nonlinear analysis of reissner plates on an elastic foundation by the bem the fundamental solutions and the boundary element method for obtaining numerical solutions of nonlinear reissner plates on an elastic foundation are presented in the paper the derivation of the fundamental solutions is mainly based on two of hu s functions and the resolution method of differential operator an incremental form of the boundary integral equations is suggested to achieve linearization of the original nonlinear equations the plate may be moderately thick or sandwich plates with or without elastic foundation finally three examples are considered to illustrate the correctness and accuracy of the proposed method

an extended boundary element method formulation for the direct calculation of the stress intensity factors in fully anisotropic materials copyright 2016 john wiley sons ltd we propose a formulation for linear elastic fracture mechanics in which the stress intensity factors are found directly from the solution vector of an extended boundary element method formulation the enrichment is embedded in the boundary element method formulation rather than adding new degrees of freedom for each enriched node therefore a very limited number of new degrees of freedom is added to the problem which contributes to preserving the conditioning of the linear system of equations the stroh formalism is used to provide boundary element method fundamental solutions for any degree of anisotropy and these are used for both conventional and enriched degrees of freedom several numerical examples are shown with benchmark solutions to validate the proposed method copyright 2016 john wiley sons ltd

transient boundary element algorithm for elastoplastic building floor slab analysis a direct boundary element algorithm is developed for the dynamic analysis of thin elastoplastic building floor slabs directly supported by columns the formulation employs the classical boundary element methodology dedicated to the analysis of elastoplastic plates the method uses the static fundamental solution of the thin elastic plate problem in this case boundary as well as interior elements are used in the space descritization of the problem this is due to the presence of plasticity and inertial effects in the integral formulation an explicit time integration algorithm employed on the incremental form of the matrix equation of motion leads to the solution of the problem simple practical examples illustrate the accuracy and the efficiency of the proposed algorithm

characterizing the statistical properties of mutual information in mimo channels we consider gaussian multiple input multiple output mimo frequency selective spatially correlated fading channels assuming that the channel is unknown at the transmitter and perfectly known at the receiver for gaussian codebooks using results from multivariate statistics we derive an analytical expression for a tight lower bound on the ergodic capacity of such channels at any signal to noise ratio snr we show that our bound is tighter than previously reported analytical lower bounds and we proceed to analytically quantify the impact of spatial fading correlation on ergodic capacity based on a closed form approximation of the variance of mutual information in correlated flat fading mimo channels we provide insights into the multiplexing diversity tradeoff for gaussian code books furthermore for a given total number of antennas we consider the problem of finding the optimal ergodic capacity maximizing number of transmit and receive antennas and we reveal the snr dependent nature of the maximization strategy finally we present numerical results and comparisons between our capacity bounds and previously reported bounds

a new method for evaluating singular integrals in stress analysis of solids by the direct boundary element method the purpose of this paper is to report on a new and efficient method for the evaluation of singular integrals in stress analysis of elastic and elasto plastic solids respectively by the direct boundary element method bem triangle polar co ordinates are used to reduce the order of singularity of the boundary integrals by one degree and to carry out the integration over mappings of the boundary elements onto plane squares the method was subsequently extended to the cubature of singular integrals over three dimensional internal cells as occur in applications of the bem to three dimensional elasto plasticity for this purpose so called tetrahedron polar co ordinates were introduced singular boundary integrals stretching over either linear triangular or quadratic quadilateral isoparametric boundry elements and singular volume integrals extending over either linear tetrahedral or quadratic hexahedral isoparametric internal cells are treated in case of higher order isoparametric boundary elements and internal cells division into a number of subelements and subcells respectively is necessary the analytical investigation is followed by a numerical study restricted to the use of quadratic quadrilateral isoparametric boundary elements this is justified by the fact that such elements as opposed to linear elements yield singular boundary integrals which cannot be integrated analytically the results of the numerical investigation demonstrate the potential of the developed concept

a sinh transformation for evaluating two dimensional nearly singular boundary element integrals a new transformation technique is introduced for evaluating the two dimensional nearly singular integrals which arise in the solution of laplace s equation in three dimensions using the boundary element method when the source point is very close to the element of integration the integrals are evaluated using in a product fashion a transformation which has recently been used to evaluate one dimensional near singular integrals this sinh transformation method automatically takes into account the position of the projection of the source point onto the element and also the distance b between the source point and the element the method is straightforward to implement and when it is compared with a number of existing techniques for evaluating two dimensional near singular integrals it is found that the sinh method is superior to the existing methods considered both for potential integrals across the full range of b values considered 0 0 01 for smaller values of b the use of the lmethod is recommended for flux integrals copyright 2006 john wiley sons ltd

fundamental solutions and boundary integral equations for reissner s plates on two parameter foundations abstract in this paper the fundamental solutions and boundary integral equations for reissner s plates on a two parameter foundation are presented the construction of the fundamental solutions and the numerical treatment of the boundary integral equations are described in detail some numerical examples are studied to demonstrate the correctness and accuracy of the formulation presented

buckling analysis of shear deformable plates by boundary element method in this paper the derivation and numerical implementation of boundary integral equations for the buckling analysis of shear deformable plates are presented plate buckling equations are derived as a standard eigenvalue problem the formulation is formed by coupling boundary element formulations of shear deformable plate and two dimensional plane stress elasticity the eigenvalue problem of plate buckling yields the critical load factor and buckling modes the domain integrals which appear in this formulation are treated in two different ways initially the integrals are evaluated using constant cells and next they are transformed into equivalent boundary integrals using the dual reciprocity method drm several examples with different geometry loading and boundary conditions are presented to demonstrate the accuracy of the formulation

highly convergent dynamic models obtained by modal synthesis with application to short wave pulse propagation a general approach for obtaining the matrices of a substructure ensuring minimum modal frequency errors of the whole structure is presented the mass and stiffness matrices of a small component domain of selected dimension are obtained by applying the modal synthesis of a limited number of close to exact modes such that after assembling a larger joined domain model the modal convergence rate of the latter should be as high as possible the goal is achieved by formulating the minimization problem for the penalty type target function representing the cumulative relative modal frequency error of the joined sample domain and by applying the gradient descent minimization method after the optimum matrices of a component domain are obtained they can be used in any structure as higher order elements or super elements the well known generalized mass matrices obtained as a weighted sum of lumped and consistent components can be treated as a special case of the presented approach the obtained dynamic models are used for modelling short transient waves and wave pulses propagating in elastic or acoustic environments by using a only a few nodal points per pulse length copyright 2004 john wiley sons ltd

boundary integration and interpolation procedures for plate bending in the direct boundary element method dbem for thin plate bending analysis the integration of the kernel shape function products can lead to complications due to a combination of factors the first is the existence of a singularity at the source point leading to the singular kernel which increases in strength as the integral equation is differentiated once for rotation again for moment and yet again for shear the second factor arises from the use of piecewise interpolation polynomials in the first part of the dbem analysis where the unspecified boundary values are computed the numerical procedures are fairly straightforward it is found in this paper that special care must be taken in calculating internal actions at domain points the problems which can be encountered are demonstrated and a modified boundary interpolation procedure is described examples are given which show the superiority of the recommended approach

boundary element modelling of flat plate floors under vertical loading the present paper develops a boundary element model for flat plate floors the floor slab is modelled using the shear deformable plate bending theory internal columns or walls are treated using internal collocation technique where three interaction generalized forces are considered at the slab column connection two bending moments in two directions and shear force in the vertical direction such forces are considered to be constant over the column cross sections the present technique takes into account the realistic geometric modelling of the column cross sections the effect of considering such geometry in the analysis of the bending moments transferred from slab to columns is studied several examples including solution of practical building slab are presented the results are compared to those obtained from other numerical methods to demonstrate the accuracy and the reliability of the present formulation the present formulation can be considered as an accurate tool to predict moment transferred from the slab to the column copyright 2004 john wiley sons ltd

analysis of orthotropic thick plates by meshless local petrov galerkin mlpg method a meshless local petrov galerkin mlpg method is applied to solve static and dynamic problems of orthotropic plates described by the reissner mindlin theory analysis of a thick orthotropic plate resting on the winkler elastic foundation is given too a weak formulation for the set of governing equations in the reissner mindlin theory with a unit test function is transformed into local integral equations on local subdomains in the mean surface of the plate nodal points are randomly spread on the surface of the plate and each node is surrounded by a circular subdomain to which local integral equations are applied the meshless approximation based on the moving least squares mls method is employed in the numerical implementation the present computational method is applicable also to plates with varying thickness numerical results for simply supported and clamped plates are presented copyright 2006 john wiley sons ltd

application of the boundary integral equation method to reissner s plate model numerical solution of reissner s model for the bending of elastic plates by an advanced boundary integral equation method is outlined construction of fundamental solutions and computational strategy is fully described implementation of the resulting one dimensional model is illustrated by two test problems including comparison to analytical solutions

the method of steepest descent for estimating quadrature errors this work presents an application of the method of steepest descent to estimate quadrature errors the method is used to provide a unified approach to estimating the truncation errors which occur when gauss legendre quadrature is used to evaluate the nearly singular integrals that arise as part of the two dimensional boundary element method the integrals considered here are of the form 1 1 h x d x x a 2 b 2 where h x is a well behaved function 0 and 1 a 1 since 0 b 1 the integral is nearly singular with a sharply peaked integrand the method of steepest descent is used to estimate the generally large truncation errors that occur when gauss legendre quadrature is used to evaluate these integrals as well as to estimate the much lower errors that occur when gauss legendre quadrature is performed on such integrals after a sinh transformation has been applied the new error estimates are highly accurate in the case of the transformed integral and are shown to be comparable to those found in previous work by elliott and johnston 2007 one advantage of the new estimates is that they are given by just one formula each for the un transformed and the transformed integrals rather than the much larger set of formulae in the previous work another advantage is that the new method applies over a much larger range of values than the previous method

an improved local well posedness result for the one dimensional zakharov system abstract the 1d cauchy problem for the zakharov system is shown to be locally well posed for low regularity schrodinger data u 0 h k p and wave data n 0 n 1 h l p h l 1 p under certain assumptions on the parameters k l and 1 p 2 where u 0 h k p k u 0 l p generalizing the results for p 2 by ginibre tsutsumi and velo especially we are able to improve the results from the scaling point of view and also allow suitable k 0 l 1 2 i e data u 0 l 2 and n 0 n 1 h 1 2 h 3 2 which was excluded in the case p 2

error estimation of quadrature rules for evaluating singular integrals in boundary element problems the efficient numerical evaluation of integrals arising in the boundary element method is of considerable practical importance the superiority of the use of sigmoidal and semi sigmoidal transformations together with gauss legendre quadrature in this context has already been well demonstrated numerically by one of the authors in this paper the authors obtain asymptotic estimates of the truncation errors for these algorithms these estimates allow an informed choice of both the transformation and the quadrature error in the evaluation of boundary element integrals with algebraic or algebraic logarithmic singularities at an end point of the interval of integration copyright 2000 john wiley sons ltd

the fundamental solution of mindlin plates resting on an elastic foundation in the laplace domain and its applications abstract the aim of this study is to investigate the method of fundamental solution mfs applied to a shear deformable plate reissner mindlin s theories resting on the elastic foundation under either a static or a dynamic load the complete expressions for internal point kernels i e fundamental solutions by the boundary element method for the mindlin plate theory are derived in the laplace transform domain for the first time on employing the mfs the boundary conditions are satisfied at collocation points by applying point forces at source points outside the domain all variables in the time domain can be obtained by durbin s laplace transform inversion method numerical examples are presented to demonstrate the accuracy of the mfs and comparisons are made with other numerical solutions in addition the sensitivity and convergence of the method are discussed for a static problem the proposed mfs is shown to be simple to implement and gives satisfactory results for shear deformable plates under static and dynamic loads

dual boundary method for assembled plate structures undergoing large deflection summary in this paper the dual boundary element method is combined with a multiregion formulation to simulate plate assembly undergoing large deflection the incremental load approach is used to treat the geometrical nonlinearity and radial basis functions are used to approximate the derivatives of the large deflection terms the dual reciprocity method is used to transfer all the domain integrals to the boundary once the solution at the boundary is obtained for the assembly a j integral for large deflection is implemented to extract the fracture parameters copyright 2011 john wiley sons ltd

nonlinear schrodinger equations and sharp interpolation estimates a sharp sufficient condition for global existence is obtained for the nonlinear schrodinger equation begin array 20 c nls 2i phi t delta phi left phi right 2 sigma phi 0 x in mathbb r n t in mathbb r end array in the case 2 n this condition is in terms of an exact stationary solution nonlinear ground state of nls it is derived by solving a variational problem to obtain the best constant for classical interpolation estimates of nirenberg and gagliardo

contact between plates by a new direct boundary integral equation formulation abstract the unilateral contact between two plates according to kirchhoff s theory is solved by using a boundary integral equation method a discretization leading to a matrix formulation is proposed to solve this problem an elimination of boundary unknowns is performed an iterative method proves successful with the example treated

taylor expansions for singular kernels in the boundary element method the problem treated is the integration of singular functions which arise in three dimensional isoparametric formulations of boundary integral equations a taylor expansion in the local parametric co ordinates is developed for the singular integrand so allowing singular terms to be integrated in closed form even for curved surface elements the remainder integral obtained by subtracting out the worst singularities is integrated by repeated gaussian quadrature two groups of tests are presented first the accuracy of the integrations has been checked for plane parallelograms for which exact solutions have been developed and for curved elements on a sphere secondly results from complete boundary element calculations based on point collocation have been compared with known analytical solutions to two problems zonal surface harmonics on a sphere and the capacitance of an ellipsoid the agreement obtained with few degrees of freedom suggests that errors which have previously been attributed to point collocation might have arisen in the numerical integration

on the convergence of the solution for a generalized zakharov system in this paper we study the limit behavior of the smooth solution for the generalized zakharov system with a magnetic field which describes the spontaneous generation of a magnetic field in a cold plasma by showing uniform bounds of solutions for this system with suitable initial data we prove that solution of the generalized zakharov system converges to the solution of the nonlinear schrodinger equation with a magnetic field

a self adaptive co ordinate transformation for efficient numerical evaluation of general boundary element integrals almost all general purpose boundary element computer packages include a curved geometry modelling capability thus numerical quadrature schemes play an important role in the efficiency of programming the technique the present work discusses this problem in detail and introduces efficient means of computing singular or nearly singular integrals currently found in two dimensional axisymmetric and three dimensional applications emphasis is given to a new third degree polynomial transformation which was found greatly to improve the accuracy of gaussian quadrature scheme s within the near singularity range the procedure can easily be implemented into existing be codes and presents the important feature of being self adaptive i e it produces a variable lumping of the gauss stations toward the singularity depending on the minimum distance from the source point to the element the self adaptiveness of the scheme also makes it inactive when not useful large source distances which makes it very safe for general usage

the direct boundary element method in plate bending the direct boundary element method based on the rayleigh green identity is employed for the static analysis of kirchhoff plates the starting point is a slightly modified version of stern s equations the focus is on the implementation of the method for linear elements and a hermitian interpolation for the deflection w the concept of element matrices is developed and the cauchy principal values of the singular integrals are given in detail the treatment of domain integrals the handling of internal supports the properties of the solution and the effect of singularities are discused numerical examples illustrate the various techniques in the appendix the influence functions for the second and third derivatives of the deflection w are given

unilateral buckling of thin elastic plates by the boundary integral equation method the unilateral buckling of thin elastic plates according to kirchhoff s theory is studied by using a boundary integral method a representation for the second member of the equation is given in the matrix formulatiea boundary unknowns are eliminated therefore the unilateral buckling problem reduces to compute the eigenvalues and the eigenvectors of a matrix depending on the contact zone with the rigid foundation an iterative process allows this zone and the buckling load to be computed the capacities of the proposed method are illustrated by four examples

a new boundary integral formulation for stream function and vorticity in axisymmetric stokes flow a boundary integral equation approach is presented to solve the flow stream function and vorticity in the axisymmetric stokes problem without swirl the governing equations expressed in these variables require that the fundamental solutions of the involved differential operators be found the fundamental solutions in a closed form suitable for numerical treatment of integral equations are obtained and their equivalent forms in infinite integral are derived by using fourier and hankel transforms a coupled system of boundary integral equations for the stream function and the vorticity is formulated by employing new fundamental solutions solution of these equations is realized by the collocation method numerical results are included for several bounded and unbounded domain problems to validate and demonstrate the effectiveness of the proposed approach

augmented levy michell equations for flexural plates abstract a new sixth order isotropic elastic and flexural plate theory is presented based on the fourth order equations of levy 1877 and michell 1900 the lack of surface loading in these levy michell equations is overcome by including the dominant flexural component of dougall s 1904 solution for a point load on the surface of a three dimensional isotropic elastic layer the augmented plate equations are arranged to fit the form of a consistent sixth order system of isotropic plate equations which include the well known work of reissner and static equations of mindlin numerical applications to two three dimensional problems with analytical solutions show good comparative results

evaluation of single layer potentials over curved surfaces the evaluation of nearly singular single layer potentials encountered in boundary element methods is treated by a new approach the potential is expressed as a sum of a one dimensional integral and a correction term that vanishes for planar surfaces the small variance of the second term s integrand allows the use of a quasi monte carlo quadrature numerical results show that a significant reduction in computational time is obtained over algorithms employing domain subdivisions

dual boundary element formulation for fracture mechanics analysis of shear deformable shells this paper presents a new boundary element formulation for fracture mechanics analysis of shear deformable shells hyper singular boundary integral equations for shear deformable shells are derived dual boundary element formulations are constructed by using traction integral equations on one side of the crack surface and displacement integral equations on the other side of the crack surface and all other boundaries five stress intensity factors two for membrane behaviour and three for shear and bending are computed several crack configurations are analysed to demonstrate the efficiency and accuracy of the proposed formulation

low regularity global well posedness for the zakharov and klein gordon schrodinger systems we prove low regularity global well posedness for the id zakharov system and the 3d klein gordon schrodinger system which are systems in two variables u r d x x r t c and n r d x x r t r the zakharov system is known to be locally well posed in u n l 2 x h and the klein gordon schrodinger system is known to be locally well posed in u n l 2 x l 2 here we show that the zakharov and klein gordon schrodinger systems are globally well posed in these spaces respectively by using an available conservation law for the l 2 norm of u and controlling the growth of n via the estimates in the local theory

the general fundamental solution of the sixth order reissner and mindlin plate bending models revisited abstract the sixth order differential equation system of the reissner and mindlin plate bending models describe mathematically the plate problem where lines normal to the mid plane before deformation remain straight and inextensible in the deformed configuration but not necessarily normal to the reference plane anymore the non normality condition is due to the consideration of transverse shearing strains disregarded in the classical bi harmonic kirchhoff plate model as the plate thickness is reduced and or the transverse shear modulus is increased the deformed configuration is less dependent of the transverse shear strains and in the limit as the plate thickness approaches zero and or the transverse shear modulus approaches the transverse shear strain effects vanish and the problem is exactly that described by the classical plate model in this paper we investigate the fundamental solutions of both the fourth order kirchhoff and the sixth order reissner and mindlin plate models we consider a transversely isotropic material and show that the fundamental solution of the bi harmonic problem can be obtained directly from the general fundamental solution of the sixth order plate problem in the limit as the plate thickness approaches zero and or the transverse shear modulus approaches this solution is in agreement with the analytical solution of an infinite thin clamped circular plate submitted to a unitary concentrated load acting at its center

evaluation of boundary integrals for plate bending the alternative to quadrature as a procedure for dealing with the integrations required in the direct boundary element method dbem is to carry out the integration analytically and code the results directly the potential benefits are efficient computer programs the avoidance of numerical instability and generally better accuracy the technique is developed in this paper serious problems arise when gauss quadrature is employed for the integration of functions which contain or are close to singularities a numerical integration approach may fail at the first stage of the analysis that is during the assembly of the discrete equations or it may fail at the subsequent stage of computing domain points near the boundary the severity of the problem is dependent both on the strength of the singularity and on geometry these points are illustrated with examples

non singular boundary integral representation of potential field gradients in this paper we derive the non singular boundary integral representation of the field gradients for two dimensional problems of classical potential field theory numerical implementation of this representation is developed too the proposed method eliminates the most inaccurate influence coefficients which arise when singular integral representations are used and the internal point approaches the boundary since the integrands in this new method are finite at any internal point accurate numerical results are achieved even in that portion of a solid which is very close to a discretized boundary two test problems are analysed in which the numerical results computed by strongly singular weakly singular and non singular integral representations are compared mutually and with exact solutions

boundary element frequency domain formulation for dynamic analysis of mindlin plates a new boundary element formulation for analysis of shear deformable plates subjected to dynamic loading is presented fundamental solutions for the mindlin plate theory are derived in the laplace transform domain the characteristics of the three flextural waves are studied in the time domain it is shown that the new fundamental solutions exhibit the same strong singularity as in the static case two numerical examples are presented to demonstrate the accuracy of the boundary element method and comparisons are made with the finite element method copyright 2006 john wiley sons ltd

accurate numerical integration of singular boundary element kernels over boundaries with curvature use of the green function for the solution of boundary value problems frequently results in singular integral equations algorithms are presented for the accurate and efficient treatment of singular kernels frequently encountered in the boundary element method bem they are based upon the use of appropriately weighted gaussian quadrature formulae together with numerical geometrical transformations of the region of integration the use of high order subdomain expansion functions for interpolation over nonplanar elements allows boundary curvature to be accommodated in particular the handling of green functions with logarithmic and r 1 behaviour are detailed volume integrals with r 2 singularity are outlined operations are performed on a simplex thus resulting in generality and ease of automation this scheme has been incorporated into boundary element method software and successfully applied to a variety of problems

simply supported plates by the boundary integral equation method plates governed by kirchhoff s equation have been analysed by the boundary integral equation method using the fundamental solution of the biharmonic equation in the case of supported plates the boundary conditions permit the uncoupling of the field equation into two harmonic equations that originate due to the nature of the fundamental solution easier integration kernels and a simpler system of equations the calculation of bending and twisting moments and transverse shear force can be formed combining derivatives of the integral equation which defines the expression of the deflection on any point of the plate the uncoupling of the biharmonic equation into two poisson s equations involves the discretization of the domain of the studied problems nevertheless the unknown quantity of the problem does not appear in the domain integrations for which a refined discretization is unnecessary in the paper however a numerical alternative is considered to express the domain integral by means of boundary integrals in this way we need only discretize the boundary of the plate making it necessary to solve a supplementary system of equations in order to calculate the coefficients of the approximation carried out

meshless local petrov galerkin mlpg method for reissner mindlin plates under dynamic load abstract a meshless local petrov galerkin mlpg method is applied to solve dynamic plate bending problems described by the reissner mindlin theory both harmonic and impact loads are considered the laplace transform is used to eliminate the time dependence of the variables for transient problems a weak formulation for the set of governing equations in the reissner mindlin theory with a unit test function is transformed into local integral equations on local subdomains in the mean surface of the plate nodal points are randomly spread on the surface of the plate and each node is surrounded by a circular subdomain to which local integral equations are applied the meshless approximation based on the moving least squares mls method is employed for the implementation unknown laplace transformed quantities are computed from the local boundary integral equations the time dependent values are obtained by the stehfest s inversion technique

analysis of three dimensional anisotropic heat conduction problems on thin domains using an advanced boundary element method abstract in this paper an advanced boundary element method bem is developed for solving three dimensional 3d anisotropic heat conduction problems in thin walled structures the troublesome nearly singular integrals which are crucial in the applications of the bem to thin structures are calculated efficiently by using a nonlinear coordinate transformation method for the test problems studied promising bem results with only a small number of boundary elements have been obtained when the thickness of the structure is in the orders of micro scales 10 6 which is sufficient for modeling most thin walled structures as used in for example smart materials and thin layered coating systems the advantages disadvantages as well as potential applications of the proposed method as compared with the finite element method fem are also discussed

a boundary integral equation method for plate flexure with conditions inside the domain a method for solving boundary value problems for thin plate flexure as described by kirchhoff s theory is proposed an integral formulation leads to a system of boundary integral equations involving values of deflection slope bending moment and transverse shear force along the edge a discretization leading to a matrix formulation is proposed to solve problems with inner conditions in the plate domain an elimination of boundary unknowns proves successful the degenerate case where the boundary is free which leads to a non invertible matrix is investigated three examples illustrate the efficiency of the method

on the cauchy problem for the zakharov system abstract we study the local cauchy problem in time for the zakharov system 1 1 and 1 2 governing langmuir turbulence with initial data u 0 n 0 t n 0 h k h lscr h l 1 in arbitrary space dimension we define a natural notion of criticality according to which the critical values of k l are 2 3 2 2 2 using a method recently developed by bourgain we prove that the zakharov system is locally well posed for a variety of values of k l the results cover the whole subcritical range for 4 for 3 they cover only part of it and the lowest admissible values are k l 1 2 0 for 2 3 and k l 0 1 2 for 1 as a by product of the one dimensional result we prove well posedness of the benney system 1 14 and 1 15 governing the interaction of short and long waves for the same values of k l

three dimensional analysis of functionally graded plates based on the state space formalism a three dimensional analysis is presented for orthotropic functionally graded rectangular plates with simply supported edges under static and dynamic loads the material properties are assumed to be variable through the thickness the governing equations for the functionally graded material fgm are developed on the state space approach in the laplace transform domain assuming constant material properties we derive the analytical solutions that can be used to validate any numerical methods for fgm plates the numerical solutions are obtained by the use of radial basis function method three examples are presented for the fgms and laminated composite the accuracy of the proposed numerical technique has been compared with the exact solutions copyright 2011 john wiley sons ltd

meshless formulations for simply supported and clamped plate problems in this paper simply supported and clamped thin elastic plates are analysed the biharmonic differential equation representing the basis of the kirchhoff theory is decomposed into two poisson equations local boundary integral equations are derived for this system of equations the meshless approximation based on the moving least squares method is employed for the implementation in the case of simply supported plates it is sufficient to use the local boundary integral equations for the case of clamped plates we propose to use a combination of the local boundary integral equations and the global ones then two groups of nodal unknowns are computed separately this leads to a reduced system of algebraic equations copyright 2002 john wiley sons ltd

hypersingular boundary integral equation for axisymmetric elasticity an axisymmetric hypersingular boundary integral formulation for elasticity problems is presented in this paper the hypersingular and strong singular fundamental solutions are derived and their singular behaviour is discussed in detail for different locations of the source point several free terms arise from the limiting process when generating hypersingular boundary integral equations including an extra one specific to the axisymmetric formulation which does not appear in two and three dimensional cases the singularity subtraction technique is used to regularize all strong singular and hypersingular integrals and their evaluation procedure is explained finally the developed formulation is assessed through simple numerical tests copyright 2001 john wiley sons ltd

data throughputs of noise limited mimo cellular systems we present the closed form approximated expressions of the cumulative distribution function of the spectral efficiency for noise limited multiple input multiple output mimo cellular systems with minimum mean square error based ordered successive interference cancellation mmse osic or zero forcing zf receivers in a composite channel model which includes both rayleigh and log normal fading when the users have independent and identically distributed i i d channels we analyze the spectral efficiency of the mimo time division multiple access tdma systems with maximum data rate scheduler numerical experiments show that these results can consistently produce highly accurate results

a boundary element method for dynamic plate bending problems abstract in this paper the fundamental solution for kirchhoff plate in the laplace transform domain is deduced and the boundary element formulation is established to study plate bending problem by use of the moment integral equation the dual boundary element equation is developed to solve the cracked plate problem subjected to dynamic loads durbin s laplace transform inversion method is used and the dynamic stress intensity factors are determined by equivalent stress technique an infinite plate containing an isolated crack or two cracks or one set of parallel cracks under heaviside load on the crack surfaces is studied the numerical results obtained demonstrate the efficiency and accuracy of the proposed formulation

blow up and nonlinear instability for the magnetic zakharov system abstract this study deals with the generalized zakharov system with magnetic field first of all we construct a kind of blow up solutions and establish the existence of blow up solutions to the system through considering an elliptic system next we show the nonlinear instability for a kind of periodic solutions in addition we consider the concentration properties of blow up solutions for the system under study at the end of this paper we establish the global existence of weak solutions to the cauchy problem of the system under consideration

on global smooth solution for generalized zakharov equations this paper considers the existence and uniqueness of the global smooth solution for the initial value problem of generalized zakharov equations in dimension two by means of a priori integral estimates galerkin method and compactness theory one has the existence and uniqueness for small initial data

bi expansion approximation of the bessel functions applied to analytical integration based bem for reissner plates the paper deals with the boundary element analysis of plates modeled by the reissner theory the integral equations are obtained in standard fashion by boundary collocation the fundamental solution is expressed in terms of modified bessel functions using different series expansions for small and large arguments the transition from one to the other form is regulated by an error based criterion for selecting the number of terms which have to be used in the series expansion attention is paid to the computational aspects influencing the accuracy of the numerical model the boundary variables are described by using a quadratic b spline interpolation and the evaluation of the boundary integrals is developed almost entirely in analytical form some numerical experiments test and compare the performances of the numerical model in particular the solution within the boundary layer is studied

some notes on singular integral techniques in boundary element analysis the paper presented here reviews the numerical techniques used currently to calculate the singular integrals and nearly singular integrals in the boundary element analysis some incorrect algorithms published before are discussed and a new numerical technique to calculate the nearly singular integral is developed the numerical results show a significant improvement in both accuracy and efficiency compared to the traditional adaptive gaussian quadrature and subdivision techniques

a boundary element formulation for geometrically nonlinear analysis of shear deformable shells abstract a new boundary element method to solve geometrically nonlinear deflection problems of shear deformable shallow shells having quadratic mid surface is presented the displacement integral equations have been derived to obtain five integral equations in term of displacements two rotations one out of plane displacement and two in plane displacements the boundary is discretised into quadratic isoparametric elements and the domain is transferred to the boundary using the dual reciprocity technique a simple yet efficient load incremental technique is developed to solve the nonlinear problem several examples are presented and the results are in good agreement with the finite element method

writing on dirty paper corresp a channel with output y x s z is examined the state s sim n 0 qi and the noise z sim n 0 ni are multivariate gaussian random variables i is the identity matrix the input x in r n satisfies the power constraint l n sum i 1 n x i 2 leq p if s is unknown to both transmitter and receiver then the capacity is frac 1 2 ln 1 p n q nats per channel use however if the state s is known to the encoder the capacity is shown to be c ast frac 1 2 ln 1 p n independent of q this is also the capacity of a standard gaussian channel with signal to noise power ratio p n therefore the state s does not affect the capacity of the channel even though s is unknown to the receiver it is shown that the optimal transmitter adapts its signal to the state s rather than attempting to cancel it

the influence of the mass matrix on the dispersive nature of the semi discrete second order wave equation abstract the application of discrete solution methods to the second order wave equation can yield a dispersive representation of the non dispersive wave propagation problem resulting in a phase speed that depends not only upon the wavelength of the signal being propagated but also upon the direction of propagation in this work the dependence of the dispersive errors on the wave propagation direction mesh aspect ratio and wave number is investigated with the goal of understanding and hopefully reducing the phase and group errors associated with the two dimensional bilinear finite element an analysis of the dispersive effects associated with the consistent row sum lumped and higher order mass matrices has led to a reduced coupling penta diagonal mass matrix that yields improved phase and group errors with respect to wavelength and propagation direction the influence of row sum lumping the finite element mass matrix is demonstrated to always introduce lagging phase and group error while a linear combination of the lumped and consistent mass matrices i e a higher order mass matrix is shown to improve the dispersion characteristics of both the reduced and full integration element using a 2 5 phase error metric the higher order mass matrix can reduce the mesh resolution requirements relative to the lumped mass matrix by nearly a factor of two in one dimension a factor of 4 in two dimensions similarly the reduced coupling mass matrix can reduce the grid requirements by a factor of approximately four relative to the lumped mass matrix a factor of 16 in two dimensions although the reduced coupling mass matrix requires additional storage relative to the lumped mass the factor of 16 reduction in grid requirements promises tremendous overall savings for computing a fixed wavelength spectrum or alternatively for resolving shorter wavelengths with a fixed grid resolution

hypersingular boundary element formulation for reissner plates in this work the hypersingular boundary element formulation for plate bending analysis based on reissner theory is presented first order taylor expansion are used to deal with the strong singularity o 1 r whereas rigid body considerations together with the taylor expansion are used to compute the hypersingular kernels o l r2 the plate boundary is discretised into quadratic isoparametric discontinuous boundary elements to satisfy the continuity requirements for the boundary unknowns several examples are tested including thin and thick plates the results show a good agreement with both the analytical solutions and the corresponding results for the standard displacement boundary element formulation 1998 elsevier science ltd all rights reserved

efficient boundary element analysis of sharp notched plates the present paper further develops the boundary element singularity subtraction technique to provide an efficient and accurate method of analysing the general mixed mode deformation of two dimensional linear elastic structures containing sharp notches the elastic field around sharp notches is singular because of the convergence difficulties that arise in numerical modelling of elastostatic problems with singular fields these singularities are subtracted out of the original elastic field using the first term of the williams series expansion this regularization procedure introduces the stress intensity factors as additional unknowns in the problem hence extra conditions are required to obtain a solution extra conditions are defined such that the local solution in the neighbourhood of the notch tip is identical to the williams solution the procedure can take into account any number of terms of the series expansion the standard boundary element method is modified to handle additional unknowns and extra boundary conditions analysis of plates with symmetry boundary conditions is shown to be straightforward with the modified boundary element method in the case of non symmetrical plates the singular tip tractions are not primary boundary element unknowns the boundary element method must be further modified to introduce the boundary integral stress equations of an internal point approaching the notch tip as primary unknowns in the formulation the accuracy and efficiency of the method is demonstrated with some benchmark tests of mixed mode problems new results are presented for the mixed mode analysis of a non symmetrical configuration of a single edge notched plate

extended isogeometric boundary element method xibem for two dimensional helmholtz problems isogeometric analysis is a topic of considerable interest in the field of numerical analysis the boundary element method bem requires only the bounding surface of geometries to be described this makes non uniform rational b splines nurbs which commonly describe the bounding curve or surface of geometries in cad software appear to be a natural tool for the approach this isogeometric analysis bem igabem provides accuracy benefits over conventional bem schemes due to the analytical geometry provided by nurbs when applied to wave problems it has been shown that enriching bem approximations with a partition of unity basis in what has become known as the pu bem allows highly accurate solutions to be obtained with a much reduced number of degrees of freedom this paper combines these approaches and presents an extended isogeometric bem xibem which uses partition of unity enriched nurbs functions this new approach provides benefits which surpass those of both the igabem and the pu bem two numerical examples are given a single scattering cylinder and a multiple scatterer made up of two capsules and a cylinder

a boundary element numerical scheme for the two dimensional convection diffusion equation in this study the theoretical and numerical fundamentals of biem techniques for the two dimensional convection diffusion problem are presented after an extended presentation of the basic integral formulation the discretizing and iterative processes for its resolution are introduced interesting remarks on general expressions versus previously published particularized results are worth mentioning a numerical solution scheme is provided which has been completely developed and designed to the physical problem posed a novel scheme based in the simultaneous solving of the potential and the gradient of the potential boundary integral equations is included a diversity of problems is tested to prove the possibilities of the method copyright 2008 john wiley sons ltd

on the numerical green s function technique for cracks in reissner s plates abstract the numerical green s function ngf technique previously proposed by the present authors is here extended to fracture mechanics problems involving reissner s plate theory the technique numerically produces a plate bending fundamental green s function that automatically includes embedded cracks to be used in the classical boundary element method bem to solve this class of problems the applications discussed include torsion bending moment and shear force loadings in addition also presented is a series of numerical results computed in terms of normalized stress intensity factors to illustrate the good accuracy of the procedure

equations of langmuir turbulence and nonlinear schrodinger equation smoothness and approximation we consider the following family of systems parametrized by e 0 which describe langmuir s turbulence in the case where initial data are sufficiently small we study the asymptotic behaviour of the solutions ee ne when e goes to zero for d 1 2 3 namely we state convergence results of ee ne to the couple e e 2 where e is the solution of the nonlinear schrodinger equation moreover in three dimensions we show that the smooth solution ee ne is defined on 0 tmax e with tmax e going to infinity as e goes to 0

fracture mechanics analysis of curved stiffened panels using bem abstract a dual boundary element method is developed for a analysis of reinforced cracked shallow shells boundary integral equations are derived from the betti s reciprocal theorem for a cracked shallow shell with transverse frames and longitudinal stiffeners the effect of frames and stiffeners are treated as a distribution of line body forces the radial basis function is used to transform domain integrals to boundary integrals stress intensity factors are evaluated from crack opening displacements the effect of curvature on the stress intensity factors is illustrated by numerical examples three examples are presented to demonstrate the accuracy of this method compared with solutions obtained using the finite element method

boundary domain element method for free vibration of moderately thick laminated orthotropic shallow shells in this paper an integral equation formulation of free vibration of moderately thick laminated orthotropic shallow shells has been established by using the method of weighted residuals and taking the static fundamental solution as the weighted function in the present formulation there are not only boundary unknowns but also domain unknowns the integral equations presented are reduced to a standard algebraic eigenvalue problem by means of the boundary domain element in the numerical implementation two kinds of different matrix formulation are presented by using two kinds of different domain elements some numerical results are presented and compared with the exact solutions in order to demonstrate the correctness and the accuracy of the present method

energy convergence for singular limits of zakharov type systems we prove existence and uniqueness of solutions to the klein gordon zakharov system in the energy space h1 l2 on some time interval which is uniform with respect to two large parameters c and these two parameters correspond to the plasma frequency and the sound speed in the simultaneous high frequency and subsonic limit we recover the nonlinear schrodinger system at the limit we are also able to say more when we take the limits separately

well posedness of the initial value problem for the korteweg de vries equation 1 1 itu axu u1xu o x t e r u x 0 uo x the kdv equation which was first derived as a model for unidirectional propagation of nonlinear dispersive long waves 21 has been considered in different contexts namely in its relation with the inverse scattering method in plasma physics and in algebraic geometry see 24 and references therein our purpose is to study local and global well posedness of the ivp 1 1 in classical sobolev spaces hs r we shall say that the ivp 1 1 is locally resp globally well posed in the function space x if it induces a dynamical system on x by generating a continuous local resp global flow it was established in the works of bona and smith 3 bona and scott 2 saut and temam 30 and kato 1 5 that the ivp 1 1 is locally resp globally well posed in hs with s 3 2 resp s 2 roughly speaking global well posedness in hs depends on the available local theory and on the conservation laws satisfied by solutions of 1 1 namely

a bem based domain meshless method for the analysis of mindlin plates with general boundary conditions abstract in this paper a bem based domain meshless method is developed for the analysis of moderately thick plates modeled by mindlin s theory which permits the satisfaction of three physical conditions along the plate boundary the presented method is achieved using the concept of the analog equation of katsikadelis according to this concept the original governing differential equations are replaced by three uncoupled poisson s equations with fictitious sources under the same boundary conditions the fictitious sources are established using a technique based on bem and approximated by radial basis functions series the solution of the actual problem is obtained from the known integral representation of the potential problem thus the kernels of the boundary integral equations are conveniently established and evaluated the presented method has the advantages of the bem in the sense that the discretization and integration are performed only on the boundary and consequently mindlin plates with general boundary conditions can be analyzed without difficulty to illustrate the effectiveness applicability as well as accuracy of the method numerical results of various example problems are presented

symmetric galerkin bem for shear deformable plates a symmetric galerkin boundary element formulation is developed for shear deformable plates a mixed strategy is used for the integration process i e partial regularization using simple solutions followed by a singularity subtraction technique for the shear equation full regularization is achieved using new kernel relationships found through a constant shear mode of deformation some of the strong singular integrals are avoided altogether by using a modified traction obtained through a very simple variable change appropriate boundary conditions are defined details of the implementation are given and several example problems solved to verify the accuracy of the proposed formulation copyright 2003 john wiley sons ltd

an efficient direct bem numerical scheme for phase change problems using fourier series abstract due to the moving boundary nature of the solidification and melting problems the application of the standard time domain boundary element formulation of the problem presents the difficulty of the numerical evaluation of the history dependence representing more and more work as time proceeds in that regard we present an algorithm based on a green s function which allows a fourier representation of the domain integral in the reinitialization scheme of the direct boundary element method formulation of the problem from which it is possible to carry out the history integration in a recursive manner to obtain the reinitialization approach in the integral representation formula the green s function corresponding to zero temperature in a box containing the original domain will be used instead of using the classical free space fundamental solution this green s function is given in terms of the original fundamental solution plus a regular solution of the heat equation inside the domain in consideration it can therefore be used in the integral representation formula of the heat equation direct formulation to obtain the solution of a heat problem in such domain the mentioned green s function can be obtained by the images method and the resulting source series can also be rewritten in terms of a double fourier series that will be used in the domain integral of the integral representation formula to transform such integral into equivalent surface integrals in this work a new reinitialization scheme has been applied to solve moving boundary problems to detect the location of the phase change interface in solidification and melting problems the numerical results were compared with analytical solutions in the case where they were available showing a good agreement between the results giving special emphasis to the interface location and the temperature distribution

global smooth solution for the klein gordon zakharov equations in this paper the initial value problem to the klein gordon zakharov equations in two dimensions is discussed without assuming that the cauchy data are small we prove the existence and uniqueness of the global smooth solution for the problem via the so called continuous method and delicate a priori estimates also the asymptotic behaviour of the solution to the k g z equations with a small parameter approaching zero is studied

on the existence and uniqueness of smooth solution for a generalized zakharov equation abstract the paper deals with the existence and uniqueness of smooth solution for a generalized zakharov equation we establish local in time existence and uniqueness in the case of dimension d 2 3 moreover by using the conservation laws and brezis gallouet inequality the solution can be extended globally in time in two dimensional case for small initial data besides we also prove global existence of smooth solution in one spatial dimension without any small assumption for initial data