problem with finite friction in this paper we are concerned with coupled volterra integral equations for rigid bodies in the frame of the hertz contact model considering an appropriate integral operator as the variable of the matrix polynomial a l matrix corresponding to the hertz model is determined knowledge of the smith decomposition forms of the l matrices enables us to characterize a single integral equation which recovers the normal stress as well as the compliance factor the presented model shows a reliable behavior and an acceptable accuracy of the l matrix approach in comparison to the recent results in the literature

versal deformations of invariant subspaces we describe a miniversal deformation of invariant subspaces with regard to a fixed endomorphism by means of a technique which can be applied to obtain explicitly miniversal deformations in a general orbit space in addition we present an application to the problem of classifying invariant subspaces

dynamic analysis of a hollow cylinder subject to a dual traveling force imposed on its inner surface abstract the dynamic behavior of a hollow cylinder under a dual traveling force applied to the inner surface is investigated in this study the cylinder is constrained at both the top and bottom surfaces not to move in the length direction but free in other directions and a dual force travels at a constant velocity along the length direction on the inner surface of the hollow cylinder the resulting governing field equations and the associated boundary conditions are ruled by the general hooke s law due to the nature of the field equations proper adjoint system of equations and biorthogonality conditions were derived in a precise and detailed manner to solve these field equations in this study the method of separation of variable is used and the method of fr o benius is employed for the differential equations in the radial direction using the field equations the eigenanalyses on both the original and its adjoint system were performed with great care which results in the eigenfunction sets of both systems the biorthogonality conditions were applied to the field equations to obtain the discretized equation for each mode using the solutions of the discretized equations that account for the boundary forcing terms the critical speed for a dual traveling force for each mode could be computed

an algorithm for computing the eigenstructure of a regular matrix polynomial abstract we give an algorithm to compute the finite zeros of a regular matrix polynomial p i e det p 0 the approach is close to that of the algorithm in 8 we use nonunitary elementary matrices instead of unitary matrices for the equivalence transformations which are somewhat cheaper in practice the danger of growth of nonunitary matrices seems to be more remote than usually supposed

computation of structural invariants of generalized state space systems in this paper we develop an algorithm for computing the zeros of a generalized state space model described by the matrix 5 tuple e a b c d where e may be a singular matrix but det a he 0 the characterization of these zeros is based on the system matrix of the corresponding 5 tuple both the characterization and the computational algorithm are extensions of equivalent results for state space models described by the 4 tuples a b c d we also extend these results to the computation of infinite zeros and left and right minimal indices of the system matrix several non trivial numerical examples are included to illustrate the proposed results

buckling of folded plate structures subjected to partial in plane edge loads by the fsdt meshfree galerkin method this paper presents a meshfree galerkin method that is based on the first order shear deformation theory fsdt to study the elastic buckling behaviour of stiffened and un stiffened folded plates under partial in plane edge loads the un stiffened folded plates are modelled as assemblies of flat plates the stiffness and initial stress matrices of the flat plates are derived by the meshfree galerkin method a treatment is implemented to modify the stiffness and initial stress matrices and the matrices are then superposed to obtain the stiffness and initial stress matrix of the entire folded plate the analytical process for stiffened folded plates is similar except that the effects of the stiffeners must be taken into account because no mesh is required the proposed method is superior for studying problems that would involve remeshing in the finite element method several examples are employed to show the convergence and accuracy of the proposed method the results obtained show good agreement with the results computed from the finite element analysis software ansys copyright 2005 john wiley sons ltd

an algebraic theory for design of controllers for linear multivariable systems part ii feedback realizations and feedback design the study of general linear multivariable systems with possibly different controlled and measured outputs is continued in this part of the paper the structure matrices defined in part i are used to solve the feedback realization problem feedback realizable transfer functions are then used to solve problems of regulator type it is shown that the solutions to problems like disturbance deeoupling output regulation and pole placement are all special cases of the solution to a more general problem finally it is shown how the results of part i and part ii can be combined to solve problems of servo type and of regulator type simultaneously

the eigenstructure of an arbitrary polynomial matrix computational aspects we give a new numerical method to compute the eigenstructure i e the zero structure the polar structure and the left and right null space structure of a polynomial matrix p these structural elements are of fundamental importance in several systems and control problems involving polynomial matrices the approach is more general than previous numerical methods because it can be applied to an arbitrary m n polynomial matrix p with normal rank r smaller than m and or n the algorithm is then shown to compute the structure of the left and right null spaces of p as well the speed and accuracy of this new approach are also discussed

an observer s information dynamics acquisition of information and the origin of the cognitive dynamics conventional information science considers an information process but traditionally uses the probability measure for random states and shannon s entropy as the uncertainty function of these states this paper presents a new approach based on an integral information measure of the random process an entropy functional ef on the trajectories of the process accumulates and encodes the process inner connections between the information states the application of a variation principle vp to the ef determines the process information path functional ipf whose extremal trajectories describe the informational dynamics of this process information dynamics with the vp invariant relations evaluate the information content of a random process expose its information code and reveal a conserved hidden information produced at an acquisition of the process information by introducing both objective and subjective information observers we consider the observers information cognitive dynamics and neurodynamics based on the ef ipf approach the universal nature of information process dynamics and regularities discovered in the information observers have many applications not only in cognitive and intelligent systems but also in different biological social and economic systems

characteristic and hyperinvariant subspaces over the field gf 2 let f be an endomorphism of a vector space v over a field k an f invariant subspace x v is called hyperinvariant respectively characteristic if x is invariant under all endomorphisms respectively automorphisms that commute with f if k 2 then all characteristic subspaces are hyperinvariant if k 2 then there are endomorphisms f with invariant subspaces that are characteristic but not hyperinvariant in this paper we give a new proof of a theorem of shoda which provides a necessary and sufficient condition for the existence of characteristic non hyperinvariant subspaces

perturbed marked reduced forms of invariant subspaces abstract the classification of invariant subspaces is an open problem related to other important ones like the carlson problem here we obtain a reduced form of these invariant subspaces as a new tool to tackle these problems in particular it allows us to prove quite easily partial results already known the key point is assigning to each invariant subspace a marked one its marked type in order to partition the set of invariant subspaces in a finite number of subsets the marked classes each one containing only one marked subspace next we parametrize minimally each marked class by means of the so called pm reduced families so that representatives of an invariant subspace its pm reduced forms appear in just one of these families

polynomial matrices and feedback for a polynomial matrix having full row rank for all values of the parameter number of rows less than number of columns a number of extra rows is constructed such that the completed square polynomial matrix is unimodular this construction is performed in a numerically reliable way using a deadbeat control algorithm for a generalized state space system which in turn represents the given polynomial matrix

structural stability of c a marked subspaces abstract given an observable pair of matrices c a we consider the manifold of c a invariant subspaces having a fixed brunovsky kronecker structure using arnold techniques we obtain the explicit form of a miniversal deformation of a marked c a invariant subspace with respect to the usual equivalence relation as an application we obtain the dimension of the orbit and we characterize the structurally stable subspaces those with open orbit

realizations in generalized state space form for polynomial system matrices and the definitions of poles zeros and decoupling zeros at infinity this paper contains three main results firstly a realization procedure is presented that brings a polynomial system matrix of a non proper multivariable system to generalized state space form such that all relevant properties including phenomena of redundancy associated with finite and infinite decoupling zeros are retained secondly new definitions are proposed for poles zeros and decoupling zeros at infinity of a general polynomial system matrix as a third result a theorem of rosenbrock 1974 e on the redundancy of lcr multiports is generalized to include the decoupling zeros at infinity

min max elementwise backward error for roots of polynomials and a corresponding backward stable root finder abstract a new measure called min max elementwise backward error is introduced for approximate roots of scalar polynomials p z compared with the elementwise relative backward error this new measure allows for larger relative perturbations on the coefficients of p z that do not participate much in the overall backward error by how much these coefficients can be perturbed is determined via an associated max times polynomial and its tropical roots an algorithm is designed for computing the roots of p z it uses a companion linearization c z a z b of p z to which we added an extra zero leading coefficient and an appropriate two sided diagonal scaling that balances a and makes b graded in particular when there is variation in the magnitude of the coefficients of p z an implementation of the qz algorithm with a strict deflation criterion for eigenvalues at infinity is then used to obtain approximations to the roots of p z under the assumption that this implementation of the qz algorithm exhibits a graded backward error when b is graded we prove that our new algorithm is min max elementwise backward stable several numerical experiments show the superior performance of the new algorithm compared with the matlab roots function extending the algorithm to polynomial eigenvalue problems leads to a new polynomial eigensolver that exhibits excellent numerical behaviour compared with other existing polynomial eigensolvers as illustrated by many numerical tests