a numerical solution of burgers equation by time discretization of adomian s decomposition method in this paper burgers equation one dimensional quasi linear parabolic pde which is used in turbulence and shock wave theory was solved by modified adomian s decomposition method with discretization in time the numerical results obtained by this method for various values of viscosity have been compared with the exact solution to show the efficiency of the method

non linear finite element formulation of kinematic limit analysis the objective of the research presented in this paper was to develop a general computational method for kinematic limit analysis problems that involve the determination of an optimal kinematically admissible velocity field of the studied structure under external loads with the failure velocity field available we can obtain a numerical estimate of the limit load exerted to the structure the general kinematic limit analysis is characterized by the minimization of the plastic potential power dissipation functional of the mechanical system this minimization problem was approached previously by linear and non linear programming schemes in this paper a new non linear solution scheme is described which is based on previous research on the regularized method the regularized functional is a convex and non linear functional whose minimum represents a viscoplastic potential power dissipation the velocity which minimizes this functional was proved to be kinematically admissible and can be obtained by the augmented lagrangian method this paper demonstrates that the non linear programming scheme is applicable to direct limit analysis the basic idea of using this optimization method is to tranform the functional with a non linear term of the first order derivatives of the velocity to a functional in which this term is uncoupled with the strain rates and in consequence the augmented lagrangian transformed functional can be solved more easily some special problems related to incompressibility and discontinuity are discussed a simple and accurate scheme is proposed to deal with the incompressibility problem and the problem of the linear mohr coulomb yield surface in the principal stress space examples of plane stress and plane strain problems are given for von mises and mohr coulomb materials numerical results are provided in graphical form which serves to illustrate the kinematic admissibility the limit loads obtained agreed well with the analytical results which demonstrates the efficiency and accuracy of the non linear computational method presented

a general algorithm for limit solutions of plane stress problems a computational approach to limit solutions is considered most challenging for two major reasons a limit solution is likely to be non smooth such that certain non differentiable functions are perfectly admissible and make physical and mathematical sense moreover the possibility of non unique solutions makes it difficult to analyze the convergence of an iterative algorithm or even to define a criterion of convergence in this paper we use two mathematical tools to resolve these difficulties a duality theorem defines convergence from above and from below the exact solution a combined smoothing and successive approximation applied to the upper bound formulation perturbs the original problem into a smooth one by a small parameter e as e 0 the solution of the original problem is recovered this general computational algorithm is robust such that from any initial trial solution the first iteration falls into a convex hull that contains the exact solution s of the problem unlike an incremental method thut invariably renders the limit problem ill conditioned the algorithm is numerically stable limit analysis itself is a highly efficient concept which bypasses the tedium of the intermediate elastic plastic deformation and seeks the most important information directly with the said algorithm we have produced many limit solutions of plane stress problems certain non smooth characters of the limit solutions are shown in the examples presented two well known as well as one parametric family of yield functions are used to allow comparison with some classical solutions

behavior of plane waves propagating through a temperature inhomogeneous region abstract description and analysis of acoustic waves in ducts with a region containing temperature inhomogeneous fluid represent a significant problem of scientific and practical interest this interest is induced by the need of understanding how temperature fields affect acoustic processes which would lead to a more efficient design and control of systems involving thermoacoustic interactions most of the works addressing these problems limit themselves to the assumption of weak temperature profile gradients or to temperature profiles which do not connect neighboring temperature homogeneous regions smoothly in our work we investigate the behavior of plane acoustic waves that enter a region with an arbitrary temperature gradient a polynomial character of the used temperature profile ensures smooth connection with constant temperature regions the one dimensional wave equation for ducts with an axial mean temperature gradient is solved analytically the derived solutions based on heun functions extend the class of published exact analytical solutions of model wave equations taking into account the medium temperature gradient due to the property that our proposed polynomial temperature function has derivatives equal to zero at points which are connected with the surrounding temperature homogeneous regions we can form more complex smooth temperature profiles for which it is possible to use the transfer matrix method

a novel augmented lagrangian based formulation for upper bound limit analysis summary this paper describes a novel upper bound formulation of limit analysis this formulation is an innovative variant of an existing two field mixed formulation based on the augmented lagrangian method also developed by the authors a natural approach is used to describe the deformation of each finite element furthermore and in contrast to the previous formulation two independent field approximations are now both used to define the velocity field defined globally and at element level it is shown that this feature allows a governing system of uncoupled linear equations to be obtained some numerical examples in plane strain conditions are presented in order to illustrate the current model performance in conclusion the potential and advantages of this new approach are discussed copyright 2011 john wiley sons ltd

the calculation of thermoacoustic oscillations thermoacoustic oscillations occur in a wide variety of practical applications in which heat is supplied to an acoustic resonator a simple geometry is investigated systematically to determine the importance of various flow parameters on the frequency of the oscillations detailed consideration of elementary examples shows that the form of the coupling between the heat input and the unsteady flow has a crucial effect on the frequency of oscillation the same elementary examples are used to compare how well if at all different calculation methods in the literature account for this influence a mean flow and a distributed region of heat input significantly complicate the analysis of thermoacoustic oscillations and are often neglected model problems are used to illustrate that mean flow effects can become significant even at modest inlet mach numbers and to indicate circumstances under which a distributed heat input may be treated as concentrated

a parameter uniform implicit difference scheme for solving time dependent burgers equations abstract a numerical study is made for solving one dimensional time dependent burgers equation with small coefficient of viscosity burgers equation is one of the fundamental model equations in the fluid dynamics to describe the shock waves and traffic flows for high coefficient of viscosity a number of solution methodology exist in the literature 6 7 8 9 and 14 but for the sufficiently low coefficient of viscosity the exist solution methodology fail and a discrepancy occurs in the literature in this paper we present a numerical method based on finite difference which works nicely for both the cases i e low as well as high viscosity coefficient the method comprises a standard implicit finite difference scheme to discretize in temporal direction on uniform mesh and a standard upwind finite difference scheme to discretize in spacial direction on piecewise uniform mesh the quasilinearzation process is used to tackle the non linearity an extensive amount of analysis has been carried out to obtain the parameter uniform error estimates which show that the resulting method is uniformly convergent with respect to the parameter to illustrate the method numerical examples are solved using the presented method and compare with exact solution for high value of coefficient of viscosity

a numerical solution of burgers equation by pseudospectral method and darvishi s preconditioning in this paper we solve the burgers equation by pseudospectral method this equation is one dimensional quasilinear partial differential equation to reduce round off error of pseudospectral method we use darvishi s preconditioning the numerical results obtained by this method for different values of viscosity have been compared with the exact solution it was seen that they were in good agreement with each other because norm infinity of error is very small

the distance between two convex sets abstract in this paper we explore the duality relations that characterize least norm problems the paper starts by presenting a new minimum norm duality mnd theorem one that considers the distance between two convex sets roughly speaking the new theorem says that the shortest distance between the two sets is equal to the maximal separation between the sets where the term separation refers to the distance between a pair of parallel hyperplanes that separates the two sets the second part of the paper brings several examples of applications the examples teach valuable lessons about the role of duality in least norm problems and reveal new features of these problems one lesson exposes the polar decomposition which characterizes the solution of an inconsistent system of linear inequalities another lesson reveals the close links between the mnd theorem theorems of the alternatives steepest descent directions and constructive optimality conditions

a 3d finite element with planar symmetry for limit analysis computations abstract a formulation for finite element limit analysis of a certain class of 3d perfectly plastic solids governed by von mises plasticity condition is presented a planar symmetry constraint for both geometry and displacement field is assumed to analyze plane problems where the variable nature of transverse dissipation must be considered a mixed locking free and low distortion sensitive element is formulated on the basis of the natural approach the solution procedure exploits the kinematic theorem of limit analysis cast in the form of a minimum problem for a convex but non smooth dissipation functional applications to a notched specimen and to a bolted joint are presented to stress the importance of transverse effects in some problems commonly modeled as purely 2d

semi infinite programming theory methods and applications starting from a number of motivating and abundant applications in 2 including control of robots eigenvalue computations mechanical stress of materials and statistical design the authors describe a class of optimization problems which are referred to as semi infinite because their constraints bound functions of a finite number of variables on a whole region in 3 5 first and second order optimality conditions are derived for general nonlinear problems as well as a procedure for reducing the problem locally to one with only finitely many constraints another main effort for achieving simplification is through duality in 6 there algebraic properties of finite linear programming are brought to bear on duality theory in semi infinite programming section 7 treats numerical methods based on either discretization or local reduction with the emphasis on the design of superlinearly convergent sqp type methods taking this differentiable point of view this paper can be considered to be complementar

computation of limit loads for computing the collapse state of a perfect plastic continuum we suggest a mixed finite element approximation to the infinite dimensional mathematical programming problem of limit analysis the convergence of the limit load to the exact solution is discussed as well as solution methods for the discrete problem finally the method is applied to a classical problem in plane strain

a numerical solution of burgers equation by finite element method constructed on the method of discretization in time abstract in this paper the galerkin finite element method constructed on the method of discretization in time was applied to solve the one dimensional nonlinear burgers equation the system of nonlinear equations obtained for each time step was solved by using the newton method in order to show the efficiency of the presented method the numerical solutions obtained for various values of viscosity were compared with the exact solutions it was seen that they were in excellent agreement

numerical solution of burgers equation with restrictive taylor approximation in this paper we have applied restrictive taylor approximation classical explicit finite difference method to the burgers equation with a set of initial and boundary conditions to obtain its numerical solution the stability region and truncation error of the new method are discussed the accuracy of the proposed method is demonstrated by the two test problems the numerical results are found in good agreement with the exact solutions

applying multiquadric quasi interpolation to solve burgers equation abstract in this paper we develop a kind of univariate multiquadric mq quasi interpolation and use it to solve burgers equation with viscosity at first we construct the mq quasi interpolation which possesses the properties of linear reproducing and preserving monotonicity next we obtain the numerical scheme by using the derivative of the quasi interpolation to approximate the spatial derivative of the dependent variable and a low order forward difference to approximate the time derivative of the dependent variable then we verify our method for two examples with distinguishing initial value condition one example is tested for three reynolds number that is r 10 r 100 and r 10 000 from the numerical experiments we see that the presented method in this paper is valid although the accuracy of the technique is not higher than hon and mao s one another example is used to examine the travelling of the shock we can improve the accuracy by selecting an appropriate shape parameter and using a higher accurate mq quasi interpolation the advantage of the resulting scheme is that the algorithm is very simple so it is very easy to implement

load capacity ratios for structures abstract for a given structure made of a perfectly plastic material with a yield stress s y we consider the load capacity ratio of the structure the largest positive number c depending only on the geometry of the structure which satisfies the following property for any loading distribution f on the structure whose maximum is f max the structure will not undergo plastic collapse as long as f max s y c independently of the distribution of the load the paper presents the mathematical aspects related mechanical notions algorithms and examples corresponding to load capacity ratios of structures

an exact solution for one dimensional acoustic fields in ducts with an axial temperature gradient abstract in this paper an approach is presented for obtaining exact analytical solutions for sound propagation in ducts with an axial mean temperature gradient the one dimensional wave equation for ducts with an axial mean temperature gradient is derived the analysis neglects the effects of mean flow and therefore the solutions obtained are valid only for mean mach numbers that are less than 0 1 the derived wave equation is then transformed to the mean temperature space it is shown that by use of suitable transformations the derived wave equation can be reduced to analytically solvable equations e g bessel s differential equation the applicability of the developed technique is demonstrated by obtaining a solution for ducts with a linear temperature profile this solution is then applied to investigate the dependence of sound propagation in a quarter wave tube upon the mean temperature profile furthermore the developed analytical solution is used to extend the classical impedance tube technique to the determination of admittances of high temperature systems e g flames the results obtained using the developed analytical solution are in excellent agreement with experimental as well as numerical results analytical solutions were also obtained for a duct with an exponential temperature profile and also for a temperature profile that corresponds to a constant convective heat transfer coefficient at the wall

complementary energy principle for elastodynamics free of volumetric locking abstract this paper proposes a complementary energy principle for elastodynamic problems in doing so the stresses and the inertial forces that satisfy the equilibrium equations a priori are chosen as basic variables and then the complementary variational formulation is established by weakly enforcing the kinematic constraints the eventual formulation is posed to be an integral equation with respect to the time dimension and can be easily applied to free and forced vibration analysis in addition the volumetric locking free property inherent in the complementary energy principle is addressed numerical study on a rectangular plate is performed to validate the proposed complementary energy principle as well as to verify the featured locking free property moreover extensions of the dynamic complementary energy principle to tackle visco elastodynamics and stokes flows are also presented

reconstruction of acoustic transfer matrices by instationary computational fluid dynamics thermoacoustic combustion instabilities are a frequently encountered problem in the operation of combustion equipment the brute force application of computational fluid dynamics to the analysis of thermoacoustic instabilities is estimated to be forbiddingly expensive for many systems of technical interest due to the high computational demands of a time and space accurate simulation of a low mach number compressible reacting flow in a complex geometry thermoacoustic systems can be modelled efficiently as networks of acoustic multi ports where each multi port corresponds to a certain component of the system e g air or fuel supply burner flame combustor and suitable terminations and is represented mathematically by its transfer matrix for some multi ports the transfer matrix can be derived analytically from first principles i e the equations of fluid motions and suitable approximations however the acoustic behavior of more complicated components e g a burner or a flame has to be determined by empirical methods by using a black box approach common in communications engineering in this work a method is introduced which allows one to reconstruct the transfer matrix of an acoustic two port from an instationary computation of the response of the two port to an imposed perturbation of the steady state firstly from the time series data of fluctuating velocity and pressure on both sides of the two port the auto and cross correlations of the fluctuations are estimated then the unit impulse responses of the multi port are computed by inverting the wiener hopf equation finally the unit impulse responses are z transformed to yield the coefficients of the transfer matrix the method is applied to the one dimensional model of a heat source with time delay placed in a low mach number compressible flow for which an analytical description can be derived from first principles computational predictions of the transfer matrix have been validated successfully against these analytical results furthermore a comparison of the novel approach presented in this paper with a method for computing the frequency response of a flame by laplace transforming its step response is carried out

computation of collapse states with von mises type yield condition a new computational approach to the problem of limit analysis with quadratic yield condition is developed and tested the problem is solved with the exact convex yield condition and the general case of unbounded yield set corresponding to unrestricted hydrostatic pressure is treated the solution method simultaneously approximates the collapse fields for stresses and flow the approach consists of two separate steps first the continuous problem is discretized by the finite element method into a finite dimensional optimization problem which turns out to be of a very specific form then this problem is solved by a suitable optimization method this way it is not necessary to be an expert in optimization in order to solve collapse problems and we can take advantage of the rapid development in optimization methods for large sparse problems without changing the discretization program the efficiency and accuracy of the method for large problems is demonstrated by solving a classical problem in the plane strain model approximately 90000 finite element nodes with 3 stress components and 2 velocity components at each node in two space dimensions this may be overkill but it shows that we are able to solve problems in three space dimensions

computations in limit analysis for plastic plates a class of mixed finite element discretizations of the problem of limit analysis for plastic plates is analysed for the discrete problem we discuss a linear programming approach based on linearization of the yield condition and a convex programming approach based on the exact mises condition applying the method to rectangular plates with uniform load and concentrated loads we get improved and new results partly in disagreement with one of our references

an upper bound limit analysis of mindlin plates using cs dsg3 method and second order cone programming the paper presents a numerical procedure for kinematic limit analysis of mindlin plate governed by von mises criterion the cell based smoothed discrete shear gap method cs dsg3 is combined with a second order cone optimization programming socp for determining the upper bound limit load of the mindlin plates the limit analysis problem of mindlin plates is formulated by minimizing the dissipation power subjected to a set of constraints of boundary conditions and unitary external work this minimization problem is then transformed into an explicit form suitable for the solution using the socp the numerical results of some benchmark problems show that the proposal procedure can provide the reliable upper bound collapse multipliers for the mindlin plates cs dsg3 is combined with socp for determining upper bound limit load of mindlin plates limit analysis problem is transformed into an explicit form suitable for solution using socp and cs dsg3 numerical results show that cs dsg3 is free of shear locking and can provide reliable upper bound collapse multipliers for mindlin plates

on plane wave propagation in a uniform pipe in the presence of a mean flow and a temperature gradient a theoretical study on the propagation of plane waves in the presence of a hot mean flow in a uniform pipe is presented the temperature variation in the pipe is taken to be a linear temperature gradient along the axis the theoretical studies include the formulation of a wave equation based on continuity momentum and state equation and derivation of a general four pole matrix which is shown to yield the well known transfer matrices for several other simpler cases

a mixed formulation and mixed finite elements for limit analysis a mixed variational principle for the limit analysis of rigid perfectly plastic continua is discussed in which the nonlinear yield condition and the associated flow rule appear through a suitably defined penalty function a mixed finite element discrete formulation is derived and a sequential unconstrained minimization technique is devised affording a complete static and kinematic solution several results are presented in both structural and soil mechanics compared with previously available exact and numerical solutions

a variational principle and an algorithm for limit analysis of beams and plates abstract a variational principle for limit analysis of beams and plates is developed from a yield function based on the frobenius matrix norm the formulation produced a pair of maximization and minimization problems with a duality relation between them exact solutions of two simple problems are presented as verification to the validity of the new variational principle an iterative algorithm is constructed to solve the minimization problem the algorithm tested successfully on the two example problems is intended for beams and plates with general loading and boundary conditions and shapes

limit analysis with the dual affine scaling algorithm the collapse state of a rigid plastic material with the linearized mises yield condition is computed we use an infeasible point variant of the dual affine scaling algorithm for linear programming which is extremely efficient for this large sparse and ill conditioned problem for a classical test problem we obtain better results than previously both for the limit load and for the collapse fields thus setting a new standard for computations in limit analysis

a general algorithm for plastic flow simulation by finite element limit analysis abstract limit analysis has been rendered versatile in many structural and metal forming problems in metal forming analysis the slip line method and the upper bound method have filled the role of limit analysis as a breakthrough of the previous work a computational approach to limit solutions is considered as the most challenging area in the present work a general algorithm for limit solutions of plastic flow is developed with the use of finite element limit analysis the algorithm deals with a generalized holder inequality a duality theorem and combined smoothing and successive approximation in addition to a general procedure for finite element analysis the algorithm is robust such that from any initial trial solution the first iteration falls into a convex set which contains the exact solution s of the problem the idea of the algorithm for limit solutions is extended from rigid perfectly plastic materials to work hardening materials by the nature of the limit formulation which is also robust with numerically stable convergence and highly efficient computing time

feedback control of combustion instabilities from within limit cycle oscillations using h loop shaping and the ν gap metric combustion instabilities arise owing to a two way coupling between acoustic waves and unsteady heat release oscillation amplitudes successively grow until nonlinear effects cause saturation into limit cycle oscillations feedback control in which an actuator modifies some combustor input in response to a sensor measurement can suppress combustion instabilities linear feedback controllers are typically designed using linear combustor models however when activated from within limit cycle the linear model is invalid and such controllers are not guaranteed to stabilize this work develops a feedback control strategy guaranteed to stabilize from within limit cycle oscillations a low order model of a simple combustor exhibiting the essential features of more complex systems is presented linear plane acoustic wave modelling is combined with a weakly nonlinear describing function for the flame the latter is determined numerically using a level set approach its implication is that the open loop transfer function oltf needed for controller design varies with oscillation level the difference between the mean and the rest of the oltfs is characterized using the gap metric providing the minimum required robustness margin for an formula see text loop shaping controller such controllers are designed and achieve stability both for linear fluctuations and from within limit cycle oscillations

a cell based smoothed finite element method for kinematic limit analysis this paper presents a new numerical procedure for kinematic limit analysis problems which incorporates the cell based smoothed finite element method with second order cone programming the application of a strain smoothing technique to the standard displacement finite element both rules out volumetric locking and also results in an efficient method that can provide accurate solutions with minimal computational effort the non smooth optimization problem is formulated as a problem of minimizing a sum of euclidean norms ensuring that the resulting optimization problem can be solved by an efficient second order cone programming algorithm plane stress and plane strain problems governed by the von mises criterion are considered but extensions to problems with other yield criteria having a similar conic quadratic form or 3d problems can be envisaged

a second order accurate linearized difference scheme for the two dimensional cahn hilliard equation the cahn hilliard equation is a nonlinear evolutionary equation that is of fourth order in space in this paper a linearized finite difference scheme is derived by the method of reduction of order it is proved that the scheme is uniquely solvable and convergent with the convergence rate of order two in a discrete l2 norm the coefficient matrix of the difference system is symmetric and positive definite so many well known iterative methods e g gauss seidel sor can be used to solve the system

quadratic b spline finite element method for numerical solution of the burgers equation abstract in this paper the one dimensional nonlinear burgers equation was converted to a set of nonlinear ordinary differential equations by the method of discretization in time and then each of them was solved by applying the quadratic b spline finite element method in order to show the efficiency of the presented method two problems were considered the numerical solutions obtained for various values of viscosity were compared with the exact solutions it is seen that the results obtained by this way are quite satisfactory

an efficient numerical scheme for burgers equation this paper applies the multiquadric mq as a spatial approximation scheme for solving the nonlinear burgers equation for comparison purposes a low order explicit finite difference approximation of the time derivative is employed by decreasing the time step of the computation it is shown that the major numerical error is from the time integration instead of the mq spatial approximation the numerical results indicate that this mq offers an excellent approximation for all possible values of reynolds number an adaptive algorithm is also developed to adjust the mq interpolation points to the peak of the shock wave which is shown to provide an improved numerical result numerical comparisons are made with most of the existing numerical schemes for solving the burgers equation

a numerical solution of burgers equation based on least squares approximation abstract burgers equation which is one dimensional non linear partial differential equation was converted to p non linear ordinary differential equations by using the method of discretization in time each of them was solved by the least squares method for various values of viscosity at different time steps the numerical solutions obtained were compared with the exact solutions it was seen that both of them were in excellent agreement while the exact solution was not available for viscosity smaller than 0 01 it was shown that mathematical structure of the equation for the obtained numerical solutions did not decay

the semi approximate approach for solving burgers equation with high reynolds number this paper presents the solution of burgers equation involving very high reynolds number re 5 we use semi implicit time difference scheme to reduce burgers equation to two point non linear ordinary differential equation and solved it by matched asymptotic expansion method

upper bound limit analysis using discontinuous velocity fields abstract a new method for computing rigorous upper bounds under plane strain conditions is described it is based on a linear three noded triangular element which has six unknown nodal velocities and a fixed number of unknown plastic multiplier rates and uses the kinematic theorem to define a kinematically admissible velocity field as the solution of a linear programming problem unlike existing formulations which permit only a limited number of velocity discontinuities whose directions of shearing must be specified a priori the new formulation permits velocity discontinuities at all edges shared by adjacent triangles and the directions of shearing are found automatically the variation of the velocity jump along each discontinuity is described by an additional set of four unknowns all of the unknowns are subject to the constraints imposed by an associated flow rule and the velocity boundary conditions the objective function corresponds to the dissipated power or some related load parameter of interest and is minimised to yield the desired upper bound since plastic deformation may occur not only in the discontinuities but also throughout the triangular elements as well the method is capable of modelling complex velocity fields accurately and typically produces tight upper bounds on the true limit load the formulation is applicable to materials whose strength is cohesive frictional purely cohesive and uniform or purely cohesive and linearly varying and thus quite general the new procedure is very efficient and always requires fewer elements than existing methods to obtain useful upper bound solutions moreover because of the extra degrees of freedom introduced by the discontinuities the linear elements no longer need to be arranged in a special pattern to model incompressible behaviour accurately

lower bound limit analysis by using the efg method and non linear programming intended to avoid the complicated computations of elasto plastic incremental analysis limit analysis is an appealing direct method for determining the load carrying capacity of structures on the basis of the static limit analysis theorem a solution procedure for lower bound limit analysis is presented firstly making use of the element free galerkin efg method rather than traditional numerical methods such as the finite element method and boundary element method the numerical implementation is very simple and convenient because it is only necessary to construct an array of nodes in the domain under consideration the reduced basis technique is adopted to solve the mathematical programming iteratively in a sequence of reduced self equilibrium stress subspaces with very low dimensions the self equilibrium stress field is expressed by a linear combination of several self equilibrium stress basis vectors with parameters to be determined these self equilibrium stress basis vectors are generated by performing an equilibrium iteration procedure during elasto plastic incremental analysis the complex method is used to solve these non linear programming sub problems and determine the maximal load amplifier numerical examples show that it is feasible and effective to solve the problems of limit analysis by using the efg method and non linear programming copyright 2007 john wiley sons ltd

a fully implicit finite difference scheme for two dimensional burgers equations the two dimensional burgers equations are discretized in fully implicit finite difference form this scheme leads to a system of nonlinear difference equations to be solved at each time step newton s method is used to solve this nonlinear system the linear system is solved by a direct method at each iteration of newton s method the accuracy of the proposed numerical scheme is examined by comparison with other analytical and numerical results the present method performs well

two dimensional elastoplasticity approximation by mixed finite elements two dimensional elastoplastic problems are used to assess the performance of a family of mixed finite elements in the non linear regime in particular four node bilinear quadrilateral elements that exhibit high accuracy in coarse meshes are used to simulate plane stress plane strain axisymmetric and shear deformable plate bending problems the excellent performance of these elements is demonstrated with a number of discriminating examples selected from the literature in addition agreement is observed in the limit load predicted by the axisymmetric solid and plate bending elements

a non linear programming method approach for upper bound limit analysis this paper presents a finite element model based on mathematical non linear programming in order to determine upper bounds of colapse loads of a mechanical structure the proposed formulation is derived within a kinematical approach framework employing two simultaneous and independent field approximations for the velocity and strain rate fields the augmented lagrangian is used to establish the compatibility between these two fields in this model only continuous velocity fields are used uzawa s minimization algorithm is applied to determine the optimal kinematical field that minimizes the difference between external and dissipated work rate the use of this technique allows to bypass the complexity of the non linear aspects of the problem since non linearity is addressed as a set of small local subproblems of optimization for each finite element the obtained model is quite versatile and suitable for solving a wide range of collapse problems this paper studies 3d strut and tie structures 2d plane strain stress and 3d solid problems copyright 2007 john wiley sons ltd

limit analysis of plates using the efg method and second order cone programming the meshless element free galerkin efg method is extended to allow computation of the limit load of plates a kinematic formulation that involves approximating the displacement field using the moving least squares technique is developed only one displacement variable is required for each efg node ensuring that the total number of variables in the resulting optimization problem is kept to a minimum with far fewer variables being required compared with finite element formulations using compatible elements a stabilized conforming nodal integration scheme is extended to plastic plate bending problems the evaluation of integrals at nodal points using curvature smoothing stabilization both keeps the size of the optimization problem small and also results in stable and accurate solutions difficulties imposing essential boundary conditions are overcome by enforcing displacements at the nodes directly the formulation can be expressed as the problem of minimizing a sum of euclidean norms subject to a set of equality constraints this non smooth minimization problem can be transformed into a form suitable for solution using second order cone programming the procedure is applied to several benchmark beam and plate problems and is found in practice to generate good upper bound solutions for benchmark problems

lower bound limit analysis by the symmetric galerkin boundary element method and the complex method abstract a solution procedure for lower bound limit analysis is presented making use of the symmetric galerkin boundary element method sgbem rather than of finite element method the self equilibrium stress fields are expressed by linear combination of several basic self equilibrium stress fields with parameters to be determined these basic self equilibrium stress fields are expressed as elastic responses of the body to imposed permanent strains obtained through elastic plastic incremental analysis the complex method is used to solve nonlinear programming and determine the maximal load amplifier the numerical results show that it is efficient and accurate to solve limit analysis problems by using the sgbem and the complex method

fourth order finite difference method for solving burgers equation abstract in this paper we present fourth order finite difference method for solving nonlinear one dimensional burgers equation this method is unconditionally stable the convergence analysis of the present method is studied and an upper bound for the error is derived numerical comparisons are made with most of the existing numerical methods for solving this equation

exact solutions to one dimensional acoustic fields with temperature gradient and mean flow an exact solution for one dimensional acoustic fields in ducts in the presence of an axial mean temperature gradient and mean flow is presented in this paper the analysis is valid for mean mach numbers such that the square of the mean mach number is much less than one the one dimensional wave equation for ducts with axial mean temperature gradient and mean flow is derived by appropriate transformations the wave equation is reduced to an analytically solvable hypergeometric differential equation for the case of a linear mean temperature profile the developed solution is applied to investigate the dependence of sound propagation in a duct on factors such as temperature gradient and mean flow the results obtained using the analytical solution compare very well with the numerical results the developed solution is also compared with an existing analytical solution

a numerical solution of burgers equation in this paper the burgers equation which is one dimensional quasi linear parabolic partial differential equation was solved by a variational method constructed on the method of discretization in time the numerical results obtained by these ways for various values of viscosity have been compared with the exact solution it was seen that they were in good agreement with each other

analytical and numerical investigation of strain hardening viscoplastic thick walled cylinders under internal pressure by using sequential limit analysis plastic limit load of strain hardening viscoplastic thick walled cylinders subjected to internal pressure is investigated numerically and analytically in the paper the paper applies sequential limit analysis to deal with the quasi static problem involving hardening material properties and weakening behavior corresponding to the strain rate sensitivity and widening deformation by sequential limit analysis the paper treats the plasticity problems as a sequence of limit analysis problems stated in the upper bound formulation rigorous upper bounds are acquired iteratively through a computational optimization procedure with the internal pressure factor as the objective function especially rigorous validation was conducted by numerical and analytical studies of thick walled cylinders in terms of the plastic limit load as well as the onset of instability it is found that the computed limit loads are rigorous upper bounds and agree very well with the analytical solutions 2007 elsevier b v all rights reserved

investigation of rotating hollow cylinders of strain hardening viscoplastic materials by sequential limit analysis the paper employs sequential limit analysis to investigate rotating hollow cylinders of nonlinear isotropic strain hardening viscoplastic materials a computational optimization procedure was developed to account for hardening material properties and weakening behavior corresponding to the strain rate sensitivity and widening deformation a sequence of limit analysis problems was then conducted to seek the corresponding plastic limit angular velocities sequentially by a general algorithm incorporated with an inner and outer iterative sequence particularly analytical solutions of plastic limit angular velocities and the onset of instability were derived for rigorous comparisons the corresponding stability condition was also obtained explicitly specifically the implicit form of the onset of instability was solved by the fixed point iteration it is found that the computed limit angular velocities are rigorous upper bounds and match well with analytical solutions

computing limit loads by minimizing a sum of norms this paper treats the problem of computing the collapse state in limit analysis for a solid with a quadratic yield condition such as for example the von mises condition after discretization with the finite element method using divergence free elements for the plastic flow the kinematic formulation reduces to the problem of minimizing a sum of euclidean vector norms subject to a single linear constraint this is a nonsmooth minimization problem since many of the norms in the sum may vanish at the optimal point recently an efficient solution algorithm has been developed for this particular convex optimization problem in large sparse form the approach is applied to test problems in limit analysis in two different plane models plane strain and plates in the first case more than 80 of the terms in the objective function are zero in the optimal solution causing extreme ill conditioning in the second case all terms are nonzero in both cases the method works very well and problems are solved which are larger by at least an order of magnitude than previously reported the relative accuracy for the solution of the discrete problems measured by duality gap and feasibility is typically of the order 10 8

automatic mesh refinement in limit analysis a strategy for automatic mesh refinement in limit analysis is combined with a recently developed computational method in the absence of estimates of the local error the strategy can be based on the deformations and on slack in the yield condition the approach is tested on standard problems in plane strain including the classical punch problem very accurate results are obtained with the use of moderate computational power

convergence analysis and validation of sequential limit analysis of plane strain problems of the von mises model with non linear isotropic hardening the paper presents sequential limit analysis of plane strain problems of the von mises model with non linear isotropic hardening by using a general algorithm the general algorithm is a combined smoothing and successive approximation cssa method in the paper emphasis is placed on its convergence analysis and validation applied to sequential limit analysis involving materials with isotropic hardening by sequential limit analysis the paper treats deforming problems as a sequence of limit analysis problems stated in the upper bound formulation especially the cssa algorithm was proved to be unconditionally convergent by utilizing the cauchy schwarz inequality finally rigorous validation was conducted by numerical and analytical studies of a thick walled cylinder under pressure it is found that the computed limit loads are rigorous upper bounds and agree very well with the analytical solutions copyright 2005 john wiley sons ltd

a mixed finite difference and boundary element approach to one dimensional burgers equation this paper presents a mixed method for the numerical solution of the one dimensional burgers equation this method uses mixed boundary elements in association with finite differences two standard problems are used to validated the algorithm comparisons are made with some of the existing numerical schemes and analytical solutions the proposed method performs well

a finite difference approach for solution of burgers equation abstract in this paper we have applied restrictive pade approximation classical implicit finite difference method to the burgers equation with a set of initial and boundary conditions to obtain its numerical solution the stability region and truncation error of the new method are discussed the accuracy of the proposed method is demonstrated by the two test problems the numerical results obtained by this method for various values of viscosity have been compared with the exact solution to show the efficiency of the method the numerical results are found in good agreement with the exact solutions

exact solution for one dimensional acoustic fields in ducts with a quadratic mean temperature profile the purpose of this letter is to present an exact analytical solution for sound propagation in ducts with a quadratic mean temperature profile using appropriate transformations the one dimensional wave equation for ducts with an axial mean temperature gradient was reduced to the hypergeometric differential equation whose solution can be expressed in terms of hypergeometric functions the analysis neglects the effects of mean flow and is therefore valid only for small mean mach numbers

a polytree based adaptive approach to limit analysis of cracked structures abstract we in this paper present a novel adaptive finite element scheme for limit analysis of cracked structures the key idea is to develop a general refinement algorithm based on a so called polytree mesh structure the method is well suited for arbitrary polygonal elements and furthermore traditional triangular and quadrilateral ones which are considered as special cases also polytree meshes are conforming and can be regarded as a generalization of quadtree meshes for the aim of this paper we restrict our main interest in plane strain limit analysis to von mises type materials yet its extension to a wide class of other solid mechanics problems and materials is completely possible to avoid volumetric locking we propose an approximate velocity field enriched with bubble functions using wachspress coordinates on a primal mesh and design carefully strain rates on a dual mesh level an adaptive mesh refinement process is guided by an l 2 norm based indicator of strain rates through numerical validations we show that the present method reaches high accuracy with low computational cost this allows us to perform large scale limit analysis problems favorably

on generalized ho der inequality inequality may apply to general paired non euclidean norms we restrict the discussion to finite dimensional spaces a theorem is established for such generalized holder inequality together with its sharpness condition the new sharpness condition involves the gradient of the norm function the previous inequalities of this type and their associated sharpness conditions become special cases of this new inequality which is a fundamental primal dual relation of two spaces defined by paired norms on their respective elements given an arbitrarily defined primal norm in one space a method is presented for constructing the dual norm in the other the generalized holder inequality is the basis for many known minimax duality theorems in applied fields particular examples of this duality are found in mathematical models of plastic behavior inequalities appear frequently in algebra geometry and analysis this form of mathematical statements is so prevalent that it is difficult to state their relevance and applications exhaustively inequalities are used to demarcate numbers vectors matrices and functions e g to be positive definite to define sets norm measures convexity of sets and functions to compare and bound functions with another function just to name a few there are books devoted exclusively to inequalities 11 a class of inequalities concerning inner products of vectors and functions can be grouped into two frequently encountered ones in literature although one is a special case of the other the schwarz inequality applies to the euclidean and hilbert spaces 2 the holder inequality extends the concept to certain non euclidean and non hilbert spaces associated with a specific family of norm measures defined by minkowski 3 we shall restrict our discussion to finite dimensional spaces a further extension of the holder inequality is presented in this paper for general paired non euclidean spaces the familiar schwarz inequality for the euclidean space r can be stated for the inner product

an artificial boundary method for the hull white model of american interest rate derivatives abstract the hull white hw model is a widely used one factor interest rate model because of its analytical tractability on liquidly traded derivatives super calibration ability to the initial term structure and elegant tree building procedure as an explicit finite difference scheme lattice method is subject to some stability criteria which may deteriorate the computational efficiency for early exercisable derivatives this paper proposes an artificial boundary method based on the partial differential equations pdes to price interest rate derivatives with early exercise american feature under the hw model we construct conversion factors to extract the market information from the zero coupon curve and then reduce the infinite computational domain into a finite one by using an artificial boundary on which an exact boundary condition is derived we then develop an implicit scheme with unconditional stability to solve the pde in the reduced bounded domain with a finite computational domain the optimal exercise strategy can be determined efficiently our numerical examples show that the proposed scheme is accurate robust to the truncation size and more efficient than the popular lattice method for accurate derivative prices in addition the singularity separating technique is incorporated into the artificial boundary method to enhance accuracy and flexibility of the numerical scheme

a class of mixed assumed strain methods and the method of incompatible modes a three field mixed formulation in terms of displacements stresses and an enhanced strain field is presented which encompasses as a particular case the classical method of incompatible modes within this frame work incompatible elements arise as particular compatible mixed approximations of the enhanced strain field the conditions that the stress interpolation contain piece wise constant functions and be l2 ortho gonal to the enhanced strain interpolation ensure satisfaction of the patch test and allow the elimination of the stress field from the formulation the preceding conditions are formulated in a form particularly convenient for element design as an illustration of the methodology three new elements are developed and shown to exhibit good performance a plane 3d elastic plastic quad an axisymmetric element and a thick plate bending quad the formulation described herein is suitable for non linear analysis

locking free discontinuous finite elements for the upper bound yield design of thick plates summary this work investigates the formulation of finite elements dedicated to the upper bound kinematic approach of yield design or limit analysis of reissner mindlin thick plates in shear bending interaction the main novelty of this paper is to take full advantage of the fundamental difference between limit analysis and elasticity problems as regards the class of admissible virtual velocity fields in particular it has been demonstrated for 2d plane stress plane strain or 3d limit analysis problems that the use of discontinuous velocity fields presents a lot of advantages when seeking for accurate upper bound estimates for this reason discontinuous interpolations of the transverse velocity and the rotation fields for reissner mindlin plates are proposed the subsequent discrete minimization problem is formulated as a second order cone programming problem and is solved using the industrial software package mosek a comprehensive study of the shear locking phenomenon is also conducted and it is shown that discontinuous elements avoid such a phenomenon quite naturally whereas continuous elements cannot without any specific treatment this particular aspect is confirmed through numerical examples on classical benchmark problems and the so obtained upper bound estimates are confronted to recently developed lower bound equilibrium finite elements for thick plates copyright 2015 john wiley sons ltd

a difference scheme for burgers equation in an unbounded domain the numerical solution of the one dimensional burgers equation in an unbounded domain is considered two artificial boundaries are introduced to make the computational domain finite on both artificial boundaries two exact boundary conditions are proposed respectively to reduce the original problem to an initial boundary value problem in a finite computational domain a difference scheme is constructed by the method of reduction of order to solve the problem in the finite computational domain at each time level only a strictly diagonal dominated tridiagonal system of linear algebraic equations needs to be solved it is proved that the difference scheme is uniquely solvable and unconditional convergent with the convergence order 3 2 in time and order 2 in space in an energy norm a numerical example demonstrates the theoretical results

method to determine cutoff frequencies for acoustic waves propagating in nonisothermal media a method to determine cutoff frequencies for linear acoustic waves propagating in nonisothermal media is introduced the developed method is based on wave variable transformations that lead to klein gordon equations and the oscillation theorem is applied to obtain the turning point frequencies physical arguments are used to justify the choice of the largest turning point frequency as the cutoff frequency the method is used to derive the cutoff frequencies in nonisothermal media modeled by exponential and power law temperature gradients for which the cutoffs cannot be obtained based on known analytical solutions an interesting result is that the acoustic cutoff frequencies calculated by the method are local quantities that vary in the media and that their specific values at a given height determine the frequency that acoustic waves must have in order to be propagating at this height to extend this physical interpretation of the acoustic cutoff frequency to nonisothermal media of arbitrary temperature gradients a generalized version of the method applicable to these media is also presented

duality theorem for a generalized fermat weber problem the classical fermat weber problem is to minimize the sum of the distances from a point in a plane tok given points in the plane this problem was generalized by witzgall ton dimensional space and to allow for a general norm not necessarily symmetric he found a dual for this problem the authors generalize this result further by proving a duality theorem which includes as special cases a great variety of choices of norms in the terms of the fermat weber sum the theorem is proved by applying a general duality theorem of rockafellar as applications a dual is found for the multi facility location problem and a nonlinear dual is obtained for a linear programming problem with a priori bounds for the variables when the norms concerned are continuously differentiable formulas are obtained for retrieving the solution for each primal problem from the solution of its dual

limit analysis of orthotropic structures based on hill s yield condition abstract the limit analysis problem which permits the direct computation of the limit load of rigid perfectly plastic solids and structures is considered with reference to anisotropic materials as a starting step attention is focused on hill s orthotropic condition for which an explicit expression of the dissipation power in terms of strain rates is established on this basis numerical procedures successfully employed in the isotropic von mises case can be used in this context as some examples illustrate

a numerical method for plastic limit analysis of 3 d structures abstract based on the upper bound theorem of plasticity the 3 d limit analysis of rigid perfectly plastic structures is formulated as a discrete nonlinear mathematical programming problem with only equality constraints by means of the finite element technique the penalty function method is used to deal with the plastic incompressibility condition a direct iterative algorithm is employed in solving this formulation at each step of the iteration the rigid and plastic zones are continually distinguished the respective constraint conditions are imposed on them and the goal function is modified appropriately the numerical difficulties caused by the nonlinearity and nonsmoothness of the goal function and the incompressibility of plastic deformation are overcome the limit load multiplier and the associated velocity field computed by the iteration procedure converge monotonically to the upper bounds of real solutions the numerical procedure has been used to carry out the limit analysis for cylindrical shells with part through slot type defects under internal pressure numerical examples are given to demonstrate the applicability of the procedure

large deformation of structures by sequential limit analysis although most structures are designed to function under small deformation their large deformation behavior can be used to estimate reliability and safety for survivorship from an accident or a natural disaster structures such as buildings bridges ships vehicles and machinery are designed with a safety factor to protect certain assets from the unexpected and unknot elements the large deformation analysis provides the rational basis for a safety factor in this paper the method of sequential limit analysis is used to compute large deformation solutions of truss and frame problems differing from the incremental method of plasticity the limit analysis method is numerically stable more effecient and requires simpler input data a duality theorem serves as the foundation of an algorithm for computing the complete static and kinematic solutions sim uhaneously and for establishing their accuracy in each step of a deformation sequence the phenom ena encountered in large deformation such as loading unloading under monotone deformation bifurcation more generally loss of uniqueness of solutions and internal contact of structural members are revealed by the sequential limit analysis presented in this paper

an mpec approach for the critical post collapse behavior of rigid plastic structures this paper presents a numerical method to identify and trace the critical post collapse response of rigid perfectly plastic structures to account for the possibility of multiple equilibrium paths the critical one is directly identified using the minimum 2nd order work criterion our proposed enhanced sequential limit analysis is formulated as an instance of the challenging class of optimization problems known as a mathematical program with equilibrium constraints mpec this mpec formulation minimizes the 2nd order work expression subject to the set of constraints describing the complete complementarity system in mixed static kinematic variables governing simultaneously the two adjacent equilibrium configurations namely the current one and its neighboring state we use a nonlinear programming based algorithm involving relaxation of the complementarity terms to solve the mpec four numerical examples are provided to illustrate application of the proposed scheme

a numerical method based on crank nicolson scheme for burgers equation abstract in this paper we present a solution based on crank nicolson finite difference method for one dimensional burgers equation burgers equation arises frequently in mathematical modeling of problems in fluid dynamics hopf cole transformation e hopf the partial differential equation u t uu x u xx commun pure appl math 3 1950 201 230 j d cole on a quasilinear parabolic equation occurring in aerodynamics quart appl math 9 1951 225 236 is used to linearize burgers equation the resulting heat equation is discretized by using crank nicolson finite difference scheme this method is shown to be unconditionally stable and second order accurate in space and time numerical results obtained by the present method have been compared with exact solution for different values of reynolds number

the one dimensional acoustic field in a duct with arbitrary mean axial temperature gradient and mean flow abstract this paper presents an analytical solution for the one dimensional acoustic field in a duct with arbitrary mean temperature gradient and mean flow a wave equation for the pressure perturbation is derived which relies on very few assumptions an analytical solution for this is derived using an adapted wkb approximation the solution is a superposition of waves travelling in either direction and thus provides physical insight it is also very easy to calculate the proposed solution is applied to ducts with a mean temperature profile which varies axially with i a linear and ii a partial sine wave profile predictions are compared to those obtained by numerically solving the linearised euler equations lees the analytical solution reproduces the acoustic field very accurately across a wide range of flow conditions which span both low and moderate to high subsonic mach numbers it always performs well when the frequency exceeds a certain value when the mean temperature profile is linear it also performs well to very low frequencies this increased frequency range for linear mean temperature profiles leads to its application to more complicated profiles in a piecewise linear manner axially segmenting the temperature profile into regions that can be approximated as linear the acoustic field is predicted very accurately as long as enough segmentation points are used and the condition for the linear mean temperature profile is satisfied k 0 where k0 is the local wave number when there is no mean flow and is the normalised mean density gradient the proposed solution is extensively compared to previous analytical solutions and is found to be more accurate and reliable especially at higher mach numbers the entropy wave generated by communication between the acoustic waves and the distributed mean temperature zone is calculated using the lees it is found to remain very small across all operating conditions such that both the entropy wave and its impact on the acoustic field can be neglected

an edge based finite element method es fem with adaptive scaled bubble functions for plane strain limit analysis abstract this paper deals with critical roles of cubic bubble functions for the edge based finite element method es fem formulation within the framework of the kinematic theorem for predicting the plastic collapse loads of structures we show that the bubble function can be scaled by a non zero coefficient alpha while the volumetric locking is entirely eliminated based on this finding the present method is designed in a very small value with a bubble function that is maximum at the center of the element this can lead to the loss of the partition of unity for easy reference the present method is termed as bes fem the significant advantage of the present method lies in the rigorous treatment of the volumetric locking free that can occur in the fully plastic range the bes fem works well with high efficiency by using triangular meshes it achieves both simplicity and computational efficiency for implementation into packages of plastic limit analyses in case of bes fem the locking issue can be solved conveniently by two schemes 1 the usual piecewise linear displacements enriched with a cubic bubble function on a primal mesh of triangular elements and 2 a projection operator of strain rates through a dual mesh associated with the edges in the mesh the optimization formulation of finite element limit analysis is written in the form of a second order cone programming socp the well established interior point solvers can be exploited efficiently the bes fem using a small number of integration points enables to solve the large scale optimization problems efficiently in addition an adaptive meshing procedure based on an alternative indicator of dissipation is also derived to further enhance the quality of the solution without increasing significantly the number of degrees of freedom of the model numerical results show the robustness of the proposed method

generalized gradients of lipschitz functionals abstract the purpose of this article is threefold i to present in a unified fashion the theory of generalized gradients whose elements are at present scattered in various sources ii to give an account of the ways in which the theory has been applied iii to prove new results concerning generalized gradients of summation functionals pointwise maxima and integral functionals on subspaces of l these last mentioned formulas are obtained with an eye to future applications in the calculus of variations and optimal control their proofs can be regarded as applications of the existing theory of subgradients of convex functionals as developed by rockafellar ioffe and levin valadier and others

an iterative algorithm for limit analysis with nonlinear yield functions abstract a mathematical programming algorithm is proposed for the general limit analysis problem plastic behavior is described by a set of linear or nonlinear yield functions abstract formulations of limit analysis are first considered and a quasi newton strategy for solving the optimality conditions is then sketched the structure of the problem arising from a finite element discretization is taken into account in order that the algorithm should be able to solve large scale problems

a family of exact transient solutions for acoustic wave propagation in inhomogeneous non uniform area ducts abstract this paper presents a family of exact solutions for quasi one dimensional transient acoustic wave propagation in ducts with mean temperature and area variations in the absence of mean flow these solutions are obtained using a transformation of the spatial and acoustic variables in a manner suggested by the wkb approximation exact travelling wave type solutions are obtained for a class of temperature and area profiles these solutions differ from the classical travelling wave solution however in that the acoustic pressure and velocity are not algebraically related by the local value of the acoustic impedance x c x although these solutions resemble the approximate high frequency wkb form of solution of the wave equation they have the interesting property that they are exact regardless of the scale of the acoustic disturbance relative to that of the inhomogeneity

a direct complementarity approach for the elastoplastic analysis of plane stress and plane strain structures this paper presents a direct complementarity approach for carrying out the elastoplastic analysis of plane stress and plane strain structures founded on a traditional finite step formulation our approach however avoids the typically cumbersome implementation of iterative predictorcorrector procedures associated with the ubiquitous return mapping algorithm instead at each predefined step the governing formulationcast in its most natural mathematical programming format known as a mixed complementarity problemis directly solved by using a complementarity solver run from within a mathematical modeling system we have chosen the industry standard general algebraic modeling system path mixed complementarity problem solver that is called from within the general algebraic modeling system environment we consider both von mises and tresca materials with perfect or hardening kinematic and isotropic behaviors our numerical tests five benchmark examples of which are presented in this paper have been carried out using models constructed from the mixed finite element of capsoni and corradi comput methods appl mech eng 1997 141 6793 which beneficially offers a locking free behavior and coarse mesh accuracy the results indicate in addition to an isochoric locking free behavior good accuracy and the ability to circumvent the difficult singularity problem associated with the corners of tresca yield surfaces

application of the heun functions to rotor vibratory gyroscope their numerical computation and accuracy estimation abstract for an asymmetric rotor vibratory gyroscope that is oscillating in an elastic suspension means the equation of motion is derived from the eurler lagrange equation and the exact solution is obtained as heun functions hfs a fast and effective method for calculating heun functions by direct calculation of solutions of the heun differential equation hde using standard numerical integration methods is developed three methods of accuracy check are employed in this case the accuracy of the numerical solutions deteriorated in the vicinity of the singularity to overcome this difficulty an optimised method for calculating the hfs is developed which give a uniform accuracy of the calculated values on the interval the optimised method for calculating the numerical hfs by means of the solution of the governing initial value problem gave acceptable accuracy in modelling the behaviour of an asymmetric rotor gyroscope

the influence of a liquid flow on sound fields confined by conical walls abstract sound propagation in conical waveguides is analyzed for the case where a background flow is maintained through the cone and points along the radial co ordinate r only a general expression for the acoustic pressure is derived and the perturbations of the acoustic field accommodated by the presence of a background flow are found by use of the green function method in the second part of this paper flow measurement properties are discussed the designation of propagation constants such as the wave number and phase speed lose much of their intuitive meaning in a conical waveguide instead the so called pseudo guide wave number and pseudo phase speed are introduced as they are well defined in the cone case and simplifies to the wave number and phase speed in the cylinder case respectively it is shown that changes due to a background flow in pseudo guide wave number pseudo phase speed and zero point crossing times all exhibit an oscillatory behavior as a function of the r co ordinate this is in contrast to the case of a cylinder where such changes become a linear function of the distance from the transmitter the oscillatory behavior in the changes in zero point crossing times as a function of r does not hamper flow measurement in the cone case since the only requirement to be fulfilled is in principle that a one to one correspondence between measured output changes in zero point crossing times and actual flow determined by v 0 at a specific receiver location exists it is shown that this requirement is fulfilled as changes in zero point crossing times depend linearly on the flow coefficient v 0 at a given r co ordinate there are however certain discrete r co ordinate values where this is not the case namely those where changes in zero point crossing times become zero for any value of v 0 in other words if the receiver is positioned near r co ordinates where zero point crossing times are at a maximum or a minimum for a given value of v 0 the truncated cone flow meter sensor is able to measure flow unambiguiosly by detection of changes in zero point crossing times induced by a background flow

a new high accuracy two level implicit off step discretization for the system of two space dimensional quasi linear parabolic partial differential equations abstract in this article we propose a two level compact implicit off step discretization for the solution of the system of 2d quasi linear parabolic partial differential equations subject to suitable initial and boundary conditions new methods for the estimates of first order space derivatives of the solution are also derived these methods are fourth order accurate in space and second order accurate in time and involve only nine spatial grid points of a single compact cell we further develop the alternating direction implicit adi scheme for a general linear parabolic equation which is shown to be unconditionally stable for the heat equation in polar coordinates the proposed methods are directly applicable to singular problems without the need of any special technique which is the main advantage of this work the method is effectively applied to the time dependent navier stokes model equations in polar coordinates numerical examples are provided to illustrate the accuracy of the methods

numerical solutions for fractional kdv burgers equation by adomian decomposition method abstract based on the symbolic computation system maple adomian decomposition method developed for differential equations of integer order is directly extended to derive explicit and numerical solutions of the fractional kdv burgers equation the fractional derivatives are described in the caputo sense according to my knowledge this paper represents the first available numerical solutions of the nonlinear fractional kdv burgers equation with time and space fractional derivatives finally the solutions of our model equation are calculated in the form of convergent series with easily computable components