numerical solution of convection diffusion problems at high peclet number using boundary elements this paper describes a boundary element scheme for solving steady state convection diffusion problems at high peclet numbers a special treatment of the singular integrals is included which uses discontinuous elements and a regularization procedure transformations are performed to avoid directly evaluating bessel functions for cauchy principal value and hypersingular integrals test examples are solved with values of peclet number up to 107 to assess the numerical scheme 1998 john wiley sons ltd

a two dimensional bi cubic b spline finite element used in a study of mhd duct flow abstract a two dimensional bi cubic b spline finite element is proposed and used within a galerkin approach to model magneto hydrodynamic duct flow excellent agreement is obtained between the numerical results and the analytic solution even for large values of the applied magnetic field

non linear steady state vibration of frames by finite element method a finite element method based on the virtual work principle to determine the steady state response of frams in free or forced periodic vibration is introduced the axial and flexural deformations are coupled by mean of the induced axial force along the element the spatial discretization of the deformations is achieved by the usual finite element method and the time discretization by fourier coefficients of the nodal displacements no unconventional element matrices are needed after applying the harmonic balance method a set of non linear algebraic equations of the fourier coefficients is obtained these equations are solved by the newtonian iteration method in terms of the fourier coefficient increments nodal damping can easily be included by a diagonal damping matrix the direct numerical determination of the fourier coefficient increments is difficult owing to the presence of peaks loops and discontinuities of slope along the amplitude frequency response curves parametric construction of the response curves using the phase difference between the response and excitation is recommended to provide more points during the rapid change of the phase i e at resonance for undamped natural vibration the method of selective coefficients adopted numerical examples on the duffing equation a hinged hinged beam a clamped hinged beam a ring and a frame are given for reasonably accurate results it is shown that the number of finite elements must be sufficient to predict at least the linear mode at the frequency of interest and the number of harmones considered must satisfy the conditions of completeness and balanceability which are discussed in detail

the member stiffness determinant and its uses for the transcendental eigenproblems of structural engineering and other disciplines transcendental stiffness matrices are well established in vibration and buckling analysis having been derived from exact analytical solutions of the differential equations for many structural members without recourse to finite element discretization their assembly into the overall structural stiffness matrix gives a transcendental eigenproblem solvable with certainty by the wittrick williams ww algorithm instead of the usual linear algebraic eigenproblem this paper establishes a normalized member stiffness determinant being the value of the stiffness matrix determinant if the member were modelled by infinitely many finite elements and its ends were clamped it is derived for beams with uncoupled axial and bernoulli euler flexural behaviour by methods applicable to any member possessing transcendental stiffnesses multiplying the product of a structure s member stiffness determinants by the determinant of its transcendental overall stiffness matrix gives a determinant which unlike the determinant of the transcendental overall stiffness matrix itself has no poles when plotted against the eigenparameter leading to a more secure eigenvalue location numerical results demonstrate the resulting advantages in addition the member stiffness determinant can give exact determinants for members with various standard end conditions and also provides limits for finite element solutions as the number of elements approaches infinity analogous advantages occur in all other disciplines where the ww algorithm is used e g fluid vibrating in pipes heat and mass diffusion and sturm liouville problems

numerical quadratures for singular and hypersingular integrals abstract we present a procedure for the design of high order quadrature rules for the numerical evaluation of singular and hypersingular integrals such integrals are frequently encountered in solution of integral equations of potential theory in two dimensions unlike integrals of both smooth and weakly singular functions hypersingular integrals are pseudo differential operators being limits of certain integrals as a result standard quadrature formulae fail for hypersingular integrals on the other hand such expressions are often encountered in mathematical physics see for example 1 and it is desirable to have simple and efficient quadrature formulae for them the algorithm we present constructs high order quadratures for the evaluation of hypersingular integrals the additional advantage of the scheme is the fact that each of the quadratures it produces can be used simultaneously for the efficient evaluation of hypersingular integrals hilbert transforms and integrals involving both smooth and logarithmically singular functions this results in significantly simplified implementations the performance of the procedure is illustrated with several numerical examples

the method of variably scaled radial kernels for solving two dimensional magnetohydrodynamic mhd equations using two discretizations the crank nicolson scheme and the method of lines mol abstract mhd equations have many applications in physics and engineering the model is coupled equations in velocity and magnetic field and has a parameter namely hartmann the value of hartmann number plays an important role in the equations when this parameter increases using different meshless methods makes the oscillations in velocity near the boundary layers in the region of the problem in the present paper a numerical meshless method based on radial basis functions rbfs is provided to solve mhd equations for approximating the spatial variable a new approach which is introduced by bozzini et al 2015 is applied the method will be used here is based on the interpolation with variably scaled kernels the methodology of the new technique is defining the scale function c on the domain r d then the interpolation problem from the data locations x j r d transforms to the new interpolation problem in the data locations x j c x j r d 1 bozzini et al 2015 the radial kernels used in the current work are multiquadrics mq inverse quadric iq and wendland s function of course the latter one is based on compactly supported functions to discretize the time variable two techniques are applied one of them is the crank nicolson scheme and another one is based on mol the numerical simulations have been carried out on the square and elliptical ducts and the obtained numerical results show the ability of the new method for solving this problem also in appendix we provide a computational algorithm for implementing the new technique in matlab software

an inverse problem for the three dimensional vector helmholtz equation for a perfectly conducting obstacle abstract a numerical algorithm for a three dimensional inverse electromagnetic scattering problem is considered for time harmonic waves the maxwell s equations are reduced to the vector helmholtz equation from the knowledge of several far fields generated by an obstacle d when hit by incoming linearly polarized plane waves the boundary d of the obstacle is reconstructed the obstacle d is supposed to be bounded connected with smooth boundary and perfectly conducting the reconstruction procedure proposed here generalizes the herglotz function method introduced by colton and monk 1 for the acoustic problem and is effective in the so called resonance region

on the free vibration analysis of spinning structures by using discrete or distributed mass models abstract the analysis of the natural frequencies and modes of vibration of a spinning structure is in general complicated by the presence of gyroscopic or coriolis forces leading to a complex hermitian dynamic stiffness or impedance matrix it is shown that if the analysis is performed by using a discrete model with n degrees of freedom the leading principal minors of the n th order dynamic stiffness matrix exhibit a type of sturm sequence property this leads to a theorem which can be used for the systematic calculation of the natural frequencies of either a discrete system which is assembled from sub structures or an assembly of distributed mass members in both of these cases the order n of the matrix is less than the number of degrees of freedom and its determinant possesses poles as well as zeros the theorem is identical with a corresponding one for non spinning structures previously derived by the authors the application of the theorem to a spinning two dimensional frame with distributed mass members is discussed in some detail

development of a block lanczos algorithm for free vibration analysis of spinning structures this paper is concerned with the development of an efficient eigenproblem solution algorithm and an associated computer program for the economical solution of the free vibration problem of complex practical spinning structural systems thus a detailed description of a newly developed block lanczos procedure is presented in this paper that employs only real numbers in all relevant computations and also fully exploits sparsity of associated matrices the procedure is capable of computing multiple roots and proves to be most efficient compared to other existing similar techniques

the galerkin boundary node method for magneto hydrodynamic mhd equation in this research a variational reformulation for magneto hydrodynamic mhd problem is derived existence and uniqueness of the weak solution are discussed the galerkin boundary node method is a boundary meshless method which uses mls basis functions to approximate solution of problems this paper tries to apply this method for a variational form of the magneto hydrodynamic mhd problem numerical experiments reveal that the method is effective and convenient for this problem

spinning finite elements abstract by means of lagrangian equations the finite element method is extended to spinning structures skeletal structures consisting of straight beam members are taken as examples explicit element matrices are given numerical solution procedures based on the newtonian algorithm are suggested the orientation of a beam member is arbitrary with reference to a rotating frame so that general spinning space structures can be considered numerical examples show the well known fact that the axial force in a beam induced by the centrifugal force has destabilizing effects while gyroscopic motion has stabilizing effects the combined effect may be either stabilizing or destabilizing depending on the boundary conditions

a solution of the eigenproblem for undamped gyroscopic systems with the lanczos algorithm this paper presents an efficient numerical solution of the quadratic eigenproblem arising in the analysis of gyroscopic systems such problems are known to reduce to a generalized linear eigenproblem defined by two real non singular matrices one symmetric and one skew symmetric for this class of problems the general lanczos algorithm for unsymmetric matrices is shown to simplify considerably and yields an efficient solution of the problem full advantage can be taken of the sparsity of the matrices and of the specific nature of gyroscopic systems numerical examples are presented which demonstrate the efficiency and accuracy of the solution procedure

geometrically non linear vibration of spinning structures by finite element method the geometrically non linear steady state vibration of spinning structures is studied full flap lag torsional gyroscopic coupling effects are considered the non linearity arises mainly from the non linear axial strain displacement relation the equations of motion are derived from lagrangian equations spatial discretization is achieved by the finite element method and steady state nodal displacements are expanded into fourier series the harmonic balance method gives a set of non linear algebraic equations with the fourier coefficients of the nodal displacements as unknowns the non linear algebraic equations are solved by a newtonian algorithm iteratively the importance of the conditions of completeness and balanceability in choosing the number of harmonic terms to be used is discussed general frame structures with arbitrary orientation in a rotating frame can be investigated by the present method rotating blades and shafts are treated as special cases examples of a rotating ring with different orientations are given the non linear amplitude frequency relation can be constructed parametrically

modal analysis of rotating shafts a body fixed axis formulation approach abstract a spinning timoshenko beam subjected to a constant moving load is analyzed using a modal expansion technique the formulation is based on a body fixed axis reference system and thus should be applicable to handle any general cross sections using this alternative approach dynamic quantities such as natural frequencies mode shapes and system responses are easily computable it is shown that simply supported spinning timoshenko beams posses two pairs of natural frequencies corresponding to each mode shape through appropriate simplifications the coupled eighth order differential equations governing the problem are degenerated into a set of uncoupled fourth order equations with this simplified theory closed form expressions for natural frequencies and system transient response are derived however one pair of the natural frequencies is lost in the process but this is acceptable as the frequencies of this pair are much higher than those of the retained pair in addition a linearized approximation of the natural frequency similar to the one given for euler bernoulli beams is also proposed for a timoshenko shaft numerical simulations are performed to demonstrate the characteristics of the response

three dimensional time harmonic electromagnetic inverse scattering the reconstruction of the shape and the impedance of an obstacle abstract a numerical method for the reconstruction of the shape and the impedance of an obstacle from time harmonic electromagnetic scattering data is presented let d be a bounded simply connected domain contained in the three dimensional euclidean space r 3 with smooth boundary d the three dimensional euclidean space is filled with an isotropic homogeneous medium we assume that d contains the origin and d is regarded as an obstacle whose electric properties are given by a boundary impedance x x d from the knowledge of the electric far fields generated by the obstacle d when hit by known time harmonic electromagnetic waves the shape d and the boundary impedance x of the obstacle are reconstructed the reconstruction algorithm is based on the herglotz function method introduced by colton and monk 1 in acoustic scattering

a subspace iteration method for the eigensolution of large undamped gyroscopic systems on presente une methode efficace et numeriquement stable pour le calcul des valeurs propres de plus petit module et des vecteurs propres associes d un probleme propre quadratique on traite un exemple numerique

lambda matrix flexibility abstract to represent an harmonically vibrating continuous system having an infinite number of degrees of freedom by means of mathematical models of a finite number of co ordinates the relation between the excitation force vector and response displacement vector the dynamic stiffness matrix d is inevitably frequency dependent it is often required to compute the dynamic flexibility matrix z which is the inversion of d a new method is presented here to express z in terms of the eigensolutions of d it is similar to the classical format except that d is no longer required to be expressible as a matrix polynomial in with constant coefficient matrices in contrast to the state variables which tend to increase the order of the matrices only physical co ordinates are concerned d may be non symmetric and defective

inverse obstacle scattering for homogeneous dielectric cylinders using a boundary finite element method a method for reconstructing the shape and the permittivity of a penetrable homogeneous cylinder is described it is the extension to penetrable cylinders of a previous work dealing with perfectly conducting cylinders a low frequency approximation is used to determine an initial guess then a rigorous boundary integral method permits us to reconstruct arbitrary shapes and complex permittivities it is based on an iterative conjugate gradient algorithm requiring the solving of two direct diffraction problems only a simple and original regularization scheme is presented which ensures the robustness of the algorithm numerical examples with lossy embedding media and additional random noise for both e spl par and h spl par polarizations are given

the meshless galerkin boundary node method for stokes problems in three dimensions the galerkin boundary node method gbnm is a boundary only meshless method that combines an equivalent variational formulation of boundary integral equations for governing equations and the moving least squares mls approximations for generating the trial and test functions in this approach boundary conditions can be implemented directly and easily despite of the fact that the mls shape functions lack the delta function property besides the resulting formulation inherits the symmetry and positive definiteness of the variational problems the gbnm is developed in this paper for solving three dimensional stationary incompressible stokes flows in primitive variables the numerical scheme is based on variational formulations for the first kind integral equations which are valid for both interior and exterior problems simultaneously a rigorous error analysis and convergence study of the method for both the velocity and the pressure is presented in sobolev spaces the capability of the method is also illustrated and assessed through some selected numerical examples copyright 2011 john wiley sons ltd

a galerkin boundary node method and its convergence analysis the boundary node method bnm exploits the dimensionality of the boundary integral equation bie and the meshless attribute of the moving least square mls approximations however since mls shape functions lack the property of a delta function it is difficult to exactly satisfy boundary conditions in bnm besides the system matrices of bnm are non symmetric a galerkin boundary node method gbnm is proposed in this paper for solving boundary value problems in this approach an equivalent variational form of a bie is used for representing the governing equation and the trial and test functions of the variational formulation are generated by the mls approximation as a result boundary conditions can be implemented accurately and the system matrices are symmetric total details of numerical implementation and error analysis are given for a general bie taking the dirichlet problem of laplace equation as an example we set up a framework for error estimates of gbnm some numerical examples are also given to demonstrate the efficacity of the method

a meshless galerkin method for stokes problems using boundary integral equations a meshless galerkin scheme for the simulation of two dimensional incompressible viscous fluid flows in primitive variables is described in this paper this method combines a boundary integral formulation for the stokes equation with the moving least squares mls approximations for construction of trial and test functions for galerkin approximations unlike the domain type method this scheme requires only a nodal structure on the bounding surface of a body for approximation of boundary unknowns thus it is especially suitable for the exterior problems compared to other meshless methods such as the boundary node method and the element free galerkin method in which the mls is also introduced boundary conditions do not present any difficulty in using this meshless method the convergence and error estimates of this approach are presented numerical examples are also given to show the efficiency of the method

three dimensional inverse obstacle scattering for time harmonic acoustic waves a numerical method a numerical method for a three dimensional inverse acoustic scattering problem is considered from the knowledge of several far fields patterns of the helmholtz equation a closed surface partial d representing the boundary of an unknown obstacle d is reconstructed the obstacle d is supposed to be acoustically soft or acoustically hard or characterized by a given acoustic impedance

fundamental solution for coupled magnetohydrodynamic flow equations in this paper a fundamental solution for the coupled convection diffusion type equations is derived the boundary element method bem application then is established with this fundamental solution for solving the coupled equations of steady magnetohydrodynamic mhd duct flow in the presence of an external oblique magnetic field thus it is possible to solve mhd duct flow problems with the most general form of wall conductivities and for large values of hartmann number the results for velocity and induced magnetic field is visualized in terms of graphics for values of hartmann number m 300

duct flow with a transverse magnetic field at high hartmann numbers finite element methods can be used for determining the flow in a straight channel under a variety of wall conductivity conditions when a uniform magnetic field is imposed perpendicular to the flow direction at high hartmann numbers oscillatory solutions are found unless sufficient points are placed within the hartmann layers in some one and two dimensional problems it appears that it is adequate to place one or two points within the hartmann layer to remove the oscillations central core values can sometimes be predicted with good accuracy even when the hartmann layers are not resolved adequately a nine point gauss point rule has been used to evaluate the stiffness and other matrices for the eight node elements copyright 2001 john wiley sons ltd