bluuebunny/crossref_metadata_2025 huggingface dataset:
Numerical prediction of separated flows
Authors: Atkins D. J. , Maskell S. J. , Patrick M. A.
Published: August 2005

Upwind and central difference schemes for laminar and turbulent flows over a step in a two‐dimensional channel are compared with each other and with experiment. Vorticity ω and stream function ψ are used as dependent variables and it is shown that an upwind difference method can give predictions which agree with experiment for high Reynolds number flows. The numerical implementation of the boundary conditions is found critically to determine the solutions obtained. Explicit prescription of ψ and ω at the inlet leads to incorrect values of the inlet velocity component perpendicular to the flow and a solution that does not agree with experiment. Experimental evidence is not available at low Reynolds numbers, but it is found that upwind differences give recirculation zones 8 per cent shorter and 8 per cent less intense than the more conventional conditionally stable central difference method.

The distribution of the false diffusion effect in the upwind scheme is considered, and it is shown by use of a simple example that previous statements as to possible minimization of this effect are not generally true.

The difficulty of determining the pressure distribution from the vorticity and stream function model is analysed and illustrated.

Further, turbulent separated flows are seen to contain regions where two‐dimensional time‐dependent flow does not exist, and conventional theories do not give good results.
The global element method for stationary advective problems
Authors: Haj A. , Phillips C. , Delves L. M.
Published: August 2005

We extend the variation principle used in the global element method for self‐adjoint elliptic problems1, to problems containing advective terms. Used with the global element formalism, the extended principle yields a uniform framework for treating advective or boundary layer problems, with the attractive feature that the implicit treatment of interface conditions between elements yields an effective decoupling between ‘boundary layer’ and ‘interior’ parts of the solution. As a numerical example, we solve the one‐dimensional model problem of Christie and Mitchell3, obtaining high accuracy for Peclet numbers up to 106 with no sign of instability. These results suggest that, given a suitable choice of global elements, the decoupling is very effective in damping the oscillations found in standard finite difference or finite element treatment.
Primitive variable finite element formulations for steady viscous flows
Authors: Hutton S. G. , Exeter M. K. , Fussey D. E. , Webster J. J. , Rigon C.
Published: August 2005

The solution of incompressible, viscous flow problems using the primitive variable finite element approach is formulated in a coherent and physically reasoned exposition. In particular, it is shown that terms associated with changes in momentum caused by lack of mass conservation should logically be included in the governing equations. Previous formulations have not considered this possibility. Numerical results are presented to show the effect of inclusion of these extra terms; however, it is concluded from the numerical results for the specific case which was tested that there is no obvious benefit obtained by including these terms.
Response of Coastal harbours
Authors: Mattioli Franco , Tinti Stefano
Published: August 2005

A numerical method able to evaluate the response of harbours of constant depth to periodic plane waves in the presence headlands of breakwaters near the harbour mouth is described and tested on a particular case.

The method, based on Green's function theory, is rather general, and can also treat the response of an off‐shore harbour, as well as the diffraction field due to only breakwaters or headlands, when the interaction with the coastline must be taken into account.
Stability analysis of plates by a complementary energy method
Authors: Sundararajan C.
Published: August 2005

A complementary energy method for the stability analysis of plates is presented. Buckling loads of rectangular plates with different boundary conditions are obtained, and the convergence of the solution is studied.
The w‐plane finite element method for the solution of scalar field problems in two dimensions
Authors: Nath B. , Jamshidi J.
Published: August 2005

A simple, efficient finite element method has been presented for the solution of a variety of scalar field problems in two dimensions. It is based on the mapping of the physical problem domain into an ‘image’ domain in the w‐plane. The governing equation(s) and the boundary conditions in the physical plane are also appropriately transformed into the w‐plane. The processes of standard finite element analysis are then implemented to obtain a solution in the w‐plane.

The method has been explained in detail, with illustrative examples where appropriate; it has several important advantages over the standard finite element method, particularly for the solution of infinite or semi‐infinite domain problems. The method has been demonstrated to be simple, efficient, economical and potentially capable of dealing with a large repartoire of two‐dimensional problems, including non‐homogeneity, nonlinearity, etc.
Finite element applications of viscoplasticity with singular yield surfaces
Authors: Mroz Z. , Sharma K. G.
Published: August 2005

The side and corner flow rules for viscoplastic materials with singular yield surfaces are discussed and applied in numerical solution of several boundary‐value problems. The differences in predictions of displacement and stress fields for different flow rules are demonstrated.
A numerical method for solving two‐point boundary value problems for nonlinear ordinary differential equations
Authors: Tewarson R. P.
Published: August 2005

A numerical method for solving two‐point boundary value problems associated with systems of first‐order nonlinear ordinary differential equations is described. It needs four function evaluations at each point and is of order h6, where h is the space chop. Results of computational experiments, which include perturbation of the initial conditions, comparing this method with other known methods are given.
On the use of central difference scheme for Navier–Strokes equations
Authors: Gupta Murli M. , Manohar Ram P.
Published: August 2005

Both the central and upwind difference schemes are commonaly employed to solve the Navier‐Stokes equations governing the two‐dimensional laminar flow of an incompressible laminar flow of an incompressible viscous fluid. By a judicious choice of a damping parameter and using direct methods for solving the systems of linear equations appearing in an iterative procedure, the central difference scheme could be made to give convergent results even for large Reynolds numbers. Using a model problem of flow through a driven square cavity it is shown that the converged results so obtained become progressively oscillatory and inaccurate as the Reynolds number increases. It is known that the central difference scheme gives more accurate results than the upwind difference scheme, at least for small values of Reynolds number. However, for a reasonably small mesh size the numerical solutions obtained by using either the central or the upwind difference scheme do not differ appreciably at low Reynolds numbers. There is a small range of Reynolds numbers for which the central difference scheme may yield more accurate results than the upwind difference scheme; however, this range is not known a priori.
Reduction of the error in eccentric beam modelling
Authors: Miller Robert E.
Published: August 2005

The usual linear shape function for approximating axial displacement in beam finite elements used as eccentric stiffeners leads to an inconsistency which can result in large errors in the deflection of plates or composite beams. The introduction of an additional degree‐of‐freedom for these elements circumvents this problem.
A method for incorporating free boundaries with surface tension in finite element fluid‐flow simulators
Authors: Ruschak Kenneth J.
Published: August 2005

A boundary‐location method is developed for finite element simulation of steady, two‐dimensional flows of Newtonian liquid with free boundaries. In the method, boundary shape and position and the velocity and pressure fields are determined simultaneously. Inertial, viscous, gravitational, and surface tension effects are included in the development. The complete set of nonlinear finite element equations is solved by a modified frontal method combined with Newton‐Raphson iteration to speed convergence. The finite element used to illustrate the method approximates the pressure as a piecewise constant function and the velocity and free boundaries as piecewise linear functions. Example calculations for flow from a slit show that the method can be effective.
A modified plasticity theory for porous metals
Authors: Gadala M. S. , Mullins M. L. , Dokainish M. A.
Published: August 2005

A plasticity theory for porous metals is proposed. A simple model of a porous materials is analysed by the finite element method. Small strain elastic–plastic analysis provides stress–strain curves, yield stressed and incremental plastic strain vectors for different void ratios. An assessment is made of an existing yield criterion for porous metals. A modified yield criterion and plastic potential function and, consequently, different plasticity equations are given. Reasonable agreement is obtained between the present numerical results and previous results in the literature.
An economical storage organization for large and small finite element systems with reference to the application of iterative approximation methods to nonlinear material behaviour
Authors: Fengels W. , Troost A.
Published: August 2005

The method of data transfer from the peripheral storage unit to the central processor unit, when dealing with large solution systems, is of greater importance, as each access of peripheral stored data interrupts the active flow of arithmetic operation in the central processor core. When solving a large number of symmetrical positive‐definite equations this generally leads to difficulties in channel interaction and priority, possibly even to the breakdown of the computer system or to uneconomical computing times. The problem increases when considering the iterative approximation of nonlinear problems; further still, when using the frontal solution method. It will be shown that this difficulty can be avoided by inserting two different types of buffers—a micro‐buffer and a macro‐buffer—into the data transfer between the central memory and an arbitrary peripheral storage unit. This method should primarily be used in those finite element (FE) programs which are based on the ‘slow’ BACKSPACE‐READ‐BACKSPACE commands, but even in the case of peripheral storage units such as magnetic discs (random access) or magnetic tape machines (working in one or two directions) the computing time and channel control can successfully be improved. A second achievement of this procedure is the possibility of applying a FE program economically, not only to large element systems and elements of a ‘higher order’ but also with good results for small element systems, e.g. when investigating nonlinear material behaviour with simple element types and geometrical structure. Another purpose of this text is to recommend the FORTRAN subroutine in the Appendix, whose novel features make it a useful supplement to ‘nonlinear’ FE programs.
Techniques for developing ‘special’ finite element shape functions with particular reference to singularities
Authors: Hughes Thomas J. R. , Akin J. E.
Published: August 2005

A concise and efficient algorithm is presented for deriving finite element shape functions from an arbitrary set of independent functions. Based on special one‐dimensional interpolatory schemes derived via the algorithm, a variety of two‐ and three‐dimensional interpolatory schemes are developed which are useful for modelling singular behaviour. The methodology presented is general and may be fruitfully applied to the development of ‘special’ finite element shape functions for a variety of other situations.
Transition finite elements for three‐dimensional stress analysis
Authors: Surana Karan S.
Published: August 2005

This paper presents isoparametric formulation for the three‐dimensional transition finite elements. The transition finite elements are necessary for applications requiring the use of three‐dimensional isoparametric solid elements and the curved shell elements. These elements provide proper connections between the two portions of the structure modelled with three‐dimensional solids and the curved shell elements. The element properties are derived and presented in detail. Numerical examples are also presented to demonstrate the accuracy and the applications of such elements in three‐dimensional stress analysis.
The synthesis of near‐optimum finite element meshes with interactive computer graphics
Authors: Shephard Mark S. , Gallagher Richard H. , Abel John F.
Published: August 2005

A new approach to the generation of near‐optimum finite element meshes is presented. Like other current methods, the procedure presented uses the results of a previous analysis to improve the idealization, but unlike other procedures a new element mesh is generated in each cycle with the aid of interactive computer graphics. The procedure generates near‐optimum two‐dimensional meshes on one cycle employing a grid optimization criterion based on variations in the strain energy density and using a software system which operates like an interactive finite element preprocessor. The example problems presented demonstrate the efficiency and flexibility of the approach.
Modification of iterative processes for improved convergence characteristics
Authors: Lawther R.
Published: August 2005

A method for improving the convergence rate of iterative processes is presented. This method monitors the sequence of approximations produced by an iterative process, and generates a new iterative process, or sequence of processes, each with more rapid convergence characteristics than the previous one. This method of process modification can be applied to many iterative techniques currently in use. Examples of application of the method are given, using both nonlinear and linear systems. In one of these examples it is shown that the method can be applied to a divergent iterative process, producing a convergent one. It is also shown how the technique can be applied to equations of one variable, yielding a method with convergence characteristics similar to those of Newton's method, but without the explicit calculation of derivatives.
An application of Keller's method to the solution of an eighth‐order nonlinear boundary value problem
Authors: Balu R.
Published: August 2005

An efficient implicit finite difference method, called the Keller's box scheme, is applied to solve an eighth‐order nonlinear two‐point boundary value problem. The example considered here is the compressible boundary layer equations at a general three‐dimensional stagnation point. The solutions obtained are compared with results from other methods and the potential advantages of the method are demonstrated.
Nonlinear analysis of liquid motion in a container subjected to forced pitching oscillation
Authors: Nakayama Tsukasa , Washizu Kyuichiro
Published: August 2005

A nonlinear analysis is carried out for the motion of the inviscid, incompressible fluid in a two‐dimensional, rigid, open container which is subjected to forced sinusoidal pitching oscillation. Firstly, the problem is defined as a nonlinear initial‐boundary value problem by the use of a governing differential equation and boundary conditions. Next, the problem is formulated in the form of a pseudo‐variational principle, which provides a basis for our discretization. The finite element method and finite difference method are used spacewise and timewise, respectively. Due to the strong nonlinearity of the problem, an incremental method is used for the numerical analysis. Numerical results obtained by the present method are compared with solutions of the linear theory and experimental data. The difference between linear and nonlinear analysis has been clearly indicated.
Numerical analysis of the steady‐state behaviour of a MOS field effect transistor
Authors: Akers Lex A. , Portnoy William M.
Published: August 2005

A numerical scheme is developed to simulate the non‐isothermal steady‐state behaviour of a MOS field effect transistor. In a desire to develop a fast, stable numerical scheme, physical instabilities were eliminated by using a simplified device model. The numerical technique developed permits a computer solution of the majority carrier transport equation, the nonlinear heat conduction equation, in which the heat generation term is obtained from the solution of the transport equation, and a number of auxiliary differential equations.

The simplified model of the MOS transistor adopted will not, of course, produce any information on the actual operation of the short channel MOS transistor of practical interest today, but the numerical scheme can be extended to simulate short channel models that are of great practical interest.
A Serendipity cubic‐displacement hybrid‐stress element for thin and moderately thick plates
Authors: Spilker Robert L. , Munir Nasir I.
Published: August 2005

A hybrid‐stress element is developed for the analysis of thin and moderately thick plates. The independent transverse displacement and rotations are interpolated by the 12‐node cubic Serendipity shape functions. All components of stress are included and 36β stress assumption is used. The element stiffness possesses correct rank and numerical results indicate that the element does not lock in the thin‐plate limit. Results obtained using the present element are compared with those obtained using a 12‐node assumed‐displacement based Mindlin plate element with reduced integration; the present hybrid‐stress element is shown to yield superior accuracy for all cases considered. In addition, the accuracy of the present element is compared against that of analogous 4‐node and 8‐node hybrid‐stress Mindlin plate elements.
A family of variable section curved beam and thick‐shell or membrane‐stiffening isoparametric elements
Authors: Jirousek J.
Published: August 2005

A family of isoparametric curved beam elements of a general, compact cross‐section is introduced. The formulation is based on beam theory and takes into account both transverse shear deformation and shear centre location. The elements exhibit the required displacement compatbility with Ahmad's superparametric thick‐shell elements and isoparametric membrane elements. Examples presented at the end of the paper illustrate the validity of the formulation and the possibility of practical application of the elements.
The finite element method for laminar flow with chemical reaction
Authors: Winters K. H. , Rae J. , Jackson C. P. , Cliffe K. A.
Published: August 2005

A finite element formulation of laminar flow with finite rate chemical reaction and heat release is made. Results are presented for steady flow in a channel, a special case of which is solved analytically, and for transverse flow around a cylinder. These illustrate the power of the finite element method for the calculation of reacting flows in complex geometries.
Solutions of boundary‐value problems by the Lanczos–Chebyshev reduction method
Authors: Chen Peter Y. P.
Published: August 2005

The reduction of liner partial differential equations for boundary‐value problems to ordinary differential equations by the Lanczos‐Chebyshev method is discussed and illustrated by applications to linear stress analysis and heat conduction in axisymmetric cylinders. Numerical examples given include eigenvalues for self‐equilibrating end load problems in hollow cylinders, and heat conduction in a semi‐infinite cylinder. Heat conduction in an infinite half‐space is treated by considering a large multi‐annular cylinder. The simplicity of the Lanczos‐Chebyshev reduction method and its speed and accuracy are demonstrated.
On the treatment of time‐dependent boundary conditions in splitting methods for parabolic differential equations
Authors: Sommeijer B. P. , van der Houwen P. J. , Verwer J. G.
Published: August 2005

Splitting methods for time‐dependent partial differential equations usually exhibit a drop in accuracy if boundary conditions become time‐dependent. This phenomenon is investigated for a class of splitting methods for two‐space dimensional parabolic partial differential equations. A boundary‐value correction discussed in a paper by Fairweather and Mitchell for the Laplace equation with Dirichlet conditions, is generalized for a wide class of initial boundary‐value problems. A numerical comparison is made for the ADI method of Peaceman‐Rachford and the LOD method of Yanenko applied to problems with Dirichlet boundary conditions and non‐Dirichlet boundary conditions.
Solution of quasi‐harmonic equations through the combined finite element‐transfer matrix method
Authors: Chiatti G. , Sestieri A.
Published: August 2005

The extension of a combined finite element‐transfer matrix method to problems governed by quasi‐harmonic equations is presented.

Particular emphasis is given to heat conduction, and numerical results are presented for this type of problem (steady and transient cases).

The principal advantage of the method with respect to finite elements concerns the minor dimension of the last matrix formulation which quite often implies a reduced computational burden.

The accuracy of the method is considered by comparing the numerical results with some available analytical solutions for slabs: an excellent agreement is effectively obtained.

No particular restrictions to the application of the method exist, and quite complex systems may be considered, provided that a suitable subdivision into strips and elements of the relevant region is carried out.
Numerical integration of linear boundary value problems in solid mechanics by segmentation method
Authors: Kant Tarun , Ramesh C. K.
Published: August 2005

Numerical integration of the system of governing equations which define a boundary value problem written down in the form of a coupled system of first‐order ordinary differential equations is shown to be a powerful technique. After presenting the basic approach the paper critically examines the numerical schemes available for situations when the boundary value problem so defined has boundary layer characteristics. One such method which is originally due to Goldberg, Setlur and Alspaugh3 is described in detail, with documentation in the form of a flow diagram and a FORTRAN listing of a working subroutine. The method is shown to be computationally efficient and reliable for the solution of a class of problems in the field of solid mechanics. Potential use of the method for the solution of magnetostatic problems is indicated.
A geodesic beam finite element for use in the‐static analysis of reinforced circular cylindrical shells
Authors: Thomas I. T. , Webber J. P. H.
Published: August 2005

The development of a geodesic beam finite element for use with a specific circular cylindrical shell finite element in the analysis of reinforced circular cylinders is described.

The basic strain and curvature change equations are given and, from these, three versions of the geodesic beam element are developed. Two of the beams have nodal degress‐of‐freedom identical with the shell element. They differ in the treatment of the terms relating to rotation about the principal normal. The first version ignores this parameter but, under certain circumstances, the stiffness matrix contains terms which can contribute to the strain energy under arbitrary rigid body movement of the beam. This deficiency is removed by applying an aspect of Koiter's theory which is used to transform the curvature change equations.

The introduction of additional rotational degress‐of‐freedom, at the end nodes of the beam element, produces a variation which is capable of accurately representing and transmitting in‐surface bending effects to an adjoining beam element.

Numerical evaluation successfully compares finite element solutions to basic problems for straight, circular and helical beams with theoretical strain energy solutions. Finally the beam is used in conjunction with a shell element to analyse an infinitely long circular cylinder, reinforced with equispaced rings, subjected to internal pressure.
Use of screw translational symmetry for the vibration analysis of structures
Authors: Whiston G. S.
Published: August 2005

A method for the exploitation of screw translation symmetry for the vibration analysis of structures is presented. The method is capable of providing significant computational economies over the use of the lower axial translational symmetry of such structures.
Three‐dimensional hybrid‐stress isoparametric quadratic displacement elements
Authors: Spilker R. L. , Singh S. P.
Published: August 2005

Two 20‐node quadratic displacement three‐dimensional isoparametric elements are developed based on the hybrid‐stress model. The elements differ in the stress interpolation used. In one case, the stress polynomials are selected to correspond approximately to the strain polynomials obtained from the displacement field, and a 57β stress field results. In the other element, complete cubic polynomials are used which are forced to satisfy the equilibrium equations and stress compatibility equations, and a 69β stress field results. Both elements possess correct rank, but only the 69β element is invariant. Results obtained using these two elements, and the corresponding 20‐node assumed‐displacement element, are compared and the 69β element is shown to be the better element. The 2 × 2 × 2 Gauss stations are also verified to be the optimal sampling points for these elements.
Approximate solution of singular integro‐differential equations in elastic contact problems
Authors: Sankar T. S. , Hoa S. V. , Fabrikant V. I.
Published: August 2005

A method for the numerical solution of singular integro‐differential equations is proposed. The approximate solution is sought in the form of the sum of a power series with unknown coefficients multiplied by a special term which controls the appropriate solution behaviour near and at the edges of the interval. The coefficients are to be determined from a system of linear algebraic equations. The method is applied to the solution of a contact problem of a disk inserted in an infinite elastic plane. Exact analytical solution is obtained for the particular case when the disk is of the same material as the plane. Comparison is made between the exact and the approximate solutions as well as with the solutions previously available in literature. The stability and the accuracy of the present method is investigated under variation of the parameters involved. The applicability of the method to the case when the boundary conditions for the unknown function are nonzero is discussed along with an illustrative example. A FORTRAN subroutine for the numerical solution of singular integro‐differential equations is also provided.
A thermodynamically consistent numerical method for transonic cascade flow simulation
Authors: Thyagaraja A.
Published: August 2005

The author's recent work on thermodynamically consistent numerical methods for the simulation of inviscid, adiabatic flow is extended to handle transonic flow problems of practical interest. The basic Singhal–Spalding scheme is developed and tested on two problems. The first one is the standard transonic nozzle flow. The computational results are shown to be in good agreement with the analytical solution. The second problem is a flow situation studied experimentlly by Sieverding. The inviscid results are in surprisingly good agreement with the principal qualitative features of the real folws. There are important quantitative discrepancies which are believed to be due to the inadequacies of the inviscid model rather than failings of the scheme itself. Arguments in support for this view are presented.
Acceleration of subspace iteration
Authors: Akl Fathy A. , Dilger Walter H. , Irons Bruce M.
Published: August 2005

An algorithm is presented and discussed which gives 40 per cent reduction in the cost of the basic subspace iteration for eigenvalues.
Elasto‐viscoplastic and elasto‐plastic large deformation analysis of thin plates and shells
Authors: Dinis L. M. S. , Owen D. R. J.
Published: August 2005

To account for plastic deformation in plate and shell structures an elasto‐viscoplastic solution algorithm is considered based on Perzyna's model for material behaviour. This algorithm can be employed to solve for time‐dependent elasto‐viscoplastic situations and by allowing steady‐state conditions to be reached, elasto‐plastic problems can also be considered.

For the large displacement elasto‐viscoplastic analysis of thin shells, an incremental stiffness procedure is employed together with a Lagrangian description of the stress and strain vectors. The Semiloof plate and shell elements are used for finite element space discretization.

The procedures developed are applied to the solution of several numerical examples and the solutions compared with results from other sources where available.
Mixed formulation finite elements for mindlin theory plate bending
Authors: Lee S. W. , Wong S. C.
Published: August 2005

Two new finite elements are developed for the Mindlin theory plate bending problem. The formulation is based on the modified Hellinger‐Reissner principle with independent transverse shear strains. Numerical examples indicate that, with properly assumed transverse shear strains, these new elements designated as PLAT8 and PLAT8H do not exhibit locking effect even for very thin plates.
A moving Petrov‐Galerkin method for transport equations
Authors: Herbst B. M. , Schoomnbie S. W. , Mitchell A. R.
Published: August 2005

A time‐dependent transport equation is solved numerically by using a Petrov‐Galerkin technique on a time‐dependent grid. A piecewise linear trial solution and piecewise Hermite cubic test functions are used. The same method is also applied to a time‐independent problem, in which case it automatically generates a grid in a way which bears some resemblance to certain existing grid‐generation techniques. Several numerical examples are given.
Dynamic programming in minimum weight design of shells
Authors: Thevendran V.
Published: August 2005

In designing a structure for a given purpose, the designer should aim at the most economical design from many points of view. Minimum weight designs may not be the most economical ones. Nevertheless, such designs provide insights into other types of design and may pave ways for improvements in design procedures. Minimum weight designs of continuum structures may be formulated as numerical optimization problems using either the finite difference method or the finite element method, and the resulting minimization problem may be solved using techniques of numerical optimization. This paper, on the other hand, considers the formulation of the minimum weight design of a spherical cap as a dynamic programming problem and its solution. The paper also discusses the advantages and limitations of the approach.
The potential due to a uniform source distribution over a triangular domain
Authors: Okon Ephraim E. , Harrington Roger F.
Published: August 2005

An exact expression is derived for the potential due to a uniform source distribution over a triangular domain. This expression, which is valid for arbitrary field points, is important for the numerical solution of electromagnetic field problems. Numerical values of the potential are calculated by using the expression obtained, and are compared with the results derived by numerical integration.
A linear finite element approach to the solution of the variational inequalities arising in contact problems of structural dynamics
Authors: Talaslidis D. , Panagiotopoulos P. D.
Published: August 2005

The present paper deals with the theoretical and numerical treatment of dynamic unilateral problems. The governing equations are formulated as an equivalent variational inequality expressing D' Alembert's principle in its inequality form. The discretization with respect to time and space leads to a static nonlinear programming problem which is solved by an appropriate algorithm. Some properties of dynamic unilateral problems are outlined and the influence of several parameters on the solution is investigated by means of numerical examples.
Free surface seepage from nonsymmetric channels
Authors: Remar J. , Bruch J. C. , Sloss J. M.
Published: August 2005

The problem of steady, two‐dimensional seepage from a nonsymmetric channel through a homogeneous porous medium underlain at a finite depth by a drain, is solved using the Baiocchi transformation and method. Because of the nonsymmetry in the problem, both free surfaces must be included in the solution domain of the problem. Thus, several interesting complexities are introduced into the solution of the problem. First, there are the two solution domain extensions (one across each free surface) and then the formulation of the new dependent variable throughout the extended solution domain. Secondly, the projection operator has two bounds in the numerical scheme. Finally, there are two compatibility conditions—one for the flowrate and one for the value of the new dependent variable at the left‐hand side free surface‐channel intersection. A secant method for the solution of two simultaneous nonlinear equations was used to obtain the values of these parameters. Results from the proposed method compared favourably with what few results were available in the literature.
On the displacement formulation of torsion of shafts with rectangular cross‐sections
Authors: Bathe Klaus‐Jürgen , Chaudhary Anil
Published: August 2005

The use of warping displacement functions for the torsional stiffness representation of beams with rectangular cross‐sections is studied. These functions can directly be employed in the displacement‐based formulation of Hermitian and isoparametric three‐dimensional beam elements for linear, elastic‐plastic or large displacement/large rotation analysis. the results of some studies are given to demonstrate the applicability and use of the proposed functions.
Uniform rational approximation on large data sets
Authors: Kaufman E. H. , McCormick S. F. , Taylor G. D.
Published: August 2005

We report on a very effective program for uniform approximation of functions (or discrete data) by generalized rational functions of any number of variables over point sets so large that conventional methods are inapplicable. The points need not be arranged in a regular pattern, but if they are, the number of points is normally limited only by the computer time available. The program extends the differential correction algorithm discussed in an earlier article in this journal by combining it with a first Remes‐type exchange procedure, while retaining the flexibility and robustness of differential correction. Furthermore, this algorithm is guaranteed to converge in theory. Testing has shown that, even when the point set is small enough for differential correction to be applied directly, this algorithm is usually faster. We discuss the algorithm and program along with several numerical examples, one of which involves more than three million data points. A FORTRAN listing with illustrative output can be obtained from the first author.
Evaluation of a new quadrilateral thin plate bending element
Authors: Batoz Jean‐Louis , Tahar Mabrouk Ben
Published: August 2005

A review of 4‐node, 12 degrees‐of‐freedom quadrilateral elements for thin plates is presented. A new element called DKQ is discussed. The formulation is based on a generalization of the efficient and reliable triangular element DKT presented in References 1 and 2 and on the rectangular element QC presented in Reference 3. These elements are derived using the so‐called discrete Krichhoff technique. A detailed numerical evaluation of the behaviour of the DKQ element for the computation of displacements and stresses for thin plate bending problems is presented and discussed. The DKQ element appears to be a simple and reliable 12 degrees‐of‐freedom thin plate bending element.
Second‐order design sensitivity analysis of mechanical system dynamics
Authors: Haug Edward J. , Ehle Paul E.
Published: August 2005

Dependence of dynamic response of nonlinear mechanical systems on design variables is analysed. An adjoint variable method is used to derive first‐ and second‐order derivatives of measures of dynamic response with respect to design variables. A computational algorithm is presented for numerical calculation of first and second design derivatives. A simple oscillator example is solved analytically and by the adjoint variable method, with identical results. A burst fire automatic weapon mechanism with linear and nonlinear damping is treated numerically. It is shown that quadratic appriximations of dynamic response, using results of second‐order design sensitivity analysis, can be substantially better than conventional linear approximations.
Rapid crack propagation and arrest in the dcb specimen—an improved numerical analysis
Authors: Perl M.
Published: August 2005

A two‐dimensional linear elastodynamic analysis of crack initiation, fast crack propagation and crack arrest in the DCB specimen is presented. The analysis is performed using the previously developed SMF2D code in its generation mode. The experimentally measured crack tip motion, as well as the specimen's geometry and its material characteristics, serve as input to the simulation. The dynamic stress intensity factor, the dynamic energy release rate and the various distributions of energies are subsequently evaluated. The numerical results are found to be in very good agreement with analytical and experimental findings.
Considerations of core storage arising from the finite element analysis of radiation diffusion‐transport benchmark problems
Authors: Ziver A. K. , Goddard A. J. H. , Ackroyd R. T.
Published: August 2005

Problems involving the diffusion and transport (angular dependence considered) of neutron radiation are frequently encountered in radiation physics and nuclear engineering. Neutron diffusion problems require substantial computer storage arising from the energy and spatial dependence, while in the case of transport problems the angular dependence of the neutron flux and of the neutron scattering process gives rise to a further considerable increase in storage. In the present work, a method has been developed which greatly eases the bandwidth problem in the solution of large systems of linear equations and algorithms have been developed to assemble and solve such systems of equations in one and two dimensions. The formalism used is the variational method and, for simplicity, linear interpolating functions have been used to derive a symmetric banded system of equations. Finite element algorithms have been implemented in the codes FEED1 and FEED2, which treat one and two space dimensions, respectively. Three benchmark problems are analysed in this paper and results are compared with finite difference discrete ordinate method solutions. It is shown that the finite element method provides fast and accurate solutions to neutron diffusion and transport problems.
Numerical operational methods for time‐dependent linear problems
Authors: Narayanan G. V. , Beskos D. E.
Published: August 2005

A general and systematic discussion on the use of the operational method of Laplace transform for numerically solving complex time‐dependent linear problems is presented. Application of Laplace transform with respect to time on the governing differential equations as well as the boundary and initial conditions of the problem reduces it to one independent of time, which is solved in the transform domain by any convenient numerical technique, such as the finite element method, the finite difference method or the boundary integral equation method. Finally, the time domain solution is obtained by a numerical inversion of the transformed solution. Eight existing methods of numerical inversion of the Laplace transform are systematically discussed with respect to their use, range of applicability, accuracy and computational efficiency on the basis of some framework vibration problems. Other applications of the Laplace transform method in conjunction with the finite element method or the boundary integral equation method in the areas of earthquake dynamic response of frameworks, thermaliy induced beam vibrations, forced vibrations of cylindrical shells, dynamic stress concentrations around holes in plates and viscoelastic stress analysis are also briefly described to demonstrate the generality and advantages of the method against other known methods.
Implicit time integration of elasto‐viscoplastic solids subject to the Mohr‐Coulomb yield criterion
Authors: Damjanić F. , Owen D. R. J.
Published: August 2005

For selected situations in geotechnical engineering, the use of implicit time integration techniques for elasto‐viscoplastic analysis is advantageous, or even unavoidable. In this paper the necessary expressions are derived for the implicit analysis of a material governed by the Mohr‐Coulomb yield criterion. In particular, detailed expressions are provided for the viscoplastic, strain rate derivative matrix Hn in a form suitable for numerical computation. Use of this algorithm is illustrated by the solution of a numerical example.
Quality of trial functions in quadratic isoparametric representation of an arc
Authors: Morley L. S. D.
Published: August 2005

An examination is made of displacement trial functions found in the quadratic isoparametric representation of an arc. Special attention is given to the quality of curvature change description and to effective manipulation of the trial functions. Various interpolation formulae are derived which have relevance to curved shell finite element design under Love‐Kirchhoff assumptions.
A comparative study on three boundary element method approaches to problems in elastodynamics
Authors: Manolis George D.
Published: August 2005

In this study, three boundary element method approaches are compared by solving a typical problem in linear elastodynamics. The first approach formulates and solves the problem in the real time domain in conjunction with a time‐stepping algorithm. The other two approaches formulate and solve the problem in the Laplace and the Fourier transformed domains, which necessitates a numerical inversion of the results to the time domain. The results obtained compare favourably with available analytic solutions. A detailed tabulation of the computer time and memory requirements of each approach is presented.
Finite element method for unbounded field problems and application to two‐dimensional taper
Authors: Orikasa Teruaki , Honma Toshihisa , Fukai Ichiro , Washisu Shin
Published: August 2005

Treatment of the finite element method for an unbounded field problem was proposed by McDonald and Wexler in 1972. Their method is superior to others, because it can exclude the singularities of Green's functions. This paper explains the treatment of the method in our 1979 letter which had some revisions of McDonald and Wexler's and calculated the time‐harmonic field problems. Examples presented are electromagnetic fields of two‐dimensional tapers which are open‐ended. Electromagnetic waves propagate in the taper and radiate from the taper to free space. In this case, the exact solutions for radiation from tapers are not available because of the complicated shape, and so the finite element method is useful in solving these problems. Electromagnetic fields of tapers involving dielectric slabs are also calculated as examples of inhomogeneous problems.
A study of nonlinear periodic systems via the point mapping method
Authors: Flashner Henryk , Hsu C. S.
Published: August 2005

It is well known that one way to treat nonlinear periodic dynamical systems governed by ordinary differential equations is to find first the corresponding point mappings. This approach has many advantages but it has a main obstacle in that it is difficult to obtain the exact mapping except in very special cases. Presented in this paper is a procedure which allows us to determine the point mapping in a polynomial form up to any specific degree of accuracy. The procedure when applied to linear periodic systems reduces to the one proposed by Friedmann et al.22 After presenting the algorithm for finding the point mappings, the method is applied to several problems in order to study the dynamical properties of the systems and to demonstrate the usefulness of the method.
Structural optimization to include material selection
Authors: Imai Kanji
Published: August 2005

The mini‐max dual method ia applied for solving the material selection structural optimization problems. A somewhat general objective function is introduced to consider structural weight and material cost simultaneously. It is expressed by the sum of scaled structural weight and material cost. The present formulation can yield minimum cost and minimum weight designs as two distinct special cases. It is shown that practically useful intermediate optimal designs can exist between the two extremes. Only truss structures are considered as a representative example. One numerical example is provided to illustrate the change in optimal material distribution when various objective functions are employed. A particular advantage in using the dual method for the material selection problem is also described.
Comparison of magnetic fields computed by finite element and classical series methods
Authors: Baker F. E. , Brown S. H. , Brauer J. R. , Gerhardt T. R.
Published: August 2005

The finite element reduced scalar potential method of calculating magnetic fields is investigated by comparing it with a classical series method. Both methods are applied to two problems having a current band surrounding a ferromagnetic shell. The magnetic field distributions obtained by both methods are shown to be in generally good agreement.
Damping and phase analysis for some methods for solving second‐order ordinary differential equations
Authors: Gladwell I. , Thomas R. M.
Published: August 2005

We consider numerical methods for initial value problems for second‐order systems of ordinary differential equations, analysing them by applying them to the test equation We discuss conditions which ensure an oscillatory numerical solution and the desirability of such a property. We also use a slightly more general test equation to derive conditions which ensure that the numerical forced oscillation is in phase with the true forced oscillation.

To illustrate the theory, we consider the damping and phase properties of some frequently used methods.
A non‐conforming piecewise quadratic finite element on triangles
Authors: Fortin M. , Soulie M.
Published: August 2005

It is shown in this paper that non‐conforming finite elements on the triangle using second‐degree polynomials can be easily built and used. Indeed they appear as an ‘enriched’ version of the standard piecewise quadratic six‐node element. This work is divided into two parts. In the first we present the basic properties of the element, namely how it can be built and basic error estimates. We also show that this element exhibits a very peculiar regularity property. In the second part we apply our element to the approximation of viscous incompressible flows and more generally to the approximation of incompressible materials.