bluuebunny/crossref_metadata_2025_split huggingface dataset:
Anisotropic parametric plate discrete elements
Authors: Palacol E. L. , Stanton E. L. 
Published: August 2005

AbstractA limitation of most plate and shell discrete elements now in use is the shape of their undeformed geometry. Typically, the plan form of these elements is a straight‐sided triangle or quadrilateral that linearly approximates the undeformed geometry while often using higher‐order polynomials to approximate the deformed geometry. This modelling difference leads to inefficiencies that can be eliminated, as demonstrated by a new parametric discrete element based entirely on bicubic Hermite polynomials. This representation of element geometry corresponds to the bicubic Coon's surface patch widely used in design, which allows a common mathematical model for design and analysis. Consideration is given to automating the generation of these patches. Solutions are presented for several plate bending and plate stretching problems. The solutions are in good agreement with closed‐form solutions and photoelastic results in the case of a stress‐concentration problem. These data demonstrate that the new parametric discrete element maintains solution accuracy for plates with curved boundaries.
Numerical solution of the integral equations for optimal sequential filtering
Authors: Kalaba R. E. , Spingarn K. 
Published: August 2005

AbstractInhomogeneous Fredholm integral equations occur frequently in communication theory where it is desired to determine optimal receivers and filters for signal detection and estimation. In this paper an initial value method is utilized to determine the Fredholm resolvent and the solution of the integral equation. Numerical results are given for a simple example. The method is of particular interest where sequential solutions are desired.
Finite element bending analysis of multilayer plates
Authors: Mawenya A. S. , Davies J. D. 
Published: August 2005

AbstractThe development of a general quadratic multilayer plate element is presented for the analysis of arbitrarily layered curved plates. In the formulation, each layer of the multilayer plate can have different orthotropic properties and can deform locally. Examples of bending problems are presented which demonstrate the applicability of the formulation.
The finite element analysis of elasto‐plastic materials by use of dislocation dipole systems
Authors: Owen D. R. J. , Prakash A. 
Published: August 2005

AbstractIt is shown how the stress field due to any prescribed continuous distribution of dislocation dipoles can be determined. This technique then forms the basis of a general method of solution of elasto‐plastic material problems. The presentation is limited to situations which conform to either plane stress or strain conditions. Some results are obtained for relatively simple geometrical and loading configurations and compared with classical plasticity solutions. Finally, the method is applied to the problem of a circular hole in a finite strip under tension.
Finite element analysis of elasto‐plastic shells
Authors: Bäcklund Jan , Wennerström Hans 
Published: August 2005

AbstractA finite element analysis applicable to elasto‐plastic shells of arbitrary shape is presented. Small‐deflection behaviour of thin shells subjected to monotonically increasing static loads is considered. The material is assumed to be originally isotropic, following the von Mises yield criterion and the Prandtl‐Reuss flow rule. A flat triangular element with twelve degrees of freedom is used in the analysis. Within each element both membrane forces and bending moments are assumed to be constant. Some numerical results are included to illustrate the merits of the element.
The rectangular plane stress element by Turner, Pian and Wilson
Authors: Fröier M. , Nilsson L. , Samuelsson A. 
Published: August 2005

AbstractOne of the first finite elements presented was that by Turner et al.1 Pian2 presented a hybrid plane stress element and Wilson et al.3 presented a non‐conforming displacement element. It is shown that the three resulting stiffness matrices are identical.
Stresses in nearly incompressible materials by finite elements with application to the calculation of excess pore pressures
Authors: Naylor D. J. 
Published: August 2005

AbstractA number of problems are analysed by the displacement method to assess the stress accuracy at very low compressibilities. ‘Parabolic’ isoparametric elements are used. It is found that the mean stress becomes grossly in error at the centre and edges of each element as the compressibility is reduced whereas the deviatoric stress components do not. All stress components retain good accuracy at the ‘reduced’ integration sampling points (2 × 2 Gauss). ‘Exact’ integration yields a similar stress distribution to ‘reduced’ but the mean stress is grossly in error at the integration points (3 × 3 Gauss). Exceptions, however, occur.These findings are interpreted, and a rule for predetermining whether or not accurate stresses can be obtained at the integrating points is suggested. Thus it is shown that the displacement method is suitable for analysing materials which for practical purposes are incompressible.A procedure is then presented for analysing porous media‐both linear and non‐linear‐by separating the stiffness into ‘effective’ and ‘pore fluid’ components. This allows excess pore pressure to be calculated explicitly. Applications to saturated soils are given which make use of the findings of the first part of the paper.
Finite element solutions for an equilateral triangle
Authors: Daly P. 
Published: August 2005

AbstractIn a two‐dimensional space of points on an equilateral triangle grid, a single difference equation holding at each node is found from the finite element formulation of the wave equation for all published polynomial orders of the functional expansion. Assuming homogeneous boundary conditions on any equilateral triangle whose edges and vertices pass through the grid points, the eigensolutions of the difference equation are found exactly and thus provide an excellent test problem for the programmer or engineer. The advantage of the present method over other formulations is that the number of linear operations required to produce the difference equation is minimal.
Cycle bases for the flexibility analysis of structures
Authors: Cassell A. C. , de C. Henderson J. C. , Kaveh A. 
Published: August 2005

AbstractTwo methods are presented for the automatic selection of a cycle basis leading to a sparse flexibility matrix for the analysis of rigid‐jointed skeletal structures.The first method having a local approach forms a maximal set of admissible minimal cycles, while the second having a global approach constructs admissible minimal cycles on the ordered chords of a shortest route tree. A cycle ordering algorithm is also given to reduce the band width of the corresponding flexibility matrix.
Spline‐blended approximation of Hartmann's flow
Authors: Gheri G. , Cella A. 
Published: August 2005

AbstractThe steady state flow problem known in magnetohydrodynamics as Hartmann's flow is converted into variational formulation and is given an approximate solution by means of the spline blended interpolation technique. The equations of motion consist of two coupled potential flow problems with homogeneous boundary conditions. The spline blended interpolation method is reduced here, because of the shape of the domain, to a cartesian product of cardinal splines with trigonometric or ordinary polynomials. ‘Exact’ boundary conditions are presented by the blending technique. The numerical results indicate that high accuracy is possible with relatively few unknowns.
The application of quasilinearization to non‐linear systems
Authors: Kelsey Stephen J. 
Published: August 2005

AbstractThis paper presents a method of solving systems of simultaneous non‐linear partial differential equations using the method of lines and the method of quasilinearization‐superposition in combination. The advantages of the method over those methods more generally used are discussed and an example of the application of the method to the two‐dimensional momentum and energy equations considering temperature‐dependent and/or shear‐rate dependent viscosity is given.
An application of least squares to one‐dimensional transient problems
Authors: Lewis Roland W. , Bruch John C. 
Published: August 2005

AbstractThe method of ‘least squares’, which falls under the category of weighted residual processes, is applied as a time‐stepping algorithm to one‐dimensional transient problems including the heat conduction equation, diffusion‐convection equation, and a non‐linear unsaturated flow equation. Comparison is made with other time‐stepping algorithms, and the least squares method is seen to offer definite advantages.
A finite element analysis of general deformation of sheet metals
Authors: Gotoh M. 
Published: August 2005

AbstractA polynomial shape function of triangular elements for finite element analysis of general deformation of sheet metals with or without orthotropic anisotropy is proposed. And general formulation for large deformation and large strain analysis with non‐linearity of material property, say plasticity, is given. Some numerical examples are examined with respect to hydraulic bulging.
Steady magnetohydrodynamic flow past a circular cylinder
Authors: Ingham D. B. 
Published: August 2005

AbstractThe steady two‐dimensional, viscous, electrically conducting flow around a circular cylinder is investigated. The flow and magnetic field are uniform and parallel at large distances from the cylinder. The equations and boundary conditions are derived for arbitrary values of R, Rmand β, where R is the Reynolds number, Rm the magnetic Reynolds number and β, the ratio of the square of the Alfvén speed to the square of the main stream speed. Because of the large number of parameters involved, the numerical solution is restricted to R = 40, Rm = 1 and infinity and 0 ⩽ β ⩽ 4. Also the cylinder is taken to be a perfect conductor, this avoids having to compute the magnetic field within the cylinder.The numerical computations for the non‐magnetic case, i.e. β = 0, are presented and are found to be in good agreement with existing results. The effect of increasing the strength of the magnetic field (i.e. increasing β) on the drag coefficient, the size and position of the standing vortex and the increasing effect of the upstream propagation of disturbances are examined.
A second order finite element method for the one‐dimensional Stefan problem
Authors: Bonnerot R. , Jamet P. 
Published: August 2005

AbstractWe describe a finite element method for the one‐dimensional Stefan problem. The elements are quadrilaterals of the space‐time plane which are determined at each time‐step in relation with the position of the free boundary. The method appears as a generalization of the classical Crank‐Nicolson scheme, since it is identical to this scheme in the case of rectangular elements; it has the advantage of providing a simple and accurate determination of the free boundary. Numerical experiments show that the order of accuracy is equal to 2.
A few remarks on the paper: ‘Parameters of Gamma and Beta distribution’
Authors: Phillips D. T. , Beightler C. S. , Éliás E. J. 
Published: August 2005

AbstractThe paper shows a procedure for estimating the shape parameter of a Gamma distribution from a sample. This procedure uses a rapidly converging iteration to solve the maximum‐likelihood equation and suggests a simple formula for determing the starting value.
A general quadrilateral plate element
Authors: Torbe I. , Church K. 
Published: August 2005

AbstractThe stiffness matrix and consistent nodal load vector for a general quadrilateral plate element are developed for both in‐plane and bending analysis. The basis chosen for the development is the hybrid stress method because

it has been shown to produce results of relatively high accuracy.
it employs only primary nodes and
all integration required in the derivations can be achieved in closed form.
Various numerical examples, relating to both plane stress and bending conditions, are considered in order to establish the validity and generality of the derivations.
Spectral analysis using Fourier Transform techniques
Authors: Resch Francois J. , Abel Rudolf 
Published: August 2005

AbstractThe present study is intended as a guide for those who wish to undertake spectral analyses using Discrete Fast Fourier Transforms. Points of particular difficulty in using Fourier Transforms are derived in some detail. Experimental results are offered to illustrate the mathematical derivations. Finally the case of a signal with discontinuities along the time‐axis is discussed.
Higher order finite element methods for the solution of compressible porous bearing problems
Authors: Rohde S. M. , Oh K. P. 
Published: August 2005

AbstractFinite element methods are used to solve hydrodynamic lubrication problems involving compressible lubricants and porous bearing solids. The particular calculation scheme permits solution at high compressibility numbers (Λ > 100) to be obtained without any numerical difficulty. Finite element and finite difference results for the porous, gas lubricated journal bearing are presented and compared.
A note on numerical computation of elastic contact problems
Authors: Francavilla A. , Zienkiewicz O. C. 
Published: August 2005

AbstractA simple procedure of obtaining flexibility matrices in terms of contact pressures at possible contact points of two bodies allows the frictionless contact pressures to be solved as a quasi‐linear problem. Iteration is limited in general to very few cycles and, as small matrices are handled, can be very economical.Excellent accuracy of this procedure is demonstrated.
Average and complete incompressibility in the finite element method
Authors: Thompson Erik G. 
Published: August 2005

AbstractThe constraint of incompressibility is incorporated into the finite element method for plane strain through the use of a Lagrange multiplier. Depending on the approximating function chosen for this multiplier, the constraint condition can be satisfied everywhere within the element or only in an average sense for the entire element. A study of these two approaches from the point of view of rate of convergence and computer time is presented.
A finite element solution program for large structures
Authors: Cheung Y. K. , Khatua T. P. 
Published: August 2005

AbstractA straightforward and general computer program for assembling and solving (using Gauss elimination technique) widely sparsed finite element matrix equations with very large bandwidth and capable of handling different degrees‐of‐freedom and variable bandwidth at different nodes, is described herein. The program assembles any type of finite elements having arbitrary number of nodes and each node may have differnt degrees‐of‐freedom. It requires only a small core memory in the computer, although a fast random access device is also needed. The two very important features of this program are (i) it does not store any zero submatrices within the band and (ii) during the solution of equations all operations dealing with zero submatrices within the band are automatically skipped and thus the savings of a considerable amount of disc storage space and computer time can be effected in many cases. Another feature is that many right hand sides can be handled simultaneously. Hence the program is very economical for structures having widely sparsed matrix equations. A listing of the computer program written in FORTRAN IV for CDC 6400 computer is readily available from the authors, but unfortunately could not be given here because of lack of space. The program is so general that it can be used to solve a wide class of finite element problems without actually having to understand fully the techniques behind it.
Calculation of stress intensity factors in three dimensions by finite element methods
Authors: Blackburn W. S. , Hellen T. K. 
Published: August 2005

AbstractFinite element methods are used to calculate the stress intensity factors for three‐dimensional geometries containing a number of depths of crack subjected to various loads. Special elements are used at the tip to represent the variation of the displacement with respect to the square root of the distance from the tip. The stress intensity factors are determined by comparison of the displacements in the special elements, by a method of virtual crack extensions, and, in one case, by an integral around the tip. With meshes containing between 50 and 100 quadratic isoparametric elements, results accurate to within 1 per cent or 4 per cent (depending on case) of known solutions are demonstrated.
Calculation of vibration frequencies by a hybrid element method based on a generalized complementary energy principle
Authors: Brandt Klaus 
Published: August 2005

AbstractBased on a generalized complementary energy principle the derivation of the element matrices is presented for calculation of natural frequencies. The degrees‐of‐freedom are not defined on nodal points but in an abstract way. No restrictions about the number of interpolation functions in the interior and at the boundaries of the element have been introduced. The exact solution of the discretized element equations leads to the dynamic stiffness matrix while the approximate solution results in a linear eigenvalue problem. Plate bending problems are used to study the convergence of frequencies depending on the degrees of interpolation functions within the element and on its boundaries and on the number of elements.
Finite element solutions of the non‐self‐adjoint convective‐dispersion equation
Authors: Prakash Anand 
Published: August 2005

AbstractFinite element formulations based on the Galerkin and variational principles have been developed for the self‐adjoint and non‐self‐adjoint problems represented respectively by the flow and convective‐dispersion equations in the cylindrical polar system of co‐ordinates. The formulation based on the variational principle is shown to be restricted to dispersion‐dominant transports only. The Galerkin method is demonstrated to be more versatile and free from convergence and stability problems. The computational scheme based on the Galerkin principle is shown to be equally valid for both convection and dispersion dominant transports. The numerical results obtained are verified with known analytical solutions. It is concluded that the suggested scheme can be used in solving a variety of field problems involving groundwater dispersion.
Cold sheet rolling, the thermoviscoelastic problem, a numerical solution
Authors: Batra R. C. 
Published: August 2005

AbstractThe coupled system of equations governing the thermomechanical deformations of a viscoelastic sheet while it is being cold rolled is solved numerically. The pertinent energy equation is solved by the finite difference method and the mechanical problem is solved by the finite element method using uniform first order rectangular elements. The developed computer program enables one to compute the complete deformation and temperature fields in the sheet. Results presented graphically include the temperature distribution, the stress distribution at the middle surface, the contact pressure distribution and the asymmetric surface deformation of the sheet.
A strategy for the solution of problems involving large deflections, plasticity and creep
Authors: Bushnell David 
Published: August 2005

AbstractA strategy for solving problems involving simultaneously occurring large deflections, elastic‐plastic material behaviour, and primary creep is described. The incremental procedure involves a double iteration loop at each load level or time. In the inner loop the material properties are held constant and the non‐linear equilibrium equations are solved by the Newton–Raphson method. These equations are formulated in terms of the tangent stiffness. In the outer loop the plastic and creep strains are determined and the tangent stiffness properties are updated with use of a subincremental algorithm. The magnitude of each time subincrement is determined such that the change in effective stress is less than a preset percentage of the effective stress. The strategy is implemented in a computer program, BOSOR 5, for the analysis of shells of revolution. Examples are given of elastic‐plastic deformations of a centrally loaded flat plate and elastic‐plastic‐creep deformations of a beam in bending. The major benefits of the subincremental technique are the increased reliability with which problems involving non‐linear plastic and time‐dependent material behaviour can be solved and the greatly relaxed requirement on the number of load or time increments needed for satisfactory results.
First Cesaro sums for high order finite elements near singularities
Authors: Rossow M. P. , Mehta A. K. , Petruska G. 
Published: August 2005

AbstractHigh order finite elements often exhibit an oscillatory behaviour near stress singularities which appears similar to the Gibbs phenomenon in the theory of Fourier series. It is known that under certain conditions the average of successive partial sums (the first Cesaro sum) of a Fourier series exhibiting the Gibbs phenomenon will converge monotonically to the function being approximated. An analogous device introduced for high order finite element approximations near a stress singularity successfully smooths the oscillations of the computed stress.
On an eigensystem routine due to K. K. Gupta
Authors: Whiston G. S. 
Published: August 2005

AbstractAn eigensystem subroutine ‘EASI’ due to K. K. Gupta is critically discussed. Some faults are pointed out and remedial measures which have been adopted in practice are presented. The result is a consistently reliable convergent algorithm which has solved narrow bandwidth problems of order up to 1000 × 1000.
A classification and survey of numerical methods for boundary value problems in ordinary differential equations
Authors: Aktas Z. , Stetter H. J. 
Published: August 2005

AbstractThe objective of the paper is a survey and classification of available numerical methods for boundary value problems with an emphasis on two point boundary value problems. In the paper a general two point boundary value problem is stated first and later available numerical methods are classified into five main groups according to their approach in numerical solution. In the next sections of the paper, each of these main groups are described and appropriate subgroups are defined and discussed.
On the elastic plastic initial‐boundary value problem and its numerical integration
Authors: Son Nguyen Quoc 
Published: August 2005

AbstractAn interative approach is proposed for the numerical analysis of elastic–plastic continua. This approach gives after convergence an implicit scheme of integration of the evolution problem, and is concerned with elastic‐perfectly plastic materials and with hardening standard materials. Under a generalized assumption of positive hardening, the proof of convergence of the iterative solutions is given. Some numerical examples by the finite element method are also discussed.
Finite element post‐buckling analysis for frames
Authors: Care R. F. , Lawther R. E. , Kabaila A. P. 
Published: August 2005

AbstractPresented in this paper is a direct method of analysis of the elastic non‐linear behaviour of frames. Emphasis is given to the method's capability of tracing the post‐buckling path from a bifurcation point although the method can also trace the non‐linear behaviour of frames with eccentricities. The method is proposed as an alternative to the main methods currently in use, the perturbation method and the incremental method. Conditions for equilibrium and stability are developed from a variational approach to the total potential. A finite element approximation is made and an efficient solution technique for the resulting non‐linear equations is developed.Results for three frames are given demonstrating good agreement with solutions generated from other approaches.