three dimensional exact solution for the vibration of functionally graded rectangular plates abstract a three dimensional exact solution is presented for free and forced vibrations of simply supported functionally graded rectangular plates suitable displacement functions that identically satisfy boundary conditions are used to reduce equations governing steady state vibrations of a plate to a set of coupled ordinary differential equations which are then solved by employing the power series method the exact solution is valid for thick and thin plates and for arbitrary variation of material properties in the thickness direction results are presented for two constituent metal ceramic functionally graded rectangular plates that have a power law through the thickness variation of the volume fractions of the constituents the effective material properties at a point are estimated by either the mori tanaka or the self consistent schemes exact natural frequencies displacements and stresses are used to assess the accuracy of the classical plate theory the first order shear deformation theory and a third order shear deformation theory for functionally graded plates parametric studies are performed for varying ceramic volume fractions volume fraction profiles and length to thickness ratios results are also computed for a functionally graded plate that has a varying microstructure in the thickness direction using a combination of the mori tanaka and the self consistent methods forced vibrations of a plate with a sinusoidal spatial variation of the pressure applied on its top surface are scrutinized

three dimensional free vibration of thick functionally graded annular plates in thermal environment the free vibration analysis of functionally graded fg thick annular plates subjected to thermal environment is studied based on the 3d elasticity theory the material properties are assumed to be temperature dependent and graded in the thickness direction considering the thermal environment effects and using hamilton s principle the equations of motion are derived the effects of the initial thermal stresses are considered accurately by obtaining them from the 3d thermoelastic equilibrium equations the differential quadrature method dqm as an efficient and accurate numerical tool is used to solve both the thermoelastic equilibrium and free vibration equations very fast rate of convergence of the method is demonstrated also the formulation is validated by comparing the results with those obtained based on the first order shear deformation theory and also with those available in the literature for the limit cases i e annular plates without thermal effects the effects of temperature rise material and geometrical parameters on the natural frequencies are investigated the new results can be used as benchmark solutions for future researches

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

reduced aliasing formulations of the convective terms within the navier stokes equations for a compressible fluid the effect on aliasing errors of different formulations describing the cubically nonlinear convective terms within the discretized navier stokes equations is examined in the presence of a non trivial density spectrum fourier analysis shows that the existing skew symmetric forms of the convective term result in reduced aliasing errors relative to the conservation form several formulations of the convective term including a new formulation proposed for cubically nonlinear terms are tested in direct numerical simulation dns of decaying compressible isotropic turbulence both in chemically inert small density fluctuations and reactive cases large density fluctuations and for different degrees of resolution in the dns of reactive turbulent flow the new cubic skew symmetric form gives the most accurate results consistent with the spectral error analysis and at the lowest cost in marginally resolved dns and les poorly resolved by definition the new cubic skew symmetric form represents a robust convective formulation which minimizes both aliasing and computational cost while also allowing a reduction in the use of computationally expensive high order dissipative filters

a multi scale formulation for compressible turbulent flows suitable for general variational discretization techniques based on the recently introduced variational multi scale vms approach to large eddy simulation les as introduced in t j r hughes l mazzei k e jansen large eddy simulation and the variational multiscale method comput visual sci 3 2001 47 59 s s collis monitoring unresolved scales in multiscale turbulence modeling phys fluids 13 6 2001 1800 1806 we present a vms formulation which can be used in the simulation of compressible flows special attention is given to obtain a vms formulation which is suitable for complex flow domains and general variational discretization techniques a generalization of the favre averaging procedure is introduced such that the formulation resembles the favre filtered navier stokes equations traditionally used in les of compressible flow and no explicit subgrid terms arise in the continuity equation also we show that with the use of discretization methods other than fourier spectral methods the vms projection no longer commutes with differentiation this results in additional subgrid scale terms which resemble the commutator error as encountered in the traditional filtering approach to les

analysis of numerical errors in large eddy simulation using statistical closure theory this paper develops a dynamic error analysis procedure for the numerical errors arising from spatial discretization in large eddy simulation the analysis is based on edqnm closure theory and is applied to the les of decaying isotropic turbulence first the effects of finite differencing truncation error aliasing error and the dynamic smagorinsky model are independently considered the time evolution of kinetic energy and spectra predicted by the analysis are compared to actual les using the navier stokes equations and good agreement is obtained the analysis is then extended to simultaneously consider all sources of error in a second order discretely energy conserving central difference les solver good agreement between the analysis and actual les is obtained the analysis is used to compare the contribution of the subgrid model to that of numerical errors and it is shown that the contribution of the subgrid scale model is much higher than the numerical errors the proposed one dimensional edqnm les model shows potential as a more general tool for the analysis of numerical error and sgs model in simulations of turbulent flow

on the effect of numerical errors in large eddy simulations of turbulent flows aliased and dealiased numerical simulations of a turbulent channel flow are performed using spectral and finite difference methods analytical and numerical studies show that aliasing errors are more destructive for spectral and high order finite difference calculations than for low order finite difference simulations numerical errors have different effects for different forms of the nonlinear terms in the navier stokes equations for divergence and convective forms spectral methods are energy conserving only if dealiasing is performed for skew symmetric and rotational forms both spectral and finite difference methods are energy conserving even in the presence of aliasing errors it is shown that discrepancies between the results of dealiased spectral and standard nondialiased finite difference methods are due to both aliasing and truncation errors with the latter being the leading source of differences the relative importance of aliasing and truncation errors as compared to subgrid scale model terms in large eddy simulations is analyzed and discussed for low order finite difference simulations truncation errors can exceed the magnitude of the subgrid scale term

modeling of biological population problems using the element free kp ritz method a degenerate parabolic equation arising in the spatial diffusion of biological population is analyzed using the mesh free kp ritz method the mesh free kernel particle estimate is employed to approximate the 2d displacement field a system of discrete equations is obtained through application of the ritz minimization procedure to the energy expressions to validate the accuracy of the results and stability of the present method convergence studies were carried out based on influences of support size and number of nodes effectiveness of the mesh free kp ritz method for biological population model is investigated by numerical examples in this paper the present results were compared with results reported in extant literature and were found to be in good agreement with the literature

vibration of thick skew plates based on mindlin shear deformation plate theory the free flexural vibration of thick skew plates is considered the total energy functional is derived based on the first order shear deformation plate theory by mindlin the newly developed pb 2 rayleigh ritz method is applied to obtain the solution the method features the versatile pb 2 ritz functions for approximating the deflection and rotation functions which comprise the product of 1 a two dimensional polynomial function p 2 and 2 a basic function b the basic function is the key to ensure the automatic satisfaction of the geometric boundary conditions at the outset since it is formed from the product of the boundary equations raised to appropriate powers natural frequency parameters for skew mindlin plates with different combinations of boundary conditions are presented the solutions where possible are verified by comparisons with those available in the open literature the effect of the poisson ratio on vibration frequencies of plates with free edges is also investigated

on the use of computational intelligence in the optimal shape control of functionally graded smart plates functionally graded material fgm plates are an essential component for most advanced integrated systems in terms of vibration and acoustic controls or condition monitoring in general these fgm plates are designed with embedded piezoelectric sensors and actuators to achieve their shape control this optimal control problem is normally required to find appropriate actuator voltage and displacement control gains that will generate the desired shape such an optimal control problem is known to be highly non linear and often posses slope and functional discontinuity that will limit the efficiency of the gradient based methods stochastic zero order population based optimization methods are ideal for solving this class of problems in this paper we introduce a stochastic zero order optimization algorithm based on the principles of learning this algorithm is embedded with three key learning strategies that control who to learn from i e leader identification and leader selection and what to learn i e information acquisition to reach a common goal the leader identification mechanism partitions the individuals into a set of leaders and a set of followers the followers interact with the leaders and move toward the better performing leaders in searching for better solutions the parameter free algorithm provides the designer with the true flexibility that is necessary to handle various forms of design problem effectively and at a computational cost that is comparable to existing stochastic optimization methods in this study numerical results are presented for the shape control of the fgm plates under a temperature gradient by optimizing i the voltage distribution for the open loop control and ii the displacement control gain values for the closed loop feedback control we also examine the effect of the constituent volume fractions of zirconia through the varying of volume fraction exponent n on the optimal voltages and gain values

an analysis of numerical errors in large eddy simulations of turbulence the reliability of numerical simulations of turbulence depend on our ability to quantify and control discretization errors in the classical literature on error analysis typically simple linear equations are studied estimates of errors derived from such analyses depend on the assumption that each dependent variable can be characterized by a unique amplitude and scale of spatial variation that can be normalized to unity this assumption is not valid for strongly nonlinear problems such as turbulence where nonlinear interactions rapidly redistribute energy resulting in the appearance of a broad continuous spectrum of amplitudes in such situations the numerical error as well as the subgrid model can change with grid spacing in a complicated manner that cannot be inferred from the results of classical error analysis in this paper a formalism for analyzing errors in such nonlinear problems is developed in the context of finite difference approximations for the navier stokes equations when the flow is fully turbulent analytical expressions for the power spectra of these errors are derived by exploiting the joint normal approximation for turbulent velocity fields these results are applied to large eddy simulation of turbulence to obtain quantitative bounds on the magnitude of numerical errors an assessment of the significance of these errors in made by comparing their magnitudes with that of the nonlinear and subgrid terms one method of controlling the errors is suggested and its effectiveness evaluated through quantitative measures although explicit evaluations are presented only for large eddy simulation the expressions derived for the power spectra of errors are applicable to direct numerical simulation as well

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

matrix characterization of mds linear codes over modules abstract let r be a commutative ring with identity n be an r module and m aij r k be a matrix over r a linear code c of length n over n is defined to be a submodule of nn it is shown that a linear code c k r with parity check matrix m i r is maximum distance separable mds iff the determinant of every h h submatrix h 1 2 min k r of m is not an annihilator of any nonzero element of n this characterization is used to derive some results for group codes over abelian groups

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

thermo electro elastic transient responses in piezoelectric hollow structures the paper presents an analytical method to solve thermo electro elastic transient response in piezoelectric hollow structures subjected to arbitrary thermal shock sudden mechanical load and electric excitation volterra integral equation of the second kind caused by interaction between elastic deformation and electric field is solved by using an interpolation method thus the exact expressions for the transient responses of displacement stresses electric displacement and electric potential in the piezoelectric hollow structures are obtained by means of hankel transform laplace transform and their inverse transforms in section 2 based on spherical coordinates the governing equation of thermo electro elastic transient responses in a piezoelectric hollow sphere is found and the associated numerical results are carried out in section 3 based on cylindrical coordinates the governing equation of thermo electro elastic transient responses in a non homogeneous piezoelectric hollow cylinder is found and the corresponding numerical results are carried out the results carried out may be used as a reference to solve other transient coupled problems of thermo electro elasticity in piezoelectric structures

signal sets matched to groups recently linear codes over z sub m the ring of integers mod m have been presented that are matched to m ary phase modulation the general problem of matching signal sets to generalized linear algebraic codes is addressed based on these codes a definition is given for the notion of matching it is shown that any signal set in n dimensional euclidean space that is matched to an abstract group is essentially what d slepian 1968 called a group code for the gaussian channel if the group is commutative this further implies that any such signal set is equivalent to coded phase modulation with linear codes over z sub m some further results on such signal sets are presented and the signal sets matched to noncommutative groups and the linear codes over such groups are discussed

free vibration of skew mindlin plates by p version of f e m abstract accurate natural frequencies and mode shapes of skew plates with and without cutouts are determined by p version finite element method using integrals of legendre polynomials for p 1 14 the hierarchical plate element is formulated based on mindlin s plate theory including rotatory inertia effects and based on a skew co ordinate system non dimensional frequency parameter and mode shapes are presented for a range of skew angle aspect ratio a b thickness width ratio h b cutout dimensions and different boundary conditions the results were verified by comparison with those available in the open literature

fully conservative higher order finite difference schemes for incompressible flow conservation properties of the mass momentum and kinetic energy equations for incompressible flow are specified as analytical requirements for a proper set of discrete equations existing finite difference schemes in regular and staggered grid systems are checked for violations of the conservation requirements and a few important discrepancies are pointed out in particular it is found that none of the existing higher order schemes for a staggered mesh system simultaneously conserve mass momentum and kinetic energy this deficiency is corrected through the derivation of a general family of fully conservative higher order accurate finite difference schemes for staggered grid systems finite difference schemes in a collocated grid system are also analyzed and a violation of kinetic energy conservation is revealed the predicted conservation properties are demonstrated numerically in simulations of inviscid white noise performed in a two dimensional periodic domain the proposed fourth order schemes in a staggered grid system are generalized for the case of a non uniform mesh and the resulting scheme is used to perform large eddy simulations of turbulent channel flow

vibration analysis of functionally graded annular plates with mixed boundary conditions in thermal environment abstract the free vibration analysis of functionally graded annular plates with mixed boundary conditions in thermal environment is carried out by the 3d elasticity theory and the chebyshev ritz method the material properties are assumed to be temperature dependent and graded in the thickness direction the mixed boundary conditions which include upper and lower surfaces partially fixed inner side partially fixed and outer side partially fixed are considered respectively the accuracy of the present approach for solving the free vibration of the plates with different boundary conditions is validated by comparing the present numerical results with the results available the effects of the different mixed boundary conditions the temperature rise the material graded index and the geometrical parameters on the eigen frequencies are studied

statistical behavior of the orthogonal subgrid scale stabilization terms in the finite element large eddy simulation of turbulent flows abstract numerical simulations have proved that variational multiscale methods vmm perform well as pure numerical large eddy simulation les models in this paper we focus on the orthogonal subgrid scale oss finite element method and make an analysis of the statistical behavior of its stabilization terms in the quasi static approximation this is done by resorting to results from classical statistical fluid mechanics concerning two point velocity pressure and combined correlation functions of various orders given a fine enough mesh with characteristic element size h in the inertial subrange of a turbulent flow it is shown that the rate of transfer of subgrid kinetic energy provided by the oss stabilization terms does not depend on h and that it equals the molecular physical dissipation rate up to a dimensionless constant that only depends on the finite element shapes for a proper redesign of the standard parameters of the formulation this is a noteworthy fact taking into account that the subgrid stabilization terms do not arise from physical considerations but from the mathematical necessity to allow equal interpolation for the pressure and velocity fields as well as to control convection therefore the obtained results contribute somehow to the line of reasoning supporting that pure numerical approaches i e without introducing additional physical models could probably suffice in the les simulation of turbulent flows

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

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

vibration characteristics and transient response of shear deformable functionally graded plates in thermal environments free and forced vibration analyses for initially stressed functionally graded plates in thermal environment are presented material properties are assumed to be temperature dependent and graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents theoretical formulations are based on reddy s higher order shear deformation plate theory and include the thermal effects due to uniform temperature variation the plate is assumed to be clamped on two opposite edges with the remaining two others either free simply supported or clamped one dimensional differential quadrature technique galerkin approach and the modal superposition method are used to determine the transient response of the plate subjected to lateral dynamic loads comprehensive numerical results for silicon nitride stainless steel rectangular plates are presented in dimensionless tabular and graphical forms the roles played by the constituent volume fraction index temperature rise shape and duration of dynamic loads initial membrane stresses as well as the character of boundary conditions are studied the results reveal that when thermal effects are considered functionally graded plates with material properties intermediate to those of isotropic ones do not necessarily have intermediate natural frequencies and dynamic responses

underlying mechanism of numerical instability in large eddy simulation of turbulent flows this paper extends our recent theoretical work concerning the feasibility of stable and accurate computation of turbulence using a large eddy simulation m ida and n taniguchi phys rev e 68 036705 2003 in our previous paper it was shown based on a simple assumption regarding the instantaneous streamwise velocity that the application of the gaussian filter to the incompressible navier stokes equations can result in the appearance of a numerically unstable term that can be decomposed into positive and negative viscosities that result raises the question as to whether an accurate solution can be achieved by a numerically stable subgrid scale model in the present paper based on assumptions regarding the statistically averaged velocity we present similar theoretical investigations to show that in several situations the shears appearing in the statistically averaged velocity field numerically destabilize the fluctuation components because of the derivation of a numerically unstable term that represents negative diffusion in a fixed direction this finding can explain the problematic numerical instability that has been encountered in large eddy simulations of wall bounded flows the present result suggests that this numerical problem is universal in large eddy simulations and that if there is no failure in modeling the resulting subgrid scale model can still have unstable characteristics that is the known instability problems of several existing subgrid scale models are not something that one may remove simply by an artificial technique but must be taken seriously so as to treat them accurately

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 lowest density mds codes let f sub q denote the finite field gf q and let h be a positive integer mds maximum distance separable codes over the symbol alphabet f sub q sup b are considered that are linear over f sub q and have sparse low density parity check and generator matrices over f sub q that are systematic over f sub q sup b lower bounds are presented on the number of nonzero elements in any systematic parity check or generator matrix of an f sub q linear mds code over f sub q sup b along with upper bounds on the length of any mds code that attains those lower bounds a construction is presented that achieves those bounds for certain redundancy values the building block of the construction is a set of sparse nonsingular matrices over f sub q whose pairwise differences are also nonsingular bounds and constructions are presented also for the case where the systematic condition on the parity check and generator matrices is relaxed to be over f sub q rather than over f sub q sup b

algebraic characterization of mds group codes over cyclic groups an n k group code over a group g is a subset of g sup n which forms a group under componentwise group operation and can be defined in terms of n k homomorphisms from g sup k to g the set of homomorphisms which define maximum distance separable mds group codes defined over cyclic groups are characterized each defining homomorphism can be specified by a set of k endomorphisms of g a matrix is associated with the k n k defining endomorphisms of the code and necessary and sufficient conditions for this matrix to define an mds code over cyclic groups is proved using this matrix characterization it is proved that over a cyclic group with m elements where m p sub 1 sup d 1 p sub 2 sup d 2 spl middot spl middot spl middot p sub m sup d m k s k mds group codes for all s k spl ges 2 do not exist if max s k spl ges min p sub 1 p sub 2 spl middot spl middot p sub m finally it is shown that the dual code of an mds group code over c sub m a cyclic group with m elements is also an mds group code

free vibration and buckling analyses of shear deformable plates based on fsdt meshfree method abstract a meshfree method based on the reproducing kernel particle approximate is employed for the free vibration and buckling analyses of shear deformable plates in this approach the first order mindlin reissner plate theory fsdt is used and the displacement shape functions are constructed using the reproducing kernel approximation satisfying the consistency condition the essential boundary conditions are enforced by a transformation method numerical examples considering various aspect ratios skew angles and boundary conditions are demonstrated to show the validity of the proposed method and satisfactory results were obtained when comparisons are made with the exact and other available numerical results existing in the literature

numerical analysis of generalized regularized long wave equation using the element free kp ritz method abstract a numerical analysis of the generalized regularized long wave grlw equation by application of the element free kp ritz method is performed to approximate the displacement field an element free kernel particle estimation is employed and a system of nonlinear discrete equations is achieved by using the ritz minimization procedure to the energy expressions validation of the present numerical solutions with the exact results has been conducted by numerical examples and evidenced a good agreement

interactions of breaking waves with a current over cut cells by design of the external and internal wave current generators the objective of this paper is to extend our efficient navier stokes solver t li p troch j de rouck wave overtopping over a sea dike j comput phys 198 2004 686 726 for modelling of interactions between breaking waves and a current over a cut cell grid based on a dynamic subgrid scale sgs model this solver is constructed by a novel vof finite volume approach coupled with surface tension when studying waves following a positive current our external generator creates the combined inflow motions of waves and a current which is viewed as one type of wavy inflow conditions for cases of waves against strong currents our internal generator describes the opposing current by incorporating the source function to the continuity and momentum equations as a net driving force acting on the fluid elements lying within the finite thickness source region the outgoing waves downstream are dissipated with a breaking type wave absorber placed in the tank extremity five test cases recommended are of distinctly different applications of interest characterized by overtopping of following waves over sloping and vertical structures under the grid refinement effects the results in 2d and 3d are in close agreement with the experimental data available in terms of the surface wave additionally the performance of convergence in computations is also investigated including full discussion for waves on beaches between 2d and 3d by visualization of the motions that describe the physics of turbulence it has been shown that our solver can capture most of the significant features in wave current interactions varying with three different current speeds positive zero negative

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

enhancement of an industrial finite volume code for large eddy type simulation of incompressible high reynolds number flow using near wall modelling abstract we present a validation strategy for enhancement of an unstructured industrial finite volume solver designed for steady rans problems for large eddy type simulation with near wall modelling of incompressible high reynolds number flow different parts of the projection based discretisation are investigated to ensure les capability of the numerical method turbulence model parameters are calibrated by using a minimisation of least squares functionals for first and second order statistics of the basic benchmark problems decaying homogeneous turbulence and turbulent channel flow then the method is applied to the flow over a backward facing step at reh 37 500 of special interest is the role of the spatial and temporal discretisation error for low order schemes for wall bounded flows present results confirm existing best practice guidelines for mesh design for free shear layers a sensor to quantify the resolution quality of the les based on the resolved turbulent kinetic energy is presented and applied to the flow over a backward facing step at reh 37 500

on the hamming distance properties of group codes under certain mild conditions the minimum hamming distance d of an n k d group code c over a non abelian group g is bounded by d n 2 consequently there exists no n k n k 1 group code c over an non abelian group g if 1

geometrically uniform codes a signal space code c is defined as geometrically uniform if for any two code sequences in c there exists an isometry that maps one sequence into the other while leaving the code c invariant geometrical uniformity a strong kind of symmetry implies such properties as a the distance profiles from code sequences in c to all other code sequences are all the same and b all voronoi regions of code sequences in c have the same shape it is stronger than ungerboeck zehavi wolf symmetry or calderbank sloane regularity nonetheless most known good classes of signal space codes are shown to be generalized coset codes and therefore geometrically uniform including a lattice type trellis codes based on lattice partitions lambda lambda such that z sup n lambda lambda 4z sup n is a lattice partition chain and b phase shift keying psk type trellis codes based on up to four way partitions of a 2 sup n psk signal set

the element free kp ritz method for free vibration analysis of conical shell panels in this paper the free vibration of conical panels is analyzed by the mesh free kp ritz method both 1 d and 2 d versions of the kp ritz approach are formulated for conical panels for conical panels with two simply supported straight edges the 1 d kp ritz version is used where the kernel particle estimation is employed in hybridized form with harmonic functions to approximate the 2 d displacement field for conical panels having arbitrary boundary conditions the displacement field is approximated by the 2 d kp ritz version with 2 d form of kernel particle functions employed the classical thin shell theory based on love s hypothesis is employed in the present analyses and based on the kernel particle concept and ritz technique the eigenequations of the frequencies of the conical panels are obtained to validate the accuracy of stability of the present method convergence studies were carried out based on the influences of the support size and the number of nodes comparisons were also made with existing results available in the open literature this study also examines in detail the effects of variation in the semi vertex angle and boundary conditions on the frequency characteristics of conical panels

geometrically nonlinear analysis of functionally graded plates using a cell based smoothed three node plate element cs min3 based on the c0 hsdt abstract a cell based smoothed three node mindlin plate element cs min3 based on the first order shear deformation theory fsdt was recently proposed for static and dynamics analyses of mindlin plates in this paper the cs min3 is extended to geometrically nonlinear analysis of functionally graded plates fgps subjected to thermo mechanical loadings in the fgps the material properties are assumed to vary through the thickness by a simple power rule of the volume fractions of the constituents the nonlinear formulation is based on the c0 type high order shear deformation plate theory c0 hsdt and the von karman strains which deal with small strains and moderate rotations in the analysis process both thermal and mechanical loadings are considered and a two step procedure is performed including a step of analyzing the temperature field along the thickness of the plate and a step of analyzing the geometrically nonlinear behavior of the fgps subjected to both thermal and mechanical loadings the accuracy and reliability of the proposed method is verified by comparing its numerical solutions with those of available other numerical results

block coded psk modulation using two level group codes over dihedral groups a length n group code over a group g is a subgroup of g sup n under component wise group operation group codes over dihedral groups d sub m with 2m elements that are two level constructible using a binary code and a code over z sub m residue class integer ring modulo m as component codes are studied for arbitrary m a set of necessary and sufficient conditions on the component codes for the two level construction to result in a group code over d sub m are obtained the conditions differ for m odd and even using two level group codes over d sub m as label codes the performance of a block coded modulation scheme is discussed under all possible matched labelings of 2m apsk and 2m spsk asymmetric and symmetric psk signal sets in terms of the minimum squared euclidean distance matched labelings that lead to automorphic euclidean distance equivalent codes are identified it is shown that depending upon the ratio of hamming distances of the component codes some labelings perform better than others the best labeling is identified under a set of restrictive conditions finally conditions on the component codes for phase rotational invariance properties of the signal space codes are discussed

a computational error assessment of central finite volume discretizations in large eddy simulation using a smagorinsky model we present a framework for the computational assessment and comparison of large eddy simulation methods we apply this to large eddy simulation of homogeneous isotropic decaying turbulence using a smagorinsky subgrid model and investigate the combined effect of discretization and model errors at coarse subgrid resolutions we compare four different central finite volume methods these discretization methods arise from the four possible combinations that can be made with a second order and a fourth order central scheme for either the convective and the viscous fluxes by systematically varying the simulation resolution and the smagorinsky coefficient we determine parameter regions for which a desired number of flow properties is simultaneously predicted with approximately minimal error we include both physics based and mathematics based error definitions leading to different error measures designed to emphasize either errors in large or in small scale flow properties it is shown that the evaluation of simulations based on a single physics based error may lead to inaccurate perceptions on quality we demonstrate however that evaluations based on a range of errors yields robust conclusions on accuracy both for physics based and mathematics based errors parameter regions where all considered errors are simultaneously near optimal are referred to as multi objective optimal parameter regions the effects of discretization errors are particularly important at marginal spatial resolution such resolutions reflect local simulation conditions that may also be found in parts of more complex flow simulations under these circumstances the asymptotic error behavior as expressed by the order of the spatial discretization is no longer characteristic for the total dynamic consequences of discretization errors we find that the level of overall simulation errors for a second order central discretization of both the convective and viscous fluxes the 2 2 method and the fully fourth order 4 4 method is equivalent in their respective multi objective optimal regions mixed order methods i e the 2 4 and 4 2 combinations yield errors which are considerably higher

explicit filtering and exact reconstruction of the sub filter stresses in large eddy simulation explicit filtering has the effect of reducing numerical or aliasing errors near the grid scale in large eddy simulation les we use a differential filter namely the inverse helmholtz operator which is readily applied to unstructured meshes the filter is invertible which allows the sub filter scale sfs stresses to be exactly reconstructed in terms of the filtered solution unlike eddy viscosity models the method of filtering and reconstruction avoids making any physical assumptions and is therefore valid in any flow regime the sub grid scale sgs stresses are not recoverable by reconstruction but the second order finite element method used here is an adequate source of numerical dissipation in lieu of an sgs model results for incompressible turbulent channel flow at re 180 are presented which show that explicit filtering and exact sfs reconstruction is a significant improvement over the standard les approach of implicit filtering and eddy viscosity sgs modelling

a further study of numerical errors in large eddy simulations numerical errors in large eddy simulations les arise from aliasing and discretization errors and errors in the subfilter scale sfs turbulence model using a direct numerical simulation dns dataset of stably stratified shear flow to perform a priori tests we compare the numerical error from several finite difference schemes to the magnitude of the sfs force this is an extension of ghosal s analysis j comput phys 125 1996 187 to realistic flow fields by evaluating different grid resolutions as well as different filter grid ratios we provide guidelines for les for a second order finite difference scheme a filter grid ratio of at least four is desired for a sixth order pade scheme a filter grid ratio of two is sufficient

wave propagation of functionally graded layers treated by recursion relations and effective boundary conditions wave propagation through a layer of a material that is inhomogeneous in the thickness direction typically a functionally graded material fgm is investigated the material parameters and the displacement components are expanded in power series in the thickness coordinate leading to recursion relations among the displacement expansion functions these can be used directly in a numerical scheme as a means to get good field representations when applying boundary conditions and this can be done even if the layer is not thin this gives a schema that is much more efficient than the approach of subdividing the layer into many sublayers with constant material properties for thin layers for which the material parameters do not depend on the layer thickness the recursion relations can be used to eliminate all but the lowest order expansion functions employing the boundary conditions this leads to a set of effective boundary conditions relating the displacements and stresses on the two sides of the layer thus completely replacing the layer by these effective boundary conditions numerical examples illustrate the convergence properties of the scheme for fg layers and the influence of different variations of the material parameters in the fg layer