bluuebunny/crossref_metadata_2025_split huggingface dataset:
Numerical approximation of one‐dimensional consolidation
Authors: Davis R. O. 
Published: August 2005

AbstractA generalized finite difference scheme is developed to represent the one‐dimensional consolidation process. The difference equations are derived from integral balance equations which represent the soil as a mixture of two constituents. No restrictions are placed on the soil constitutive properties or stratigraphy. An approach to stability analysis for the scheme is outlined, and an example problem is presented.
A note on the estimation of critical damping in dynamic relaxation
Authors: Bunce J. W. 
Published: August 2005

AbstractA new way of estimating critical damping in dynamic relaxation is proposed using the concept of a mass‐dependant load vector, a postulate concerning vibrations and Rayleigh's principle. The method should be particularly appealing in those not uncommon circumstances where the actual loads are approximately proportional to the masses for then the computer time required in evaluating the various constants would actually be a part of the problem‐solving time.
Optimum design of hypertatic structures
Authors: Majid K. I. , Anderson D. 
Published: August 2005

AbstractThe task of optimum design of structures is one that involves non‐linear Programming. This is particularly the case when deflection as well as stress limitation are imposed as design criteria. In this paper a Fundamental approach is presented for the minimum weight design of statically indeterminate elastic structure subject to non‐linear deflection and stress constrains.The matrix force method is adopted to formulate the problem. The constraints thus derived prove to have separable variables and therefore can be linearized in a piecewise manner. The computation aspects concerning the restricted entry in to the simplex tableau are briefly discussed and illustrative examples are given to verify the validity of the proposed method.
Note on the ‘Alpha’‐constant stiffness method for the analysis of non‐linear problems
Authors: Nayak G. C. , Zienkiewicz O. C. 
Published: August 2005

AbstractA procedure for the acceleration of convergence in non‐linear analysis using the modified Newton–Raphson problem is described. The process has been found useful in plasticity and large deformation studies and its application elsewhere can be envisaged.
A finite element method for block adjustment problems of photogrammetry
Authors: Utku Senol 
Published: August 2005

AbstractIt is shown that the finite element method can be used advantageously in generating the normal equations of a given photogrammetric network for block adjustments. In this method aerial (or spatial) photographs of a block are processed one at a time, in any random order, to generate the portion of the coefficient matrix between the main diagonal and the variable band and the right hand vector of the normal equations, related with the adjustments to the control points. Any known information related with the adjustments may be imposed, and an internal control point relabelling scheme may be used during the assembly process, in order to minimize the actual computer storage area and the solution time requirements. The paper shows the analogies between the linear equilibrium problems of structural mechanics, and the block adjustment problems of photogrammetry, in order to enable the students of both fields to use the same computer software. In this context, plate‐point adjustment matrices and plate‐point load vectors for the adjustment problem (corresponding to the element stiffness matrices and the element load vectors of equilibrium problems) are defined and explicit expressions are given.
Note on an approximate method for computing consistent conjugate stresses in elastic finite elements
Authors: Oden J. T. , Reddy J. N. 
Published: August 2005

AbstractA technique is described wherein improved stresses can be computed in finite element models based on displacement approximations. The method is based on the idea of consistent stress approximations and it approximates such stresses using the notion of a domain of influence of the stress intensity at a nodal point. Considerable improvement in accuracy of the stresses is obtained with little difficulty.
Stresses in a partly yielded notched bar—An assessment of three alternative programs
Authors: Owen D. R. J. , Nayak G. C. , Kfouri A. P. , Griffiths J. R. 
Published: August 2005

AbstractThe results of three finite element stress analysis programs are compared for the problem of the elasto–plastic bending of a notched beam under plane strain conditions. Both Tresca and von Mises yield criteria are considered and the numerical results are compared with an available analytical solution based on slip‐line field theory. The general conclusion is drawn that finite element methods can be used with confidence in elasto–plastic stress analysis.
A numerical method for the analysis of longitudinal elastic–plastic stress wave propagation
Authors: Ondracek E. , Haddow J. B. 
Published: August 2005

AbstractA numerical method for the analysis of one‐dimensional propagation of elastic–plastic stress waves in cylindrical bars is proposed. The method is based on the division of the bar into elements of finite length and the solution of the equations of motion for these elements.Numerical results are presented for semi‐infinite bars and a finite bar fixed at one end.
Solution of quadratic matrix equations for free vibration analysis of structures
Authors: Gupta K. K. 
Published: August 2005

AbstractAn efficient digital computer procedure and the related numerical algorithm are presented herein for the solution of quadratic matrix equations associated with free vibration analysis of structures. Such a procedure enables accurate and economical analysis of natural frequencies and associated modes of discretized structures.The numerically stable algorithm is based on the Sturm sequence method, which fully exploits the banded form of associated stiffness and mass matrices. The related computer program written in FORTRAN V for the JPL UNIVAC 1108 computer proves to be substantially more accurate and economical than other existing procedures of such analysis. Numerical examples are presented for two structures: a cantilever beam and a semicircular arch.
Direct numerical solution of three‐dimensional equations containing elliptic operators
Authors: Martin E. Dale 
Published: August 2005

AbstractA direct three‐dimensional elliptic solver is presented for application in a wide class of numerical methods for solving partial differential equations in physics and engineering. The derived algorithm and FORTRAN code implement Buzbee, Golub and Nielson's proposed extension of Buneman's Cyclic‐Reduction Poisson solver to three dimensions. Both a ‘most direct’ cyclic reduction and a revised method (to eliminate roundoff error difficulties) are derived. Tests on an IBM 360/67 computer, using various optional combinations of subroutines, showed significant differences in accuracy and computing time, with the optimum subroutine combination depending on mesh size.
Application of the Fast Fourier Transform to linear systems in civil engineering
Authors: O'Brien M. A. , Fitzgerald J. J. , Dillon E. C. 
Published: August 2005

AbstractThe Fast Fourier Transform is employed as a method of Laplace transform inversion to solve problems in the civil engineering fields of visco‐elasticity and hydrology. When these problems are accurately represented by a linear time‐invariant model, it is shown that the Fast Fourier Transform inversion procedure is often more accurate than standard convolution and inversion techniques. The speed and accuracy of solution resulting from this application of the Fast Fourier Transform is illustrated by referring to case studies solved on an IBM 1130 computer, model 3D processor with 32K memory.
Optimization of complex structures to satisfy static, dynamic and aeroelastic requirements
Authors: Rao S. S. 
Published: August 2005

AbstractA structural optimization problem is considered in which the design requirements include restrictions on the strength, stability, frequency and flutter characteristics of the structure. One of the central concerns of this phase of the work has been to overcome the problems inherent in analysing the dynamic and aeroelastic behaviour of structures with many degrees of freedom. The multiweb delta wing structure under supersonic flight conditions is the model upon which this exploratory study is based. The finite element idealization, with three different kinds of elements, is used to model the wing structure. The constant stress triangular plate elements, the rectangular shear panels and the pin‐jointed bar elements are used to represent, respectively, the cover skins, webs and stringers of the wing structure. The design problem is formulated as a minimum weight optimization problem and is solved by using non‐linear programming techniques. Computationally efficient schemes are developed for the necessary derivatives of the behaviour constraints. Numerical examples are presented to illustrate the feasibility and the computational effectiveness of the method.
Restrictions in the application of automatic mesh generation schemes by ‘isoparametric’ co‐ordinates
Authors: Steinmueller G. 
Published: August 2005

AbstractTo obtain meshes of reasonable form there have to be made some restrictions in the application of automatic mesh generation schemes using ‘isoparametric’ co‐ordinates. In this present paper it will be shown that such restrictions exist for plane meshes. The results figured here are also valid for three‐dimensional meshes.
Buckling under combined loading of thin, flat‐walled structures by a complex finite strip method
Authors: Plank R. J. , Wittrick W. H. 
Published: August 2005

AbstractA finite strip method is presented for determining the initial buckling stresses of any structure consisting of a series of thin flat isotropic plates rigidly connected together at their longitudinal edges. Each plate may be subjected to a combination of longitudinal and transverse compression, longitudinal in‐plane bending, and shear, and it is assumed that the buckling mode, of whatever type, is sinusoidal in the longitudinal direction. Due to the presence of shear, the perturbation forces and displacements which occur at the edges of component plates during buckling are out of phase, and this is accounted for by defining their magnitudes in terms of complex quantities. Stiffness matrices relating the amplitudes of these forces and displacements are derived using an approximate method based upon assumed displacement functions across the width of the plate. It is shown how the method can be used to calculate natural frequencies of prismatic structures, and finally an indication of the accuracy of the method is given together with some illustrative results.
Least square‐finite element for elasto‐static problems. Use of ‘reduced’ integration
Authors: Zienkiewicz O. C. , Owen D. R. J. , Lee K. N. 
Published: August 2005

AbstractA least square based finite element algorithm is developed for some elasto‐static problems. In the formulation both stresses and displacements appear as simultaneous variables. In two dimensional (plane) analysis, parabolie isoparametric elements are used. Considerable improvement of performance is obtained with a numerical integration based on 2 × 2 Gauss point distribution over more accurate integration schemes. Reasons for this are presented.The formulation is extended in the section ‘General least square formulation’ to beams and plates with a similar success of ‘reduced’ integration.
Finite elements in the solution of electromagnetic induction problems
Authors: Donea J. , Giuliani S. , Philippe A. 
Published: August 2005

AbstractThis paper describes a method of solving electromagnetic induction problems by means of the finite element technique. A variational equation associated with the differential equation for the vector potential is formulated and solved via the concept of finite elements. Sinusoidal driving currents and linear, isotropic, but inhomogeneous media are assumed. A typical example is included in order to illustrate the suggested solution technique.
Observations regarding assumed‐stress hybrid plate elements
Authors: Cook Robert D. , Ladkany Samaan G. 
Published: August 2005

AbstractEdge displacement of assumed‐stress hybrid plate elements are commonly chosen as either linear, quadratic or cubic functions of the edge co‐ordinate. The present paper examines the effect of this choice on the acceptability, accuracy, and possible zero energy modes of elements based on a linear stress field. It is concluded that triangular elements may be preferable to quadrilaterals, and that linear edge displacements are not desirable.
Representation of singularities with isoparametric finite elements
Authors: Benzley S. E. 
Published: August 2005

AbstractThe development of a generalized quadrilateral finite element that includes a singular point at a corner node is presented. Inter‐element conformability is maintained so that monotone convergence is preserved. The global‐local concept of finite elements is used to formulate the complete set of equations. Examples of crack tip singularities are given.
A new triangular element for finite difference solution of axisymmetric conduction problems in cylindrical co‐ordinates
Authors: Mahata Prafulla C. , McNary Orlo 
Published: August 2005

AbstractThe triangular element is one of the most useful finite difference elements for the potential problems because of its versatility in fitting irregular boundary, in connecting one element type to another, and in changing grid fineness. Such triangular elements find many applications in conduction problems in cartesian co‐ordinates. This paper presents a new triangular element for the finite' difference solution of axisymmetric conduction problems in cylindrical co‐ordinates. The validity of the proposed triangular element is analyzed, and its workability is demonstrated using three selected examples. Also, an industrial application highlights the advantageous characteristics of the triangular element, and gives a comparison with known results obtained by finite element method.
Computer analysis of a rotating axial‐turbomachine blade in coupled bending‐bending‐torsion vibrations
Authors: Fu C. C. 
Published: August 2005

AbstractBasic equations are derived for a comprehensive computer analysis for an equivalent lumped parameter system which simulates a pre‐twisted, rotating or non‐rotating. Timoshenko beam in coupled bending‐bending‐torsion vibrations. These equations enable one to develop straightforwardly digital computer programs for studying vibration problems related to compressor or turbine blades in turbomachinery as well as in other structural dynamics applications. The validity of the lumped parameter approach is established through a free vibration study. Good agreement between the present computer results and those obtained theoretically or experimentally by other investigators is demonstrated. In particular, it is found that the natural frequencies obtained in the free vibration study for all beams examined converge from below the exact values at a convergence rate of N−4, where N is the total number of the lumped parameters used in the computer simulation. The rapid rate of convergence shows that the mathematical model used in deriving the basic equations can adequately represent the type of beams under consideration. The known convergence rate also provides an estimate on the accuracy of the computer results, and a means to improve these results by extrapolation.
Calculation of transient temperature fields with finite elements in space and time dimensions
Authors: Köhler W. , Pittr J. 
Published: August 2005

AbstractA program is demonstrated which apart from linear finite elements in time also includes elements with shape functions of the second and third degree. The algorithm for discretization in the time dimension is described and, using the example of a parabolic time element, the coefficients required to form the global system are given. By various test examples the efficiency of the process is examined by comparison with the customary difference method. Generally, with finite elements in time, the solution has better stability. Comparing the time required for calculation with the accuracy of the solution it would appear that in examining problems where boundary conditions are constant in time, higher order time elements are no improvement over the linear time element. However, for the purpose of reproducing periodic processes, higher order time elements offer an advantage in that one is not limited to linear variations of the boundary conditions within the element. Thus, for example, the temperature curve for parabolic variation of the surface temperature can be reproduced with close approximation by two time elements per period and a shape function of the third degree.
The torsional stiffness of prismatic members with sections divisible into rectangles
Authors: Golley B. W. , Cashman J. D. 
Published: August 2005

AbstractA method of determining the torsional stiffness of a wide range of structural sections, both homogeneous and composite, is presented. Prandtl's stress function along the boundaries of component sections is approximated by finite Fourier series with coefficients chosen to minimize a functional. An example indicates that the stiffness may be determined to acceptable accuracy by the solution of very few equations.
Discrete (Legendre) orthogonal polynomials—a survey
Authors: Neuman C. P. , Schonbach D. I. 
Published: August 2005

AbstractThe discrete (Legendre) orthogonal polynomials, (DLOP's) are useful for approximation purposes. This set of mth degree polynomials {Pm(K, N)} are orthogonal with unity weight over a uniform discrete interval and are completely determined by the normalization Pm(O, N) = 1. The authors are employing these polynomials as assumed modes in engineering applications of weighted residual methods. Since extensive material on these discrete orthogonal polynomials, and their properties, is not readily available, this paper is designed to unify and summarize the presently available information on the DLOP's and related polynomials. In so doing, many new properties have been derived. These properties, along with sketches of their derivation, are included. Also presented are a representation of the DLOP's as a product of vectors and matrices, and an efficient computational scheme for generating these polynomials.
Variational principles and the patch test
Authors: De Veubeke B. Fraeijs 
Published: August 2005

AbstractThe patch test is shown to be contained in the variational formulations of the finite element methods at the assembling level, all of which require the vanishing of the virtual work of interface connection loads. By a systematic introduction of stress generating functions, attention is drawn to the fact that any given finite element model can be assembled in two different ways: either by identification of a set of boundary displacements (leading to the direct stiffness method), or by identification of a set of local stress function values (leading to the dual direct flexibility method). Looking at any conjugate couple (generalized displacement‐generalized surface traction) at an interface, one is strongly transmitted, the other weakly. Discretization of the zero virtual work condition at an interface of plate bending models, by means of Legendre polynomial expansions, allows a systematic construction of so‐called ‘non‐conforming’ elements that pass the patch test. They are in fact identified with weakly conforming, but strongly diffusive, hybrids, and the lowest degree element (quadratic) is in fact the Morley constant‐moment element. Examples are given for higher degree displacement fields.The case of plate stretching elements can be handled by duality, the difficulties being here associated with the requirements for diffusivity. Non‐diffusive elements that pass the zero interface virtual work test can be constructed systematically and are identifiable with weakly diffusive, but strongly conforming, hybrids of the type first proposed by T. H. H. Pian.
Finite difference analysis for laminar flow heat transfer in concentric annuli with simultaneously developing hydrodynamic and thermal boundary layers
Authors: Coney J. E. R. , El‐Shaarawi M. A. I. 
Published: August 2005

AbstractThe results of a finite difference analysis are presented for the problem of incompressible laminar flow heat transfer in concentric annuli with simultaneously developing hydrodynamic and thermal boundary layers, the boundary conditions of one wall being isothermal and the other wall adiabatic. This corresponds to the fundamental solution of the third kind according to the four fundamental solutions classified by Reynolds, Lundberg and McCuen1.Firstly, the hydrodynamic entry length problem, based on the boundary layer simplifications of the Navier–Stokes equations, was solved by means of an extension of the linearized finite difference scheme used previously by Bodia and Osterle2 to solve a similar problem between parallel plates. The energy equation is then solved, using the velocity profiles previously obtained, by means of an implicit finite difference technique.The accuracy of the numerical solution was checked by comparing results for the annulus of radius ratio 0.25 with the avaiable solution of Shumway and McEligot3.
Effect of shear deformations and rotary inertia on optimum beam frequencies
Authors: Kamat M. P. 
Published: August 2005

AbstractAccounting for shear deformations and rotary inertia effects, necessary condition for optimum fundamental frequency of a vibrating beam of constant volume and with a given distribution of non‐structural mass, is obtained through the calculus of variations. Minimum cross‐section of the beam is controlled by the introduction of an inequality constraint. A finite element displacement formulation is then used in an iterativve manner to arrive at the optimum fundamental frequency and the corresponding material distribution for the discretized beam models with various boundary conditions. A comparison is then made with the corresponding results of an Euler beam.
Sampling techniques in the analysis of Power‐System transients
Authors: McCarthy T. O. 
Published: August 2005

AbstractA detailed investigation of analytical approaches to the determination of transients on Power Systems has been undertaken1, the main features of which are presented in this paper. The shortcomings of conventional travelling‐wave methods, particularly where long power lines constitute complex sub‐systems, have led to a numerical solution approach based on a discrete form of the Laplace Transform which has been labelled the ‘Fast Laplace Transform’ (FLT). The method allows efficient treatment of a wide variety of linear problems including, in particular, cases involving frequency‐dependent parameters.An examination of continuous evaluation procedures, which are subject to truncation difficulties and to inefficient usage of computer time, is followed by a review of frequency domain sampling methods. 4,5,11 The FLT inversion technique is described with emphasis on the efficient use of computer time.The method is illustrated by application to a number of switching studies and comparison with travelling‐wave solutions is made. Problems involving frequency‐dependent ground impedance, even where ground resistivity varies with depth, are easily simulated.