bluuebunny/crossref_metadata_2025 huggingface dataset:
Added mass computation by the boundary integral method
Authors: Deruntz John A. , Geers Thomas L.
Published: August 2005

Computational techniques for the treatment of fluid‐structure interaction effects by discrete boundary integral methods are examinde. Attention is focused on the computation of the added mass matrix by finite element methods for a structure submerged in an infinite, inviscid, incompressible fluid. A general computational procedure is presented that is based upon a variational approach involving the assumption of constant source strength over each surface element. This is followed by an analysis of the discretization error for a spherical body that is then used to develop a hierarchy of computational schemes. These schemes are than evaluated numerically in terms of ‘fluid boundary modes’ for a submerged spherical surface. One scheme has been found to be surprisingly accurate in relation to its computational demands.
Node Reordering algorithms for water network analysis
Authors: Gay R. K. L. , Chin K. K. , Chua S. H. , Chan C. H. , Ho S. Y.
Published: August 2005

The node Admittance matrices for Water Networks are normally sparse and symmetrical. Advantage may be taken of these properties to reduce the amount of computational time and memory required to solve them. Two node reordering algorithms and an economic system of storing input data are described. The node reordering algorithms minimize the number of fill‐ins which would occur in the solution of the node admittance matrix. Only non‐zero elements are stored and operated on. Subroutines for the node reordering algorithms and storge of input data, written in FORTRAN IV are included.
Sor vs. conjugate gradients in a finite element discretization
Authors: Fried Isaac , Metzler Jim
Published: August 2005

Sucessive Overrlaxation and Conjugate Gradients are used to solve the linear algebraic system set up with finite elements for the discretization of a plane, linear, head conducting problem. It is numerically shown that even with the optimal overrelaxation factor SOR is hardly superior to CG which is decisively simpler to program.
A note on quarter‐point triangular elements
Authors: Wait R.
Published: August 2005

Recently1−3 alternative methods of constructing triangular elements that reproduce strain singularities at crack‐tips have been suggested. The differences and similarities between the approaches are considered in this note.
Cross‐country sailplane flight as a dynamic optimization problem
Authors: Pierson Bion L. , De Jong Jan L.
Published: August 2005

A minimum−time, thermal−to−thermal sailplane trajectory optimization problem is formulated as a non−linear optimal control problem. Numerical solutions are obtained using a gradiaent projection algorithm which incorporates conjugate directions of search. Further insight into the nature of the solutions and the computational process is ontained through an analysis of the linearized sailplane dynamics and the necessary conditions for optimality. Numerical results are presented for two sailplane types and various values of thermal strength and distance between thermals. An additional problem is formulated and solved for the case of bounded control rate.
Finite element analysis of laminated composite plates
Authors: Panda Suresh C. , Natarajan R.
Published: August 2005

A finite element analysis technique for an arbitrarily laminated anisotropic plate is described. A superparametric quadratic plate element with five degrees‐of‐freedom per node is used in the analysis. A stress‐strain relation is derived from a three‐dimensional approach to the problem. The volume integration of the stiffness matrix is evaluated by numerical integration using the Gauss quadrature formula with 2 × 2 × 2 sampling points. A variety of laminated plate problems is solved and the results are compared with the exact solutions, which demonstrate the validity of the method.
A new finite element technique for the analysis of steady viscous flow problems
Authors: Ikegawa M.
Published: August 2005

A new finite element technique for two‐dimensional viscous incompressible fluid flow problems is presented in this paper. The vorticity transport equation is integrated in a small control volume, which results in the conservation law of vorticity. The finite element technique is applied to this equation together with the continuity equation, where simple linear triangular elements with three nodes are used for the formulation. Resulting sets of algebraic equations are solved by the use of a kind of relaxation method. Numerical results for viscous flow past a cavity show good agreement with experimental results.
An optimization procedure for stress concentrations by the finite element technique
Authors: Schnack Eckart
Published: August 2005

Load‐free notch surfaces of bodies made of a linear‐elastic, homogeneous, isotropic material are optimized within given variation domains by means of an interation procedure so that the occurring maximum tangéntial stress is reduced to a minimum. The hypothesis of a constant tangential stress distribution for obtaining minimal notch stresses proposed by R. V. Baud has been confirmed by means of the Fade‐away Law of the notch stress theory. The finite element method is applied for calculating the displacement and stress field of the styructure. An increment procedure is used for determing the displacement field after every iteration step, which permits the calculation of the displacement quantities with sufficient accuracy in a single step. Numerical solutions and their comparison with analytical solutions and stress results obtained with the aid of photo‐elasticity confirm the usefulness of this procedure. The known optimization methods1,2 differ from those used in the present paper.
Finite element discretization of open‐type axisymmetric elements
Authors: Basu Prodyot K. , Gould Phillip L.
Published: August 2005

A series of open‐type elements which are compatible with axisymmetric thin shell elements have been dervied. These elements allow the effects of intermediate openings and discrete support systems for rotational shells to be realistically modelled in the dynamic regime. Also, consistent load vectors for several common cases are derived.

The availablility of these elements in a public domain computer program enhances the possibility for modelling systems which are basically axisymmetric but which include intermediate or end supports using a rotational shell code.
LORA—an accurate four node stress plate bending element
Authors: Robinson John , Haggenmacher Gernot W.
Published: August 2005

A simple and accurate four‐node quadrilateral plate‐bending element based on stress assumptions is presented. Initial theremal strains and transverse shear stresses are included. The derivation is straightforward and without gimmicks and no numerical integration is necessary. The element behaves well for a wide range of aspect ratios with excellent convergence characteristics. The element is now being used in a practical warped configuration and with anisotropic material properties in the Lockheed‐California Company NASTRAN system.
Finite element incremental contact analysis with various frictional conditions
Authors: Okamoto Noriaki , Nakazawa Masaru
Published: August 2005

The use of contacting components such as gear teeth in mesh and shrink‐fitted shafts is very common in engineering practice. This paper deals with the development of a theoretical method which gives a solution for non‐linear contact problems with irreversibility resulting from stick‐slip phenomenon.

The method is based on the finite element method and load incremental theory. The geometrical and the statical boundary conditions on contact surfaces are treated as additional conditions being independent of stiffness equations. As a result, the algorithm of calculation is simplified and only a part of the simultaneous equations related to the contact surfaces is required to be solved instead of the overall stiffness equations at each step. Furthermore, the magnitude of load causing a change in a contact condition of one contact nodepair is taken as a load increment, in analogy with the incremental iterative procedure for elastic‐plastic problems. Therefore, the method provides a general and efficient method for analysis and design of such problems.

As illustrative examples, the stick‐slip behaviour of turbo‐alternator end‐bells and other problems are discussed. The calculated results show a reasonable agreement with experimental data and other solutions.
An algorithm for multipoint constraints in finite element analysis
Authors: Abel John F. , Shephard Mark S.
Published: August 2005

A method of introducing general constraint equations into finite element matrix equations is described. The characteristics of the method are that it requires no reordering or condensation of the equations, no large matrix operations, and no increase in the number of unknowns. The method is suitable for application in minicomputer implementations of finite element analysis unless a large number of constraints is to be applied.
A collocation finite element method for potential problems in irregular domains
Authors: Frind Emil O. , Pinder George F.
Published: August 2005

A potentially powerful numerical method for solving certain boundary value problems is developed. The method combines the simplicity of orthogonal collocation with the versatility of deformable finite elements. Bicubic Hermite elements with four degrees‐of‐freedom per node are used. A subparametric transformation permits the precise positioning of the collocation points for maximum accuracy as well as a unique representation of irregular boundaries. It is shown that by taking advantage of the boundary conditions, a minimum number of collocation points can be used.

The method is particularly suitable for potential and mass transport problems where a C1 continuous solution is required. In contrast to the Galerkin approach, it does not require the evaluation of basis function products and numerical integration, also the coefficient matrix contains only about half as many non‐zero terms as the corresponding Galerkin coefficient matrix. This results in approximately a 90 per cent reduction in formulation and a 50 per cent reduction in solution operation, as compared with the Galerkin finite element method, for this type of problem. Examples show that the accuracy of the collocation solution is as good as or better than that of the Galerkin solution.
Substructure variational analysis of the vibrations of coupled fluid–structure systems. Finite element results
Authors: Morand Henri , Ohayon Roger
Published: August 2005

The finite element method is used for the computation of the variational modes of the system composed of an elastic tank partially filled with a compressible liquied. We propose, on the one hand, a direct approcach based on a three field mixed variational formulation, and, on the other hand, a variational modal interaction scheme allowing the use of the acoustic eigenmodes of the liquid in a rigid motionless enclosure and the hydroelastic modes of the enclosure. Numerical results show the advantage of the second procedure.
Curved finite elements and shell theories with particular reference to the buckling of a circular arch
Authors: Batoz J. L.
Published: August 2005

The choice of strain‐displacement relations to fomulate curved finite elements for the geometrically nonlinear analysis of deep thin shells of general shape is discussed. It is clearly demonstrated on a simple arch problem how the strain‐displacement relations can affect the buckling pressure and it is concuded that inconsistent expressions should be avoided.
Numerical determination of a class of generalized stress intensity factors
Authors: Ioakimidis N. I. , Theocaris P. S.
Published: August 2005

A modification of the collocation method for the numerical solution of Cauchy‐type singular integral equations appearing in plane elasticity and, especially, crack problems is proposed. This modification, based on a variable transformation, applies to the case when the unknown function of the singular integral equation behaves like A(x − c)α + B(x − c)β, where α < 0, 0 < β − α < 1, near an endpoint c of the integration interval. In plane elasticity such a point is either a crack tip or a corner point of the boundary of the elastic medium. Thus the method seems to be quite efficient for the numerical evaluation of generalized stress intensity factors near such points. A successful application of the method to the classical plane elasticity problem of an antiplane shear crack terminating at a bimaterial interface was also made.
Smooth interfacing of finite element models
Authors: Harvey John W. , Clark Wesley C.
Published: August 2005

A technique for smoothing the transition between structural components modelled with dissimilar finite element meshes is presented. The interface mismatch is assigned a potential of dislocation, which is minimized with respect to selected kinematic parametes of the mating surface. This leads to linear constraints between the caididate representations of the mating surface which essentially dictate a least‐square error in dislocaiton. The constraints are enforced by the Lagrange multiplier or reduced stiffness technique. Numerical results indicate gradual transition in the predicted stresses neighbouring the interface. Existing computer codes which permit multipoint constraint specifications are readily available to implement the technique.
The computation of three‐dimensional rolling contact with dry friction
Authors: Kalker J. J.
Published: August 2005

In this paper the computer code Duvorol, dealing with the computation of three‐dimensional rolling contact with dry friction, is described. It is based on the variational principle of Duvaut and Lions for dry friction, which leads to an incremental theory. The relevant properties of Duvorol are:

Generality. All half‐space steady‐state rolling contact problems with Hertzian normal contact can be treated.

Reliability. The total tangential force is always found with reasonable accuracy by a standard discretization.

Speed. On an IBM 370/158 the calculation of a case then takes only several seconds.
Inelastic bending of beam including transverse shear
Authors: Bagchi D. K.
Published: August 2005

An incremental force–displacement relation is derived using the finite element matrix method to study the inelastic bending of beams including transverse shear. Solutions are obtained for the case of a cantilever beam with a point load and a simply supported beam with distributed loading considering and also ignoring the effect of transverse shear. They show good agreement for those cases where solutions are available. Also, the effect of transverse shear is found to be quite significant.
An algorithm for discrete Chebyshev linear approximation with linear constraints
Authors: Roberts F. D. K. , Barrodale I.
Published: August 2005

We describe a dual linear programming algorithm for solving the discrete Chebyshev (or l∞) approximation problem subject to any type of linear constraints. The numerical results provided here indicate that the present algorithm is an efficient extension of the Barrodale and Phillips Chebyshev algorithm, to which it reduces in the absence of constraints.
Numerical implementation of the ‘summed progressing wave’ formalism. computation of short‐time and long‐time transients
Authors: Gamby D. , Lamy R.
Published: August 2005

A mixed initial‐boundary value problem associated with a hyperbolic integro‐differential system is solved by means of the ‘summed progressing wave’ formalism. Once the numerical problem has been set, the pertaining solution methods are described. A simple approximate solution is also proposed. Attenuation functions are calculated through a novel method using the semi‐group property exhibited by the exponential of an integro‐differential operator. The long‐time solution of the problem at hand can be brought out owing to this procedure.
Line search methods for extended penalty function environments
Authors: Davis Caleb S.
Published: August 2005

Univariate minimization is considered for constrained optimization with the Kavlie‐Moe extended interior penalty. An algorithm is derived using a linear‐plus‐hyperbolic fit suggested by R. L. Fox for interior penalties. A linear extension to the linear‐plus‐hyperbolic permits rapid convergence with extended interior alties. However, constraint deletion and approximation of remaining constraints before each minimization also characterize the environment. These and other complexities impede accurate fitting of larger intervals. Thus, following Murray, a mixed strategy is adopted with function comparison reductions of interval size to supplement curve fitting.

Analysis shows how quadratic and cubic fit searches break down under certain limiting conditions of interior, extended and exterior penalties. A quadratic‐extended linear curve derived for exterior penalties and the linear‐plus‐hyperbolic similarly fail on extended interior penalties. Examples of constrained optimization with extended interior penalties were run on the Stanford IBM 370/168 computer. A stiffened two‐panel box provides eight optimization variables with many constraints on demensions and against failure. The extended linear‐plus‐hyperbolic surpasses cubic and linear‐plus hyperbolic fitting, especially when the Fiacco‐McCormick multiplier for the penalty becomes small. The value of feedback from curve fitting to decide function comparison use is also illustrated.
An historical note on the finite element method
Authors: Williamson Frank
Published: August 2005

Some comparisons between the finite element method and two early methods in the calculus of variations are presented.
Automatic reduction of frontwidth for finite element analysis
Authors: Razzaque Abdur
Published: August 2005

An algorithm is presented for reducing the frontwidth of finite element meshes. The technique takes an arbitrary input scheme and reorders the elements so as to reduce the frontwidth. A number of examples are presented to demonstrate the reliability and effectiveness of the method.
Solution of the Pontriagin–Vitt equation for the moments of time to first passage of the randomly accelerated particle by the finite element method
Authors: Bergman L. A. , Heinrich J. C.
Published: August 2005

The Pontriagin–Vitt equation governing the mean of the time of first passage of a randomly accelerated particles has been studied extensively by Franklin and Rodemich.1 In their paper is presented the analytic solution for the two‐sided barrier problem and solutions by several finite difference procedures.

This note demonstrates solution of the problem by a Petrov–Galerkin finite element method using upstream weighting functions,2 shown to give rapidly convergent results. In addition, the equation is generalized to include higher statistical moments, and solutions for the first few ordinary moments are reported.
Generalization of selective integration procedures to anisotropic and nonlinear media
Authors: Hughes Thomas J. R.
Published: August 2005

A new finite element procedure is introduced for the analysis of nearly‐incompressible media. The approach may be simply implemented by a small change of the standard technique, and is applicable to arbitrary anisotropic and/or nonlinear media. The procedure is shown to specialize to the selective integration and mean‐dilatation formulations under appropriate hypothesis.
Finite element calculations on a micro‐computer
Authors: Verruijt A.
Published: August 2005

A method is presented for solving field problems using a finite element formulation, to be executed with the aid of a micro‐computer. In order to reduce the requirements regarding memory space, the coefficients of the matrix defining the system of equations are not stored, but calculated when they are needed, in a modification of the usual finite element procedure. The method is applicable to all problems for which Gauss–Seidel iteration converges, and can handle problems involving more than 100 degrees‐of‐freedom on a computer with 8,000 bytes memory. Computing time may run up to several minutes per cycle of iteration, but on a small, personal computer, this is still acceptable.
Smoothing of data with errors in more than one variable
Authors: Thomson P. F.
Published: August 2005

Numerical experiments on the stepwise smoothing of non‐uniformly‐spaced‐two‐dimensional arrays of data by a simple and computationally inexpensive method have been performed. The method can readily be extended to more than two dimensions and the degree of smoothing can be improved by iteration. The method appears to be most efficient when the orientation of the reference axes is close to that of the curves which the data follow.
The use of time domain diakoptics in time discrete models of fields
Authors: Johns P. B. , Akhtarzad K.
Published: August 2005

The principles of diakoptics are extended to time domain solutions and the technique is applied to the solution of fields by introducing space approximating polynomials. Since transmission‐line networks provide time‐discrete models suitable for exact numerical analysis, the topic is approached by tearing these transmission‐line models and then showing how reconnection is made in the time domain.
Numerical results from large deflection beam and frame problems analysed by means of elliptic integrals
Authors: Mattiasson Kjell
Published: August 2005

Numerical evaluations of elliptic integral solutions of some large deflection beam and frame problems are presented. The values are given in tabular form with up to six significant figures. The numerical technique used for evaluating the elliptic integrals is described.
Singular finite element efficiency in estimating stress intensity factors
Authors: Staab G. H. , Sun C. T.
Published: August 2005

Singular finite element displacement functions for linear elastic fracture mechanics applications are investigated. The displacement fields are expressed in terms of polynomials. These polynomials are expanded in varying degrees of r and θ in order to examine the effect of the number and type of terms on the solution to various problems with known solutions. Methods of estimating the stress intensity factors for mode 1 and mode 2 are presented. Numerical results evaluating the effect of various r and θ terms on the solutions are presented.
Mixed models and reduced/selective integration displacement models for nonlinear analysis of curved beams
Authors: Noor Ahmed K. , Peters Jeanne M.
Published: August 2005

Simple mixed models are developed for the geometrically nonlinear analysis of deep arches. A total Lagrangian description of the arch deformation is used and the analytical formulation is based on a form of the nonlinear deep arch theory with the effects of transverse shear deformation included. The fundamental unknowns consist of the six internal forces and generalized displacements of the arch, and the element characteristic arrays are obtained by using Hellinger–Reissner mixed variational principle. The polynomial interpolation functions used in approximating the forces are one degree lower than those used for approximating the displacements, and the forces are discontinuous at the interelement boundaries.

The equivalence between the mixed models developed herein and displacement models based on reduced integration of both the transverse shear and extensional energy terms is discussed. The advantages of mixed models over equivalent displacement models are outlined. Numerical results are presented to demonstrate the high accuracy and effectiveness of the mixed models developed, and compare their performance with other mixed models reported in the literature.
Adaptive mesh refinement processes for finite element solutions
Authors: Rheinboldt Werner C.
Published: August 2005

The nature of adaptive processes is reviewed using as an example a specific finite element problem. Several possible formulations for the objective of mesh refinement processes are given. For the most natural of these objectives the A*‐algorithms of artificial intelligence turn out to provide a solution process which is known to be optimal in a certain sense. But practically, there is insufficient information and these processes tend to be inefficient. On the other hand, if the objective is replaced by a strictly local objective based on Pareto‐optimality, the error estimates of the resulting mesh sequence are shown to exhibit the order of convergence which is known to be best possible for the type of elements used.
A uniform strain hexahedron and quadrilateral with orthogonal hourglass control
Authors: Flanagan D. P. , Belytschko T.
Published: August 2005

The treatment of zero energy modes which arise due to one‐point integration of first‐order isoparametric finite elements is addressed. A method for precisely isolating these modes for arbitrary geometry is developed. Two hourglass control schemes, viscous and elastic, are presented and examined. In addition, a convenient one‐point integration scheme which analytically integrates the element volume and uniform strain modes is presented.
Continuous families of Lax‐Wendroff schemes
Authors: Cushman John H.
Published: August 2005

Families of difference schemes are developed for both the linear and nonlinear inviscid Burger's equation and a system of shallow water equations. Single‐step and two‐step (Lax–Wendroff type) families are described and comparisons are made with other difference schemes.

The schemes are developed using a very limited portion of a space–time continua, coupled with Galerkin's method applied over a few triangular elements. The elements are geometrically flexible as a function of a geometry factor α, creating the idea of difference families.

Stability is commented on, including the continuous relationship between stability and the families of schemes as a function of α. Numerical results are presented and commented on for the system of shallow water equations and the inviscid Burger's equation. Several areas for future research are described.
Collocation methods and the solution of conduction–convection problems
Authors: Herbst B. M.
Published: August 2005

The upwinded finite element method was introduced for the solution of conduction–convection problems by considering the model problem, u″‐Ku′=0, K>0, subject to the boundary conditions u(0)=1, u(1)=0. In this paper we consider the solution of this problem by the collocation method using piecewise cubic Hermite polynomials and a uniform grid. We consider the collocation points to be arbitrary parameters which enable us to express the collocation points in terms of the upwinding parameter of the upwinded finite element method. Various choices of the collocation points, including values which lead to complete accuracy in the nodal function values as well as the nodal values of the derivatives are discussed. Finally, we discuss the application of these points to slightly more general problems. Numerical results illustrating the behaviour of these points are given.
Finite element analysis of harmonic waves in layered and fibre‐reinforced composites
Authors: Minagawa S. , Nemat‐Nasser S. , Yamada M.
Published: August 2005

The problem of harmonic waves in layered and fibre‐reinforced composites is solved by a method of finite elements. Piecewise linear approximating functions are used for the displacement and stress fields in a mixed variational formulation, recently proposed by one of the writers in the form of a new quotient. Numerical computations are made for approximate phase‐velocities of harmonic waves in layered composites, where asymmetric and symmetric triangular meshes, and square meshes with interior nodes, are used. To illustrate the accuracy and effectiveness of the method, these approximate solutions are compared with those given by means of exponential test functions, and the exact ones by Rytov, etc. Calculations are also performed for harmonic waves in fibre‐reinforced composites. Dispersion curves for these waves are obtained and displayed graphically.
A comparison of localized finite element formulations for two‐dimensional wave diffraction and radiation problems
Authors: Taylor R. Eatock , Zietsman J.
Published: August 2005

Two of the most promising localized finite element methods are compared: the boundary series element method, in which a series of eigenfunctions is used to represent the far field solution; and the boundary integral element method, in which an integral equation is satisfied at the boundary between localized finite element and outer regions. The methods are applied to water of arbitrary depth. The theory of the two methods is summarized, and typical numerical results are discussed. Consideration is given to the well‐known hydrodynamical reciprocal relations, and to the phenomenon of ‘irregular’ frequencies. The relative merits of the two methods are established.
Finite difference solution of a system of first‐order partial differential equations
Authors: Henwood D. J. , Whiteman J. R. , Yettram A. L.
Published: August 2005

A finite difference solution of a system of first‐order partial differential equations, using a central difference scheme, is presented. The equations describe the linear elastic behaviour of a thick rectangular plate resting on an elastic foundation and carrying an arbitrary transverse load. The lateral edges of the plate are unstressed. The main deflections and stresses predicted by the method for a particular case are given, together for purposes of comparison, with results from a finite element analysis.
A two‐level implicit scheme for the numerical solution of the linearized vorticity equation
Authors: Shoucri Magdi M.
Published: August 2005

A numerical scheme is developed to study the stability of the linearized vorticity equations. The linear growth rates of Kelvin‐Helmholtz instabilities resulting from a velocity shear are calculated numerically. The theory of neutrally stable waves, in two dimensions, is extended to include the cases where the stream function is zero or periodic at the boundary, and is verified numerically for the case of a velocity profile having the shape of a cosine function. The instability growth rates of the oscillations in the neighbourhood of the neutrally stable waves are calculated numerically and are shown to be in very good agreement with the theory. The results are also of interest in relation to studies on the instabilities of a two‐dimensional guiding‐centre plasma, and also in the study of the diocotron instability in electronics.
Comparison of boundary element and finite element methods in the inelastic torsion of prismatic shafts
Authors: Mukherjee Subrata , Morjaria Mahesh
Published: August 2005

The accuracy and computational efficiency of the boundary element and the finite element methods are compared in this paper for problems of time‐dependent inelastic torsion of prismatic shafts. Several cross‐sections and two types of twisting history are considered in the numerical examples. The shaft material is assumed to obey an elastic‐time hardening creep constitutive model.
The boundary element method applied to the analysis of two‐dimensional nonlinear sloshing problems
Authors: Nakayama Tsukasa , Washizu Kyuichiro
Published: August 2005

This paper deals with an application of the boundary element method to the analysis of nonlinear sloshing problems, namely nonlinear oscillations of a liquid in a container subjected to forced oscillations. First, the problem is formulated mathematically as a nonlinear initial‐boundary value problem by the use of a governing differential equation and boundary conditions, assuming the fluid to be inviscid and incompressible and the flow to be irrotational. Next, the governing equation (Laplace equation) and boundary conditions, except the dynamic boundary condition on the free surface, are transformed into an integral equation by employing the Galerkin method. Two dynamic boundary condition is reduced to a weighted residual equation by employing the Galerkin method. Two equations thus obtained are discretized by the use of the finite element method spacewise and the finite difference method timewise. Collocation method is employed for the discretization of the integral equation. Due to the nonlinearity of the problem, the incremental method is used for the numerical analysis.

Numerical results obtained by the present boundary element method are compared with those obtained by the conventional finite element method and also with existing analytical solutions of the nonlinear theory. Good agreements are obtained, and this indicates the availability of the boundary element method as a numerical technique for nonlinear free surface fluid problems.
Practical stability test for finite elements with reduced integration
Authors: Hayes Linda J.
Published: August 2005

An easy to use stability test is presented for finite elements which are under‐ or selectively‐integrated. This test is reminiscent of the patch test in that it must be applied only to one prototype element, and it is a sufficient test for the nonsingularity of the global coefficient matrix. The minimum number of integration points which can be used with each of several common one‐, two‐ and three‐dimensional elements for a variety of steady‐state and time‐dependent, scalar boundary value problems are given.
Mesh refinement and iterative solution methods for finite element computations
Authors: Carey Graham F. , Humphrey David L.
Published: August 2005

Global and element residuals are introduced to determine a posteriori, computable, error bounds for finite element computations on a given mesh. The element residuals provide a criterion for determining where a finite element mesh requires refinement. This indicator is implemented in an algorithm in a finite element research program. There it is utilized to automatically refine the mesh for sample two‐point problems exhibiting boundary layer and interior layer solutions. Results for both linear and nonlinear problems are presented. An important aspect of this investigation concerns the use of adaptive refinement in conjunction with iterative methods for system solution. As the mesh is being enriched through the refinement process, the solution on a given mesh provides an accurate starting iterate for the next mesh, and so on. A wide range of iterative methods are examined in a feasibility study and strategies for interweaving refinement and iteration are compared.
On the computation of numerical derivatives by cubic splines
Authors: Tewarson R. P.
Published: August 2005

A method for improving the computational accuracy of numerical derivatives based on cubic splines and computed from a given set of function values with possible errors is described. The method incorporates smoothing, a derivative profile and/or numerical derivatives in the computational process by solving a pentadiagonal system of linear equations. Results comparing the derivatives computed by the present method, cubic spline and finite differences are given.
Application of the boundary integral equation method to Reissner's plate model
Authors: Weeën F. Vander
Published: August 2005

Numerical solution of Reissner's model for the bending of elastic plates by an advanced boundary integral equation method is outlined. Construction of fundamental solutions and computational strategy is fully described. Implementation of the resulting one‐dimensional model is illustrated by two test problems, including comparison to analytical solutions.
Discrete transfinite mappings for the description and meshing of three‐dimensional surfaces using interactive computer graphics
Authors: Haber Obert , Abel John F.
Published: August 2005

A system for describing three‐dimensional surfaces in a form suitable for finite element analysis is described. The system makes extensive use of real‐time interactive computer graphics techniques for both input and display. Discrete transfinite mappings are used as the mathematical basis for the surface representation. The mathematical basis and the reasons for choosing this form of representation are discussed. Explicit forms of the mappings based on Lagrange polynomial interpolation functions are presented. Finally, the interactive graphics procedures for defining finite element meshes are described.
Boundary layer refinements in convective diffusion problems
Authors: Kanarachos A.
Published: August 2005

The paper outlines a numerical procedure for the finite element solution of convective diffusion problems with significant convective terms using conventional (not upwinded) Galerkin methods in connection with ‘boundary‐layer type’ elements. The underlying argument in the sequel is that the poor stability properties of conventional Galerkin methods are caused by the insufficient approximation of eigensolutions. These are located at some sections of the boundary and are only present within a generally very thin layer. Consequently, the identification of these layers and the satisfactory approximation of the eigensolutions are necessary and totally sufficient for a satisfactory solution. In the following we intend to present this procedure, its theoretical background and selected numerical results.
A mixed formulation and mixed finite elements for limit analysis
Authors: Casciaro Raffaele , Cascini Leonardo
Published: August 2005

A mixed variational principle for the limit analysis of rigid‐perfectly plastic continua is discussed, in which the nonlinear yield condition and the associated flow rule appear through a suitably defined ‘penalty’ function. A mixed finite element discrete formulation is derived and a sequential unconstrained minimization technique is devised, affording a complete (static and kinematic) solution. Several results are presented in both structural and soil mechanics, compared with previously available (exact and numerical) solutions.
A direct automated procedure for frictionless contact problems
Authors: Mahmoud Faten Faheem , Salamon Nicholas J. , Marks Walter R.
Published: August 2005

The solution of elastostatic bodies in frictionless contact is obtained by an automated direct method which exploits the theory of linear elasticity and circumvents the need for the inclusion of artificial interface elements, mathematical programming techniques or computation of contact pressure. The method is simple and economical to use and can be easily appended to existing numerical schemes such as the finite element method. The formulation and numerical algorithm are presented for body combinations which are independent of relative tangential displacements along the contact surface. The method is illustrated through an elementary example amenable to hand calculation. Numerical results for more realistic problems are given and compared to known solutions. It is concluded that the method provides a powerful means for both the analysis and design of contacting bodies when used in conjunction with a finite element computer program.
Optimal arrangement of holes in a two‐dimensional heat conductor by a special boundary integral method
Authors: Barone M. R. , Caulk D. A.
Published: August 2005

The position, size and surface temperature of circular holes inside a two‐dimensional heat conductor are optimized to produce a minimum variation in surface temperature over a portion of the outer boundary. This problem, whic arises in thermal desing of moulds and dies, resembles those encountered in structural shape optimization because the internal geometry of the heat conductor depends on the design variables. In this paper, some of the traditional difficulties associated with shape optimization are overcome by analysing steady heat conduction with a special boundary integral method developed for two‐dimensional regions with circular hole. This approach eliminates the need to regenerate a finite element mesh over the interior of the region each time the geometry is changed during the design process. It also increases the efficiency of the analysis by reducing the number of unknowns in the numerical discretization of the region. Since the objective function depends only on the boundary temperatures, there is no need to determine temperatures in the interior.

The analysis method is applied to two problems arising in optimal thermal design of compression moulds. These examples show that the number of holes choson for the design strongly affects their resulting optimal arrangement as well as the ultimate uniformity of the cavity surface temperature.
High order methods for elliptic partial differential equations with singularities
Authors: Houstis Elias N. , Rice John R.
Published: August 2005

This paper reports on an experimental study of the effectiveness of high order numerical methods applied to linear elliptic partial differential equations whose solutions have singularities or similar difficulties (e.g. boundary layers, sharp peaks). Three specific hypotheses are established with high levels of statistical confidence to support the general conclusion: there is a strong correlation between the order of a method and its efficiency. Higher order is better.
A finite element formulation of uncoupled thermoviscoelastic response of plane problems for all admissible values of Poisson's ratio
Authors: Srinatha H. R. , Lewis R. W.
Published: August 2005

A variational theorem and the finite element method of solution are presented for the solution of thermoviscoelastic stress analysis of linear materials, valid for all admissible values of Poisson's ratio. An illustrative example is included.
Plastic analysis of torsion of a prismatic beam
Authors: Baba Shunsuke , Kajita Tateo
Published: August 2005

Finite element formulation for stress analysis of a twisting beam is developed. The formulation is effective for a prismatic beam with solid section as well as a thin‐walled beam, and can be applied both to a pure‐torsion problem and a warping‐torsion problem. The formulation is of a great advantage to an elastic‐plastic torsion problem. The formulation does not stand on the assumption of a thin‐walled structure, and therefore torsional rigidity of the section can be evaluated exactly without using the so‐called Saint‐Venant's torsional constant. Torsional rigidity is, in this paper, evaluated directly by a warping function of the section. Warping function is evaluated numerically due to shape of the section, due to progress of plastic region and due to effect of finite displacement (finite rotation, small strain). Pure‐torsion and warping‐torsion of a rectangular beam and an H‐beam, which have an elastic‐plastic material property, are analysed, and the extension to the finite displacement problem is discussed. Many numerical examples are provided in order to check the accuracy of the formulation.
Static analysis of shallow shells of arbitrary shape—a new approach
Authors: Bucco D. , Mazumdar J. , Sved G.
Published: August 2005

A simple, efficient and economical numerical technique for the analysis of shallow shells‐of arbitrary shape is presented. The technique is based upon the method of constant‐deflection contours combined with the well‐known finite element method. In the proposed method the elemental stiffness matrix is derived from a system of two consistent partial differential equations for two scalar functions using Galerkin's method. Several representative examples are included to indicate the effectiveness of the method.
A comparison of discretization methods for the shallow water equations
Authors: Praagman Niek
Published: August 2005

Numerical solutions of the shallow water equations obtained both by finite element methods and finite difference methods are compared. The numerical results show that the way in which the boundary is discretized has an important but local influence. Furthermore, the role of empirical parameters is shown to be of at least the same local importance.
The thermal history of a composite cylinder girth welded by TIG
Authors: Grill A.
Published: August 2005

A mathematical model for the calculation of the three‐dimensional thermal history of a composite cylinder, during girth welding by the TIG method, is presented. The solution is obtained by the alternating direction implicit finite difference method. The model takes into consideration the distribution of the heat input from the welding arc, the heat losses from the cylinder by radiation and convection, the dependence of the physical properties of the metal on the temperature and the solid‐liquid phase transformation. The effects of the efficiency coefficient of the welding arc, of the effective arc radius and of heat transfer coefficients on the thermal history are presented.
Another kind of numerical instabilities of the integral approach to the interior boundary‐value problem for the two‐dimensional Helmholtz equation
Authors: Mattioli Franco
Published: August 2005

In a previous paper it has been proved by the author that the integral equations arising from the application of Green's formula to the Helmholtz equation in a limited domain can show a certain type of numerical instability, if a real Green's function is used. It has been also proved that such instabilities cannot arise if a complex Green's function is employed.

However, it has been found in this latter case also that numerical instabilities can occur. This has been proved and thoroughly analysed for a circular domain, and a technique of avoiding these instabilities has been devised.

Furthermore, when this technique is followed, very accurate results can be obtained, regardless of wavenumber used. Thus, only three or four segments are sufficient to describe a wavelength, contrary to what until now has been obtained, i.e. that at least six segments are always necessary. This last result has been shown to be valid also for geometries other than the circular one.
Error growth in transient large displacement calculations
Authors: Wright Joseph P. , Baylor John L.
Published: August 2005

Nonlinear problems are widely acknowledged as being more difficult to solve numerically than linear problems. Various kinds of errors contribute to this difficulty and in this paper some of these errors will be described and illustrated by solving certain large displacement problems using eight‐noded isoparametric brick elements in space and an explicit integration method in time. First, approximation errors in time integration are illustrated, with violation of energy conservation being used as an indicator of the increased difficulties encountered in solving large displacement problems. Next, round‐off errors and order of operations are discussed and illustrated for the case of a cube that is impulsively set in rotation about its centre of mass. Simple tests of invariance with respect to translation and rotation are shown to be interesting and potentially useful. Finally, approximation errors in spatial discretization, especially those associated with incomplete or inconsistent integration over the element volume, are illustrated for a large deflection beam problem.
A mixed variational principle for finite element analysis
Authors: Day Michael L. , Yang T. Y.
Published: August 2005

A mixed variational principle is developed and utilized in a finite element formulation. The procedure is mixed in the sense that it is based upon a combination of modified potential and complementary energy principles. Compatibility and equilibrium are satisfied throughout the domain a priori, leaving only the boundary conditions to be satisfied by the variational principle. This leads to a finite element model capable of relaxing troublesome interelement continuity requirements. The nodal concept is also abandoned and, instead, generalized parameters serve as the degrees‐of‐freedom. This allows for easier construction of higher order elements with the displacements and stresses treated in the same manner. To illustrate these concepts, plane stress and plate bending analyses are presented.