bluuebunny/crossref_metadata_2025 huggingface dataset:
Application of quasi‐linearization to studies on diffusioin flames
Authors: Sriramulu V.
Published: August 2005

A method by which the numerical difficulties that one encounters while attempting to solve the differential equations which describe a diffusion flame can be circumvented is the quasi‐linearization technique. Application of this method in conjunction with difference approximations transforms the equations into tri‐diagonal matrices which can be inverted by the Thomas method. Since this is an iterative method initial profiles are generated by employing Burke‐Schumann kinetics. This method is found to be superior to the marching techiques that are frequently used in the analyses of diffusion flames.
The application of the least squates finite element method to Abel's integral equation
Authors: Balasubramanian R. , Norrie D. H. , De Vries G.
Published: August 2005

Abel's integral equation is the governing equation for certain problems in physics and engineering, such as radiation from distributed sources. The finite element method for the soultion of this non‐linear equation is presented for problems with cylindrical symmetry and the extension to more general integral equations is indicated. The technique was applied to an axisymmetric glow discharge problem and the results show excellent agreement with previously obtained solutions.
Finite element analysis of elastic–plastic materials displaying mixed hardening
Authors: Axelsson K. , Samuelsson A.
Published: August 2005

The problem of non‐radial loading (in the stress space) of structures of elastic–plastic metals is discussed. A concept of combined isotropic and kinematic hardening is proposed. For a material displaying such mixed hardening, constitutive equations are derived and incorporated in a finite element program for the analysis of elastic–plastic 2D‐structures. When determining the numerical solution of the non‐linear equations, the program enables the investigator to select an optimal combination of step by step and iteration procedures. The computed results are compared with experimental results and with results from calculations based on the overlay model, Reference 25.
A numerical method for the determination of optimal surface temperatures of steel ingots
Authors: El‐Gidny T. M. , Townsend P.
Published: August 2005

A numerical method is presented for the determination of control temperatures to be applied to the surface of a steel ingot to induce a predetermined temperature distribution within the ingot. The one‐dimensional case of an infinite plate is considered and the problem converted to one of static optimization which is then solved using a partial quadratic interpolation technique.
Computation of the limit load and elasto–plastic bending of thin plates
Authors: Mercier Bertrand
Published: August 2005

We use the mixed equilibrium finite element method of Hellan–Herrmann,1‐5 for solving the problem of elasto–plastic bending and limit load for a thin plate.

We give also some results for the elastic case, for which exact solutions are known.
Hybrid‐stress models for elastic–plastic analysis by the initial‐stress approach
Authors: Spilker R. L. , Pian T. H. H.
Published: August 2005

Two alternative numerical methods are presented, based on the assumed‐stress hybrid finite element model and the initial‐stress approach, for the elastic–plastic small‐deflection analysis of structures under static loading. The use of the initial‐stress approach results in a set of simultaneous linear algebraic incremental equations to be solved at each loading step, with the elastic stiffness matrix remaining unchanged throughout the loading process and the effects of plasticity included as equivalent element loads. The derivation of these alternative methods differs in the assigning of the incremental stress which satisfies equilibrium; in one case it is the actual stress increment while in the other it is a fictitious stress increment. An equilibrium imbalance correction is included in each of these methods to prevent drifting of the solution during the incremental process. Example solutions are presented which demonstrate the accuracy of the two methods and permit comparisons of the relative efficiencies of the two methods.
Families of consistent conforming elements with singular derivative fields
Authors: Stern Morris
Published: August 2005

Families of two‐and three‐dimensional finite elements are constructed for use in modelling fields with singular derivatives. The elements are complete over linear fields, conform with regular elements, and are easily programmed. A low order exact quadrature rule is also derived for element stiffness calculations.
A physical interpretation of the artifice used in frequency analysis of unsupported structures
Authors: Pramila A.
Published: August 2005

A physical interpretation of the method—adding αM to the stiffness matrix—used in frequency analysis of unsupported structures is suggested. The proper choice of α is discussed and a relation between angular natural frequencies of structures with and without elastic support is given.
A direct linear system solver with small core requirements
Authors: Recuero A. , Gutierrez J. P.
Published: August 2005

This paper present an algorithm and its corresponding FORTRAN IV program which solves a system of simultaneous equations of the type generated in structural analysis. It is based on the Gauss elimination method, so it is a direct method. But it only needs to have in core as many equations as it can contain, with a minimum of two. The program offers the following advantages: (a) Takes into account zeros to avoid operations. (b) Considers very big numbers in the diagonal, corresponding to boundary conditions, to avoid operations. (c) It can handle several load cases either simultaneously or in groups, at choice.
Finite element analysis of stress intensity factors for plane extension and plate bending problems
Authors: Yagawa G. , Nishioka T.
Published: August 2005

This paper deals with the finite element calculation of the stress intensity faactors for plane extension and plate bending problems. On the basis of the plate theory including the effect of transverse shear deformation, the influences of plate thickness, crack length and plate width on the stress intensity faotors are investigated. The numeriacal analyses are carried out using the superposition method of analytical and finite element solutions. It is found that the present stress intensity factors calculated for cracked plates under plane extension as well as bending compare favorably with the analytical ones.
Nonlinear rebound of a rod after impact against a deformable barrier
Authors: Garnet Hyman , Armen Harry
Published: August 2005

The nonlinear impact of a vehicle against a deformable barrier and its subsequent rebound from that barrier are simulated. A one‐dimensional elastoplastic model represents the vehicle as a series of rod finite elements and the barrier as a single mass, nonlinear spring. The solution procedure utilizes variable time step integration, contains an error control and eliminates numerical instabilities. A limited study assesses the influence of system parameters on both structure and occupants. The chief objective, however, is to establish the feasibility of the proposed treatment of this class of problems. Some results obtained appear, at first, to contradict intuition. It is observed that modelling a deformable barrier as rigid can lead to unconservative results with respect to structural response of the vehicle.
Application of backward differentiation methods to the finite element solution of time‐dependent problems
Authors: Zlatev Zahari , Thomsen Per Grove
Published: August 2005

The application of finite element methods to parabolic partial differential equations leads to large linear systems of first‐order ordinary differential equations. Very often these systems are stiff and difficulties arise in their numerical solution. We attempt to analyse the problem of how to select numerical methods for the solution of such linear systems.
On an efficient use of CST elements
Authors: Subramanian G. , Krishnan A.
Published: August 2005

Similar and similarly oriented CST elements have the same stiffness matrix, and therefore similar shapes generated by the assembly of such elements possess the same stiffness matrix. This property and the matrix condensation technique may be judiciously combined to simplify the study of large structures, which may otherwise incur large core requirements and time and involve the solution of a great number of equations. In this paper the idea is developed to indicate its full potential. In illustration, results from examples on the determination of stresses around a small hole in a large plate are presented.
Residual correction applied to a sequence of block tridiagonal matrices
Authors: Brown R. Leonard
Published: August 2005

The decomposition of a block tridiagonal matrix into the product of block lowe and upper matrices is described. The cost of solving a block tridiagonal system of equations is given and compared to profile gaussian elimination. The desirability of a less expensive method is coupled to physical intuition about a common problem of solving a slowly varying sequence of such systems to motivate an iterative method based on residual correction. The method is described and convergence criteria are derived. An expression of the cost is developed and is shown to compare favourably with decomposition in many cases. Problems and advantages in computer implementation of the method are discussed and results of tests of a particular implementation on a well‐known problem are given.
The order of numercial quadrature in two dimensions
Authors: Thatcher R. W.
Published: August 2005

In this paper the order of certain two‐dimensional quadrature formulae is discussed and it is shown that their degree and order are not related in the same simple way as they are for one‐dimensional rules.
A fast algorithm for triangular plate bending element
Authors: Joseph K. T. , Rao K. Singa
Published: August 2005

This communication presents a simple algorithm to compute the stiffness matrix for a triangular plate bending element, without numerical integration. This brings about a substantial saving in computer time.
Conforming approximations for Kirchhoff plates and shells
Authors: Peano Alberto
Published: August 2005

Finite element interpolations of arbitrary polynomial degree which are exactly and minimally C1 continuous across interelement boundaries are studied. A perspective view of the techniques proposed by other authors is presented and some new possibilities are considered. The problem is discussed with reference to the plate and shell finite element approximations, based on the principle of minimum potential energy. The approach also permits identification of sufficient conditions for guaranteeing full rank of stiffness matrices based on modified principles of potential energy. The results of this analysis can be used to investigate the linear dependencies among nodal variables which also occur in the formulation of other fourth‐order problems.
An accurate method for two‐point boundary value problems
Authors: Walker J. D. A. , Weigand G. G.
Published: August 2005

A new second‐order accurate method for the solution of two‐point boundary value problems on a uniform mesh is given; the local truncation error is obtained for use with the deferred correction process. The method is compared with existing second‐order techniques and is shown to produce more accurate results for a number of linear and nonlinear example problems.
Finite element representation and pressure stiffness in shell stability analysis
Authors: Loganathan K. , Chang S. C. , Gallagher R. H. , Abel J. G.
Published: August 2005

In the light of recent contributions by Batoz1 and Hibbitt,2 two aspects of finite element formulations for shell stability analysis are examined. The first is the consistency of the shell strain‐displacement equations employed; the second is the proper representation of ‘follower forces’—pressures that are always normal to the deforming surface. Numerical studies of an arch indicate that improper representation of either of these factors can have a significant effect on predicted buckling loads. Numerical studies of an arch indicate that improper representation of either of these factors can have a significant effect on predicted bukling loads.
Forbidden nodes for curved finite elements
Authors: Stephenson J. W. , Manohar R.
Published: August 2005

It is shown here that certain interpolating polynomials of degrees four and five may not always be uniquely defined on triangular‐shaped elements which have one curved side. Conditions which indicate non‐uniqueness are given, together with some geometrical interpretations concerning the location of the node on the curved side. A numerical example is given to demonstrate that there ar curves for which every point is unsuitable to be chosen as a node.
Transition finite elements for axisymmetric stress analysis
Authors: Surana Karan S.
Published: August 2005

This paper presents isoparametric finite element formulation for special classes of elements referred to as ‘transition elements’ for axisymmetric stress analysis. The transition elements are necessary for applications requiring the use of both axisymmetric solids and axisymmetric shells. These elements permit transition from the axisymmetric solid portion of the structure to the axisymmetric shell portion. The element properties are derived and presented in detail. Numerical examples are also presented to demonstrate the accuracy and applications of such elements.
An integrated load increment method for finite elasto–plastic stress analysis
Authors: Cheng S. Y. , Hsu T. R. , Too J. J. M.
Published: August 2005

A new computational scheme, named the ‘Integrated Load Increment’ method (ILI), has been developed to handle elasto–plastic analysis of solids by the finite element variational technique. This scheme allows considerably larger loading steps to be applied to the structure without deviating from its nonlinear, load‐deformation relationship. It has been shown that these relationships can be evaluated by integrating the nonlinear constitutive equations within each load increment under certain conditions. A numerical example on a pressurized thick‐walled cylinder indicates that a 240 per cent improvement in computational efficiency and substantial reduction of loading steps over the conventional load incremental method can be achieved by the ILI technique.
Quadratic reduction for the eigenproblem
Authors: Johnson C. P. , Craig R. R. , Yargicoglu A. , Rajatabhothi R.
Published: August 2005

A quadratic method is presented for solving the eigenvalue problem of a structural system having a large number of degrees‐of‐freedom. The eigenproblem is reduced to a smaller problem by condensing the system stiffness and mass using Guyan reduction. Application of a set of corrective displacements to the reduced system subsequently leads to an eigenproblem of quadratic form involving an additional mass term. To obtain the solution to the reduced problem, inverse iteration with spectrum shifts based on the eigenvalues of the Guyan problem is used. The resulting eigenvalues and mode shapes represent a corrected Guyan approximation to the solution of the unreduced system. In addition, it is shown that the amount of improvement over the Guyan solution can be approximated by employing a first‐order error analysis procedure. Numerical examples of vibrations of a bar, a beam and a plate demonstrate that the solutions obtained from the quadratic reduction procedure are very accurate and require relatively little additional computational effort in comparison with the solutions of the corresponding linear eigen‐problem. The relationship of the present method to that proposed by Przemieniecki is illustrated by an example.
Nonlinear programming applied to the optimum control of a gas compressor station
Authors: Osiadacz A.
Published: August 2005

The paper concerns the problem of optimal control of a compressor station of natural gas supplied with motor‐compressor. A mathematical model of the object considered is formulated. The control of a compressor station is variable staircase function. The objective function, taking into account the cost of energy consumed by the motor‐compressor during each time interval, is proposed. Moreover, it is assumed that the values of suction pressure, compression pressure and the compressor station capacity are given. The optimization problem stated consists in evaluating the number of simultaneously operating motor‐compressors and determining such a distribution of the capacity that the total unit fuel consumption in each time interval is minimized subject to the constraints imposed. The paper presents an algorithm of automatic search for the optimal values of the operating parameters of the compressor station. The algorithm proposed can be implemented on a digital computer. The method presented has been verified experimentally on the controlled object.
Numerical instabilities of the integral approach to the interior boundary‐value problem for the two‐dimensional Helmholtz equation
Authors: Mattioli F.
Published: August 2005

The integral equations arising from the Green's formula, applied to the two‐dimensional Helmholtz equation defined in a limited domain, are considered and the presence of instabilities in their numerical solution, when a real Green's function is adopted, is pointed out.

A complete study has been carried out for a circular domain and the conditions under which such instabilities can occur in a domain of arbitrary geometry have been investigated. In particular, it has been shown that in every case the use of a complex Green's function is able to avoid their presence.
A brief review of techniques for generating irregular computational grids
Authors: Thacker W. C.
Published: August 2005

This review attempts to place in perspective the wide variety of computer methods which are available for constructing irregular computational grids. Several different approaches exist for each aspect of the construction task: creation of the points, recognition of neighbouring points that define grid elements, enumeration of the points with indices, optimization of the positions of the points for computational advantage, and variation of point density throughout the grid.
Nonlinear analysis via global–local mixed finite element approach
Authors: Noor Ahmed K. , Peters Jeanne M.
Published: August 2005

A computational algorithm, based on the combined use of mixed finite elements and classical Rayleigh–Ritz approximation, is presented for predicting the nonlinear static response of structures; The fundamental unknowns consist of nodal displacements and forces (or stresses) and the governing nonlinear finite element equations consist of both the constitutive relations and equilibrium equations of the discretized structure. The vector of nodal displacements and forces (or stresses) is expressed as a linear combination of a small number of global approximation functions (or basis vectors), and a Rayleigh–Ritz technique is used to approximate the finite element equations by a reduced system of nonlinear equations. The global approximation functions (or basis vectors) are chosen to be those commonly used in static perturbation technique; namely a nonlinear solution and a number of its path derivatives. These global functions are generated by using the finite element equations of the discretized structure.

The potential of the global–local mixed approach and its advantages over global–local displacement finite element methods are discussed. Also, the high accuracy and effectiveness of the proposed approach are demonstrated by means of numerical examples.
Stress‐intensity factor computation in three dimensions with quarter‐point elements
Authors: Ingraffea Anthony R. , Manu Corneliu
Published: August 2005

A consistent method for computing stress‐intensity factors from three‐dimensional quarter‐point element nodal displacements is presented. The method is generalized to permit functional evaluation of stress‐intensity factors along the crack front. Embedded, surface, and corner crack problems are solved using the proposed technique. Results are compared to previous finite element and boundary element solutions. The comparison shows that use of the functional evaluation technique allows a dramatic decrease in problem size while still maintaining engineering accuracy. Next, a three‐dimensional stress‐intensity factor calibration of an unusual specimen configuration is presented. By taking advantage of the proposed technique, the calibration was performed with little difference in cost over the more usual two‐dimensional approach. Moreover, the three‐dimensional solution revealed intersting behaviour that would have been undetected by a two‐dimensional solution. Finally, the results of a study on optimum size of the quarter‐point element are presented. Surprisingly, Poisson ratio is shown to have marked effect on optimum element size.
Dynamic aspects of the error in eccentric beam modelling
Authors: Miller Robert E.
Published: August 2005

The usual linear shape function for approximating axial displacements in beam finite elements used as eccentric stiffeners or as portions of composite cross‐sections, leads to an error in the static deflection. A modified element reduces this error. The behaviour of these two elements under free vibration is examined. The linear element is shown to be in considerable error in the dynamic case also.
Optimal finite element solutions to diffusion–convection problems in one dimension
Authors: Barrett J. W. , Morton K. W.
Published: August 2005

Petrov–Galerkin methods have been proposed by several authors to eliminate the inaccuracies and oscillations obtained with Galerkin methods when applied to diffusion–convection problems at high Péclet numbers: the difficulty is to select the appropriate test space for a given trial space. We investigate here choices of test space which either exactly or approximately symmetrize the associated bilinear form and so retain the optimal character of the approximate solution. This is the key to high accuracy and superconvergence, and optimal recovery techniques are proposed to obtain the maximum information from the approximations. Examples are given to show how the position and thickness of boundary layers may be estimated with relatively coarse meshes.
Bounds on discretization error by special reduced integration of the lagrange family of finite elements
Authors: Kelly D. W.
Published: August 2005

An analysis is presented which indicates that special reduced integration of the displacement compatible Lagrange family of finite elements can give numerical models preserving characteristics of equilibrium formulations. A number of examples show that bounds on the discretization error can be obtained in both an energy norm and locally. The process is therefore recommended for error analysis and for the assessment of the reliability of displacement compatible finite element solutions.
Improved stress evaluation under thermal load for simple finite elements
Authors: Pittr J. , Hartl H.
Published: August 2005

The method of initial strain is replaced by a method of initial displacements and applied to simple four‐noded membrane and shell elements. The thermal stresses in nodes are improved for quadrilaterals and hexahedrons, which have a discrepancy between interpolation functions for temperature (linear) and strains (constant). To get initial displacements, the singular element stiffness matrix has to be inverted. Minor changes in subroutine MINV3 (enclosed version STDMNV) were made to do this.
Multiparameter shape optimization of elastic bars in torsion
Authors: Dems Krzysztof
Published: August 2005

The problem of optimal design of the shape of an internal or external boundry of an elastic bar in torsion is formulated by assuming the boundary shape is described by a set of prescribed shape functions and a set of shape parameters. The optimization procedure is reduced to determination of these parameters. For constant volume or material cost constraint, the optimality conditions are derived for the case of maximizing of torsional rigidity of elastic bars of linear material. The optimal shape problem is next formulated by means of the finite element method and the interative solution algorithm is discussed by using the optimality crieria. Several simple numerical examples are included.
An alpha modification of Newmark's method
Authors: Wood W. L. , Bossak M. , Zienkiewicz O. C.
Published: August 2005

This paper discusses the Bossak–Newmark algorithm, which is an extension of the well‐known Newmark algorithm1 for the numerical integration of the equations of discretized structural dynamics problems. The extra parameter introduced here enables the method (when used on the test equation ẍ = −ω2x) to be simultaneously second order, unconditionally stable and with positive artificial damping.

Comparisons are made with another modification of Newmark introduced by Hilber, Hughes and Taylor2.
A numerical solution for integral equations
Authors: Aguirre‐Ramirez G. , Shashani A. O.
Published: August 2005

A method for the numerical approximation for the solution of Fredholm integral equations of the second kind is presented. The approximation is obtained using cubic B‐splines as co‐ordinate functions in the variational formulation of the problem.
High order polynomial elements with isoparametric mapping
Authors: Hoppe Viggo
Published: August 2005

Finite elements with polynomial interpolation functions of a degree higher than 2 are used comparatively little on large FEM systems, except in shell elements. However, the author has had several years' experience in the use of the so‐called ‘isoparametric, reduced Hermitian element’,4 Which has behaved excellently in an industrial as well as an educational environment. The reason for the interest in the Hermitian concept is that the overcompatibility of the element reduces the number of unknowns, the solution time and the discontinuities in stresses between elements.

Explicit formulae for the family of interpolation polynomials of order q and degree p = 2q + 1 are given and hierarchical Hermite elements are introduced. The families of Hermite and serendipity elements are isomorphic and the latter may thus be extended to arbitrary high order.

For some problems the equidistant node configuration in Lagrange elements of degree 3 and higher is not optimal with respect to smoothness, and a new type of element, the ‘Lobatto element’, is introduced.

The methods consistently produce results of an accuracy which is above the requirements of usual engineering applications, but in graphics smoothness of curves is important for a convincing representation. The methods are of particular interest in industries working with structures composed of almost linear materials with well‐known properties.
Finite rotation effects in numerical integration of rate constitutive equations arising in large‐deformation analysis
Authors: Hughes Thomas J. R. , Winget James
Published: August 2005

An improved algorithm is presented for integrating rate constitutive equations in large‐deformation analysis. The algorithm is shown to be ‘objective’ with respect to large rotation increments.
Continuously deforming finite elements for the solution of parabolic problems, with and without phase change
Authors: Lynch Daniel R. , O'Neill Kevin
Published: August 2005

A number of transport problems are complicated by the presence of physically important transition zones where quantities exhibit steep gradients and special numerical care is required. When the location of such a transition zone changes as the solution evolves through time, use of a deforming numerical mesh is appropriate in order to preserve the proper numerical features both within the transition zone and at its boundaries.

A general finite element solution method is described wherein the elements are allowed to deform continuously, and the effects of this deformation are accounted for exactly. The method is based on the Galerkin approximation in space, and uses finite difference approximations for the time derivatives. In the absence of element deformation, the method reduces to the conventional Galerkin formulation.

The method is applied to the two‐phase Stefan problem associated with the melting and solidification of A substance. The interface between the solid and liquid phase form an internal moving boundary, and latent heat effects are accounted for in the associated boundary condition. By allowing continuous mesh deformation, as dictated by this boundary condition, the moving boundary always lies on element boundaries. This circumvents the difficulties inherent in interpolation of parameters and dependent variables across regions where those quantities change abruptly.

Basis functions based on Hermite polynomials are used, to allow exact specification of the flux‐latent heat balance condition at the phase boundary. Analytic solutions for special cases provide tests of the method.
Elasto visco‐plastic flow with special attention to boundary conditions
Authors: Shimazaki Yoji , Thompson Erik G.
Published: August 2005

In this paper we analyse a simple but non‐trivial steady‐state creeping elasto visco‐plastic (Maxwell fluid) radial flow problem, paying particular attention to the effects of the boundary conditions. Solutions are obtained by integration of a governing equation on stress, using the Runge‐Kutta method for initial value problems and finite differences for boundary value problems. A more general approach by the finite element method, which solves for the velocity field rather than the stress field, and which is applicable to a wide range of problems, is presented and tested using the radial flow example.
Nonlinear analysis of portal frames
Authors: Simitses G. J. , Giri J. , Kounadis A. N.
Published: August 2005

A kinematically nonlinear analysis of unbraced, rigid‐jointed, portal frames, rotationally restrained at the base and subjected to eccentric concentrated and/or uniformly distributed loads, is presented. Through this analysis the complete behaviour, including the primary path and postbuckling path (whenever it exists), is evaluated. Moreover, through parametric studies, the effects of bar slenderness ratio, load eccentricity and amount of rotational restraint are assessed. Through this method it is also possible to assess the effect of member lengths and member lengths and member bending stiffnesses.
Large deflections and large amplitude vibrations of axisymmetric circular plates
Authors: Reddy J. N. , Huang C. L. , Singh I. R.
Published: August 2005

This paper is concerned with conventional and mixed finite element analysis of large deflection bending and free vibration of axisymmetric circular plates including shear deformation. Conventional and mixed finite element formulations are presented. Numerical results are included for isotropic as well as orthotropic, circular and annular plates under various edge conditions and loadings.
The application of quasi‐Newton methods in fluid mechanics
Authors: Engelman M. S. , Strang G. , Bathe K.‐J.
Published: August 2005

The use of quasi‐Newton methods is studied for the solution of the nonlinear finite element equations that arise in the analysis of incompressible fluid flow. An effective procedure for the use of Broyden's method in finite element analysis is presented. The quasi‐Newton method is compared with the commonly employed successive substitution and Newton‐Raphson procedures, and it is concluded that the use of Broyden's method can constitute an effective solution strategy.
On computational strategies for problems involving plasticity and creep
Authors: Levy A. , Pifko A. B.
Published: August 2005

This paper discusses computational strategies for elastic‐plastic‐creep behaviour. These computational strategies, based on the tangent stiffness and initial strain techniques, include solution algorithms, modelling techniques and constitutive relations.

A predictor‐corrector iterative and non‐iterative scheme is presented for combined plasticity and creep. This scheme has been incorporated into the three‐dimensional, isoparametric element, module (HEX) of the Grumman PLANS finite element program for nonlinear analysis and used for the problems presented in this paper.

The concept of modelling for inelastic behaviour is demonstrated by introducing a variable set of inelastic integration points within a finite element at which stresses and strains are monitored.

In order to perform a meaningful analysis, one must understand and justify the employed constitutive relations. To this end, work at Oak Ridge National Laboratory in justifying constitutive relations for high‐temperature nuclear reactor components is referred to.

An analysis of a test model of a nuclear reactor inlet nozzle operating at high temperatures is presented to demonstrate some of the computational strategies discussed.
A selective relaxation iterative solution technique for nonlinear structural analysis problems
Authors: Wellford L. Carter , Sen Halis
Published: August 2005

A series of algorithms, to solve the nonlinear algebraic equations resulting from nonlinear finite element models, are proposed. These algorithms involve a selective relaxation of the corrections defined by the modified Newton method. The resulting techniques accelerate the convergence of the modified Newton method. The improved convergence rate is obtained at the expense of a small increase in storage requirements. The results of numerical experiments, on certain nonlinear elasticity problems, are presented to verify the developed techniques.
Basis functions for general Hsieh‐Clough‐Tocher triangles, complete or reduced
Authors: Bernadou Michel , Hassan Kamal
Published: August 2005

In this note, we give the basis functions (shape functions) for Hsieh‐Clough‐Tocher triangles, complete or reduced. In order to take the best advantage of symmetry and for simplicity, we derive these functions for a general triangle by using simultaneously the ‘area co‐ordinates’ and the so‐called ‘eccentricity parameters’. We conclude with some remarks concerning the implementation.
The mixed finite element method applied to two‐dimensional elastic contact problems
Authors: Tseng Jorgito , Olson Mervyn D.
Published: August 2005

The application of the mixed finite element method to two‐dimensional elastic contact problems is investigated. Since in the mixed method, both displacements and stresses are retained as variables, it is found that all the contact conditions—displacement as well as stress—can be approximated directly. A significant novelty is that some of the displacement variables are treated as natural boundary conditions in the contact region. In cases where the contact region is independent of the applied loading, an iterative procedure is used to establish the sliding and adhering portions of the contact region. In cases where the contact region is a function of the applied loading, for example progressive contact, an incremental formulation is employed to describe the discretized contact stages before invoking the former iterations. Several numerical examples are presented and the results are compared with those from the conventional potential energy or displacement finite element method.
A general two‐dimensional, graphical finite element preprocessor utilizing discrete transfinite mappings
Authors: Haber Robert , Shephard Mark S. , Abel John F. , Gallagher Richard H. , Greenberg Donald P.
Published: August 2005

Finite element preprocessor programs have been developed in recent years in order to expedite the task of data preparation. A key decision in the design of these programs is the choice of a method for automated mesh generation. Three popular methods (Laplacian, isoparametric and transfinite mappings) are compared. Transfinite mappings with boundary information represented in discrete form are found to possess distinct advantages for the task of mesh generation.

A two‐dimensional preprocessor program utilizing the discrete transfinite mappings is described. Interactive computer graphics techniques are used extensively to facilitate data preparation and display. The geometry‐generating routines are general, and may be used in any finite element application. A specialized graphical ‘attribute editor’ for structural mechanics problems is also described. This editor provides an efficient method of specifying boundary conditions, material properties, loads, etc.
An algorithm for the solution of very large banded unsymmetric linear equation systems
Authors: Stabrowski M. M.
Published: August 2005

This paper presents an algorithm and corresponding FORTRAN program for the solution of unsymmetric banded linear equation systems. The algorithm is based on the Crout method. A special technique, called double windowing, enables the solution of very large equation systems with a total equation number reaching 30,000 and a full bandwidth in excess of 1,000. Special attention was devoted to minimization of peripheral processor time (communication with backing disc memory). An appendix lists the complete program for Cyber series computers (CDC).
Stint/CD: A stand‐alone explicit time integration package for structural dynamics analysis
Authors: Underwood Philip , Park K. C.
Published: August 2005

This paper is a user's guide for the stand‐alone explicit direct time integration package STINT/CD for structural dynamics analysis. STINT/CD uses an automatic variable time increment central difference method. The purpose, function, limitations and usage of the package are described. A FORTRAN listing of STINT/CD is given along with a sample problem which illustrates its usage and performance.
Quadratic and cubic transition elements
Authors: Hussain M. A. , Vasilakis J. D. , Pu S. L.
Published: August 2005

Quadratic and cubic quadrilateral isoparametric elements are investigated for use as transition elements for use a crack tip elements. Computations for a single element are explicitly carried out using a symbolic algebraic manipulation program and in addition to the desired square root singularity, additional singularities are revealed. Cubic transitional elements were used for a double‐edge crack problem and only marginal improvement is found for a well‐laid out grid.
Eigensolution using lagrangian interpolation
Authors: Iyer M. S.
Published: August 2005

A computationally efficient and accurate solution technique for large‐order eigenvalue problems with small to medium bandwidth is presented. The algorithm—called the Sub‐Polynomial Iteration (SPI) method—solves for the eigenvalues and corresponding eigenvectors. directly without any transformation to the standard form. The method is an efficient combination of several separate techniques including Sturm sequence, Lagrangian polynomial interpolation, inverse iteration with shift and Gram‐Schmidt orthogonalization. Computer run times for a set of sample solution indicate the efficiency of the SPI method.
Plane isoparametric hybrid‐stress elements: Invariance and optimal sampling
Authors: Spilker R. L. , Maskeri S. M. , Kania E.
Published: August 2005

Formulation and applications of the hybrid‐stress finite element model to plane elasticity problems are examined. Conditions for invariance of the element stiffness are established for two‐dimensional problems, the results of which are easily extended to three‐dimensional cases. Next, the hybrid‐stress functional for a 3‐D continuum is manipulated into a more convenient form in which the location of optimal stress/strain sampling points can be identified. To illustrate these concepts, 4‐ and 8‐node plane isoparametric hybrid‐stress elements which are invariant and of correct rank are developed and compared with existing hybrid‐stress elements. For a 4‐node element, lack of invariance is shown to lead to spurious zero energy modes under appropriate element rotation. Alternative 8‐node elements are considered, and the best invariant element is shown to be one in which the stress compatibility equations are invoked. Results are also presented which demonstrate the validity of the optimal sampling points, the effects of reduced orders of numerical integration, and the behaviour of the elements for nearly incompressible materials.
Computation of limit loads
Authors: Christiansen Edmund
Published: August 2005

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.
Stereo decomposition subroutines for three‐dimensional plotter programs
Authors: Pammer Z. , Szabo L.
Published: August 2005

Two‐dimensional distributions and three‐dimensional element meshes are usually plotted in axonometric projection. Stereo decomposition can make the plots of complicated functions and structures more synoptical; the object appears in three dimensions. The method can be useful for the display of displacements and model shapes of three‐dimensional structures as well.
An approximate solution of the annular crack problem
Authors: Mastrojanni E. N. , Kermanidis T. B.
Published: August 2005

A method is presented for the approximate solution of the axisymmetric problem of an annular crack Embedded in an infinite elastic solid and subjected to a normal internal pressure. The numerical results Obtained for the stress intensity factors are in good agreement with those obtained by Smetanin2.
Mixed interpolation in primitive variable finite element formulations for incompressible flow
Authors: Jackson C. P. , Cliffe K. A.
Published: August 2005

This paper shows that mixed interpolation is required because of the nature of the pressure terms in the equations. These lead to finite element equations which in many circumstances do not uniquely determine the pressure, if the same interpolations are used for pressure and velocities.

Several new combinations of pressure and velocity interpolation are analysed with the aid of a novel diagrammatic technique. In particular we consider some very interesting combinations in which, over nearly all the flow, the pressure and velocity are approximated on elements by biquadratic polynomials which are continuous across element boundaries.

The theory of this paper is shown to be in complete agreement with numerical experiment.
C1 quintic interpolation over triangles: Two explicit representations
Authors: Barnhill R. E. , Farin G.
Published: August 2005

Two explicit representation of a C1 quintic interpolant over triangles are given. These representations are derived by generalization of Coons' methods and Bernstein‐Bézier methods, respectively.
Elastic‐plastic analysis of plates by the hybrid‐stress model and initial‐stress approach
Authors: Spilker R. L. , Munir N. I.
Published: August 2005

Two alternative hybrid‐stress‐based functionals are examined for the incremental elastic‐plastic static analysis of single layer plates. Material nonlinear effects are incorporated via the initial‐stress approach so that an equivalent nodal force vector is defined and the stiffness remains constant throughout the incremental loading. The alternative functionals differ in the incremental stress which is assumed to satisfy equilibrium; in the first, it is the actual stress increment, and in the second it is the elastic stress increment. Results are presented for two example problems, and comparisons of the alternative functionals and plausible iteration schemes are given. The effects of variation of pertinent solution parameters are also shown. A 4‐node hybrid‐stress plate element based on a Mindlin‐type displacement field is used for most cases; however, limited results are also presented using an 8‐node plate element, thus permitting comparisons of the relative efficiencies of the two elements.
Calculation of sensitivity derivatives in thermal problems by finite differences
Authors: Haftka Raphael T. , Malkus David S.
Published: August 2005

The transient thermal analysis of large aerospace vehicles such as the space shuttle requires models with thousands of degrees‐of‐freedom. The design of thermal protection systems for such vehicles requires the repetitive thermal analysis of the vehicle and the calculation of sensitivities—derivatives of the transient response with respect to design parameters. When the number of design parameters is large, the cost of the sensitivity calculations may become prohibitive. The present work is concerned with reducing the computational cost and errors in sensitivity calculations with one of the simplest available methods—the finite difference approach. A technique for calculating simultaneously the nominal and perturbed solutions required for the finite difference derivative is proposed. An expression for the optimum value of the perturbation parameter is obtained which permits reducing the computational error. An insulated cylinder is used as an example which demonstrates that significant improvements in accuracy and efficiency may be obtained.
On the accuracy of polynomial finite elements for crack problems
Authors: Johnson A. R.
Published: August 2005

A square tensile sheet with symmetric edge cracks is analysed by the finite element method to demonstrate the accuracy obtained with polynomial elements when the mesh patterns are chosen on the basis of the element's interpolation functions. Numerical results are provided for the accuracy of the total strain energy, the stress intensity factor, and the numerical condition of the global stiffness matrix. The stress intensity factor is determined to within 1.0 per cent accuracy using quadratic (linear strain) triangular elements with only 138 degrees‐of‐freedom.
Discrete and non‐discrete mixed methods for plate bending analysis
Authors: Fujii Fumio
Published: August 2005

For plate bending analysis, both discrete and non‐discrete mixed methods are presented by using spline functions in the Hellinger‐Reissner variational principle. Piecewise spline interpolation with local supports and overall spline interpolation with boundary knots are applied to each of two mixed functionals. The prescribed boundary conditions can be considered by multiple boundary knots. The convergence behaviour of the mixed methods presented is studied. Numerical examples show that a high degree of accuracy can be obtained due to continuous properties in the high derivatives of the employed shape functions. The proposed mixed methods are found to be very competitive with other numerical methods for plate bending problems.
Dispersion analysis of finite element semidiscretizations of the two‐dimensional wave equation
Authors: Mullen Robert , Belytschko Ted
Published: August 2005

The dispersive properties of finite element semidiscretizations of the two‐dimensional wave equation are examined. Both bilinear quadrilateral elements and linear triangular elements are considered with diagonal and nondiagonal mass matrices in uniform meshes. It is shown that mass diagonalization and underintegration of the stiffness matrix of the quadrilateral element markedly increases dispersive errors. The dispersive properties of triangular meshes depends on the mesh layout; certain layouts introduce optical modes which amplify numerically induced oscillations and dispersive errors. Compared to the five‐point Laplacian finite difference operator, rectangular finite element semidiscretizations with consistent mass matrices provide superior fidelity regardless of the wave direction.
Finite element operators: Inexpensive evaluation of upwind schemes
Authors: Hansen J. S. , Von Flotow A. H.
Published: August 2005

This paper introduces the notion of the finite element operator, and shows its application to the evaluation of several upwind finite element schemes. It is demonstrated that these operators supply good qualitative information on the performance of these schemes in an inexpensive as well as visual manner. In addition, this method gives insight into grid dependent effects which often characterize finite element solutions.