vibration analysis by discrete singular convolution this paper explores the utility of a discrete singular convolution algorithm for vibration analysis a number of different realizations of singular convolution kernels are selected to illustrate the present algorithm vibration analysis of strings rods beams diatomic molecules membranes waveguides and thin plates are utilized to test numerical accuracy and speed of convergence of the present approach numerical experiments indicate that the discrete singular convolution is a simple and reliable algorithm for vibration analysis

discontinuous galerkin finite element methods for second order hyperbolic problems abstract we prove a priori and a posteriori error estimates for a finite element method for linear second order hyperbolic equations based on a space time finite element discretization with the basis functions being continuous in space and discontinuous in time

vibration of twisted and curved cylindrical panels with variable thickness abstract a numerical procedure with an exact strain displacement relationship of twisted and curved cylindrical panels having variable thickness derived by considering the green strain tensor on general shell theory is presented using the principle of virtual work and the rayleigh ritz method with algebraic polynomials as in plane and transverse displacement functions the accuracy and applicability of the procedure are verified by comparing the present results with previous experimental and theoretical results for several panels the effects of variation ratio of thickness in chordwise and lengthwise directions twist and curvature both in two directions aforementioned on vibrations of cylindrical panels are studied in detail and typical vibration mode shapes are plotted to demonstrate the effects

free vibrations of rectangular plates with interior point supports abstract a new approach for the representation of point supports in the vibration analysis of plates was presented in earlier work 1 3 the approach was based on simulating a point support on a free edge as a zero of a flexibility function representing a fictitious elastic restraint distribution over the free edge the application of this approach to a variety of problems concerning rectangular plates with point supports located on the free edges was demonstrated in subsequent studies 4 5 the present study provides an extension of the flexibility function approach to the problem of rectangular plates with interior point supports in the analysis a rectangular plate is considered with two opposite edges simply supported and classical boundary conditions on the other two edges with one or more interior point supports along the line perpendicular to the simply supported edges extensive numerical results for a range of problem parameters have been obtained the results show the versatility of the flexibility function approach in the vibration analysis of rectangular plates with arbitrarily located interior point supports

numerical analysis of free vibrations of laminated composite conical and cylindrical shells discrete singular convolution dsc approach a numerical study on the free vibration analysis for laminated conical and cylindrical shell is presented the analysis is carried out using love s first approximation thin shell theory and solved using discrete singular convolution dsc method numerical results in free vibrations of laminated conical and cylindrical shells are presented graphically for different geometric and material parameters free vibrations of isotropic cylindrical shells and annular plates are treated as special cases the effects of circumferential wave number number of layers on frequencies characteristics are also discussed the numerical results show that the present method is quite easy to implement accurate and efficient for the problems considered

discontinuous galerkin method based on peridynamic theory for linear elasticity modeling of discontinuities shock waves crack surfaces etc in solid mechanics is one of the major research areas in modeling the mechanical behavior of materials among the numerical methods the discontinuous galerkin method dgm poses some advantages in solving these problems in this study a novel formulation for dgm is derived for elastostatics based on the peridynamic theory derivation of the proposed formulation is presented numerical analyses are performed for different problems and the numerical results are compared to that of the known exact solutions of the problems the proposed weak formulation is stable and coercive peridynamic discontinuous galerkin formulation is found to be robust and successful in modeling elastostatic problems copyright 2011 john wiley sons ltd

discontinuity capturing operators for elastodynamics finite element methods are presented which include discontinuity capturing operators to accurately solve elastodynamics problems exhibiting sharp gradients in their solution e g wave propagation the formulation involves finite element discretization of the temporal domain as well as the usual finite element discretization of the spatial domain linear least squares terms are included that enhance the stability of the space time finite element method nonlinear discontinuity capturing operators are presented that result in more accurate capturing of wave fronts in transient solutions while maintaining the high order accuracy of the underlying linear algorithm in smooth regions stability of the discontinuity capturing formulation is proved and a convergence proof is given for a particular choice of the discontinuity capturing operator numerical results are presented that demonstrate the effectiveness of the proposed discontinuity capturing operators for elastodynamics

proof nets garbage and computations we study the problem of local and asynchronous computation in the context of multiplicative exponential linear logic mell proof nets the main novelty is in a complete set of rewriting rules for cut elimination in presence of weakening which requires garbage collection the proposed reduction system is strongly normalizing and confluent

dsc ritz method for the free vibration analysis of mindlin plates this paper introduces a novel method for the free vibration analysis of mindlin plates the proposed method takes the advantage of both the local bases of the discrete singular convolution dsc algorithm and the pb 2 ritz boundary functions to arrive at a new approach called dsc ritz method two basis functions are constructed by using dsc delta sequence kernels of the positive type the energy functional of the mindlin plate is represented by the newly constructed basis functions and is minimized under the ritz variational principle extensive numerical experiments are considered by different combinations of boundary conditions of mindlin plates of rectangular and triangular shapes the performance of the proposed method is carefully validated by convergence analysis the frequency parameters agree very well with those in the literature numerical experiments indicate that the proposed dsc ritz method is a very promising new method for vibration analysis of mindlin plates copyright 2004 john wiley sons ltd

on the validity of a proof that the discrete singular convolution dsc lagrange distributed approximation function ldaf method is inferior to high order finite differences a few families of counterexamples are provided to a proof that the discrete singular convolution dsc lagrange distributed approximation function ldaf method is inferior to high order finite differences journal of computational physics 214 538 549 2006

discrete singular convolution and its application to the analysis of plates with internal supports part 2 applications part 2 of this series of two papers presents the applications of the discrete singular convolution dsc algorithm the main purpose of this paper is to explore the utility test the accuracy and examine the convergence of the proposed approach for the vibration analysis of rectangular plates with internal supports both partial internal line supports and complex internal supports are considered for 21 square plates of various combinations of edge support conditions the effects of different size shape and topology of the internal supports and different boundary conditions on the vibration response of plates are investigated the partial internal line supports may vary from a central point support to a full range of cross or diagonal line supports several closed loop supports such as ring square and rhombus and their combinations are studied for complex internal supports convergence and comparison studies are carried out to establish the correctness and accuracy of the dsc algorithm the dsc results are compared with those in the available literature obtained by using other methods numerical results indicate that the dsc algorithm exhibits controllable accuracy for plate analysis and shows excellent flexibility in handling complex geometries boundary conditions and support conditions copyright 2002 john wiley sons ltd

free vibration of laminated composite and sandwich plates using global local higher order theory abstract in this paper the global local higher order theory is used to study the free vibration of laminated composite and sandwich plates this global local theory can satisfy the free surface conditions and the geometric and stress continuity conditions at interfaces and the number of unknowns is independent of the layer numbers of the laminate based on the higher order theory a refined three noded triangular element satisfying c1 weak continuity conditions is presented for general laminated composite plates results obtained from present global local higher order theory have been found in good agreement with those obtained from three dimensional elasticity theories moreover this theory is still suitable for analysis of laminated plates with arbitrary layouts and soft core sandwich plates whereas numerical results show that the global higher order and first order theory overestimate natural frequency for these special structures this theory cannot only calculate the natural frequencies but can accurately predict the modal stress distributions in the thickness direction without any smooth techniques

wavelets generated by using discrete singular convolution kernels this paper explores the connection between wavelet methods and an efficient computational algorithm the discrete singular convolution dsc many new dsc kernels are constructed and they are identified as wavelet scaling functions two approaches are proposed to generate wavelets from dsc kernels two well known examples the canny filter and the mexican hat wavelet are found to be special cases of the present dsc kernel generated wavelets a family of wavelet generators proposed in this paper are found to form an infinite dimensional lie group which has an invariant subgroup of translation and dilation if dsc kernels form an orthogonal system they are found to span a wavelet subspace in a multiresolution analysis

numerical solution of the helmholtz equation with high wavenumbers this paper investigates the pollution effect and explores the feasibility of a local spectral method the discrete singular convolution dsc algorithm for solving the helmholtz equation with high wavenumbers fourier analysis is employed to study the dispersive error of the dsc algorithm our analysis of dispersive errors indicates that the dsc algorithm yields a dispersion vanishing scheme the dispersion analysis is further confirmed by the numerical results for one and higher dimensional helmholtz equations the dsc algorithm is shown to be an essentially pollution free scheme furthermore for large scale computation the grid density of the dsc algorithm can be close to the optimal two grid points per wavelength the present study reveals that the dsc algorithm is accurate and efficient for solving the helmholtz equation with high wavenumbers copyright 2003 john wiley sons ltd

a unified approach for the solution of the fokker planck equation this paper explores the use of a discrete singular convolution algorithm as a unified approach for numerical integration of the fokker planck equation the unified features of the discrete singular convolution algorithm are discussed it is demonstrated that different implementations of the present algorithm such as global local galerkin collocation and finite difference can be deduced from a single starting point three benchmark stochastic systems the repulsive wong process the black scholes equation and a genuine nonlinear model are employed to illustrate the robustness and to test the accuracy of the present approach for the solution of the fokker planck equation via a time dependent method an additional example the incompressible euler equation is used to further validate the present approach for more difficult problems numerical results indicate that the present unified approach is robust and accurate for solving the fokker planck equation

free vibration of line supported rectangular plates using a set of static beam functions the free vibration of thin orthotropic rectangular plates which may be continuous over a number of intermediate line supports in one or two directions is analyzed by the rayleigh ritz method a new set of admissible functions which are the static solutions of a point supported beam under a series of sine loads is developed the eigenfrequency equation for the plate is derived by minimizing the potential energy a very simple and general computer programme has been compiled the basic concept to form the set of static beam functions is very clear and requires no complicated mathematical knowledge some numerical results presented are compared with those obtained by other numerical methods in the literature it is shown that this set of static beam functions has some advantages in terms of computational cost application versatility and numerical accuracy especially for the plate problem with a large number of intermediate line supports and or when higher vibrating modes need to be calculated

coherence for sharing proof nets sharing graphs are an implementation of linear logic proof nets in which a redex is never duplicated in their usual formulation sharing graphs present a problem of coherence if the proof net n reduces by standard cut elimination to n then by reducing the sharing graph of n we do not obtain the sharing graph of n we solve this problem by changing the way the information is coded into sharing graphs and introducing a new reduction rule absorption the rewriting system is confluent and terminating the proof exploits an algebraic semantics for sharing graphs

dsc analysis of free edged beams by an iteratively matched boundary method this communication introduces a novel scheme for the treatment of free edge supports in the analysis of beams by using the discrete singular convolution dsc algorithm accommodating free edges has been a challenging issue in the dsc analysis of beams plates and shells an iteratively matched boundary imb method is proposed to overcome the difficulty numerical experiments are carried out to demonstrate that the proposed imb method works very well in dealing with arbitrary combinations of beam edge supports

a ritz vibration analysis of doubly curved rectangular shallow shells using a refined first order theory integral expressions for strain and kinetic energies in vibration analysis of shear deformable doubly curved shallow shells are presented although the formulation follows the first order shear deformation theory the consideration of lame parameters for the transverse shear strain through shell thickness which have been hitherto neglected by other researchers shows linear distribution functions instead of constant values if the lame parameters were dropped finite higher order two dimensional orthogonal polynomials pb 2 functions previously used in thin shell analyses 3 6 have been generalized from three to five degrees to account for the additional rotation fields of a moderately thick shell these global shape functions satisfy the kinematic boundary conditions at the outset the excellent performance and versatility of the computational methodology of the pb 2 ritz method are illustrated in representative numerical simulations the resultant matrix size is far smaller than other discretization methods and yet accurate solutions can be obtained the validity of the results is verified through direct comparisons the discrepancy of various formulations with and without the lame parameters is presented and discussed

on the use of space time finite elements in the solution of elasto dynamic problems with strain discontinuities abstract the use of a discontinuous galerkin dg formulation for the solution of elasto dynamic problems with discontinuities in the displacement gradients is examined comparisons with exact solutions are presented the paper demonstrates that space time finite element methods based on a dg formulation can be very effective in the study of dynamic solid solid phase transitions as well as dynamic fracture

free vibration analysis of beams and rectangular plates with free edges by the discrete singular convolution in this paper free vibration of beams annular plates and rectangular plates with free boundaries are analyzed by using the discrete singular convolution dsc a novel method to apply the free boundary conditions is proposed detailed derivations are given to validate the proposed method eight examples including the free vibrations of beams annular plates and rectangular plates with free boundaries are analyzed two kernels the regularized shannon s kernel and the non regularized lagrange s delta sequence kernel are tested dsc results are compared with either analytical solutions or and differential quadrature dq data it is demonstrated that the proposed method to incorporate the free boundary conditions is simple to use and can yield accurate frequency data for beams with a free end and plates with free edges thus the proposed method for applying the boundary conditions extends the application range of the dsc

discrete singular convolution and its application to the analysis of plates with internal supports part 1 theory and algorithm this paper presents a novel computational approach the discrete singular convolution dsc algorithm for analysing plate structures the basic philosophy behind the dsc algorithm for the approximation of functions and their derivatives is studied approximations to the delta distribution are constructed as either bandlimited reproducing kernels or approximate reproducing kernels unified features of the dsc algorithm for solving differential equations are explored it is demonstrated that different methods of implementation for the present algorithm such as global local galerkin collocation and finite difference can be deduced from a single starting point the use of the algorithm for the vibration analysis of plates with internal supports is discussed detailed formulation is given to the treatment of different plate boundary conditions including simply supported elastically supported and clamped edges this work paves the way for applying the dsc approach in the following paper to plates with complex support conditions which have not been fully addressed in the literature yet

mathematical modeling of vibration problem of nano sized annular sector plates using the nonlocal continuum theory via eight node discrete singular convolution transformation abstract in the present study free vibration analysis of nano sized annular sector plate is analyzed using the nonlocal continuum theory the method of discrete singular convolution dsc is used for numerical computations firstly equation of motion of thin plates is formulated via nonlocal elasticity then irregular physical domain is transformed into a rectangular domain by using geometric coordinate transformation the dsc procedures are then applied to discretization of the transformed set of governing equations and related boundary conditions the effects of nonlocal parameter mode numbers sector angle and radius ratio on the vibration frequencies are investigated in detail it is seen that the size effects are significant in vibration analysis of nano scaled annular sector plates and need to be included in the mechanical model

vibrations of mindlin rectangular plates with elastically restrained edges using static timoshenko beam functions with the rayleigh ritz method abstract a set of static timoshenko beam functions is developed as the admissible functions for the free vibration analysis of mindlin rectangular plates with uniform elastic translational and or rotational edge constraints by the use of the rayleigh ritz method this set of beam functions is made up of two parts the transverse deflection functions and rotation functions which are the static solutions of a timoshenko beam under the transverse loads of a fourier sinusoidal series distributed along the length of the beam therefore the effect of shear deformation on the admissible functions is taken into account in fact the beam is considered to be a unit width strip taken from the rectangular plate in a direction parallel to the edge of the plate and has the end supports corresponding to the edge conditions of the particular plate under consideration it can be seen that the method is sound theoretically each of the beam functions is a polynomial function of not more than third order plus a sine or cosine function for all cases and the change of the boundary supports only results in a corresponding change of the coefficients of the low order polynomial therefore a unified program with little computational efforts can be easily developed for the vibration analysis of mindlin rectangular plates with arbitrary boundary conditions and thickness span ratios the accuracy and efficiency of the proposed method are demonstrated by comparison and convergency studies finally sets of reasonably accurate natural frequencies are presented which can serve as a supplement to the database of vibration characteristics of moderately thick plates

proof of unconditional stability for a single field discontinuous galerkin finite element formulation for linear elasto dynamics abstract a discontinuous galerkin dg finite element method fem for the solution of linear elasto dynamic problems is revisited and modified the new dg fem is based on a method originally proposed by comput methods appl mech engrg 84 1990 327 and recently adapted by comput methods appl mech engrg 191 46 2002 5315 for the solution of dynamic solid solid phase transitions as the fem formulations in both the cited works have been found not to be unconditionally stable in cases where the underlying fem grid is completely unstructured this paper offers a modification of these formulations yielding a single field dg fem that is unconditionally stable without any restrictions on the grid structure furthermore an energy conserving variant of the formulation is also suggested

free vibration analysis of symmetric laminated skew plates by discrete singular convolution technique based on first order shear deformation theory in this study free vibration of laminated skew plates was investigated discrete singular convolution dsc method is used for numerical solution of vibration problems the straight sided quadrilateral domain is mapped into a square domain in the computational space using a four node element by using the geometric transformation typical results are presented for different geometric parameters and boundary conditions it is concluded from the results that the skew angle have considerable influence on the variations of the frequencies with fibre orientation angle and number of layers in the laminate the results obtained by dsc method are compared with those obtained by analytical and numerical approaches it is shown that reasonable accurate results are obtained present work also indicates that the method of dsc is a promising and potential approach for computational mechanics copyright 2009 john wiley sons ltd

option valuation by using discrete singular convolution this paper explores the utility of a discrete singular convolution dsc algorithm for solving the black scholes equation both european and american style options which include all nontrivial plain option pricing problems are considered to test the accuracy and to examine the efficiency of the present algorithm adaptive meshes are constructed to enhance the performance of the dsc algorithm all the present results are validated either by the analytical solution or by the standard binomial tree method extensive comparisons are carried out with two standard finite difference schemes and two binomial models of high speed convergence numerical experiments reveal that the present approach is accurate efficient and reliable for financial derivative valuations

discrete singular convolution element method for static buckling and free vibration analysis of beam structures a new version of discrete singular convolution dsc algorithm called the dsc element method is proposed the new method combines the high computational efficiency and accuracy of the original dsc algorithm with the convenience and generality of the finite element method in application to structural analysis the shortage existing in the original dsc algorithm has been overcome besides the proposed method provides a unique way to apply various boundary conditions in using dsc algorithm two types of dsc beam element are presented and a variety of problems such as static buckling and free vibrations with discontinuities in geometry or load have been successfully solved by the proposed method numerical results show that the proposed dsc element method is an accurate and efficient method for analyzing beam structures

multi field spacetime discontinuous galerkin methods for linearized elastodynamics we extend the single field spacetime discontinuous galerkin sdg method for linearized elastodynamics of abedi et al 1 to multi field versions a three field method in displacement velocity and strain is derived by invoking a bubnov galerkin weighted residuals procedure on the system of spacetime field equations and the corresponding jump conditions a two field formulation in displacement and velocity and the one field displacement formulation of 1 are obtained from the three field model through strong enforcement of kinematic compatibility relations all of these formulations balance linear and angular momentum at the element level and we prove that they are energy dissipative and unconditionally stable as in 1 we implement the sdg models using a causal advancing front meshing procedure that enables a patch by patch solution procedure with linear complexity in the number of spacetime elements numerical results show that the three field formulation is most efficient wherein all interpolated fields converge at the optimal o hp 1 rate for a given mesh size the three field model delivers error values that are more than an order of magnitude smaller than those of the one and two field models the three field formulation s efficiency is also superior independent of whether the comparison is based on matching polynomial orders or matching convergence rates

a low order locking free hybrid discontinuous galerkin element formulation for large deformations abstract in this work a hybrid discontinuous galerkin dg quadrilateral element formulation is presented as usual in hybrid formulations the interior of the elements is treated separately from the skeleton which represents the element boundaries these are kinematically decoupled i e displacement jumps can occur between the skeleton and the interior of the elements the global degrees of freedom dofs are defined on the skeleton as the displacements at the corners which allows the implementation into existing finite element codes as usual in hybrid dg formulations the degrees of freedom in the interior are condensed out on the element level leading to the same number of global degrees of freedom as for continuous bilinear elements instead of using conventional shape functions in the interior the deformation gradient f is assumed constant within the element furthermore f is connected to the skeleton degrees of freedom via the weak form this leads to a very simple formulation and implementation the element is tested for several computational examples from the literature special choices of the penalty parameter are investigated which are partially derived analytically it is found that the element is free of volumetric and shear locking moreover the convergence is similar to that of other well known locking free finite element formulations

matched interface and boundary mib for the implementation of boundary conditions in high order central finite differences high order central finite difference schemes encounter great difficulties in implementing complex boundary conditions this paper introduces the matched interface and boundary mib method as a novel boundary scheme to treat various general boundary conditions in arbitrarily high order central finite difference schemes to attain arbitrarily high order the mib method accurately extends the solution beyond the boundary by repeatedly enforcing only the original set of boundary conditions the proposed approach is extensively validated via boundary value problems initial boundary value problems eigenvalue problems and high order differential equations successful implementations are given to not only dirichlet neumann and robin boundary conditions but also more general ones such as multiple boundary conditions in high order differential equations and time dependent boundary conditions in evolution equations detailed stability analysis of the mib method is carried out the mib method is shown to be able to deliver high order accuracy while maintaining the same or similar stability conditions of the standard high order central difference approximations the application of the proposed mib method to the boundary treatment of other non standard high order methods is also considered

vibration frequencies of simply supported polygonal sandwich plates via kirchhoff solutions this study is concerned with the free vibration of general polygonal sandwich plates based on the reissner mindlin shear deformation plate theory the polygonal plate considered is simply supported on all its straight edges it will be shown herein that the vibration frequencies of such sandwich plates may be computed from their well known kirchhoff plate counterparts via an exact relationship this exact relationship should be useful for the development of approximate vibration formulae for sandwich plates of other shapes boundary and loading conditions and may also serve in checking vibration frequencies computed from shear deformable plate analysis software

free vibration analysis of multiple stepped beams by the discrete singular convolution in this paper free vibration of beams with multiple step changes are successfully analyzed by using the modified discrete singular convolution dsc the jump conditions at the steps are used to overcome the difficulty in using ordinary dsc for dealing with ill posed problems an nth order interpolation polynomial is established on each side of the step then two or three jump conditions together with two continuous conditions at steps are used to relate the two polynomials five examples are analyzed results obtained by the modified dsc and existing solutions are compared it is seen that the dsc results agree well with existing analytical numerical and experimental data it is also found that the dsc results are even more accurate than the data obtained by the differential quadrature element method for much higher mode frequencies the present research extends the application range of the dsc algorithm

interpolation in the limit of increasingly flat radial basis functions abstract many types of radial basis functions such as multiquadrics contain a free parameter in the limit where the basis functions become increasingly flat the linear system to solve becomes highly ill conditioned and the expansion coefficients diverge nevertheless we find in this study that limiting interpolants often exist and take the form of polynomials in the 1 d case we prove that with simple conditions on the basis function the interpolants converge to the lagrange interpolating polynomial hence differentiation of this limit is equivalent to the standard finite difference method we also summarize some preliminary observations regarding the limit in 2 d

the fictitious foundation approach to vibration analysis of plates with interior point supports abstract a new approach to the continuum representation of interior point supports in the vibration analysis of plates is proposed the plate is assumed to be supported by a fictitious non uniform winkler foundation the flexibility distribution of the winkler foundation represented by a flexibility function is such that it has a zero value at the point support locations but assumes large values resulting in negligible restraint over the rest of the plate domain the improvization of the point supports as a special case of the flexibility distribution of the elastic foundation allows one to solve the problem in a single domain in contrast to the multiple domain solutions available in the literature the application of this approach namely the fictitious foundation approach is demonstrated by considering the free vibration of a simply supported rectangular plate with interior point supports also presented is a single domain application of the impulse function approach to plates with interior point supports involving the representation of the concentrated reactions at the point support locations by a double fourier series expansion of the impulse function the results obtained by using these single domain approaches are compared with those obtained by using the multiple domain flexibility function approach presented in an earlier study by the authors the new approach presented in this paper namely the fictitious foundation approach for the simulation of interior point supports in plates provides a method for absorbing the discrete discontinuities in the force field in the interior of the plate into the governing differential equation and obtaining a continuum representation of the solution in a single domain of the plate

a novel scheme for the discrete prediction of high frequency vibration response discrete singular convolution mode superposition approach abstract this study introduces a novel scheme for the discrete high frequency forced vibration analysis based on discrete singular convolution dsc and mode superposition ms approaches the accuracy of the dsc ms is validated for thin beams and plates by comparing with available analytical solutions the performance of the dsc ms is evaluated by predicting spatial distribution and discrete frequency spectra of the vibration response of thin plates with two different boundary conditions the frequency spectra of the time harmonic excitation forces are in the form of ideal and band limited white noise so that the natural modes in the frequency band are provoked the solution exposes high frequency response behaviour definitely therefore it is hoped with this paper to contribute the studies on the treatment of uncertainties in the high frequency design applications

dsc solution for flow in a staggered double lid driven cavity a benchmark quality solution is presented for flow in a staggered double lid driven cavity obtained by using the wavelet based discrete singular convolution dsc the proposed wavelet based algorithm combines local methods flexibility and global methods accuracy and hence is a promising approach for achieving the high accuracy solution of the navier stokes equations block structured grids with pseudo overlapping subdomains are employed in the present simulation a third order runge kutta scheme is used for the temporal discretization quantitative results are presented apart from the qualitative fluid flow patterns the prevalence of rich features of flow morphology such as two primary vortex patterns merged single primary vortex patterns and secondary eddies makes this problem very attractive and interesting the problem is quite challenging for the possible existence of numerically induced asymmetric flow patterns and elliptic instability important computational issues like consistence convergence and reliability of the numerical scheme are examined the dsc algorithm is tested on the single lid driven cavity flow and the taylor problem with a closed form solution the double lid driven cavity simulations are cross validated with the standard second order finite volume method copyright 2003 john wiley sons ltd

a time discontinuous implicit variational integrator for stress wave propagation analysis in solids this paper proposes a time discontinuous and space continuous variational integration tdsc vi method for accurate elastic stress wave propagation computations in one dimensional bar the algorithm employs a limiter akin to classical artificial viscosity treatment to mitigate the deleterious gibbs jumps across the stress discontinuities and a parametrized consistent mass to alleviate dispersion error when the stepsizes are different from the courant stability limit which becomes necessary for elastic unloading and internal reflections in plastic deformation problems stability and accuracy analyses of the proposed tdsc vi method are carried out and compared with several well known traditional integration algorithms numerical experiments are carried out with the proposed implicit and explicit methods which show that the proposed methods perform favorably compared to the trapezoidal rule and the central difference method

solution of vibration problems for shallow shells of arbitrary form by the r function method an effective method for the free vibration of arbitrary plan form shallow shells is proposed the algorithm is based on the r function theory and variational ritz method the effectiveness of the method offered is illustrated by examples of shallow shells of a complex plan form at different boundary conditions three types of curvatures are considered which are the spherical circularly cylindrical and of hyperbolic paraboloid shape a number of the test problems were solved to check the veracity of the proposed method the comparison between the obtained results and those available in the literature was carried out

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

a pb 2 ritz formulation for flexural vibration of shallow cylindrical shells of rectangular planform abstract this paper presents a free flexural vibration analysis of shallow cylindrical shells of rectangular planform with arbitrary combinations of free simply supported and clamped boundaries the pb 2 ritz method previously used in the plate analysis by one of the authors is now extended to shallow shell studies the ritz approach along with the in plane and transverse displacements assumed in the form of orthogonal polynomials is used to formulate the problems numerical results for the vibration frequencies for wide ranges of aspect ratio shallowness ratio and thickness ratio are presented several selected contour plots of the mode shapes for six different combinations of boundary conditions are presented as usual the accuracy of the present method is illustrated by convergence tests and comparison with the well established results from the literature

vibration analysis of multi span plates having orthogonal straight edges abstract an accurate numerical technique is developed for flexural vibration of rectangular and l shaped plates continuous over rigid supports with arbitrary number of spans a set of orthogonally generated two dimensional plates function is used in the rayleigh ritz method to determine the natural frequencies of the plate systems several numerical examples are presented and the results obtained where possible are compared with the known solutions in the literature the present method is proven to be extremely versatile in solving a broad class of the aforementioned problems

discrete singular convolution for the sine gordon equation abstract this paper explores the utility of a discrete singular convolution dsc algorithm for the integration of the sine gordon equation the initial values are chosen close to a homoclinic manifold for which previous methods have encountered significant numerical difficulties such as numerically induced spatial and temporal chaos a number of new initial values are considered including a case where the initial value is exactly on the homoclinic orbit the present algorithm performs extremely well in terms of accuracy efficiency simplicity stability and reliability

eigenfrequencies of line supported rectangular plates abstract a set of series consisting of a combination of free vibrating beam functions and polynomials is used as the admissible functions in the rayleigh ritz method to study the problem of the flexural vibration of thin uniform thickness orthotropic rectangular plates which may be continuous over several supports in one or two directions in practice which kind of free vibrating beam functions are used is determined by the boundary conditions of the plate the starting order of the beam eigenfunctions and the number of terms in the polynomials in each direction depend on the number of intermediate line supports in that direction the coefficients of the polynomials are decided by the boundary conditions of the plate and the locations of the line supports some numerical results are given for the simply supported and or clamped rectangular plates with two and three spans in one and two directions it is demonstrated that the method may be used to tackle such plate problems and has considerable accuracy and fast convergence compared with the available results the difficulty of application not being greater than any other methods

lagrange distributed approximating functionals lagrange distributed approximating functionals ldafs are proposed as the basis for a new collocation type method for accurately approximating functions and their derivatives both on and off discrete grids example applications are presented to illustrate the use of ldafs for solving the schr umlt o dinger equation and fokker planck equation ldafs are constructed by combining the daf concept with the lagrange interpolation scheme copyright ital 1997 ital the american physical society

postbuckling behavior of bi axially compressed arbitrarily straight sided quadrilateral functionally graded material plates abstract in this paper the problem of the postbuckling behavior of biaxial compressed straight sided functionally graded material fgm plates of quadrilateral shape is studied the plate considered is subjected to in plane loads on all four edges a computational framework based on an improved moving least squares imls approximation for the field variables is developed for the analysis the solution procedures involved a transformation from the physical domain to a computational domain and then discrete the nonlinear governing equation using the imls ritz method the first order shear deformation theory fsdt with the von karman nonlinearity is employed a nonlinear solution to the postbuckling of quadrilateral fgm plates is computed through the modified newton raphson method combined with the arc length iterative algorithm a stabilized conforming nodal integration scheme is employed to improve computational efficiency and eliminate shear and membrane locking the validity and accuracy of the numerical results are established through convergence studies to the best of the authors knowledge the problem has not been attempted in the open literature

free vibration analysis of continuous rectangular plates vibration characteristics of rectangular plates continuous over full range line supports or partial line supports have been studied by using a discrete method concentrated loads with heaviside unit functions and dirac delta functions are used to simulate the line supports the fundamental differential equations are established for the bending problem of the continuous plate by transforming these differential equations into integral equations and using the trapezoidal rule of the approximate numerical integration the solution of these equations is obtained green function which is the solution of deflection of the bending problem of plate is used to obtain the characteristic equation of the free vibration the effects of the line support the variable thickness and aspect ratio on the frequencies and mode shapes are considered by comparing the numerical results obtained by the present method with those previously published the efficiency and accuracy of the present method are investigated

exact correspondence between eigenvalues of membranes and functionally graded simply supported polygonal plates we use reddy s third order plate theory to study buckling and steady state vibrations of a simply supported functionally gradient isotropic polygonal plate resting on a winkler pasternak elastic foundation and subjected to uniform in plane hydrostatic loads young s modulus and the poisson ratio for the material of the plate are assumed to vary only in the thickness direction effects of rotary inertia are considered the problem of determining the critical buckling load or the vibration frequency of the plate is found to be analogous to that of ascertaining the frequency of a membrane clamped at the edges and whose shape coincides with that of the plate the critical buckling load and the vibration frequency are shown to be positive some available results for plates symmetric about the mid plane can be retrieved from the present analysis

vibration of moderately thick cylindrical shallow shells a first order shear deformation theory is employed for the vibration analysis of shallow cylindrical shells of rectangular planform a general method of solution based on the ritz extremum energy principle and two dimensional polynomial is developed to examine the effects of thickness and curvature on the vibrating response of shells having various boundary constraints convergence and comparison studies are conducted to justify the accuracy of the eigenvalues numerical results are presented to demonstrate the capability of the present method and to provide new data for design purposes sets of new vibration mode shapes are also presented to illustrate the vibratory characteristics of the shells

dsc ritz method for high mode frequency analysis of thick shallow shells this paper addresses a challenging problem in computational mechanics the analysis of thick shallow shells vibrating at high modes existing methods encounter significant difficulties for such a problem due to numerical instability a new numerical approach dsc ritz method is developed by taking the advantages of both the discrete singular convolution dsc wavelet kernels of the dirichlet type and the ritz method for the numerical solution of thick shells with all possible combinations of commonly occurred boundary conditions as wavelets are localized in both frequency and co ordinate domains they give rise to numerical schemes with optimal accurate stability and flexibility numerical examples are considered for mindlin plates and shells with various edge supports benchmark solutions are obtained and analyzed in detail experimental results validate the convergence stability accuracy and reliability of the proposed approach in particular with a reasonable number of grid points the new dsc ritz method is capable of producing highly accurate numerical results for high mode vibration frequencies which are hitherto unavailable to engineers moreover the capability of predicting high modes endows us the privilege to reveal a discrepancy between natural higher order vibration modes of a mindlin plate and those calculated via an analytical relationship linking kirchhoff and mindlin plates copyright 2004 john wiley sons ltd

free vibration of a solid plate of arbitrary shape lying on an arbitrarily shaped ring support this paper is concerned with a method for solving problems of vibrating plates of arbitrary shape lying on arbitrarily shaped inner ring supports to treat the inner ring support the reaction force of the support is assumed to be an external unknown force the exact solution of the equation of motion in polar co ordinates is applied the boundary conditions along the edge and the support are satisfied directly by means of the fourier expansion collocation method which has bee developed in the author s previous reports numerical calculations have been carried out for a solid polygonal plate on an annular ring support and a solid circular plate on a elliptical ring support

relationships between classical and shear deformation theories of axisymmetric circular plates the exact relationships between the deflections slopes rotations shear forces and bending moments of a third order theory and those of the classical theory and the first order shear deformation theory for axisymmetric bending of isotropic circular plates are developed the relationships enable one to obtain the solutions of the third order theory from any known classical or first order theory solutions of axisymmetric circular plates for any set of boundary conditions and transverse loads the relationships may also be used to develop finite element models of axisymmetric bending of circular plates according to the first order and third order theories

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

a novel approach for the analysis of high frequency vibrations abstract despite much effort in the past few decades the numerical prediction of high frequency vibrations remains a challenging task to the engineering and scientific communities due to the numerical instability of existing computational methods however such prediction is of crucial importance to certain problems of pressing practical concern as pointed out by langley and bardell 1998 the aeronautical journal102 287 297 this paper introduces the discrete singular convolution dsc algorithm for the prediction and analysis of high frequency vibration of structures both a beam and two span plates are employed as test examples to demonstrate the capability of the dsc algorithm for high frequency vibration analysis a completely independent approach the levy method is employed to provide exact solutions for a cross validation of the proposed method the reliability of the dsc results is also validated by convergence studies remarkably extremely accurate and stable results are obtained in this work e g the relative dsc errors for the first 7100 modes of the beam and the first 4500 modes of the two span plates are all

a new algorithm for solving some mechanical problems this paper explores the utility of a discrete singular convolution algorithm for solving certain mechanical problems benchmark mechanical systems including plate vibrations and incompressible flows are employed to illustrate the robustness and to test accuracy of the present algorithm numerical results indicate that the present approach is very accurate efficient and reliable for solving the aforementioned problems

vibratory characteristics of cantilevered rectangular shallow shells of variable thickness in this paper a comprehensive study on the modeling of vibratory response of variable thickness cantilevered shallow cylindrical shells of rectangular planform is carried out through the principle of minimum total energy the equations of stretching and bending strain energies kinetic energy and the associated boundary conditions of the shells are derived the present model is developed based on the ritz formulation with the assumption of sets of mathematicall y complete admissible two dimensional polynomials to approximate the in plane and transverse displacement amplitude functions a basic function is introduced in the approximate method to enforce automatic satisfaction of the kinematic boundary conditions sets of comprehensive reasonably accurate vibration frequencies of the shallow shells are presented for wide ranges of aspect ratio thickness variation ratios and shallowness ratio these results where possible are verified by comparing with other established experimental and theoretical solutions few selected contour plots for the first known mode shapes of these cylindrical shells of variable thickness are included

parsing mell proof nets we propose a new formulation for full weakening and constants included multiplicative and exponential mell proof nets allowing a complete set of rewriting rules to parse them the recognizing grammar defined by such a rewriting system confluent and strong normalizing on the new proof nets gives a correctness criterion that we show equivalent to the danos regnier one

on the vibration of shells with timoshenko mindlin type shear deflections and rotatory inertia equations of motion of shells are formulated in curvilinear co ordinates that are consistent with assumptions made in the timoshenko beam and also the mindlin plate equations this consistency is proven by obtaining the timoshenko and mindlin equations from the derived shell equations by geometrical reduction the implication of the timoshenko type shear is illustrated by constrasting the free vibration behavior of the special case of a cylindrical shell with the behavior of the timoshenko beam and the mindlin plate

computational interpretations of linear logic abstract we study girard s linear logic from the point of view of giving a concrete computational interpretation of the logic based on the curry howard isomorphism in the case of intuitionistic linear logic this leads to a refinement of the lambda calculus giving finer control over order of evaluation and storage allocation while maintaining the logical content of programs as proofs and computation as cut elimination in the classical case it leads to a concurrent process paradigm with an operational semantics in the style of berry and boudol s chemical abstract machine this opens up a promising new approach to the parallel implementation of functional programming languages and offers the prospect of typed concurrent programming in which correctness is guaranteed by the typing

the flexural vibration of rectangular plates with point supports abstract orthogonally generated polynomial functions are used in the lagrangian multiplier method to study the free flexural vibration problem of point supported thin flat rectangular plates the analysis applies to isotropic and specially orthotropic plates having any combination of clamped simply supported or free edges with arbitrarily located point supports and to plates which are continuous over line supports parallel to the plate edges numerical results are presented for a number of specific problems illustrating the accuracy and versatility of the approach and which include natural frequencies and nodal patterns for a point supported plate which is continuous over two perpendicular line supports

vibration of triangular plates point supports mixed edges and partial internal curved supports a numerical method which is a hybrid form of the rayleigh ritz method and the lagrangian multiplier method is presented in this paper for the vibration analysis of general triangular plates with complicated supported conditions these support conditions include internal clamped or simple point supports mixed periphery boundary conditions and partial internal curved supports several plate examples are used to illustrate the method apart from the limiting cases of some of these triangular plates with point supports where existing results are available for comparison the frequency parameters presented in this paper are new they should be valuable to designers in some industrial applications

a global continuum ritz formulation for flexural vibration of pretwisted trapezoidal plates with one edge built in abstract the development of a continuum ritz model for twisted plate vibration on the basis of minimization of the energy functional is presented this method involves the use of a set of orthogonally generated pb 2 shape functions to approximate the transverse and in plane deflections in this paper a two dimensional recurrence formula is proposed to generate this set of functions during the orthogonalization process a basic function is introduced to each transverse and in plane displacement to ensure the automatic satisfaction of the essential boundary conditions the whole process can be easily implemented numerically and the accuracy of the method can be achieved by increasing the number of terms used in the polynomial functions following the above procedures a governing eigenvalue equation is derived this equation is solved to determine the vibration response of trapezoidal plates with initial twist in order to verify the validity and reliability of this method in addition to the convergence study the present results are compared with the available values from the literature where possible

a general discontinuous galerkin method for finite hyperelasticity formulation and numerical applications a discontinuous galerkin formulation of the boundary value problem of finite deformation elasticity is presented the primary purpose is to establish a discontinuous galerkin framework for large deformations of solids in the context of statics and simple material behaviour with a view toward further developments involving behaviour or models where the dg concept can show its superiority compared to the continuous formulation the method is based on a general hu washizu de veubeke functional allowing for displacement and stress discontinuities in the domain interior it is shown that this approach naturally leads to the formulation of average stress fluxes at interelement boundaries in a finite element implementation the consistency and linearized stability of the method in the non linear range as well as its convergence rate are proven an implementation in three dimensions is developed showing that the proposed method can be integrated into conventional finite element codes in a straightforward manner in order to demonstrate the versatility accuracy and robustness of the method examples of application and convergence studies in three dimensions are provided copyright 2006 john wiley sons ltd

free vibration of generally supported rectangular kirchhoff plates state space based differential quadrature method the title problem is investigated using the differential quadrature method based on the state space formalism the plates with mixed boundary conditions may cross over one way internal rigid line supports that impose zero transverse displacement constraints differential quadrature procedure is applied in the direction of line supports while exact solution is sought in the transfer domain perpendicular to the line supports using the state space method to avoid numerical instability in the transfer matrix method joint coupling matrices are introduced mainly according to the continuity conditions at line joints natural frequencies of rectangular kirchhoff plates with general boundary conditions are calculated and compared with the results from other methods effects of location of internal line supports and the mixed boundary conditions on the frequency parameters are discussed copyright 2006 john wiley sons ltd

call by name call by value call by need and the linear lambda calculus abstract girard described two translations of intuitionistic logic into linear logic one where a b maps to a b and another where it maps to a b we detail the action of these translations on terms and show that the first corresponds to a call by name calculus while the second corresponds to call by value we further show that if the target of the translation is taken to be an affine calculus where controls contraction but weakening is allowed everywhere then the second translation corresponds to a call by need calculus as recently defined by ariola felleisen maraist odersky and wadler thus the different calling mechanisms can be explained in terms of logical translations bringing them into the scope of the curry howard isomorphism our results extend neatly to translations of extensions for recursion in the call by name and call by value calculi and in general to extensions for products and for the corresponding untyped systems