bluuebunny/crossref_metadata_2025 huggingface dataset:
Inertia loading in finite element analysis of structures subject to compound motion
Authors: Barlow John
Published: August 2005

The problems associated with the stress analysis of structures subjected to body force loading due to compound motion are outlined. An economic method for calculating equivalent nodal loading, for use in a finite element displacement analysis, is proposed in which the element discretization and consistent mass matrices are used to advantage. The relevant equations, relating to the rigid body dynamics of compound motion, are appended in matrix notation. Validity of the method is demonstrated by an analysis of the stresses, due to gyroscopic and centrifugal forces, in an aero engine blade model.
Domain mappings for the numerical solution of partial differential equations
Authors: Oberkampf William L.
Published: August 2005

Independent variable transformations of partial differential equations are examined with regard to their use in numerical solutions. Systems of first order and second order partial differential equations in conservative and nonconservative form are considered. These general equations are transformed using generalized mapping functions and important computational features of the transformed equations are discussed. Examples of mappings which regularize domains are given involving various types of partial differential equations. These mappings are of particular importance in finite difference approximations because of the ease with which a mesh can be adapted to regions formed by co‐ordinate lines.
The incremental perturbation method for large displacement analysis of elastic‐plastic structures
Authors: Yokoo Yoshitsura , Nakamura Tsuneyoshi , Uetani Koji
Published: August 2005

A procedure of applying the perturbation method is presented for the incremental numerical analysis of materially and combined non‐linear problems of discrete and discretized structral systems. Small but finite strain and stress increments are strictly distinguished from the strain rates and stress rates, respectively. It is shown that, by applying the perturbation procedure not only to the non‐linear strain‐displacement relations and equilibrium equations, but also to the constitutive equations in terms of rate quantities, all the governing equations can be satisfied to any desired accuracy at every instantaneous configuration in between the starting and terminal points of an incremental step. The proposed method provides also means of finding, to a desired accuracy, every point on an equilibrium path of a discrete system at which a new element will start yielding or unloading and possible critical points on the path. The significance of the proposed method is expected to be appreciated particularly in numerical investigations of critical behaviours and post‐buckling behaviours.
The solution of ill‐conditioned linear systems arising from Fredholm equations of the first kind by steepest descents and conjugate gradients
Authors: Squire William
Published: August 2005

It is shown that the methods of steepest descents and conjugate gradients give smooth solutions of the ill‐conditioned systems of linear equations obtained by the discretization of Fredholm equations of the first kind without the use of any regularization techniques. A modification of the usual method of steepest descents is described which is equivalent to applying two cycles of the usual method with very little additional work. A number of examples are worked including one with a degenerate kernel in which the algebraic system is singular.
On a numerical solution of the supersonic panel flutter eigenproblem
Authors: Gupta K. K.
Published: August 2005

An automated digital computer procedure is presented in this paper which enables efficient solution of the eigenvalue problem associated with the supersonic panel flutter phenomena. The step‐by‐step incremental solution procedure is based on an inverse iteration technique which effectively utilizes solution results from the previous step in determining such results during the current solution step. Also, the computations are limited to the determination of a few specific roots only, which are expected to contain the flutter mode, and this is achieved at each step without having to compute any other root.

The structural discretization achieved by the finite element method yields highly banded stiffness, mass, and aerodynamic matrices; the aerodynamic matrix evaluated by the linearized piston theory is real but unsymmetric in nature. The solution algorithm presented in this paper fully exploits the banded form of the associated matrices, and the resulting computer program written in FORTRAN V for the JPL UNIVAC 1108 computer proves to be most efficient and economical when compared to existing procedures of such analysis. Numerical results are presented for a two‐dimensional panel flutter problem.
A thick finite strip solution for static, free vibration and stability problems
Authors: Benson P. R. , Hinton E.
Published: August 2005

A finite strip method for the analysis of plate bending problems is described. This method, which takes into account the effects of transverse shear deformation, is applied to the static analysis of a curved plate and then to the free vibration and stability of thick and thin plates.
Numerical evaluation of a class of singular double integrals by symmetric pairing
Authors: Squire William
Published: August 2005

Two quadrature rules based on nodes in a rhombus are used to evaluate integrals over a square with integrands which are singular on a diagonal. The rules are also compared for non‐singular integrals with an equivalent product Gauss rule.
A quadrature method for finite intervals
Authors: Squire William
Published: August 2005

The quadrature rule for a finite interval obtained by transforming to an infinite range and applying the midpoint rule is examined. It is found that the condition required to make the quadrature exact for a constant integrand imposes severe practical limits. The method is very good for integrands with singularities near the endpoints but ineffective for oscillatory integrands.
An iterative method for the design of symmetrical Joukowski airfoils of specified chord and maximum thickness
Authors: Pitoniak J. E. , Shanebrook J. R. , Lemmo A. C.
Published: August 2005

An iterative method is developed for designing symmetrical Joukowski airfoils of specified chord and maximum thickness. The method has been programmed for a digital computer and results for a particular airfoil design are given.
Efficient optimal design of structures by generalized steepest descent programming
Authors: Arora J. S. , Haug E. J.
Published: August 2005

The purpose of this paper is to present refinements in a steepest descent algorithm for optimal design of structures and numerical experience that demonstrates its numerical efficiency. The algorithm is based on a state space optimization technique that was initially developed and applied to optimal control problems. Design constraints are divided into four distinct subsets, the special characteristics of which are exploited to improve computational efficiency of the algorithm. Some further improvements in structural analysis, design sensitivity analysis, and constrained steepest descent programming calculations are presented. Optimum designs for three test problems are obtained and convergence rates are compared with results presented in the literature.
Rubber covered rolls—the thermoviscoelastic problem. A finite element solution
Authors: Batra R. C. , Levinson M. , Betz Eric
Published: August 2005

The coupled thermomechanical behaviour of a layer of thermorheologically simple material bonded to a uniformly rotating rigid cylinder and indented by another rigid cylinder is studied by the finite element method. The various approximations necessary to reduce the problem to one of tractable size and the computational methods used are discussed in some detail. The complete thermal, deformation and stress fields may be computed. Some results, computed for a grid using ‘rectangular’ elements, presented graphically include the temperature distribution, the stress distribution near the bond surface, the contact pressure distribution and the asymmetric surface deformation of the rubberlike layer.
A Poisson equation solver for rectangular or annular regions
Authors: King Hartley H.
Published: August 2005

A FORTRAN subroutine is presented which solves the system of simultaneous linear equations associated with the finite difference representation of the Poisson equation for rectangular or annular regions. The code is arranged to require minimum storage, and all possible operations involving known zeros and ones are suppressed. Single subscripting is employed to minimize execution time.
Efficient least squares finite elements for two‐dimensional laminar boundary layer analysis
Authors: Lynn Paul P. , Alani Kawan
Published: August 2005

This paper presents the formulations of essentially one‐dimensional least squares and Galerkin‐least squares finite elements for the numerical solution of two‐dimensional laminar boundary layer equations. An iterative technique to cope with the non‐linearity of the boundary layer equations, in conjunction with the least squares finite element method, is proposed. Through exhaustive numerical investigations in the retarded flow over a plate, flow past a circular cylinder, the flow past an elliptic cylinder, the accuracy and applicability of the proposed method are demonstrated.
A numerical model for the simulation of two‐dimensional convective‐dispersion in shallow estuaries
Authors: Narayanan M. , Shankar N. Jothi
Published: August 2005

A numerical model for describing two‐dimensional convective‐dispersive processes in tidally influenced shallow bays in given. The model uses a multi‐stage implicit technique with finite difference formulation, for solving the basic mass balance equation for a conservative constituent. The basic inputs to this model consist of instantaneous tidal velocities and depths obtained from an operational tidal hydrodynamic model.

The sensitivity of the output concentrations to the variation of dispersion coefficients is investigated. Application of the model to a practical situation is demonstrated by considering Galveston Bay. Texas, U.S.A. The transport model is operated to generate results which are compared with measurements from dye release studies made in a physical model of Galveston Bay.
On the finite element solution of an exterior boundary value problem
Authors: Wood Winifred L.
Published: August 2005

This paper compares three methods for dealing with an exterior boundary value problem by the Finite Element Method, one of which involves using an infinite element. The methods are illustrated by application to the problem of ground water flow round a tunnel with permeable invert. The use of a special trial function with a variable parameter in the infinite element gives a particularly efficient method of solution.
Difference schemes for second order hyperbolic equations
Authors: Jain M. K. , Ahuja Raj , Bhattacharyya S.
Published: August 2005

Implicit difference methods for the wave equation in two space variables have been discussed with the help of a stability diagram. The difference methods of intermediate accuracy 0(h4+k2) have been determined. A method of order of accuracy 0(h2+k2) with minimum truncation error has also been found.
An iterative technique for fitting exponentials
Authors: Lal M. , Moore E.
Published: August 2005

An interative method to fit the function \documentclass{article}\pagestyle{empty}\begin{document}$\mathop \[y = \sum\nolimits_i^n { = 1} a_i e^{lix}\] $\end{document} to data is considered. The technique used is that of inversion of a linear differential operator with constant coefficients. This method reproduces the parameters for mathematically precise data and gives satisfactory results when the data are affected by random errors.
Effective numerical treatment of boundary integral equations: A formulation for three‐dimensional elastostatics
Authors: Lachat J. C. , Watson J. O.
Published: August 2005

The field equations of three‐dimensional elastostatics are transformed to boundary integral equations. The elastic body is divided into subregions, and the surface and interfaces are represented by quadrilateral and triangular elements with quadratic variation of geometry and linear, quadratic or cubic variation of displacement and traction with respect to intrinsic co‐ordinates. The integral equation is discretized for each subregion, and a system of banded form obtained. For the integration of kernel‐shape function products, Gaussian quadrature formulae are chosen according to upper bounds for error in terms of derivatives of the integrands. Use of the integral formulation is illustrated by the analysis of a prestressed concrete nuclear reactor pressure vessel.
Stiffness matrix for a non‐prismatic beam‐column element
Authors: Chugh Ashok K. , Biggers S. B.
Published: August 2005

An algorithm is presented which generates an element stiffness matrix for non‐prismatic beam‐column members using Newmark's numerical procedure of successive approximations. The resulting element stiffness matrix on element co‐ordinates is fond to be in excellent agreement with those available for limiting cases. An approximate stability analysis conducted on the covergence of the numerical scheme shows that the proposed algorithm is stable. The critical buckling loads for various and conditions are computed as part of the computational scheme. A computer program listing in FORTRAN IV is included which will handle essentially and order and/or kind of non‐prismaticity of beam elements. The results are presented in the conventional and convenient coefficient format.
Computer plotting of stress contours in excavated slopes
Authors: Kalkani E. C.
Published: August 2005

The contouring of stresses in two‐dimensional slopes is done quickly and efficiently by using the computer and an incremental plotter. The computer program developed here interpolates in two directions between centroids of finite elements at which the stresses are given, determines contour line co‐ordinates, and plots the contours. This program can be easily modified to plot stresses produced by other two‐dimensional finite element analysis programs as long as the arrangement of elements in the mesh is similar.
Stress intensity factors in anisotropic plates using singular isoparametric elements
Authors: Foschi Ricardo O. , Barrett J. D.
Published: August 2005

A conformable displacement model is presented for the finite element analysis of stress intensity factors in linear elastic fracture mechanics. The method is an extension to anisotropic materials of the one developed by Benzley for isotropic materials. Very good agreement is shown for the case of inclined cracks in an orthotropic plate between finite element results and those obtained by least squares collocation of stress functions.
Computation of rational product approximations
Authors: Henry Jackson N.
Published: August 2005

Let F be a continuous real‐valued function defined on [−1, 1] × [−1,1]. For purposes of simplifaction in some numerical processes, one may desire to have an approximation of the function F. We present a known method of approximation called the best rational product approximation. When developing this approximation to F, certain types of discontinuities may arise. We develop a slight variation of a known technique to overcome such discontinuities. With this modified technique, it is then possible to develop a computer program to compute the approximation of F. A brief discussion of this program is presented along with some of the results which we have obtained.
Improved quadratic elements
Authors: Chang Anthony T.
Published: August 2005

A general method to formulate improved quadratic elements is presented. Derivation of the method is based on more accurate shape functions that take into account effects of governing differential equations. These new shape functions have the same form as those of the standard eight‐node quadratic element. Therefore, they may be easily adapted into existing programs.

The new quadratic element is compared with both standard and standard condensed quadratic elements. To show relative merits of different quadratic elements eigenvalue tests are performed. Several examples ranging from field problems, plane stress and bar vibration are used to demonstrate the applicability of this approach.
Finite element residual schemes for unconfined flow
Authors: Desai Chandrakant S.
Published: August 2005

A finite element procedure based on residual potential or flow concept is proposed for free surface flow through porous media. A preliminary example is solved by using the proposed procedure.
The finite element solution of dissipative electromagnetic surface waveguides
Authors: McAulay A. D.
Published: August 2005

A finite element method is developed for investigating the propagation of high frequency electromagnetic waves along closed or open (surface) waveguides containing dissipative materials and having a cross section of arbitrary shape. The complex propagation constants and associated complex electromagnetic fields are determined as a function of frequency for possible modes of propagation. The method is verified by applying it to structures of simple shape for which analytical results may be calculated for comparison. Waveguides considered include a waveguide filled with dissipative material, a dissipative dielectric rod, a dielectric coated wire and a conducting wire.
Optimal structural design under dynamic loads
Authors: Feng T‐T. , Arora J. S. , Haug E. J.
Published: August 2005

This paper presents an algorithm for optimal design of elastic structures, subjected to dynamic loads. Finite element, modal analysis and a generalized steepest descent method are employed in developing a computational algorithm. Structural weight is minimized subject to constraints on displacement, stress, structural frequency, and member size. Optimum results for several example problems are presented and compared with those available in the literature.
Triangular quarter‐point elements as elastic and perfectly‐plastic crack tip elements
Authors: Barsoum Roshdy S.
Published: August 2005

Triangular and prismatic quadratic isoparametric elements, formed by collapsing one side and placing the mid‐side node near the crack tip at the quarter point, are shown to embody the (1/√r) singularity of elastic fracture mechanics and the (1/r) singularity of perfect plasticity. The procedure of performing the fracture analysis for the case of small scale yielding is discussed, and the finite element results are compared with theoretical results.

The proposed elements have wide application in the fracture analysis of structures where ductile fracture is investigated. They permit a determination of the relationship between crack tip field parameters, loading, and geometry. And for a given fracture criterion can be applied to the prediction of fracture in structures such as pressure vessels under in service conditions.
Solution of a complex quadratic eigenvalue problem
Authors: Gignac Donald A.
Published: August 2005

A complex quadratic eigenvalue problem of order n (n = 20, 30, 40,…) encountered in an investigation of pipe flow was reduced to that of computing the eigenvalues of either a real or a complex matrix of order 2n, depending on the linearization technique used. To get satisfactory results using the CDC 6000 series computer, double‐precision versions of certain widely used and highly regarded eigenvalue subroutines were required. Although the modified subroutines used for the real matrix computations required less core than those used for the complex matrix, the calculation time was not significantly faster than that for the complex matrix. The use of ‘balancing’ subroutines merits further investigation.
A note on an element ordering scheme
Authors: Bykat A.
Published: August 2005

This paper contains an algorithm for the ordering of elements in the finite element method, which can be utilized in the Non‐assembly Method of the author and in the Frontal Solution Method of B. M. Irons.
A numerical method of solving Fredholm integral equations applied to current distribution and inductance in parallel conductors
Authors: Deeley E. M. , Okon E. E.
Published: August 2005

If the resistance of a conductor is negligible compared with the reactance and if radiation effects are ignored the inductance and current distribution may be obtained by using perfectly‐conducting models. In this paper the distribution of current in a system of infinitely‐long, perfectly‐conducting straight conductors of arbitrary cross‐section is shown to satisfy an integral equation of Fredholm type and a general digital procedure for solving this equation, and hence for determining inductance, is given.

The relative advantages of stepped, piecewise‐linear and piecewise quadratic approximations to the current distribution are studied using arrangements of strip conductors and of isolated rectangular conductors having known current distributions. The advantageous effect of varying the width of the sections used in the computation is also established. It is shown that inductance estimates accurate to within 0·1 per cent can be obtained with a relatively small number of sections and that for a large number of sections the inductance converges on the theoretical value. The paper also examines current distribution and inductance for ‘go‐and return’ systems of rectangular conductors, as well as for two paralleled conductors with remote return, and compares the inductances obtained with previous derivations.
Finite element analysis of non‐linear static and dynamic response
Authors: Mondkar D. P. , Powell G. H.
Published: August 2005

The paper presents the theoretical and computational procedures which have been applied in the design of a general purpose computer code for static and dynamic response analysis of non‐linear structures. A general formulation of the incremental equations of motion for structures undergoing large displacement finite strain deformation is first presented. These equations are based on the Lagrangian frame of reference, in which constitutive models of a variety of types may be introduced. The incremental equations are linearized for computational purposes, and the linearized equations are discretized using isoparametric finite element formulation. Computational techniques, including step‐by‐step and iterative procedures, for the solution of non‐linear equations are discussed, and an acceleration scheme for improving convergence in constant stiffness iteration is reviewed. The equations of motion are integrated using Newmark's generalized operator, and an algorithm with optional iteration is described. A solution strategy defined in terms of a number of solution parameters is implemented in the computer program so that several solution schemes can be obtained by assigning appropriate values to the parameters. The results of analysis of a few non‐linear structures are briefly discussed.
Eccentrically loaded sandwich panels
Authors: Tatsa E. Z. , Levy M.
Published: August 2005

The paper deals with the design of eccentrically loaded sandwich panels in civil engineering structures. A theoretical analysis taking into account the non‐linear stress–strain properties of the materials and the influence of shear deformations is proposed. A computer program based on the described algorithm is used to solve a numerical example. It is found that the Newton–Raphson procedure both in the solution of strains at individual sections and in the step by step procedure over the whole structure converges rapidly. Thus the method is suitable for the evaluation of the critical load due to strength failure or loss of stability.
Application of least square collocation technique in finite element and finite strip formulation
Authors: Kwok W. L. , Cheung Y. K. , Delcourt C.
Published: August 2005

A new approach in the formulation of finite elements using the concepts of least squares in conjunction with collocation is developed. No numerical integration is required in the stiffness formulation and the resulting matrix has the advantage of being always symmetrical. This approach has also been applied to the finite strip method and provides a means for rapid and accurate analysis of high order partial differential equations. The accuracy and versatility of the method are demonstrated by several examples.
Substructured macro elements based on locally blended interpolation
Authors: Cavendish James C. , Gordon William J. , Hall Charles A.
Published: August 2005

In this paper we describe a new class of locally refined macro finite elements which are especially amenable to the use of substructuring techniques for the efficient solution of the resulting idealization. The tools and guidelines illustrated by the examples of modelling crack tips, point load singularities and singularities at re‐entrant corners should enable an analyst to construct other such blended macro elements specifically tailored to his particular class of problems. The use of such substructured macro elements in finite element calculations permits substantial reduction in the manual effort of data preparation and the computational cost of numerical solution.
A theoretical study of thermal stress relief in thin shells of revolution
Authors: Cameron I. G. , Pemberton C. S.
Published: August 2005

A numerical method is given for examining the effect of uniformly heating thin shells of revolution which have an initial stress state. It is assumed that the yield strength decreases with temperature so that significant plastic flow takes place. The note includes a detailed study of this annealing effect on a finite length cylinder which has been given an initial state of stress by removing a longitudinal strip from it and rejoining the edges. The spread of the plastic regions with increasing temperature is followed and it is shown that the peak stress following a heating and cooling cycle is about 10–20 per cent in excess of the yield strength of the material at the peak temperature attained.
A numerical method for two‐dimensional Navier–Stokes equation by multi‐point finite differences
Authors: Saitoh Takeo
Published: August 2005

A numerical scheme with a high degree of accuracy has been developed for the full Navier–Stokes equations. The method utilizes the multi‐mesh points for space and time derivatives in order to improve the truncation error. Whereas the existing numerical method employing the finite difference scheme, e.g. the explicit, pure implicit, Crank–Nicolson, and DuFort–Frankel schemes, has the truncation errors of the order (Δx)2, Δx being the spatial mesh length, the one for the present method is generally of the order (Δx)3. A numerical example is shown for a natural convection flow in a square box and the results are compared with those of Cormack et al. One order of magnitude reduction of the computing time for a constant degree of accuracy was attained for the two‐dimensional problems. Furthermore, a two order of magnitude reduction is to be expected when the method is applied for the three‐dimensional Navier–Stokes equations.
Isoparametric, finite element, variational solution of integral equations for three‐dimensional fields
Authors: Jeng G. , Wexler A.
Published: August 2005

An improved numerical method, based on a variational approach with isoparametric finite elements, is presented for the solution of the boundary integral equation formulation of three‐dimensional fields. The technique provides higher‐order approximation of the unknown function over a bounding surface described by two‐parameter, non‐planar elements. The integral equation is discretized through the Rayleigh–Ritz procedure. Convergence to the solution for operators having a positive‐definite component is guaranteed. Kernel singularities are treated by removing them from the relevant integrals and dealing with them analytically. A successive element iterative process, which produces the solution of the large dense matrix of the complete structure, is described. The discretization and equation solution take place one element at a time resulting in storage and computational savings. Results obtained for classical test models, involving scalar electrostatic potential and vector elastostatic displacement fields, demonstrate the technique for the solution of the Fredholm integral equation of the first kind. Solution of the Fredholm equation of the second kind is to be reported subsequently.
On the approximation of convection problems in fluid dynamics
Authors: Griffiths D. F.
Published: August 2005

It is well‐known that oscillatory result when cerntral difference of finite element approximations are suoght for convective and boundary layer flows unless the grid length is sufficiently small. A priori limits on the grid spacing, bleow which the solutions are oscullation freee, are derived form one‐dimensional idenlizations of these problems and result form boundaryb layer theiry.
Comparative criteria for finite‐difference formulations for problems of fluid flow
Authors: Runchal Akshai K.
Published: August 2005

This paper concerns a technique for providing quantitative and qualitative answers to the questions related to accuracy and stability of finite‐difference schemes. It is applicable to both the unsteady and the steady flows. The application of the technique provides comparative information about the amplitudes and the speeds of propagation of the numerical and analytic solutions. The difference between the two solutions is characterized in terms of a ‘false’ propagation speed and ‘false’ diffusion parameters for the numerical schemes.

The technique is applied to a number of commonly used finite‐difference schemes and it is concluded that the use of central differences for the convective terms and/or explicit formulations tends to increase the amplitudes and wave speeds. The opposite effects on the amplitudes and wave speeds are produced by upwind or ‘donor’ cell differences and/or implicit formulations.
Derivatives of eigenvectors of locally modified structures
Authors: Hirai Itio , Kashiwaki Mitsuhiro
Published: August 2005

In this study a method for obtaining the derivatives of eigenvectors of a locally modified structure with respect to a design variable is presented. Eigensolution to the locally modified structure is expressed by equations consisting of the condensed matrices only which refer to the modified part. The analysis presented herein is developed in conjunction with eigensolution to the modified structure, and the derived fundamental equations are also represented by the same type of condensed matrices only. So, advantages are realized both in computational effort and in computer storage, if the modified part is small compared with the unmodified part. To find exact results, complete eigensolution to the unmodified structure needs to be given. Approximate results are obtained from a few lower eigenvectors and eigenvalues. A pin‐jointed truss is solved as a numerical example.
An experimental–numerical hybrid technique for three dimensional stress analysis
Authors: Chandrashekhara K. , Jacob K. Abraham
Published: August 2005

The paper describes a numerical method for determining the stress distribution in the interior of a three‐dimensional body using experimentally determined surface stresses, and the interior displacements from surface displacements. The normal and shear stresses inside the body are obtained by solving Laplace's equation in terms of sum of normal stresses together with the three‐dimensional compatibility equations in terms of stresses, using the finite difference technique, when the stresses on the surface of the body are known. On the other hand if surface displacements are known (from which strain components could be determined) then displacement components in the interior of a body can be determined by solving Laplace's equation in terms of sum of normal strains together with the three‐dimensional equilibrium equations in terms of displacements. It is shown that axi‐symmetric problems can also be solved in an identical way by transforming the equations into cylindrical co‐ordinates. The application of the method has been illustrated through several examples.
A least squares finite element approach to unsteady gas dynamics
Authors: Polk John F. , Lynn Paul P.
Published: August 2005

A numerical technique for solving unsteady gas dynamic equations is presented. The technique is based on least squares finite element concepts with elements that are constructed in both space and time. Both linear and quadratic interpolation is used on individual elements. The technique is tested against a problem whose solution is known so that numerical accuracy can be ascertained.
Finite element analysis of steady‐state elasto‐visco‐plastic flow by the initial stress‐rate method
Authors: Dawson Paul R. , Thompson Erik G.
Published: August 2005

A viscous approximation for steady creeping flow is extended to include the effect of elastic strains. Two examples are presented which illustrate both the method and the need for including elastic strains in the analysis of steady‐state visco‐plastic flows.
Closed form elastic‐plastic stiffness matrix for axisymmetric finite elements
Authors: Rich T. P.
Published: August 2005

This note presents the closed form equations for the stiffness terms in the elastic‐plastic stiffness matrix for axisymmetric finite elements. The element considered is a triangular ring element characterized by linear displacement relationships and an averaged state of stress. The physical law is modelled by the incremental theory of plasticity utilizing the Prandtl‐Reuss flow rule and von‐Mises Yield Criterion. Results are presented comparing stiffness terms as computed by numerical integration to those computed from the closed form equations. Significant errors in stiffness terms arising from numerical integration are observed for axisymmetric elements located near the line of axial symmetry as a result of the logarithmic nature of some of the stiffness terms.
A finite element formulation for large elastic‐plastic deformation analysis of polycrystals and some numerical considerations on polycrystalline plasticity
Authors: Gotoh M.
Published: August 2005

A finite element formulation for large elasto‐plastic deformation of polycrystalline materials is proposed in incremental form. The effect of rotation of crystal axes besides usual element rotaion is taken into account. Some numerical considerations on polycrystalline plasticity (i.e. stress‐strain curves for several proportional loadings, effect of change of loading path on stress‐strain curve, subsequent yield loci for uniaxial and equi‐biaxial loadings and so forth) are given for the case of small deformation by using a plate model which consists of 121 square FCC crystals.
An identification method applied to an orthotropic plate bending experiment
Authors: Kernevez J. P. , Knopf‐Lenoir C. , Touzot G. , Verchery G.
Published: August 2005

The paper presents a method of identification of material behaviour parameters. The method is applied to a simple example: the identification of orthotropic parameters using a plate bending test. A number of results are presented concerning the choice of numerical algorithm, the experimental protocole (number and locations of test points, loading) and the sensitivity of the method on experimental errors.
Higher‐order horizontally‐curved beam finite element including warping for steel bridges
Authors: El‐Amin Fathalla M. , Kasem Mohamed A.
Published: August 2005

The flexural stiffness for a horizontally curved beam element is developed for nodal parameters wi, (∂w/∂s)i, βi, (∂β/∂s)i, (∂2β/∂s2)i, (∂3β/∂s3)i by assuming a cubic displacement function for vertical deflection w, and a seventh order polynomical function for the angle of twist β, along the length of the curved beam. The element gives good accuracy with even coarse mesh for the analysis of horizontally‐curved steel beam with open thin‐walled bisymmetrical cross‐section.

Warping restraint is considered in the derivation of the stiffness matrix, which has considerable influence on the behavior and design of steel bridges curved in‐plan. The results obtained from such a new element are compared with those given by a lower order finite element, developed previously by the first author, and with theoretical solutions for the particular problem.
Application of the adaptive random search to discrete and mixed integer optimization
Authors: Kelahan R. C. , Gaddy J. L.
Published: August 2005

In this study, a random search technique, previously applied to continuous optimization problems, is adapted and applied to discrete and mixed integer problems. The development of the method and the procedure for applying the method are discussed in detail. Three discrete and one mixed integer problems, efficiencies can be made. The radom search procedure demonstrated perfect reliability in locating the optima. Improved efficiencies resulted for each of the examples are improved optimal solutions were found in two cases.
Optimal design of dynamically loaded continuous structures
Authors: Haug Edward J. , Feng T‐T.
Published: August 2005

A computational algorithm is developed and applied for optimization of beam and plate structures, subject to constraints on transient dynamic response. A continuous design formulation is retained, with dynamic response governed by partial differential operator equations. Adjoint equations are employed for sensitivity analysis and a function space gradient projection optimization approach is presented. Finite element analysis methods are applied for solution of the system dynamic and adjoint differential equations. Displacement constrained beam and plate minimum weight examples are solved, with a variety of boundary conditions.
Two step explicit finite element method for tsunami wave propagation analysis
Authors: Kawahara Matsuto , Takeuchi Norio , Yoshida Takaharu
Published: August 2005

Numerical analysis of tsunamis applying the finite element method is presented based on the shallow water wave equation. To discretize time, a two step explicit method is used. The scheme is the extension of the Lax‐Wendroff finite difference method. The present finite element method is used for the analysis of the Tokachi‐oki Earthquake tsunami problem and compared with the tide gauge records. The conclusion of this paper is that the present method is suitable for the prediction of the tsunami wave propagation problem.
The indirect design of fluid channels using a global variational method with trial functions not satisfying the prescribed boundary conditions: II cupling method
Authors: Hendry J. A.
Published: August 2005

A global variational method (GVM) not requiring the boundary conditions to be incorporated in the trial functions is described. The method is outlined for a linear differential equation and the extensions necessary to handle the non‐linear problem of the indirect design of a compressible fluid channel described. The method requires a suitable estimate of a parameter, but the results obtained for the non‐linear problem indicate that the actual value of this parameter is not critical (provided that a sufficeintly large number of trial functions is used). Comparisons are made with the results from an alternative GVM approach described in Davies and Hendry.1
Plasticity analysis by a non‐conforming plane element
Authors: Cochet J. F. , Dhatt G. S. , Aribert J. M.
Published: August 2005

A non‐compatible rectangular element with 12 degrees‐of‐freedom (DF) has been developed by Wilson et at.5 for analyzing 2‐dimensional problems. The superior convergence properties of this element as compared with the 8 DF element for linear elasticity problems with important bending have been demonstrated in References 2, 5. The purpose of this study is to assess the compartive efficiency of these two rectangular elements for an estimation of collapse loads in plasticity problems. For convenience, the 12 DF and 8 DF element will be represented by Q6 and Q4 respectively.
Solution of water networks by sparse matrix methods
Authors: Chin K. K. , Gay R. K. L. , Chua S. H. , Chan C. H. , Ho S. Y.
Published: August 2005

A computer program for Water Network analysis has been developed usingy sparse matrix techniques for solution. The method used is the successive linearization method where the set of equations [Q]=[Y][H] is solved. In the process, two subroutines for node reordering to preserve sparsity of the Jacobian matrix and a subroutine for solving the matrix by the Doolittle method are included. The method is user oriented and requires a minimum amount of input data and effort. Networks of up to 200 nodes and 300 pipes may be analysed on an IBM 1130 computer with 16K words of memory.
Large deflection analysis of frame structures by fictitious forces
Authors: Kohnke Peter C.
Published: August 2005

A new procedure is presented for the analysis of geometrically non‐linear frame structures. It assumes small strains and uses ‘fictitious forces’ based on the rotation from the initial configuration. The procedure also uses total displacements rather than incremental displacements. The procedure is valid for rotation up to 180 degrees and converges in a relatively small number of iterations.
Three‐dimensional finite element analysis for through‐wall crack in thick plate
Authors: Yagawa G. , Nishioka T.
Published: August 2005

A superposition method, in which analytical and finite element solutions are combined through the variational principle, is presented for determining the three‐dimensional stress intensity factors of the through‐wall crack. Cumbersome volume integral due to the singular terms at the crack tip is carried on by applying the least squares methods to the results obtained by the Legendre‐Gauss quadrature. Several numerical calculations are made based on the present method, showing that the three‐dimensional effects cannot be neglected especially for the cases of larger Poisson's raito. The comparison of the present method with the other finite element methods proposed for determining the three‐dimensional stress intensity factors indicates that the former has the obvious superiority to the latters in respect to the numbers of elements and nodal points necessary to obtain reasonable results.
A finite difference perturbation procedure for non‐linear elastic stability problems
Authors: Naschie M. S. El , Galaly I. , Athel S.
Published: August 2005

A finite difference perturbation scheme is developed which allows a simple solution to a wide class of non‐linear difurcation problems. The analysis shows that in order to determine the inital post bucking behaviour accurately, it is not necessary to solve more than the linear eigenvalue difference equation with similar accuracy.
Lumped mass matrices with non−zero inertia for general shell and axisymmetric shell elements
Authors: Surana Karan S.
Published: August 2005

A diagonal lumped mas formulation with non−zero inertia terms is presented for Ahmad's general shell element. The effect of co−ordinate transformation of the mas matrix is demonstrated. Due to arbitray co−ordinate transformation on nodal variables, the diagonal lumped mas matrix becomes a banded matrix of half bandwidth three. It is shown that with some approximations this matrix can be made diagnoal without effecting the results appreciably. Numerical examples are presented to illustrate the accuracy of the formulation. Similar lumped mass matrix formulation is also given for axisymmetric shell elements.
Thin plate semiloof element for structural analysis–including stability and natural vibrations
Authors: Martins R. A. F. , Owen D. R. J.
Published: August 2005

This paper presents a thin plate element formulated along parallel lines to the general three−dimensional Semiloof shell element. This plate version possesses only one half of the total number of degrees−of−freedom of the shell element and has the advantqage that the formulation of the strains and other terms is very much simplified. The element is first assessed in static situations and then its performance in the solution of eigenvalue problems is considered.
Central difference approximations to the heat transport equation
Authors: Lillington J. N. , Shepherd I. M.
Published: August 2005

This paper analyses the oscillatory nature of central difference approximations to the heat transport equation when convection is the important mechanism of heat transport. The effects of three different boundary conditions, various heat source profiles, the Peclet Number and the parity of the number of meshes on the amplitudes of these oscillations are described. A boundary condition is presented which suppresses the oscillations to insignificant amplitudes in the one−dimensional situation.
An accurate method of dynamic condensation in structural analysis
Authors: Leung Andrew Yee‐Tak
Published: August 2005

A new and efficient method of dynamic condensation is presented. It reduces the order of dynamic matrices without intoroducing further approximation by representing the passive co−ordinates in terms of the active ones exactly. The resulting frequency dependent eigenvalue problem is solved by a combined technique of Sturm sequence and subspace iteration. Examples are given for a space frame and a substructure problem. Results are compared to the complete solution.
On the Zienkiewicz three− and four−time−level schemes applied to the numerical integration of parabolic equations
Authors: Wood W. L.
Published: August 2005

The Zienkiewicz three− and four−time level schemes as proposed for vibration problems1 and adapted for the numerical integration of the diffusion equation after finite element discretization. Conditions are found for A0 stability and the methods are studied for their representation of the solution of y1=−λy. Methods used by various authors for linear and non−linear parabolic problems are compared. For the three time−level scheme a Liniger exponential fit of e−λ0Δt with a larger value of λ0Δt and the fully implicit scheme give the most promising results. The four time−level scheme is so much less amenable to control as to make it unsuitable for these problems.
The collapsed cubic isoparametric element as a ingular element for crack probblems
Authors: Pu S. L. , Hussain M. A. , Lorensen W. E.
Published: August 2005

For the 12−node quadrilateral isoparametric elements, it is shown that the inverse square root singularity of the strain field at the crack tip can be obtained by the simple technique of collapsing the quadrilateral elements into triangular elements around the crack tip and placing the two side nodes of each side of the triangles at 1/9 and 4/9 of the length of the side from the tip. This is analogous to placing the mid−side nodes at quarter points in the vicinity of the crack tip for the quadratic isoparametric elements. The advantages of this method are that the displacement compatibility is satisfied throughout the region and that there is no need of special crack tip elements. The stress intensity factors can be accurately obtained by using general purpose programs having isoparametric elements such as NASTRAN.
The numerical solution of two‐dimensional, steady flow problems by the finite element method
Authors: Moult A. , Burley D. , Rawson H.
Published: August 2005

Finite element equivalents of the equations governing shearing and buoyancy driven flows are derived, and reduced to upwind forms suitable for the solution of problems in which the Reynolds and Rayleigh numbers are large. A modification to the central difference iterative method is studied which increases the Reynolds and Rayleigh numbers for which a central difference form may be used. A comparison is made between the results obtained using the central and upwind forms of the finite element method and those predicted by finite difference methods in the case of flow in a cavity. A mesh refinement study is made. The upwind forms of the finite element equations are applied to the solution of a complex flow problem involving the flow of glass in a throated furnace in the case of constant‐ and temperature‐ dependent viscosity and conductivity.