bluuebunny/crossref_metadata_2025_split huggingface dataset:
Creep analysis of reinforced and prestressed concrete structures under non‐uniform temperature distributions, using elastic solutions
Authors: Jordaan I. J. , Khalifa M. M. A. 
Published: August 2005

AbstractThe analysis of stresses and deformations in concrete structures subjected to temperature gradients is described. As a result of the spatial variation of temperature, the creep compliance is a function of position. Previous work has shown that the constitutive equations for concrete creep can be expressed in a form which is invariable although ageing is included in the analysis. Thus viscoelastic methods can be used and correspondence principles can be developed; emphasis is placed in the present work on those which are based on the Laplace transform. A particular form is described, in which replacement of the elastic modulus by a function of the transformed creep compliance gives transformed values of stress; these values are easily obtained numerically by the finite element method using elastic analyses. The transformed values of stress are then expressed as approximate functions of the transformed creep compliance; inversion of the ensuing functions gives the stress as an approximate function of time. Two applications are given; the first considers a simple axially loaded column with reinforcement and the second deals with a thick cylinder subjected to a temperature gradient.
Security assessment of gas networks
Authors: Li P. M. , Hindi K. S. , Brameller A. 
Published: August 2005

AbstractA measure of the severity of a pipeline failure is the minimum reduction in load in the network necessary to ensure that no node falls below its minimum pressure. The expected loss of sales is calculated as the product of the minimum reduction in load and the expected duration of the period during which the pipeline will be in the inoperable state, and thus reflects both the severity and the frequency of the failure. Consequently, this index, whose evaluation involves network theory, optimization and probability theory, serves as a measure of the insecurity of the gas network.The security index can be evaluated for all points within a system, providing a basis of comparison between the relative vulnerability of different parts. The relative level of security of different design proposals can also be assessed using this index.
Compact computation of natural frequencies and buckling loads for plane frames
Authors: Williams F. W. , Howson W. P. 
Published: August 2005

AbstractExisting theory is assembled to give a method which needs only the core of a mini‐computer to calculate the eigenvalues of large rigidly jointed plane frames with certainty, the eigenvalues being natural frequencies and critical load factors in free vibration and buckling problems, respectively. The method is illustrated by annotated listings of vibration and buckling programs, each involving under two hundred Fortran statements and with low number storage requirements (see Table I). The use of the programs as ‘black boxes’ is fully explained, with illustrative examples.The member theory used is the ‘exact’ classical Bernoulli‐Euler uniform member theory. Possible applications include: evaluation of answers from approximate methods; calculation of critical loads for substitution in the modified Merchant‐Rankine formula to estimate collapse loads of frames; and calculation of shifts in natural frequencies caused by structural damage, in connection with structural integrity monitoring of inaccessible structures.
Superposition method of finite element and analytical solutions for transient creep analysis
Authors: Yagawa G. , Miyazaki N. , Ando Y. 
Published: August 2005

AbstractBased on the Lagrange multiplier's concept, a superposition method of analytical and finite element solutions has been developed to solve efficiently various non‐linear and/or time‐dependent problems in structural mechanics. According to the theory, the transient creep behaviour of a cantilever beam is analysed as an expository example.
A finite element convergence study for accelerating flow problems
Authors: Gartling D. K. , Nickell R. E. , Tanner R. I. 
Published: August 2005

AbstractThe convergence properties of several non‐linear solution procedures were examined with respect to the accelerated flow of a fluid in a converging channel (the Hamel problem), using two different finite element computer programs with different elemental construction. The Reynolds number varied from that for creeping flow to 1088 without exceeding the radius of convergence. Special attention was given to the successive substitution and Newton–Raphson solution algorithms, with a significant advantage in rate of convergence noted for the latter.
Nodal grafting for crack propagation studies
Authors: Ingraffea A. R. 
Published: August 2005

AbstractA simple, efficient method for propagating cracks through a finite element mesh is presented: nodes, borrowed from other points in the mesh, are ‘grafted’ along the advancing crack front. The method requires neither an increase in bandwidth nor a mesh regeneration. It can be easily implemented in any existing program using iso(sub)parametric elements of at least quadratic order.
Computational efficiency of non‐linear programming methods on a class of structural problems
Authors: Carpenter W. C. , Smith E. A. 
Published: August 2005

AbstractResults are presented of an investigation as to the computational efficiency of several non‐linear programming algorithms on the constrained structural weight optimization of plane trusses and plane stress plates. The optimization algorithms considered are the methods of sequential linear programming, of feasible directions based on Zoutendijk's procedure P1, and of sequential unconstrained minimizations using the methods of Powell, Stewart, Fletcher–Powell, and Newton. Results are presented on computational efficiency as a function of number of design parameters and as a function of the function evaluation effort to derivative evaluation effort ratio.
Temperature load on thick curved shell elements
Authors: Wergeland J. H. 
Published: August 2005

AbstractTemperature load on a shell is usually represented as initial strains in the tangent plane directions of the shell, since strains in shell surface normal directions are neglected. It is shown, however, that this simplification may give rise to significant errors for thick curved shell elements. A procedure to overcome this problem is presented. In particular the eight‐node subparametric thick shell element is considered.
An implicit‐iterative solution of the heat conduction equation with a radiation boundary condition
Authors: Williams S. D. , Curry Donald M. 
Published: August 2005

AbstractIn predicting temperatures with an implicit finite difference method there is a tendency for the surface temperature to oscillate if a non‐linear radiation boundary condition is imposed. An iterative method is described which eliminates these oscillations in temperature prediction.Several examples are given that allow a comparison with other implicit methods. These examples are for cases which are typical of those that arise in practical applications. The results demonstrate that the method is remarkable in its ability to predict surface conditions without the debilitation of other methods in regard to step size control, along with the ease of incorporating it into the solution routine.
A cost comparison of two static condensation‐stress recovery algorithms
Authors: Cook Robert D. , Shah Vikram N. 
Published: August 2005

AbstractWe consider finite elements that have internal degrees‐of‐freedom. These d.o.f. are condensed before elements are assembled into the structure, and must be recovered later for use in element stress computation. References 1 and 2 describe two different ways to do the calculations. This paper compares the computational costs of the two methods. Test runs were made to assess costs. Relative costs depend on several factors. The factors are discussed, and suggestions are made as to the better method in various circumstances.
Solution of non‐linear differential equations by discrete least squares
Authors: Eason E. D. , Mote C. D. 
Published: August 2005

AbstractA general‐purpose technique has been developed for solving non‐linear partial differential equations. A set of approximating functions with undetermined parameters is used to evaluate the differential equation and boundary conditions at discrete points, forming a set of residuals to be minimized. The parameters which minimize the sum of squared residuals are determined by a non‐linear least‐squares minimization technique. Initial value problems are solved by integrating the equations with respect to time at the fitting points by a predictor‐corrector algorithm. The resulting formulation is independent of the form of the problem and the approximating functions, so that a broad class of problems may be solved with a single computer program. The technique is applied to several boundary and initial value problems in one and two spatial dimensions. The tecnique is applied to several boundary and initial value problems in one and two spatial dimensions.
An integral method for computing the inductance and the a.c. resistance of parallel conductors
Authors: Deeley E. M. , Okon E. E. 
Published: August 2005

AbstractIn a previous paper1 a method was described for computing the current distribution and inductance of systems of infinitely‐long, perfectly‐conducting, straight conductors. The method relied on the solution of a Fredholm Integal equation of the first kind, and in the present paper the method is extended to equations of the second kind in order to study the inductance and a.c. resistance factor of resistive for which approximate formulas and experimental results exist, with which the method is in good agreement over a range of grequencies of particular practical practical interest. Results have also been obtained for rectangular conductors connected in parallel.
Adaptive step size selection for use with the continuation method
Authors: Schmidt William F. 
Published: August 2005

AbstractAn adaptive procedure for selecting the step size when incremental or continuation methods are used to solve sets of non‐linear equations is presented. The increment size is limited by requiring the corrective iteration procedure employed to reduce the drifting error to be within a contractive boundary at each level. The usefulness of the procedure is extended by the development of a set of conditions for detecting impending divergence of the corrective iteration process. These conditions, used in conjunction with the step size selection procedure permit the continuation of the solution through highly non‐linear regions and also provide a simple means of isolating a limit point, if one exists. Two additional benefits of the procedure are an effective convergence criterion for terminating the iteration process and a simple means for switching between the Newton‐Rephson and modified Newton‐Raphson iteration procedures. The paper concludes with a number of example problems, three are hyperelastic bodies at finite strain and the final example is the large displacement analysis of an elastic beam. The results illustrate that the procedure is computationally inexpensive, using only information normally obtained in a non‐linear analysis, flexible in the sense that a dense or sparse distribution of points along the total solution curve may be obtained, and effective, normally requiring less total computational effort than a constant step size procedure.
Analysis of explicit difference methods for a diffusion‐convection equation
Authors: Siemieniuch J. L. , Gladwell I. 
Published: August 2005

AbstractWe consider the numerical solution of a model one‐dimensional diffusion‐convection equation by a variety of explicit finite difference methods including conventional central and upwind replacements of the convection terms. We discuss commonly observed phenomena such as instability, unwanted oscillations in the numerical solution, and numerical diffusion and we present an analysis of these effects by simple mathematical techniques.
Convective difference schemes and Hermite interpolation
Authors: Fischer Karsten 
Published: August 2005

AbstractA new method for numerically solving the convection equation is presented. The reduction of numerical errors is achieved by introducing an auxiliary variable and solving an auxiliary equation for the latter. The method is based on a Hermite interpolation of the convected quantity. Three explicit numerical versions of the method are investigated and compared with some of the most widely used schemes, and it is shown that the new method gives better physical results. Arguments are given that the usual mathematical series expansions do not work sufficiently well in that context. Instead of using linear stability analyses the quality of the method is investigated by numerical experiments.
Specification of skew conditions in finite element formulation
Authors: Mangalgiri P. D. , Dattaguru B. , Ramamurthy T. S. 
Published: August 2005

AbstractFields exhibiting skew symmetry occur frequently in structural problems. There are many situations where non‐skew‐symmetric functions are conveniently used to analyse these skew fields. Specification of force and displacement conditions on the skew axis reduces the analysis to a half of the domain. The difficulty in using such conditions in an FEM analysis is their non‐explicit nature. A method of overcoming this difficulty is developed using concept of generalized forces and displacements.
A comparison of Galerkin, collocation and the method of lines for partial differential equations
Authors: Hopkins T. R. , Wait R. 
Published: August 2005

AbstractA number of numerical methods for parabolic paritial differential equations are discussed, they all reduce a single partial differential equation to a system of ordinary differential equations by discretization in the space variable(s). The discretizations can be finite element approximations (Galerkin and collocation) or finite difference approximations (methods of lines). The performances of the different methods are compared when used in conjunction with a variable time‐step ordinary differential equation integrator. Tables of results are given and the suitability of the discretizations is discussecd.
A quintic conforming plate bending triangle
Authors: Caramanlian C. , Selby K. A. , Will G. T. 
Published: August 2005

AbstractA new family of conforming triangular plate bending elements, based on the Displacement Method of formulation, is developed in detail in Reference 9. The elements can be of any order n−4, and do not present excess nodal continuties at the corner nodes. For a given element, the assumed vertical displacement w consists of a polynomial expansion supplemented by three rational function. Polynomial completeness is of order n for even n, and of order n‐1 for odd values of n. This family is proposed as a desirable alternative to refined triangular elements which incorporate all three curvatures as corner node variables,8 or require constraint equations to enforce inter‐element compatibility,10 The purpose of this paper is to describe the quintic member of the family. The traditional difficulties associated with the discontinuous curvatures of the rational functions are solved in a straightforward fashion. The element has the same good accuracy as the other, well‐known, quintic triangle, 3,4,8 and some additional advantages accruning from the simplicity of its nodal variables. A similar performance can be anticipated with the other members of the family.
Improved finite difference formulas for boundary value problems
Authors: Gawain T. H. , Ball R. E. 
Published: August 2005

AbstractThis paper deals with the numerical solution of linear differential equations of fourth order by finite differences. It points out significant (but usually overlooked) errors which result from the conventional method of imposing the boundary conditions in such problems. Revised finite difference formulas are derived which apply near the boundaries and which eliminate the above errors. Three commonly encountered boundary conditions ar econsidered. These correspond, in the terminology of beam analysis, to a clamped end, to a simply supported end and to a free end. The improvement in accuracy that can be achieved with the revised formulas is illustrated by two representative examples. The revised formulas are shown to reduce the overall error of the numerical solution by a factor of about five in a typical case.
An improved algrorithm for heat conduction problems with phase change
Authors: Morgan K. , Lewis R. W. , Zienkiewicz O. C. 
Published: August 2005

AbstractThe algorithm in a earlier paper by Comini et al1 for handling the phase change in transient non‐linear heat conduction problems is simplified and improved. Two examples involving phase change are solved using quadratic isoparametric elements and it is demonstrated that very good accuracy may be achieved.
Finite element methods for an optimal steady‐state control problem
Authors: Meric R. A. 
Published: August 2005

AbstractAn optimal steady‐state control problem governed by an elliptic state equation is solved by several finite element methods. Finite element discretizations are applied to different variational formulations of the problem yielding accurate numerical results as compared with the given analytical solution. It is sated that, for minimum computational effort and high accuracy, ‘mixed’ finite elements requiring only C° continuity, and approximating the control and state functions simultaneously are better suited to similar ‘fourth order’ problems.
Finite‐difference solution of an elliptic partial differential equation with discontinuous coefficients
Authors: Chmielewski G. E. , Hoffman G. H. 
Published: August 2005

AbstractAn algoritm is presented for point relaxation of an elliptic partial diferential equation at a grid station where its coefficient are discontinuous. Such equations can arise from the use of skewed co‐ordinate system based on discotinuous reference functions (lengths) to map a complicated physical geometry onto a simple computational domain. Efficary of the scheme is illustrated by examples involving potential flow in a sharply bent channel and in a conical diffuser.
Block iterative finite element preprocessed scheme for simulation of large non‐linear problems
Authors: Voss Clifford I. , Pinder George F. 
Published: August 2005

AbstractThe ‘Block Iterative Finite Element Preprocessed Scheme’ (BIFEPS) for finite element simulation combines two independent steps. In the ‘finite element preporcessing step’, spatial information about the finite element mesh is analysed and all integrals arising from the application of the Galerkin method are evaluated and stored on a permanent sequential storage unit (such as tape or disk). In the ‘block iterative step’, the preprocessed information is retrieved from permanent storage and the matrix equation is assembled and solved in an efficient manner according to a generalization of the block successive over‐relaxation iterative method. Significant advantages over common finite element simulation techniques are achieved in terms of both computer core requirements and execution time. Numerical experiments show that the advantages of BIFEPS are greatest for large, non‐linear simulation problems.
An analysis of a cubic isoparametric transformation
Authors: Woodford G. , Mitchell A. R. , McLeod R. 
Published: August 2005

AbstractThe general nine point isoparametric transformation is analysed with respect to a triangle with two straight sides and one curved side. Point placements are determined on the curved side which ensure that the Jacobian of the transformation remains positive inside and on the boundary of the triangle. Special cases of the transformation are considered which lead to implied curves of the form of symmetric cubics, parabolas, and explicit cubics respectively, thus enabling isoparametric transformations to match a variety of boundary shapes.
A stable finite element simulation of convective transport
Authors: Ben‐Sabar Ehud , Caswell Bruce 
Published: August 2005

AbstractA finite element simulation of the equations of momentum and energy transport in fluids has been implemented with triangular elements. An attempt is made to single out the reasons for numerical instabilities reported by other investigators for convection–diffusion transport operations in fluid mechanics when the ratio of the convective to the diffusive terms, measured by the Reynolds and Peclét numbers, is of the order of a hundred. To this end, the equations are solved for several problems to permit a direct comparison with results of other formulations. It is shown that the appearance of instability can be delayed by a proper choice of boundary conditions, and its intensity can be reduced through the use of triangular finite elements. Results agree very well with theoretical solutions for particular test problems including flows with large convection effects, large dissipation effects and fluids with temperature dependent properties.
A variable thickness, curved beam and shell stiffening element with shear deformations
Authors: Ferguson G. H. , Clark R. D. 
Published: August 2005

AbstractA family of 2‐D and 3‐D superparametric curved beam elements are introduced as a special form of general 2‐D and 3‐D isoparametric continuum elements. Each beam ‘subelement’ is rectangular incross section, however several elements may be offset and overlayed for the analysis of structural members of quite general section properties. A number of examples are presented in order to illustrate the validity and range of application of the element.
Displacement oscillation in plane quadratic isoparametric elements in orthotropic situations
Authors: Holt J. S. , Hope P. S. 
Published: August 2005

AbstractLong thin test specimens of orthotropic material are modelledby quadratic isoparametric finite elements in plane strain. Displacement oscillations occur down the long free edge of themodel with both reduced (2 × 2) and full (3 × 3) integration, themagnitude of the oscillations being affected by element aspectratio and the elastic constants of the material. The rate ofdiffusion of stress as predicted by the classical shear‐lag theory, being dependent on the material constants, is reflectedin the displacement oscillations near the load in 3 × 3integration. In 2 × 2 integration, however, this effect is swampedby the build‐up of oscillations away from the restraints in alowenergy deformation mode which becomes dominant as the elementaspect ration is increased. These latter voscillations arepredicted by the illconditioning of the structural stiffnessmatrix measured by a solution diagonal decay factor.
An explicit numerical method for solving transient combined heat conduction and convection problems
Authors: Gane C. R. , Stephenson P. L. 
Published: August 2005

AbstractThis paper describes an explicit numerical method for solving transient combined heat conduction and convection problems. Applications include the cooling of many types of engineering plant; for example, stator and rotor windings of turbogenerators and high voltage underground cables. The Du Fort–Frankel and the fully implicit finite difference schemes have been used to solve the conduction and convection equations, respectively. It is shown that, with a suitable order of calculation, the overall method becomes explicit. Computational procedures are outlined and stability, accuracy and convergence are considered. Numerical examples are given to illustrate the use of the method and to validate some of the theoretical points. Results have also been obtained using existing numerical methods and have been compared with those from the proposed method. For certain problems, it is shown that the proposed method uses less overall computing time than other methods such as that devised by Crank and Nicolson.