bluuebunny/crossref_metadata_2025 huggingface dataset:
The mixed finite element method in plane elasticity
Authors: Mirza F. A. , Olson M. D.
Published: August 2005

Studies of the convergence and performance of the mixed finite element method in plane elasticity are reported. A completeness criterion is proposed, and convergence rates for stresses and strain energy, as predicted elsewhere, are quoted. An eigenvalue analysis of the mixed element matrix is carried out for various combinations of interpolations for displacements and stresses in a triangular and a rectangular element, and the results are discussed in relation to the completeness criterion. Finally, a triangular element with linear interpolations for stresses and displacements is formulated and its use is demonstrated on several numerical examples.
Effect of shear deformation on post‐buckling behaviour of columns
Authors: Holla V. K. , Prathap G. , Varadan T. K.
Published: August 2005

The post‐buckling behaviour of a cantilever column of variable moment of inertia with tip load is studied by means of a simple numerical iterative scheme. The governing equation of equilibrium is formulated using the axial and transverse displacement quantities, and applying linear constitutive and nonlinear kinematic relations. Numerical results obtained by numerical iterative procedure are presented in the form of curves showing the relation between non‐dimensional tip‐deflection and non‐dimensional load for different values of shear correction factors and taper ratios.
An investigation of first‐ and second‐order mixed plate‐bending elements
Authors: Akay H. U.
Published: August 2005

Numerical convergence of first‐ and second‐order plate‐bending elements is investigated. Using iso‐parametric formulation, general bilinear and biquadratic quadrilaterals, with the three moment components and the transverse deflection as dependent variables, are obtained. The same elements are also used as degenerate triangles by collapsing one side. A constant bending moment patch test, applied numerically to the elements, indicated poor performance for linear triangles, while the bilinear, quadratic and biquadratic elements behaved well, with exact results in uniform meshes. Further numerical examples showed the same general trend as the patch test. Although bilinear, quadratic and biquadratic elements were always able to yield the correct solutions with mesh refinements, the linear triangles were in general unable to do so.
Finite difference analysis for developing laminar flow in circular tubes applied to forced and combined convection
Authors: Collins M. W.
Published: August 2005

The complete two‐dimensional partial differential equations for developing laminar flow in a circular tube have been treated by a finite difference analysis. Property variation with temperature, especially that of viscosity, is allowed for in a flexible manner. The continuity and momentum equations, and then the energy equations, are solved by direct elimination at each axial step, and marching procedure used in the axial direction. A new technique is that the stepwise energy balance is rigidly satisfied throughout by using it as a constituent equation in place of the ‘explicit’ wall thermal boundary condition normally used.

The analysis predicts the complete developing hydrodynamic and thermal fields, together with friction factors and heat transfer coefficients. It has been tested for a range of fluid velocity and thermal boundary conditions and for various fluids, including high viscosity oils, water and air.

Data for constant wall heat flux have already been published. 1,2 Predictions for constant wall temperature presented here are for forced and combined convection and are compared with experimental data of Test3 and Zeldin and Schmidt4.
On the optimality of the pointwise accuracy of the finite element solution
Authors: Fried Isaac
Published: August 2005

Closed form finite element solutions are obtained for the uniformly loaded membrane in Rn, n = 2,3 discretized with first‐order elements. It is verified on this model that the pointwise error in the displacement is 0(h2 log 1/h). Slopes converge pointwise at the optimal rate 0(h).
Design oriented analysis of imperfect truss structures—part II—approximate analysis
Authors: Rosen Aviv , Schmit Lucien A.
Published: August 2005

An approximate analysis method for calculating local and system geometric imperfection influences on the displacements, stresses and buckling load of imperfect truss structures, is developed. The structural response, as a function of the design variables, is expressed in this approximate analysis which is much faster and cheaper than the ‘accurate’ analysis. The accurate analysis for a particular design is used as a base for each approximate analysis which then gives the response information needed for other designs in the neighbourhood about the base point design. Comparison of the approximate behaviour predictions with accurate results based on the more refined analysis methods shows that the quality of the proposed approximate analysis procedure is adequate for guiding a structural design procedure. It is evident that the approximate analysis is capable of describing the nonlinear behaviour of the structure, but when nonlinearity increases, the quality of the approximate analysis tends to deteriorate.
Improvement of MacCormack's scheme for Burgers' equation. Using a finite element method
Authors: Lucchi Ciro W.
Published: August 2005

A brief description of the finite element method to be used is given. It is then shown how various finite difference schemes for the wave and Burgers' equations can be achieved, in particular the predictor‐corrector method of MacCormack. By the finite element method a more efficient predictor‐corrector scheme is also obtained. Furthermore, the study tends to show that terms of the general form ∂(uvw)/∂x should be discretized by considering u,v and w as separate variables instead of taking the product uvw as a single variable as is often done with equations written in conservative (divergence law) form.
Substructuring in linear and nonlinear analysis
Authors: Dodds Robert H. , Lopez L. A.
Published: August 2005

The procedures for utilizing substructuring and static condensation in structural analysis are well known. However, until recently there have been no general‐purpose structural mechanics computer systems that offer multi‐level substructuring combined with a convenient method for defining the structural model. Now that such systems are available, engineers must decide when substructuring techniques are useful. Substructuring, with and without condensation, has proved to be highly efficient in the analysis of certain classes of structure. It can reduce computer costs by a factor of from 2 to 100. Yet, indiscriminate use of condensation may result in unnecessary and expensive computations. This paper examines the advantages and disadvantages of substructuring relative to data entry and computational efficiency. Guidelines are proposed for engineers to follow when using substructuring in the analysis of linear and nonlinear structures. The FINITE system is used to illustrate actual implementation of substructuring features in a general purpose finite element system.
A generalized automatic mesh generation scheme for finite element method
Authors: Imafuku Ichiei , Kodera Yoichi , Sayawaki Masaaki , Kono Makoto
Published: August 2005

This paper presents a generalized method which generates linear, triangular, quadrilateral and pentahedral elements for the finite element method. Depending on geometrical and material variations, the region to be discretized is manually divided into blocks such as lines, triangles, quadrilaterals, pentahedrons and hexahedrons in several appropriate co‐ordinate systems. However, no connectivity information of the adjacent blocks is required by the user as input. The continuity of the generated nodal co‐ordinates and element configurations at the block interface are automatically maintained to describe the geometry of structures, no matter how these five types of blocks are connected. Furthermore, a mesh grading algorithm which generates reliable mesh grade distributions in the interior of the triangular and quadrilateral blocks is established corresponding to the arbitrarily defined subdivision numbers for each edge line of blocks. This algorithm is extended to the mesh grading in the interior of the hexahedral and pentahedral blocks. Element numbers are also renumbered in this scheme, in addition to node numbers, in order to increase the computational efficiency of the global matrix assembly. Additional facilities, i.e. loading data generation, boundary condition data generation and so on, are also discussed. An illustrative and a practical example are given to demonstrate the capabilities of this scheme.
Band‐schemes vs. frontal‐routines in nonlinear structural analysis
Authors: Agrawal A. B. , Mufti A. A. , Jaeger L. G.
Published: August 2005

This paper evaluates the relative merits of the band‐schemes over the frontal‐routines in the solution of the linearized algebraic equations resulting from a nonlinear structural analysis. Through examples it is shown that the use of the former in the nonlinear analysis programs results in considerable savings in computer time. This is especially so when the structure under consideration is subject to dynamic loads due to earthquakes or simulated ground motions.
Computation of pareto optima in structural design
Authors: Carmichael D. G.
Published: August 2005

The structural design problem is acknowledge to be commonly multi‐criteria in nature. The various bases for multi‐criteria optimization methodologies are outlined and a computationally viable method for generating Pareto optimal solutions is adopted for the structural design problem where the criteria may be non‐commensurable. A numerical example on optimal truss design illustrating non‐commensurable criteria is given.
Analysis of error growth for explicit difference schemes in conduction–convection problems
Authors: Griffiths D. F. , Christie I. , Mitchell A. R.
Published: August 2005

A detailed study is made of the error growth associated with explicit difference schemes for a conduction‐convection problem. It is shown that the error can become arbitrarily large after a finite number of time steps even though it ultimately decays to zero. Certain ambiguities reported in the literature can thereby be resolved.
Comparison between a finite element and a composite method for a three‐dimensional potential problem
Authors: Trkov A. , Wood W. L.
Published: August 2005

This paper is concerned with the solution of the three‐dimensional potential problem for electromagnetic river gauging. It extends previous ideas of joining finite elements in an interior region to one infinite external element treated by the boundary integral method1,2 to this case where there are two external infinite elements representing the river and the ground. The boundary continuity conditions on the infinite river–ground interface, as well as the internal–external interfaces, are dealt with by introducing a variational principle with relaxed continuity requirement3.
A procedure to obtain a fully stressed shape of elastic continuum
Authors: Oda Juhachi , Yamazaki Kouetsu
Published: August 2005

In this paper, a procedure for obtaining a fully stresses shape of elastic continuum under arbitrary design conditions is proposed, by using the optimum distribution of the material properties such as the Young's modulus or the plate thickness. By using this technique, the optimum multiple‐connected shape can be created from the original shape of simply body. The optimum shape of a road‐pole subjected to an uniformly distributed load is determined by using the technique, and from the results the effectiveness of the technique is examined numerically.
A penalty plate‐bending element for the analysis of laminated anisotropic composite plates
Authors: Reddy J. N.
Published: August 2005

A C0 (penalty) finite element is developed for the equations governing the heterogeneous laminated plate theory of Yang, Norris and Stavsky. The YNS theory is a generalization of Mindlin's theory for homogeneous, isotropic plates to arbitrarily laminated anisotropic plates and includes shear deformation and rotary inertia effects. The present element can also be used in the analysis of thin plates by appropriately specifying the penalty parameter. A variety of problems are solved, including those for which solutions are not available in the literature, to show the material effects and the parametric effects of plate aspect ratio, length‐to‐thickness ratio, lamination scheme, number of layers and lamination angle on the deflections, stresses, and vibration frequencies. Despite its simplicity, the present element gives very accurate results.
The hybrid‐stress model for thin plates
Authors: Spilker Robert L. , Munir Nasir I.
Published: August 2005

The assumed‐stress hybrid finite element model is examined for application to the bending analysis of thin plates. A hybrid‐stress functional is defined by using a Mindlin‐type displacement assumption and including all components of stress. The Euler equations and matrix formulation corresponding to this functional are examined to assess the effects of plate thickness, and a rationale is presented for the selection of stress assumptions so that locking is avoided in the thin plate limit. To illustrate these concepts, a series of linear displacement quadrilateral elements are derived and tested, and the best of these elements is identified for suggested implementation in general‐purpose computer programs.
A triangular finite element mesh generator for fluid dynamic systems of arbitrary geometry
Authors: Kleinstreure Clement , Holdeman Jonas T.
Published: August 2005

A two‐dimensional finite element mesh generator capable of discretizing arbitrarily shaped flow regions is described. This economical, interactive computer code, written in FORTRAN IV and employing PLOT 10 software together with TEKTRONIX graphics terminals (4000 series or similar devices), generates a triangular network of variable element density according to the geometry and local kinematic flow patterns of a given fluid flow problem. The algorithm is an easy‐to‐use preprocessor and mesh generator delivering for a particular source program suitable input data which contribute to a higher degree of accuracy, efficiency and flexibility of the numerical scheme.

The code was tested for the triangularization of the confluence region of the Ohio and Tennessee rivers with two islands forming subchannels of different sizes.
A fully nonlinear analysis of heat and mass transfer problems in porous bodies
Authors: Thomas H. R. , Morgan K. , Lewis R. W.
Published: August 2005

The finite element method is used to analyse heat and mass transfer problems in porous media, in which the thermophysical properties are allowed to vary as functions of temperature and moisture. An example is given of the application of the method to the problem of timber drying.
Stresses in bonded connections using finite elements
Authors: Carpenter Associate Professor William C.
Published: August 2005

A finite element formulation for the adhesive of a lap joint is presented. The element is based on the assumptions common to the theories of Goland and Reissner and Ojalvo and Eidinoff. Deficiencies of the lap joint theories of those workers and of a previous finite element formulation of the adhesive are pointed out and the covergence of the new formulation to their results is discussed. Experimentally determined extreme fibre strains in the adherends are compared with those determined numerically using the new finite element formulation.
Oscillation limits for weighted residual methods applied to convective diffusion equations
Authors: Jensen Ole Krogh , Finlayson Bruce A.
Published: August 2005

Convection–diffusion equations are difficult to solve when the convection term dominates because most solution methods give solutions which oscillate in space. Previous criteria based on the one‐dimensional convection–diffusion equation have shown that finite difference and Galerkin (linear or quadratic basis functions) will not give oscillatory solutions provided the Peclet number times the mesh size (Pe Δx) is below a critical value. These criteria are based on the solution at the nodes, and ensure that the nodal values are monotone. Similar criteria are developed here for other methods: quadratic Galerkin with upwind weighting, cubic Galerkin, orthogonal collocation on finite elements with quadratic, cubic or quartic polynomials using Lagrangian interpolation, cubic or quartic polynominals using Hermite interpolation, and the method of moments. The nodal values do not oscillate for collocation or moments methods with Hermite cubic polynomials regardless of the value of Pe Δx.

A new criterion is developed for all methods based on the monotonicity of the solutions throughout the domain. This criterion is more restrictive than one based only on the nodal values. All methods that are second order (Δx2) or better in truncation error give oscillatory solutions (based on the entire domain) unless Pe Δx is below a critical value. This value ranges from 2 for finite difference methods to 4·6 for Hermite, quartic, collocation methods.
A note on upwinding and anisotropic balancing dissipation in finite element approximations to convective diffusion problems
Authors: Kelly D. W. , Nakazawa S. , Zienkiewicz O. C. , Heinrich J. C.
Published: August 2005

In one dimension, Petrov—Galerkin nonsymmetric weighting for the convective diffusion equation can be interpreted as an added dissipation. The addition of an appropriate amount of dissipation can therefore give the same oscillation‐free solutions as the ‘unwinding’, Petrov—Galerkin, finite element methods. The ‘balancing dissipation’ is optimally chosen so that excessive dissipation does not occur. A scheme is presented for extending this approach to two‐dimensional problems, and numerical examples show that the new method can be used with improved computational efficiency.
Dynamics of complex shells of revolution with arbitrary stiffness and density distributions
Authors: Sheinman Izhak , Zamir Israel
Published: August 2005

A general analytical and numerical procedure, based on the linear theory, is outlined for the elastic stress and deflection analysis of complex shells of revolution with arbitrary stiffness and density distributions, under arbitrary static and dynamic loads. The equations of motion admit shear deformation and rotary inertia. A numerical solution is obtained by recourse to Fourier expansion for the circumferential direction, to finite differences for the meridonial direction, and to Houbolt's method for the time domain. Numerical results are presented.
A note on the combined isotropic–kinematic workhardening rule
Authors: Allen David H.
Published: August 2005

The Ziegler modification of the Prager hardening rule has been used in conjunction with a combined isotropic–kinematic workhardening rule in order to predict the Bauschinger effect during cyclic loadings. There has been some controversy as to whether the above workhardening rule predicts a stress increment which is consistent with the yield condition. The purpose of this communication is to establish the combined hardening rule as a consistent statement in order to clarify its correctness.
On the relationship between a continuous update method of multipliers and the generalized reduced gradient method
Authors: Root R. R. , Ragsdell K. M.
Published: August 2005

The method of multipliers1–3 (MOM) is a transformation technique which has enjoyed considerable popularity in recent years. The algorithmic philosophy is similar to conventional penalty function methods in that a constrained nonlinear programming problem is transformed into a sequence of unconstrained problems. In the standard MOM approach, the multipliers are updated after each unconstrained search. In this paper we investigate methods which involve continuous updating of the penalty parameters and design variables. We demonstrate that this continuous updating scheme is equivalent to the generalized reduced gradient method4,5 applied to a certain dual problem. Computational results are given which suggest that the continuous updating MOM is not as efficient as one might reasonably hope.
A study of three‐node triangular plate bending elements
Authors: Batoz Jean‐Louis , Bathe Klaus‐JÜRgen , Ho Lee‐Wing
Published: August 2005

An assessment of flat triangular plate bending elements with displacement degrees‐of‐freedom at the three corner nodes only is presented, with the purpose of identifying the most effective for thin plate analysis. Based on a review of currently available elements, specific attention is given to the theoretical and numerical evaluation of three triangular 9 degrees‐of‐freedom elements; namely, a discrete Kirchhoff theory (DKT) element, a hybrid stress model (HSM) element and a selective reduced integration (SRI) element. New and efficient formulations of these elements are discussed in detail and the results of several example analyses are given. It is concluded that the most efficient and reliable three‐node plate bending elements are the DKT and HSM elements.
A lower bound for the two‐dimensional Helmholtz equation
Authors: Helps J. D. , Daly P.
Published: August 2005

A variational expression (Temple's formula), requiring C1 continuity, is used to transform the two‐dimensional Helmholtz equation into a matrix equation. Finite element techniques are used and homogeneous Neumann or Dirichlet boundary conditions are assumed. It is demonstrated that under certain conditions lower bounds to the eigenvalues are obtained.
Note on the modified Aitken accelerator for use in the residual force method
Authors: Atrek Erdal
Published: August 2005

Some considerations regarding the application of the modified Aitken accelerator to solution of problems of elasto‐plasticity by the residual force method are discussed. An efficient technique for continuing iterations after an acceleration is given.
Development of a unified numerical procedure for free vibration analysis of structures
Authors: Gupta K. K.
Published: August 2005

This paper presents the details of a unified numerical algorithm and the associated computer program developed for the efficient determination of natural frequencies and modes of free vibration of structures. Both spinning and nonspinning structures with or without viscous and/or structural damping may be solved by the current procedure; in a addition, the program is capable of solving static problems with multiple load cases as well as the quadratic matric eigenproblem associated with a finite dynamic element structural discretization. A special symmetric matrix decomposition scheme has been adopted for matrix triangularization, which renders the program rather efficient and economical. Also, a novel bisection scheme is described that further accelerates the solution convergence rate, particularly for the case of repeated roots.

The associated computer program adopts and out‐of‐core solution strategy, thereby enabling effective solutions to be achieved for large, complex, practical structures. A complete listing of the program written in FORTRAN V, for the UNIVAC 1100/82 computer, along with the source deck is available for ready use.
Minimum cost design of framed structures by the mini‐max dual method
Authors: Imai Kanji , Shoji Mikio
Published: August 2005

Minimum cost design of a framed structure is considered by using the mini‐mas dual method. Stress and/or displacement constraints are imposed as behavioural constraints. The minimum cost design problem has a discrete objective function and discrete design variables. A sequence of approximate optimization problems in created by using the first‐order Taylor series expansion for displacements with respect to the reciprocals of cross‐sectional areas and moments of inertia. Each approximate problem is solved in the dual space. Two simple structural examples are given to show the appropriateness and efficiency of the proposed procedure. Approximate solutions are obtained within five structural analysis.
Efficient calculation of numerical values of a polyhedral function
Authors: Pissanetzky Sergio , Basombrío Fernando G.
Published: August 2005

Some applications require the repeated calculation of numerical values of a polyhedral function at points specified by their co‐ordinates. The function is usually defined by some simple interpolation over each of the finite elements of a given mesh. A necessary step for the calculation of the value of the function at a given point is to determine to which element the point belongs. Such a determination can be efficiently accomplished by establishing a correspondence between the cells of some suitably defined regular mesh and the finite elements. Then, for each given point, the cell to which the point belongs is determined and the elements associated with that cell are inspected. This method is described and discussed in the text, and compared with two other less efficient methods with the help of numerical examples.
Kubik: An automatic three‐dimensional finite element mesh generator
Authors: Pissanetzky Sergio
Published: August 2005

This paper describes an automatic mesh generator for finite element problems in three dimensions, called KUBIK, KUBIK is based on a modular concept. First, a set of modules is generated, each with its own mesh inside. Then, the modules are placed in contact, and a matrix describing the connectivity of the entire mesh is determined. Finally, the geometry of the mesh is specified and all nodal co‐ordinates are determined by the computer. The user's labour required to specify a mesh which represents a certain physical configuration resumbles the labour involved when the configuration has to be specified to the machine shop workers who are supposed to build it.

The modules are independent, except for the compatibility requirements between modules which are to be placed in contact. Structures of any degree of complexity can in principle be obtained using KUBIK. Only two types of modules are required, except when helicoidal structures are to be generated, in which case it is convenient to use a third type. The finite elements used are distorted cubes, but they can be divided into tetrahedra, prisms of pyramids. Nodes are placed at the corners of the cubes, and additional nodes can be introduced if desired in order to obtain other types of finite elements in use. Infinite elements of quadrilateral cross‐section are also a standard feature of KUBIK, and can be divided in order to obtain infinite prisms of triangular cross‐section.

KUBIK can also generate two‐dimensional meshes, including meshing of a three‐dimensional surface for use with boundary elements.
The fourth‐dimention concept in the finite element analysis of transient heat transfer problems
Authors: Chung K. S.
Published: August 2005

This study presents the finite element analysis for the transient heat transfer problems by introducing the Fourth‐dimension concept. Time is treated as an additional dimension in the solution domain thereby Increasing the number of dimensions by one. For instance, a three‐dimensional transient problem can be considered as a four‐dimensional problem in the x, y, z, t domain and a two‐dimensional transient problem can be considered as a three‐dimensional steady‐state problem in the x, y, t domain, respectively. The variational principle of the finite element method and the techniques existing for steady‐state problems can be directly utilized. Numerical calculations were performed for heat conduction problems, laminar‐turbulent convective heat transfer problems, and radiative heat transfer problems.
Infinite elements with 1/rn type decay
Authors: Lynn Paul P. , Hadid Hassoun A.
Published: August 2005

This paper presents a method of developing a family of 1/rn type infinite elements for the analysis of problems definite in unbounded media. The proposed method is a direct extension of the conventional finite element method. The resulting improper integrals are integrated exactly over the infinite element domains. Two numerical examples in elastic half‐space static problems are investigated to illustrate the applicability and accuracy of the method. The use of the proposed infinite elements yields excellent results and preserves all the advantages of the finite element method.
A comparative study on the elastic‐plastic collapse strength of initially imperfect deep spherical shells
Authors: Kao Robert
Published: August 2005

A finite difference method for the large deformation elastic‐plastic analysis of spherical caps is applied to predict the collapse strength of initially imperfect deep spherical shells. Twelve uniformly loaded hemispherical shell models with flat spots at their apex are analysed. For each model, a number of shallow spherical regions containing the flat spot are selected from its domain. One of these selected shallow regions yields a minimum buckling pressure; this minimum value is taken as the theoretical buckling load for the shell model under consideration. Present solutions are in good agreement with existing experimental and empirical results. The good comparison suggests that initially imperfect deep spherical shells may be analysed by using a much simpler mathematical model—the spherical cap—and thus the analytical cost may be greatly reduced. This also demonstrates that the collapse of imperfect spherical shells is primarily a local phenomenon and therefore dependent on local geometry. Consequently, the presence of initial imperfections must be fully taken into consideration in any large deformation inelastic buckling analysis before such analysis can be expected to quantitatively predict the collapse strength of practical shell structures.
Structural analogies for scalar field problems
Authors: Everstine Gordon C.
Published: August 2005

This paper describes how general‐purpose finite element structural analysis computer programs can be used, without modification, to solve various scalar field equations such as the wave equation, the Helmholtz equation, Laplace's equation, Poisson's equation, the heat equation and the telegraph equation, as well as mixed field problems (such as coupled structural‐acoustic problems) which involve these equations.
Cubic spline boundary elements
Authors: Ligget James A. , Salmon James R.
Published: August 2005

The boundary integral method is formulated and applied using cubic spline interpolation along the boundary for both the geometry and the primary variables. The cubic spline interpolation has continuous first and second derivatives between elements, thus allowing the accurate calculation of derivative dependent functions (on the boundary) such as velocity in potential flow. The spline functions also smooth the geometry and can represent curved sections with fewer nodes.

The results of numerical experiments indicate that the accuracy of the boundary integral equation method is improved for a given number of elements by using cubic spline interpolation. It is, however, necessary to use numerical quadrature. The quadrature slows calculation and/or degrades the accuracy. The numerical experiments indicate that most problems run faster for a given accuracy using linear interpolation. There seems to be a class of problems, however, which requires higher order interpolation and/or continuous derivatives for which the cubic spline interpolation works much better than linear interpolation.
Transient forced vibration of rotationally periodic structures
Authors: Fricker A. J. , Potter S.
Published: August 2005

The calculation of the response of rotationally periodic structures to transient forces and prescribed motions is considered. The work extends the work previously described by Thomas1 in which only the free and harmonic forced vibration problems were considered. It is assumed that the finite element method is to be used, so that the equation of motion of the structure contains a finite number of degrees‐of‐freedom whose responses are governed by mass, stiffness and damping matrices. It is shown that an exact solution to the equation of motion of the idealized full structure can be obtained by solving the equation of motion of a single substructure for a number of different spatial Fourier harmonics of force (and hence response). A modal method of solving this equation is described. a brief description of the implementation of the method in a suite of computer programs, and the application of the programs to a practical problems, is also given.
Quadrilateral element with semi‐radial singularity mapping
Authors: Okabe Masayuki
Published: August 2005

The singularity mapping elementology based on the constant and semi‐radial field conditions is presented in an originally quadrilateral finite element. With the complete evaluations of singularities in the stress and strain as well as of the strain energy finiteness, it is demonstrated that this singularity element family is highly versatile. Differences and some identities between the semi‐radial mapping and the so‐called quarter‐point mapping are also examined.
Influence of aerodynamics on the critical parameters of thermal ignition
Authors: Kordylewski Włodzimierz
Published: August 2005

A numerical analysis of the critical conditions of thermal ignition for a two‐dimensional cylindrical reactor with flow field occurrence was carried out. The critical conditions of thermal ignition were defined as bifurcation points of the limit type. The dependence of the bifurcation points on aerodynamics was analysed by a sequential variation of the Peclet number. The flow field in the reactor was generated previously by a numerical solution of the Navier‐Stokes equations.

The nonlinear parabolic equation of heat balance and linear eigenvalue boundary problems occurring in the proposed non‐stationary method for calculating the bifurcation points was solved numerically using the finite difference technique.

It was shown that the critical points of thermal ignition form a surface bounded by the line of ‘limit of criticality’ in the parameter space. For large values of the Peclet number, the dependence of the critical parameter of ignition on Peclet number becomes linear.
Finite element solution of the Navier–Stokes equations in rotating flow
Authors: Bar‐Yoseph P. , Blech J. J. , Solan A.
Published: August 2005

The viscous incompressible rotating flow in a shrouded rotor geometry is solved by the finite element method, using the complete three‐dimensional (axisymmetric) Navier‐Stokes equations. Solutions to classical as well as to previously unsolved rotating flow problems are given and discussed.
A cubic triangular element with local continuity—an application in potential flow
Authors: Wu Erh‐Rong
Published: August 2005

A triangular element is developed using a complete third‐degree polynomial as the interpolation function. The nodal variables include the function and its first‐order derivatives. A local continuity condition, which implements the conservation of the normal gradients of the interpolation function along the three boundaries of the element, is provided as a remedy for the nonconformity of the first‐order derivatives in conventional C° elements. The element is applied to potential flow problems. Numerical results for the flow over a cylinder and the flow through a draft tube elbow of a hydraulic turbine confirm the validity and the accuracy of this new cubic element. A comparison of this element with a C° triangular element is made by checking their differences from an analytical solution for the flow over the cylinder. This element appears to be more accurate than the C° element.
An axisymmetric infinite element
Authors: Medina Francisco
Published: August 2005

A parametric infinite element is presented for solving axisymmetric problems under non‐axisymmetric forcing functions where the considered domain is assumed infinite. The element accuracy is compared against the exact solution for two classical problems: Boussinesq's and Cerruti's. Boussinesq's problem for a rigid circular plate is also presented. For these problems, using relatively simple displacement functions, the element provides a reasonable infinite domain representation.
On fredholm integral equations of the first kind occurring in synthesis of electromagnetic fields
Authors: Adamiak Kazimierz
Published: August 2005

The paper demonstrates that Fredholm integral equations of the first kind

equation image

with the kernel K(x, s)=(x–s)k/[1+(x–s)2]n occur while solving problems of synthesis of electrostatic and magnetic fields. Numerical results for the solution of one of the equations obtained by the regularization method are provided, with two ways of regularization being employed—that of Tikhonov and that of Lavrentev.
A finite element method with a hybrid lagrange line for fluid mechanics problems involving large free surface motion
Authors: Wellford L. Carter , Ganaba Taher H.
Published: August 2005

In this paper, free surface flow problems involving large free surface motion are analysed using finite element techniques. In solving these problems a spatially fixed Eulerian mesh is employed, in conjunction with a moving Lagrangian free surface line. The coupling, between the equations valid on the free surface and the equations valid on the fluid domain, is carried out using hybrid finite element techniques. Physical problems involving solitary wave propagation, sloshing dynamics and porous media flow are analysed to demonstrate the developed technique.
Uniform rational approximation by differential correction and remes‐differential correlation
Authors: Kaufman Edwin H. , Leeming David J. , Taylor G. D.
Published: August 2005

We present two self‐contained programs which have given excellent results for uniform approximation of functions (or discrete data) by generalized rational functions. The first program is an extension of a program published in 1975 which uses a linear programming approach known as the differential correction algorithm. The present version is more robust, and allows for the use of a multiplicative weight function and restrictions on the values of the approximating function. These features make the program more suitable for applications such as digital filter approximation. The second program uses a combination of the Remes and differential correction algorithms which combines some of the good features of both algorithms. Given here is a discussion of the algorithms together with several examples. A FORTRAN listing can be obtained from the first author.
Statics of thin‐walled pretwisted beams
Authors: Krenk S. , Gunneskov O.
Published: August 2005

The displacement and strain fields of thin‐walled pretwisted beams are prescribed in terms of generalized displacements for extension, bending, torsion and warping. Differential equations and boundary conditions are obtained from the elastic potential energy functional without assuming coincidence of the beam axis with any of the structural axes. This procedure gives a unique consistent definition of sectional moments and generalized forces. Some simple explicit formulae are derived for homogeneous tension–torsion. For the general case a computer code is developed on the basis of discretized generalized displacements and a modified energy functional, devised to obtain consistent lengthwise variation of the stresses and a unique decomposition of the torsional moment. Examples show agreement with analytical results for cylindrical beams and illustrate the various coupling effects for beams with pretwist. They also demonstrate the usefulness of the explicit formulae for homogeneous tension–torsion.
An algorithm for frontwidth reduction
Authors: Pina Heitor L. G.
Published: August 2005

This paper presents an algorithm for obtaining a small frontwidth. This feature is of interest when employing the frontal technique for solution of systems of linear equations in the finite element method. The performance of the algorithm is assessed by several examples at the end of the paper.
Quasistatic indentation of a rubber‐covered roll by a rigid roll
Authors: Batra R. C.
Published: August 2005

The nonlinear elastic problem involving the indentation of a slightly compressible rubber‐like layer bonded to a rigid cylinder and indented by another rigid cylinder is analysed by the finite element method. Both the geometric and material nonlinearities are accounted for. The finite element formulation of the problem is based upon a variational principle recently proposed by Cescotto and Fonder, and is valid for both slightly compressible and incompressible materials. The results computed and presented graphically include the shape of the indented surface, the pressure distribution over the contact surface, and the stress distribution at the bond surface. For the same contact width, the results for the compressible material are found to differ significantly from those for the case when the rubber‐like layer is assumed to be incompressible.
Analytical selection of masters for the reduced eigenvalue problem
Authors: Shah V. N. , Raymund M.
Published: August 2005

Masters are defined as the degrees‐of‐freedom that are retained in the reduced eigenvalue problem. Various qualitative guidelines to select masters are published in the literature, but it is difficult to apply them to complex structures. In this paper a computational algorithm to select masters for complex structures is presented. This algorithm is based on a guideline14 which assures that the associated Guyan reduction process is valid. This algorithm eliminates one degree‐of‐freedom at a time satisfying the guideline, and preserves lower frequencies in the reduced eigenvalue problem. The algorithm presented in this paper is used to select masters for four different structural models. The natural frequencies of the associated reduced eigenvalue problems are calculated and compared with those calculated from the full eigenvalue problems.
On the rates of convergence of the finite element method
Authors: Babuska Ivo , Szabo Barna
Published: August 2005

The rate of convergence of the finite element method is a function of the strategy by which the number of degrees‐of‐freedom are increased. Alternative stragegies are examined in the light of recent theoretical results and computational experience.
A smoothing technique for reduced integration penalty methods in contact problems
Authors: Kikuchi Noboru
Published: August 2005

The paper presents a smoothing technique to the oscillated contact pressure obtained by penalty methods for a class of unilateral contact problems in linear elasticity. The main result is to show that the smoothed contact pressure satisfies the so‐called Babuska–Brezzi condition which dominates the convergence of the penalty method. One numerical example is described.
Finite element analysis of rotating flow in a skewed shrouded rotor geometry
Authors: Bar‐Yoseph P. , Blech J. J. , Solan A.
Published: August 2005

The effect of slight shroud skewness on rotating flow in an enclosed rotor geometry is modelled as a perturbation about axisymmetric flow. Solutions are obtained by the finite element method. Mixed and penalty finite element formulation are employed.
A family of conforming finite elements for deep shell analysis
Authors: Sander G. , Idelsohn S.
Published: August 2005

The problem related to the derivation of conforming deep shell finite elements is examined in the light of the thin shell theory and using the classical Loves strain energy formulation. A family of quadrangular finite elements allowing for variable curvature is developed. It is shown how an exact conformity of the displacements can be ensured in a large number of cases.

Various static and dynamic applications are used to illustrate the advantages of these elements.
An ‘upwind’ finite element method via numerical intergration
Authors: Payre Guy , De Broissia Michel , Bazinet Jacques
Published: August 2005

Upwind finite element schemes remove spurious oscillations that occur in the solution of diffusion convection equations. Up to now these schemes lose part of their accuracy when the Peclet is large. As an improvement, it is proposed to move the integration nodes along the ‘streamlines’ before evaluating the elementary convection matrices. The displacements of the nodes along the streamlines, which are one‐dimensional manifolds, are calculated analogously to well‐known one‐dimensional formulae. The last section of this paper illustrates this new method with the help of four examples which show its validity.
Numerical solution of heat conduction problems by parabolic time‐space element
Authors: Tham L. G. , Cheung Y. K.
Published: August 2005

In this paper, heat conduction problems are solved by a quasi‐variational approach. A parabolic time–space element based on the above formulation is developed, and the stability of the above scheme is established. The results indicate that the scheme is suitable for various auxiliary conditions and that it is unconditionally stable.
An experimental investigation of the use of isoparametric and rational basis elements in a fluid flow problem
Authors: Keast Patrick , Woodford Gregory
Published: August 2005

Three competing finite element techniques are applied to a simple flow problem in a region with curved boundaries. Only three‐sided elements are considered. The techniques are (1) straight‐sided elements, (2) isoparametric elements, both of which use polynomial bases, and (3) curved elements using rational basis functions. The broad conclusions are that both curved‐edge techniques are much superior to their straight‐sided equivalent and that rational basis functions are quite successful in practice but require slightly more effort to implement, and cost a little more in computer time. From the point of view of efficiency, isoparametric elements seem to be the best choice.
Internally discontinuous finite elements for moving interface problems
Authors: Steven Grant P.
Published: August 2005

All physical process change with time and although physicists and engineers often freeze them to simplify their model studies, this is not always possible. Add to this the existence of several subregions within the modelling domain with different physical properties, the size and number of which change with time, and one has produced what might appear to be an intractable problem. Previous studies have shown that adaptive grids are an inconvenient way of modelling such moving interface problems and suggested that the use of a fixed grid with special discontinuous elements affords an efficient solution technique.

This work presents and develops the characteristic matrices for two such elements, namely a quadratic triangle with an internal interface modelled by two straight lines and a quadratic isoparametric element. Both these elements are tested against an analytical solution to a simple Poisson equation. Such tests reveal the performance of the proposed elements to be satisfactory except for the definition of gradients near the interface.
Semi‐implicit transient analysis procedures for structural dynamics analysis
Authors: Park K. C. , Housner J. M.
Published: August 2005

A semi‐implicit direct time integration procedure is presented which avoids factorization of the implicit difference solution matrix. The procedure, if properly implemented, requires only vectorial calculations and hence needs the same computer core space as explicit integration procedures. Guidelines for splitting the stiffness matrix into upper and lower matrices are established, which among other things are designed to satisfy a correct transmission of rigid‐body motions from element (or grid) to its adjacent elements.
A rational function approximation for the integration point in exponentially weighted finite element methods
Authors: Flaherty Joseph E.
Published: August 2005

A rational function is presented for approximating the function f(z)=coth z‐1/z that appears in several exponentially fitted or weighted finite difference and finite element methods for convection‐diffusion problems. The approximation is less expensive to evaluate than f(z) and provides greater accuracy than the doubly asymptotic approximation when z = O(n1).