bluuebunny/crossref_metadata_2025 huggingface dataset:
Finite element analysis of rubber‐like materials by a mixed model
Authors: Scharnhorst Thomas , Pian Theodore H. H.
Published: August 2005

A Reissner type variational principle is utilized to formulate a mixed finite element model for a finite‐strain analysis of Mooney‐Rivlin rubber‐like materials. An incremental and stationary Lagrangian formulation is adopted. The functional consists of incremental displacements and incremental hydrostatic and distortional stresses as variables. In the finite element formulation the displacements are interpolated in terms of nodal displacements while the two different strss components are approximated independently. The stress parameters for the distortional stresses are eliminated at the element level and the resulting matrix equations for each incremental solution involve the incremental nodal displacements and the average hydrostatic pressure in each element as unknowns. Four‐node quadrilateral plane stain elements were used to analyze the inflation of an infinitely long thick‐walled cylinder subjected to internal pressure. Both resulting displacements and stresses are found to converge to exact values as the magnitude of the loading increments is decreasing.
The aperiodic behaviour of a rigid shaft in short journal bearings
Authors: Holmes A. G. , Ettles C. M. M. , Mayes I. W.
Published: August 2005

A study is presented of the symmetrical steady‐state motion of a rigid shaft supported by two ‘short’ (Ocvirk) journal bearings. The equations of motion for a balanced or unbalanced shaft were solved using numerical ‘initial value problem’ techniques. Frequency analysis, which was used to determine the components of the steady‐state motion, confirmed that, for most conditions, the motion was asymptotically periodic comprising a small number of components—principally at synchronous and half synchronous frequency. However, a region of the operating space was found, in which the motion was complex and did not settle to a limit cycle. An estimate of the extent of this region is given and the suspected cause investigated.
Contcat stress minimization by contour design
Authors: Haug Edward J. , Kwak Byung M.
Published: August 2005

A sequential linear programming method is developed for contour design of elastic bodies to minimize contact stresses when two bodies are pressed together by extrenally applied loads. Constraints on the amount of acceptable contour modification are imposed, based on kinematic functions to be performed by the two mating bodies. The teachique is illustrated through solution of a simple example and a more practical bearing contact design problem.
Application of displacement and hybrid strees methods to plane notch and crack problems
Authors: Schnack Eckart , Wolf Michael
Published: August 2005

For calculating stress concentration factors at plane notches and stress intensity factors at plane cracks a system of finite elements is proposed which uses specially developed triangular hybrid stress elements at the notches and cracks and combines them with triangular elements acording to the displacement method. In formulating the stresses at the notches the Fade‐away Law formulated by Neuber has been taken into consideration; for the cracks, formulations are used which exactly contain the stress distribution of Irwin's equations. The quick convergence and high degree of accuracy of this approach are demonstrated by way of test examples.
Transition elements to be used with quarter‐point crack‐tip elements
Authors: Lynn Paul P. , Ingraffea Anthony R.
Published: August 2005

A generalization of the (r−1/2) strain or stress singularity capability of the quadratic isoparametric element is presented. It is shown that, by variable placement of the side‐nobe between quarter‐ and mid‐point, the point of singularity sensed by the element can be controlled. By using eight‐noded quadrilateral isoparametric elements with appropriately placed side‐nodes as transition elements between the quarter‐point crack‐tip trinagular and remaining non‐singular elements, stress intensity factors may be computed with higher accuracy.
Stability of the centred finite difference scheme for the three‐dimensional equations of elastodynamics
Authors: Schoenberg Michael , Nathaniel Rina
Published: August 2005

The displacement equations of motion for elastodynamics in 3 space dimensions are approximated by difference equations using 2nd order centred finite differences in space and time. The stability criterion of the difference scheme without boundary conditions is taken to be that condition on the ratio of step sizes which prevents the growth of an arbitray disturbance, and it requures the ratio of time step size to the space grid size to be less than a certain function of the ratio of the shear wave speed to the compressional wave speed. For this ratio less than 0.5, the condition is more stringent than that obtained by a simple extension from the two‐dimensional case.
A balanced expansion technique for constructing accurate finite difference advection schemes
Authors: Chan Robert K.‐C.
Published: August 2005

A new procedure, called the Balanced Expansion Technique (BET), is employed to construct accurate finite difference advection schemes that, for the model equation considered, are neutrally stable. By applying BET systematically, the phase error can be made as small as one wishes. Test calculations with one‐dimensional problems have confirmed the expected accuracy of these methods.
Consistent diagonal mass matrices and finite element equations for one‐dimensional problems
Authors: Schreyer Howard L.
Published: August 2005

The conventional dynamic variational approach and finite element base functions lead to non‐diagonal consistent mass matrics which are inappropriate for use with an explicit time integration scheme. In this work, it is shown that if orthogonal base function are used with a mixed variational formulation, then consistant diagonal mass matrices and corresponding sets of spatially discretized field equations are obtained. Although the approach is quite general, the theory is purposely illustrated by a detailed development for one set of base functions. Central difference time integration is incorporated for applications to one‐dimensional wave propagation and to Euler‐Bernoulli beams. Numerical examples are provided for elastic and elastic‐plastic materials.
An application of the Roberts' minimal degree algorithm to initial value problems
Authors: Henry Jackson N. , Henry Myron S. , Taylor Donald C.
Published: August 2005

Three algorithms are used to compute polynomial approximate solutions to initial value problems. One algorithm is based on the Roberts' minimal degree algorithm, whereas the other two algorithms utilize variants of the second algorithms of Remes. Our analysis indicates that the algorithm based on the Roberts' minimal degree algorithm is superior to the others considered.
A compact computer program for calculating buckling stresses and natural frequencies of vibration of prismatic plate assemblies
Authors: Williams F. W. , Wright C. J.
Published: August 2005

Low cost and increasing capability favour the use of mini‐computers as design tools. The 336 statement Fortran program which is listed and explained was developed to use such small computers efficiently. It calculates the buckling stresses, or the natural frequencies of vibration, of prismatic assemblies of longitudinally compressed isotropic plates. Various refinements have been used to keep the array requirements very small, including the ability to handle sub‐structures very flexibly and to use radial and tangential axes to define polygonal sub‐structures or structures.
An iterative algorithm to build continuous stress and displacement solutions
Authors: Cantin G. , Loubignac G. , Touzot G.
Published: August 2005

An iterative algorithm is presented: it builds a continuous stress and displacement solution starting from the solution of a classical displacement finite element analysis. The modified solution satisfies the virtual work principle, and is much better than the starting solution. The algorithm is very easily included in existing programs. A number of examples shows the efficiency of the method.
The shear deformation of profiled metal sheeting
Authors: Davies J. M. , Lawson R. M.
Published: August 2005

In the stressed‐skin analysis of metal structures it is vital to have a simple yet accurate treatment of the shear deformation of profiled metal sheeting. A suitable theory is developed in this paper for the two important cases of sheeting fastened to the supporting structure through every and alternate troughs of the corrugations. Various practical factors are taken into account. The results of an extensive series of numerical investigations are presented as a simple equation and a set of tables.
Application of the finite element method to an optimal control problem
Authors: Nakamichi J. , Washizu K.
Published: August 2005

The finite element method is applied to a typical problem in the optimal control theory. A finite element formulation is first set up, and then applied, as an example, to a problem of minimizing the transfer time of a low‐thrust rocket vehicle between the orbits of Earth and Mars. A procedure which combines the gradient projection technique with the Newton‐Raphson method is introduced to obtain numerically the solution of the minimum time transfer problem from the discretized functional. Numerical results show that the application of the finite element method to optimal control problems seems promising as well as encouraging.
Stability of explicit‐implicit mesh partitions in time integration
Authors: Belytschko Ted , Mullen Robert
Published: August 2005

The stability of time integration for a semidiscretization of structures and continua where the mesh is partitioned into subdomains integrated simultaneously by explicit and implicit methods is considered. Stability in energy is proven for linear systems subject to the Courant condition in the explicit subdomain for a central difference explicit and trapezoidal implicit integrator. Numerical examples are presented to demonstrate the procedure.
High order difference schemes for the wave equation
Authors: Iyengar Satteluri R. K. , Mittal R. C.
Published: August 2005

ADI difference schemes for the solution of the wave equation with variable coefficients are given. Mckee1 has given a formula of order O(k2 + h4), while Ciment and Leventhal2 have given a formula of order O(k4 + h4). Both the formulas are conditionally stable with the condition λ√c λ √3−1. In this paper we have derived uncoditionally stable ADI schemes of orders O(k2 + h2) and O(k2 + h4). These schemes allow large time steps and the computational effort is thus reduced. Numerical experiments suggest the usefulness of our formulas.
A.D.I. Methods for the solution of transient heat conduction problems in r−θ geometry
Authors: Evans D. J. , Gane C. R.
Published: August 2005

In this paper, the application of a particular class of computational methods, the alternating direction implicit methods applied to the solution of time dependent heat conduction problems in regions involving circular symmetry is presented.
On the stream function‐vorticity finite element solutions of Navier‐Stokes equations
Authors: Campion‐Renson Anne , Crochet Marcel J.
Published: August 2005

The stream function‐vorticity method for solving Navier‐Stokes equations with finite elements is often disregarded in view of the necessity of an iterative proceudre for satisfying the boundary conditions. The present work shows briefly that such iterations are unnecessary. Sample solutions for flows in a square cavity and in a channel with a step show good agreement with existing solutions.
Hybrid stress finite element model for non‐linear shell problems
Authors: Horrigmoe Geir
Published: August 2005

The present paper describes a hybrid stress finite element formulation for geometrically non‐linear analysis of thin shell structures. The element properties are derived from an incremental form of Hellinger‐Reissner's variational principle in which all quantities are referred to the current configuration of the shell. From this multi‐field variational principle, a hybrid stress finite element model is derived using standard matrix notation. Very simple flat triangular and quadrilateral elements are employed in the present study. The resulting non‐linear equations are solved by applying the load in finite increments and restoring equilibrium by Newton‐Raphson iteratioin. Numerical examples presented in the paper include complete snap‐through buckling of cylindrical and spherical shells. It turns out that the present procedure is computationally efficient and accurate for non‐linear shell problems of high complexity.
Blended infinite elements for paraboblic boundary value problems
Authors: Cavendish James C. , Hall Charles A. , Zienkiewicz O. C.
Published: August 2005

A common method for numerically approximating two‐point parabolic boundary value problems of the form ut = L[u]+f(u) defined of the semi‐infinite strip S = [0, 1]×[0, ∞] is to first discretize the spatial operator in the differential equation and then solve for the time evolution. Such an approach typically involves solving a system of algebriaic equations at a sequence of time steps. In this paper we take a different approach and subdivide S into a collection of semi‐infinite substrips Si = [xi, xi+1]×[0, ∞], and use blending function techniques to derive finite parameter functions ei(x, t) defined on Si. Spectral matching methods are used in deriving ei to ensure that (u − ei) can be made small on Si. Galerkin's method, with associated integration sover the entire space‐time domain S, is then used to generate approximations to u(x, t) based upon the so defined infinite element (ei, Si). Approximations are hence found for all (x, t) in S by solving one well structed system of algebraic equations. We apply the method to several linear and non‐linear problms.
Limit analysis of structures formed from rigid blocks
Authors: Livesley R. K.
Published: August 2005

In this paper a technique previously developed for the analysis of rigid‐plastic structural frames is adapted to provide a formal procedure for finding the limit load of any structure formed from rigid blocks. In this procedure the load factor is maximized subject to the euilibrium equations of the structure and linear constraints imposed by criteria of failure at the block interfaces.

In part I of the paper it is assumed that the limiting shear force associated with sliding at a block interface is independent of the normal component of force across the interface. This assumption means that the normality rule is satisfied, so that the upper‐ and lower‐bound theorems of classical limit analysis apply. This part includes a description of computer program for the collapse analysis of masonry arches with joints incapable of carrying tension.

In part II the limit on the Shear force at a block interface is assumed to be that associated with Coulomb friction. It is not difficult to extend the computational algorithm described in part I to deal with this situation. However, the failure mechanism computed by the algorithm will not necessarily satisfy the normality rule. The corresponding limit load may therefore be an over‐estimate of the true failure load, even though it is computed by a lower‐bound (equilibrium) approach. A criterion is established for testing the validity of a failure load computed in these circumstances.
Calculation of optimum feedback gains for output constrained regulators
Authors: Petkovski Dj J. B.
Published: August 2005

A new and a simple algorithm for approximate calculation of optimal output‐constrained feedback regulators is presented. computational simplicity is achieved by using properties of weakly coupled linear systems. The algorithm has been shown to be very effective in solving high dimensional control problems.
Improved three point integration schemes for triangular finite elements
Authors: Reddy C. T.
Published: August 2005

Symmetric three point quadrature schemes are at present available for triangles for exact integration of polynomials of degree 2. There are other possible symmetries, which provide higher accuracies. Exact integration of polynomials of a higher degree is possible. General formulations are made and a set of three integration points for improved accuracy is given.
Isoparametric elemetns for cross‐sepctional properties and stress analysis of beams
Authors: Surana Karan S.
Published: August 2005

This paper presents an isoparametric finite element formulation for the torsion and the flexure due to end shears for the beam cross‐sections of arbitrary shape. Isoparametric line elements are developed using this formulation for the beam cross‐sections consisting of very thin wall open or close multicells. Isoparametric transition elements are also developed for the beam cross‐sections consisting of both thin wall sections and solid like sections. Numerical examples are presented to demonstrate the accuracy and the applications of such elements.
Derivation of a new stiffness matrix for helically armoured cables considering tension and torsion
Authors: Knapp R. H.
Published: August 2005

A new element stiffness matrix is derived for straight cable elements subjected to tension and torsion. The cross‐section of a cable, which may consist of many different structural components, is treated in the following as a single composite element. The derivation is quite general; consequently, the results can be used for a broad category of cable configurations. Individual helical armourning wires, for instance, may have unique geometric and material properties. In addition, no limit is placed on the number of wire layers. Furthermore, compressibility of the central core element can also be considered. The equations of equilibrium are first derived to include ‘internal’ geometric non‐linearties produced by large deformations (axial elongation and rotatioin) of a straight cable element. These equations are then linearized in a consistent manner to give a liner stiffness matrix. Linear elasticity is assumed throughout. Excellent agreement with experimental results for two different cables validates the correctness of the analysis.
A new eight‐node solid element
Authors: Bretl John L. , Cook Robert D.
Published: August 2005

We present a new three‐dimensional finite element, with the customary three displacement d.o.f. at each corner but no internal d.o.f. It passes the patch test and, for rectangular elemtents, exactly models pure bending. In numerical tests, the new element is found to be both accurate and efficient. It has the added advantage that its bending and twisting stiffnesses can be individually adjusted.
Curvilinear finite difference method for biharmonic equation
Authors: Lau P. C. M.
Published: August 2005

The essence of the proposed curvilinear finite difference solution method is the direct solution of the transformed fourth order partial differentiall equation using the finite difference expressions based on the flexible structure so that the geometry generality of the finite element method can be approached. The examples of applications indicte that the curvilinear mesh can be used and the boundary condition on the curved boundary can be easily and accurately prescribed.
A comparasion of three resequencing algorithms for the reduction of matrix profile and wavefront
Authors: Everstine Gordon C.
Published: August 2005

Three widely‐used nodal resequencing algorithms were tested and compared for their ability to reduce matrix profile and root‐mean‐square (rms) wavefront, the latter being the most critical parameter in determining matrix decomposition time in the NASTRAN finite element computer program. The three algorithms are Cuthill–McKee (CM), Gibbs–Poole–Stockmeyer (GPS), and Levy. Results are presented for a diversified collection of 30 test problems ranging in size from 59 to 2680 nodes. It is concluded that GPS is exceptionally fast, and, for the conditions under which the test was made, the algorithm best able to reduce profile and rms wavefront consistently well. An extensive bibliography of resequencing algorithms is included.
A numerial experiment on orthonormalization process
Authors: Cheng S. Y. , Agarwal K. M.
Published: August 2005

A numerical experiment has been conducted to check theeffectiveness and reliablity of the orthnormalization process tosolve two‐point boundary value problems. This process in usedalong with the method of superposition in the linear case andwith the quasilinearization and then the method of superpositionin the non‐linear case.
A cubic extended interior penalty function for structural optimization
Authors: Prasad B. , Haftka R. T.
Published: August 2005

This paper describes an optimization procedure for the minimum weight design of complex structures. The procedure is based on a new cubic extended interior penalty function (CEIPF) used with the sequence of unconstrained minimization technique (SUMT) and Newton's method. The Hessian matrix of the penalty function is approximated using only constraints and their derivatives. The CEIPF is designed to minimize the error in the approximation of the Hessian matrix, and as a result the number of structural analyses required is small and independent of the number of design variables. Three example problems are reported. The number of structural analyses is reduced by as much as 50 per cent below previously reported results.
A numerical method for analysis of bounded metalworking processes
Authors: Sekhon G. S. , Shishodia K. S. , Sharma P. C.
Published: August 2005

This paper describes a numerical procedure for the solution of metalworking problems of a strain‐hardening material. The overall metalworking process is split up into a number of stages and the governing equations for a typical stage are set up in terms of incremental displacements. The incremental deformation occurring in each successive stage is found by an interative numerical procedure based on the concept of piecewise linearization. The ‘composite’ solution yields the distribution of stress and strain in the work material at various stages of the process. Finally, application of the method to finite axisymmetric compression is described.
An accurate method of dynamic substructuring with simplified computation
Authors: Leung Yee‐Tak
Published: August 2005

A new dynamic substructuring method is presented. The substructures are identified by their fixed‐interface modes and the condensed stiffness and mass matrices at zero vibration frequency. Physical co‐ordinates are used instead of the modal co‐ordinates to make the condition of compatibility between elements applicable. The dimension of the fundamental matrices is equal to the number of interface co‐ordinates for each substructure. All information needed to formulate the fundamental matrices may be obtained experimentally. Both discrete and continuous parameter models are considered.

A number of numerical examples are given and the method is compared with the other methods of dynamic substructure. It is shown that the numerical accuracy lost in the ordinary eigenvalue economization process may be recovered by the present method.
A finite element model for plasma simulation in multipoles
Authors: Hennart J. P. , England R. , Martin J. G. , Melendez L. L.
Published: August 2005

A numerical model is proposed to simulate the space‐time behaviour of a low‐density plasma in a linear multipole. Semi‐discrete Galerkin techniques are used in conjunction with triangular finite elements. For both space and time discretizations, special techniques are developed to numerically separate the effect of rapid diffusion along the field lines from the slow perpendicular diffusion. Numerical results are exhibited to show how these techniques succeed in eliminating the problems caused by the strong anisotropy of the diffusion coefficient in the strongly curved and very inhomogeneous multipole configuration.
Reconsiderations on singularity or crack tip elements
Authors: Yamada Y. , Ezawa Y. , Nishiguchi I. , Okabe M.
Published: August 2005

Various singularity finite elements proposed so far are reviewed and their correlations are discussed. The method adopted in the comparative study is based on the singularity mapping or transformation technique. It is suggested that a compact design of computational routines is materialized by using the element which embodies singularity transformation and can be compatible with the notion of using the variable‐number‐nodes element in the general‐purpose computer programs.
Spurious modes in two‐dimensional isoparametric elements
Authors: Bićcanić N. , Hinton E.
Published: August 2005

The reasons for the presence of spurious modes in plane isoparametric elements are examined. Eigenvalue and eigenvector analyses of stiffness matrices for single elements and unconstrained and constrained meshes reveal the types of mechanisms and near‐mechanisms that can be expected when reduced or selective integration techniques are used with quadrilateral elements in the analysis of plane strain problems.
On consistent finite difference formulae for ordinary differential equations
Authors: Miller R. E.
Published: August 2005

This paper presents a finite difference method for two‐point boundary value problems described by fourth‐order ordinary differential equations which results in consistency of truncation errors. It is demonstrated that the order of the formulae used to approximate the boundary conditions must be higher than those used for similar derivative terms in the differential equation. A generalization of the method to differential equations of order n is discussed. The procedure is illustrated with a numerical example.
The solution of nonlinear finite element equations
Authors: Matthies Hermann , Strang Gilbert
Published: August 2005

An algorithm is described which appears to give an efficient solution of nonlinear finite element equations. It is a quisi‐Nowton method, and we compare it with some of the alternatives. Initial tests of its application to both material and geometric nonlinearities are discussed.
The concept of fictitious loading
Authors: Salonen E‐M.
Published: August 2005

The concept of fictitious external loading being in exact equilibrium with the internal stresses in a structure is introduced. It is employed in conjunction with the principle of virtual work in an effort to examine certain details of the finite element displacement method in an alternative way.
Automatic local refinement for irregular rectangular meshes
Authors: Simpson R. Bruce
Published: August 2005

The use of local mesh refinements for the generation of meshes for the finite element or finite difference methods is studied. A class of rectangular meshes which admit restricted local refinements, referred to as irregular rectangular meshes, is introduced and its representation discussed. Properties of algorithms for mesh refinements are discussed from the viewpoints of termination with a mesh in the specified class, memory utilization, symmetry and fragmentation of the mesh.
Interpolation by fast Fourier and Chebyshev transforms
Authors: Monro Donlad M.
Published: August 2005

Transform methods for the interpolation of regularly spaced data are described, based on fast evaluation using discrete Fourier transforms. For periodic data adequately sampled, the fast Fourier transform (FFT) is used directly. With undersampled or aperiodic data, a Chebyshev interpolating polynomial is evaluated by means of the FFT to provide minimum deviation and distributed ripple. The merits of two kinds of Chebyshev series are compared. All the methods described produce an interpolation passing directly through the given values and are applied easily to the multi‐dimensional case.
A remark on the numerical evaluation of stress intensity factors by the method of singular integral equations
Authors: Ioakimidis N. I. , Theocaris P. S.
Published: August 2005

A modification of the numerical techniques of solution of Cauchy‐type singular integral equations and determination of stress intensity factors at crack tips in plane elastic media is proposed. This technique presents some advantages under appropriate geometry conditions.
Smoothing techniques for certain primitive variable solutions of the Navier–Stokes equations
Authors: Lee Robert L. , Gresho Philip M. , Sani Robert L.
Published: August 2005

Several types of smoothing technique are considered which generate continuous approximation (i.e. nodal values) for vorticity and pressure from finite element solutions of the Navier–Stokes equations using quadrilateral elements. The simpler schemes are based on combinations of linear extrapolation and/or averaging algorithms which convert elementwise. Gauss point values to nodal point values. More complicated schemes, based on a global smoothing technique which employ the mass matrix (consistent or lumped), are also presented.

An initial assessment of the accuracy of the several schemes is obtained by comparing the approximate vorticities with an analytical function. Next, qualitative vorticity comparisons are made from numerical solutions of the steady‐state driven cavity problem. Finally, applications of smoothing techniques to discontinuous pressure fields are demonstrated.
Checking the topological consistency of a finite element mest
Authors: Preiss K.
Published: August 2005

Algorithms are described for checking the topological consistency of two‐ or three‐dimensional meshes. Two‐dimensional meshes may include mixtures of triangles, quadrilaterals and other polygons with optional edge or centre nodes; three‐dimensional meshes may include mixtures of cuboids and tetrahedra with optional edge; sie or internal nodes.
Three‐dimensional computer code for dynamic response of solids to intense impulsive loads
Authors: Johnson Gordon R. , Colby Dwight D. , Vavrick Daniel J.
Published: August 2005

Earlier publications demonstrated the capability of the EPIC‐3 code to perform high velocity impact computations in three dimensions.1,2 These capabilities were demonstrated with simplified material and sliding surface models in a core‐contained computer program. This paper presents recent developments which include more comprehensive material and sliding surface formulations, and an expanded computer program which can handle problems of unlimited size by beffering data between disc files and core. The EPIC‐3 code is based on an explicit, finite element, Lagrangian formulation which uses constant strain tetrahedral elements.
On the construction and numerical solution of transmission‐line and lumped network models of Maxwell's equations
Authors: Brewitt‐Taylor C. R. , Johns P. B.
Published: August 2005

It is sometimes convenient to express a numerical algorithm in terms of a network model. The physical picture given can often help the engineer to visualize the properties of the method. In field problems, a lumped network model corresponds to a space discrete field while a transmission‐line model corresponds to a field which is discrete in space and time. In this paper, the relationship is given between the lumped network models and transmission‐line network models used in the steady‐state solution of Maxwell's equations in two and three space dimensions. The use of dual networks is also discussed. An analysis is given for the velocity of waves travelling in any direction across the networks and this is used to compare the accuracy of the models. The use of diakoptics or substructures for the solution of large networks is outlined and this is illustrated by a compound two‐dimensional example.
Transformation of dependent variables and the finite element solution of nonlinear evolution equations
Authors: Čermák Libor , Zlámal Miloš
Published: August 2005

Transformation of dependent variables as, for example, the Kirchhoff transformation, is a classical tool for solving nonlinear partial differential equations. This approach is used here in connection with the finite element method and explained first in case of nonlinear heat conduction problems without phase change. The main applications of the method given in the paper concern a nonlinear degenerate parabolic equation for fluid flow through a porous medium and Stefan (moving boundary) problems.
Growth of planar cracks induced by hydraulic fracturing
Authors: Mastrojannis E. N. , Keer L. M. , Mura T.
Published: August 2005

A method is proposed for the study of growth, under normal internal pressure, of pre‐existing hydraulically induced planar cracks. The continuous growth process is approximated by a stepwise one, and during each growth step the volume of fluid within the crack cavity is assumed constant. The normal distance through which each point on the crack edge moves outwards is controlled by the level of stress intensity factor KI at each point, and the crack‐resistance characteristics of the material, which can be expressed by some critical level of KI, denoted by KIC. For the present study, that distance was assumed proportional to (KI − KIC)4 for KI > KIC. The evaluation of KI at the crack edge is achieved by utilizing the method discussed by Mastrojannis et al.1 The proposed method was applied to the study of the initial stage of growth of a circular crack under linearly varying normal pressure, and of an elliptical crack under uniform normal pressure.
Finite element analysis of free jet impingement
Authors: Obee Timothy N. , De Witt Kenneth J.
Published: August 2005

An analysis of axisymmetric free jet impingement on to finite disks was performed using the finite element method. The method employed the velocity potential as the dependent variable and six‐node triangle elements to represent the region of flow. The analysis was divided into three parts corresponding to three distinct regions of the flow: (1) In the disk region, the free jet impinged on to a finite disk which was oriented normal to the flow. The jet was subjected to zero or normal gravity and to surface tension effects of varying degrees. (2) Upon leaving the disk region, the jet entered the plume region where it was acted upon internally by surface tension and externally by zero or normal gravity. (3) In the collision region, the flow from the plume region collided symmetrically at some downstream area about the axis of symmetry. The major result achieved from this investigation was the development of techniques to locate the free surface in all three regions for a range of conditions. The velocity profiles along selected lines of constant values of the potential were determined, and a successful comparison was made between the numerical results and existing experimental data.
Finite plane strain deformations of rubberlike materials
Authors: Batra R. C.
Published: August 2005

A finite element program capable of analysing finite plane strain deformations of incompressible rubberlike (Mooney–Rivlin) materials has been developed. Two problems, namely a long wall loaded uniformly in two directions and a thick‐wall cylindrical pressure vessel loaded internally, have been solved. The computed values of displacements, strains, stresses and hydrostatic pressure agree very closely with their values obtained analytically.
The evaluation of the error term in some numerical quadrature formulae: An addendum
Authors: Smith H. V.
Published: August 2005

In a previous paper the author deduced a method of evaluating the error term arising in some quadrature formulae. This method depended on the analytic evaluation of a Hilbert transform. The result is now extended to all quadrature formulae used for the calculation of integrals over finite intervals by approximating the Hilbert transform.
The limitations of the patch test
Authors: Stummel F.
Published: August 2005

A simple approximation by nonconforming finite elements is presented that passes the patch test of Irons and Strang but does not yield approximate solutions converging to the solution of the given boundary value problem. It is constructed from continuous piecewise linear functions perturbed by step functions. Further, strange convergence properties of such approximations are explained in all details because they may be typical for the behaviour of nonconforming finite elements violating the basic precondition for convergence.
Direct analysis of elastic–plastic structures with ‘overlay’ materials during cyclic loading
Authors: Zarka J.
Published: August 2005

Several computer codes have incorporated the ‘overlay’ material models: the volume element, which is characteristic of the material, is composed of sub‐elements with different kinematic hardening, perfectly plastic or even viscoplastic flow rules and different elastic properties, these sub‐elements exhibiting all, however, the same total strain.1,2

In this paper it is demonstrated how the simple mathematical framework we first proposed for elastic‐plastic structures with kinematic hardening material,3 and we extended to some elastic viscoplastic ones,4 can easily be applied to these particular ‘overlay’ materials.

One of the interesting advantages of this approach is a straightforward analysis of structural response under cyclic loadings by applying the linear elastic analysis.
A method for space truss analysis in the post‐buckling range
Authors: Schmidt Lewis C. , Gregg Bernhard M.
Published: August 2005

A dual load method of truss analysis is presented that allows highly nonlinear member behaviour to be followed. In particular, a brittle type of strut behaviour is considered. The method assumes that the inelastic strut response is known and that piecewise linearization of the behaviour is acceptable. An example is given to illustrate the type of problem that can be handled. The example involves negative stiffness of the members and consequently attention must be given to the equation solving procedure for the structure. A comparison is made with some observed test results.
Nonlinear vibrations of thick plates using mindlin plate elements
Authors: Raju K. Kanaka , Hinton E.
Published: August 2005

Large amplitude vibrations of Mindlin plates are studies using Lagrangian, isoparametric, quadrilateral elements with selective integration. Square, rectangular, circular and elliptical plates with clamped and simply supported boundary conditions are considered.
An approximate laplace transform inversion using exponential series representation
Authors: Novotný Bohuslav
Published: August 2005

A numerical Laplace transform inversion technique is described, which is a modification of the inversion method using an exponential series representation. By adding an auxiliary function and using Erdélyi's inversion formula, the proposed technique provides the inverse approximation with improved accuracy near t = 0. Numerical illustrations shows that this procedure also works in cases when the original method of schapery fails to give satisfactory results.
A first‐order blending method for triangles based upon cubic interpolation
Authors: Nielson Gregory M.
Published: August 2005

A new method for interpolating in triangles is described. Bivariate cubic polynomials are utilized to define an interpolant which assumes arbitrary position and slope on the entire boundary of a triangular domain. Some examples and applications are discussed.
Numerical analysis of a generalized plane elastica
Authors: Miller R. E.
Published: August 2005

This article presents the derivation of a very straightforward approximate procedure for the analysis of a continuous flexible member. Since very large deformations are anticipated, a shooting method is utilized along with Newton‐type iteration for improved estimates. The resulting computer program is used to compare with exact solutions for a new examples.
Eigensolution for large structural systems with substructures
Authors: Arora Jasbir S. , Nguyen D. T.
Published: August 2005

A method for calculating natural frequencies and mode shapes of large structural systems with substructures and the subspace iteration is developed. The method uses only substructural stiffness matrices and the mass matrix for each finite element of the system. The mass matrix for the entire structure or any of its substructures need not be computed. However, efficiency of the method is improved when mass matrix for the entire structure is computed and saved in the computer core. No approximating assumptions are made. Thus, natural frequencies and mode shapes for the finite element model employed are the same with or without the substructuring algorithm. This is demonstrated by computing first ten natural frequencies and the corresponding mode shapes for an open truss helicopter tail‐boom structure.
Thermodynamic considerations in the numerical simulation of steady compressible flow
Authors: Thyagaraja A.
Published: August 2005

The notion of thermodynamic consistency of a finite difference scheme is introduced in connection with steady compressible flow simulation. This concept requires that the finite difference scheme must lead to solutions which are consistent with the Second Law of Thermodynamics, whatever the grid sizes employed. Thus, in addition to the usual consistency with the conservation equations of mass, momentum and energy, the solutions of the finite difference equations must satisfy thermodynamic restrictions. The scheme proposed by Singhal and Spalding for the computation of plane, isentropic flow is generalized in a thermodynamically consistent way to handle inviscid, adiabatic but non‐isentropic plane flow. Numerical solutions are obtained for a model problem using both the original and the extended methods. The results are compared with analytical predictions of shock‐expansion theory. The effectiveness and the thermodynamic consistency of the new formulation is demonstrated.
An algorithm for the solution of a third‐order eigenvalue problem
Authors: Schajer G. S. , Mote C. D.
Published: August 2005

A simple, rapidly convergent procedure is described for solving a third‐order symmetric eigenvalue problem Au = λ Bu typically arising in vibration analysis. The eigenvalue problem is represented in terms of its variational dual, the Rayleigh quotient, and the eigenosolution is obtained through a topographical search for points of quotient stationarity. The associated computer routine is compact and can easily be incorporated within the calling program. Degenerate eigensolutions cause no difficulty. An example FORTRAN routine is given.
A method for the automatic generation of triangular elements on a surface
Authors: Cohen Howard D.
Published: August 2005

An algorithm is given to discretize a polygon or curved surface into triangular arrays. The method first involves the manual division of the array into quadrilaterals with specified numbers on rows and columns. The individual points are then filled in automatically and elements are automatically generated. A point of particular importance is that the number of columns or rows may be made to change. A subroutine is given to perform this task.
A mesh refinement method for transient heat conduction problems solved by finite elements
Authors: Pammer Z.
Published: August 2005

This paper deals with the finite element calculation of those transient temperature fields which develops in a body, due to a sudden change in temperature of fluid being in contact with the surface. A special co‐ordinate transformation is applied to approach the temporal change of the surface temperature. By analysing the interpolability of the temperature distribution it is proved that the sizes of elements near to the surface are critical in this respect. For the sizes of critical elements situated on the boundaries of the body, criteria formed from dimensionless numbers are determined, by the use of which a subdivision method is described. The application of the method is presented on a two‐dimensional heat conduction problem, and the results are compared with the analytical solution.
Finite element analysis of laminar flow in the entrance region of ducts
Authors: Comini G. , Giudice S. Del , Strada M.
Published: August 2005

This paper presents a generally applicable approach to developing laminar flow problems in straight ducts of arbitrary shape. A three‐level central alogrithm which does not require iterations is used to march ahead with the solution in the axial direction.

The calculation procedure can be implemented by utilizing, with minor modifications, any standard finite element code for linear heat conduction.

Several illustrative examples demonstrate accuracy and versatility of the proposed technique.
Some novel applications on the Frontal concept
Authors: Abbas Syed F.
Published: August 2005

This paper describes the hitherto unpublicized flexibilities inherent in the longevity‐based Frontal concept of Irons. Diverse applications such as Guyan‐reduced superelement generation, substructuring, matrix storage in Frontal form, Frontal matrix multiplication and Frontal Subspace Iteration method are discussed. It is observed that most of these extensions require only minor modifications to Irons'original program. The first part of the paper reviews the development in the Frontal method so far. Part II describes the experiences related to the largest multi‐algorithm Frontal package reported to date. Suggestions for a simplified Frontal algorithm are also given and would be useful to those who wish to write their own solver, or improve an existing one. An algorithm and a computer program for Frontal multiplication are also provided.
Pressure marching schemes that work
Authors: Richards C. W. , Crane C. M.
Published: August 2005

Numerical solutions for two‐dimensional or axisymmetric viscous fluid flow problems are usually based on the stream function/vorticity formulation. Frequently, however, the pressure distribution is of prime interest. Difficulties have been reported in the literature with the use of obvious pressure marching schemes. Consequently, several investigators have preferred to use an iterative method which involves solving a Poisson equation with Neumann boundary conditions. In this paper, the fundamental cause of failure of the marching schemes is investigated. The authors introduce the concept of compatible pressure and vorticity schemes and show that lack of compatibility has been the principal reason for the poor results obtained using marching schemes. Compatible pressure marching methods are developed and shown to give good results. Comparisons are made between the Poisson equation method and the compatible marching method. To make the comparisons meaningful, special test cases with analytical solutions have been used.
An algorithm for defining a single near‐optimum mesh for multiple‐load‐case problems
Authors: Shephard Mark S.
Published: August 2005

A method for defining a single near‐optimum finite element discretization for multiple‐load‐case problems is described. An example problem is included to demonstrate the application of the multiple‐load‐case algorithm. A comparison to a fine uniform mesh is also included to indicate the computational efficiencies possible with such a procedure. †Assistant Professor; formerly Research Assistant, Department of Structural Engineering, Cornell University, Ithaca, New York, U.S.A.
Irregular finite element meshes in elastodynamics
Authors: Fried Isaac
Published: August 2005

Grading rules for consistent and lumped elements are opposite. Optimal mass matrices on finite difference considerations are very sensitive to mesh grading. Sensitivity of the solution accuracy to the mesh ratio increases with element order.