bluuebunny/crossref_metadata_2025_split huggingface dataset:
A further look at Newmark, Houbolt, etc., time‐stepping formulae
Authors: Wood W. L. 
Published: August 2005

AbstractThis paper looks at some well‐known methods for the numerical integration of the vibration equation from the point of view of various groupings of the independent equations involved. New forms are given of the general three‐parameter method introduced by Zienkiewicz.1 Some new one‐step methods are introduced; these are of great practical importance because of the ease with which the size of time step can be changed.
The post‐processing approach in the finite element method—Part 2: The calculation of stress intensity factors
Authors: Babuška I. , Miller A. 
Published: August 2005

AbstractIn the context of a model problem we describe post‐processing techniques for the calculation of generalized stress intensity factors as well as displacements, stresses, etc., near corner points. We discuss two broad classes of methods, one involving an ‘influence’ function, and the other related to the well‐known energy release principle of fracture mechanics. An error analysis is sketched and two numerical examples are given to illustrate the effectiveness of the techniques.
Limit analysis of fastener groups under eccentric load
Authors: Kamtekar A. G. , Wittrick W. H. 
Published: August 2005

AbstractRigid‐plastic theory is used to predict the failure load of connections made up of groups of fasteners which are subjected to a force applied in the plane of the connection. The failure mechanism consists of one of the plates making up the connection rotating relative to the other about a point in the plane of the connection. This point may coincide with the position of a fastener in which case it is shown that difficulties arise in the computation. Conditions are given for predicting whether this situation will arise and methods are developed for overcoming these and other difficulties that are encountered in the computation. Two computer programs which were developed to do the calculations are described.
Analytical integration formulae for linear isoparametric finite elements
Authors: Babu D. K. , Pinder G. F. 
Published: August 2005

AbstractExact and approximate analytical expressions can be derived for integrals arising in finite element methods, employing isoparametric linear quadrilaterals in two space dimensions with bilinear basis functions. The formulae associated with rectangular elements, arbitrarily oriented in space, can be shown to be a special case. The proposed method provides considerable savings in computational effort, in comparison with a numerical method that employs Gaussian quadrature procedures. In addition, the method, when applied to a quadrilateral inscribable in a circle, can be shown to produce better accuracy than the associated (2 × 2) Gaussian quadrature formulae.
Least squares strain smoothing for the eight‐node serendipity plane stress element
Authors: Jeyachandrabose C. , Kirkhope J. 
Published: August 2005

AbstractLeast square strain smoothing is applied to the popular eight‐node serendipity quadrilateral plane stress element. Substitute shape functions, derived from the least squares principle, are provided explicitly for smoothing the strain matrix. It is found that the spurious shear straining modes appearing in the unsmoothed formulation are now completely eliminated. The nodal stress values can thus be computed directly without any smoothed extrapolation from the Gauss‐point stresses.
Limitations for the use of an exact formula for receptance reanalysis
Authors: Brandon John A. 
Published: August 2005

AbstractThe receptance matrix of a system after a modification of rank k < n to system matrices (of ordern) may be derived from the receptance matrix of the original system by solution of a system of linear equations of order k. In this paper it is shown that it is desirable to impose a much more conservative condition on the system of equations than simple solvability. The possible consequences of breaching this conservative condition are developed and discussed.
A finite element analysis of metal‐forming problems with an elastic‐viscoplastic material model
Authors: Chandra Abhijit , Mukherjee Subrata 
Published: August 2005

AbstractA finite element formulation for elastoviscoplasticity problems in the presence of large strains and deformations is presented in this paper. The formulation is capable of using any of a class of combined creep‐plasticity constitutive models with state variables for the description of material behaviour. The specific problem considered is plane strain extrusion using the constitutive model originally proposed by Hart. Numerical results are presented for sample problems and the important effects of extrusion speed and friction (at the die–workpiece interface) on the residual stresses in an extruded sample are investigated. The computer program developed here is quite general and can be modified to solve problems for other manufacturing processes like rolling, sheet forming, etc.
A direct search package for unconstrained minimization
Authors: Rao M. V. C. , Chandra K. S. 
Published: August 2005

AbstractA new direct search package is presented. Typical test functions solved establish the robustness and efficiency of the package. The most significant features of the package are that it works satisfactorily even in single precision and requires much less memory. It needs only the function values and the unidimensional search is totally dispensed with. Methods such as different descent techniques, the RMS procedure, the co‐ordinate movement technique and the gallop–canter equalization scheme form the sequence of strategies.
An efficient zooming method for finite element analysis
Authors: Hirai Itio , Wang Bo Ping , Pilkey Walter D. 
Published: August 2005

AbstractIn this paper, an efficient, exact zooming technique is developed which employs static condensation and exact structural reanalysis methods. For a multiple level of zooming such that the successive level of zooming is contained within the prior levels of zoom, repeated application of static condensation will reduce the system to one that is associated only with the degrees‐of‐freedom (dof) of the original model. Then, application of an exact static reanalysis technique permits the displacements at the dof of the original model that are contained in the final zoomed portion of the structure to be obtained first. Next, the response external to the zoom, as well as the response of additional dof within various levels of zooming, can be computed. With the triangular factor of the stiffness matrix of the original system available, this approach involves only the solution of a system of equations of small order. The proposed method is demonstrated by a numerical example.
Finite element criteria for some shells
Authors: Morley L. S. D. 
Published: August 2005

AbstractSimple solutions are extracted from the exact compatibility equations of inextensional bending for a special class of shell shapes, and it is speculated that these solutions provide useful criteria towards evaluating finite elements for these and closely related shapes. Curved finite elements of a quadratic parametric representation, which do not belong to the special class, are then studied. By using a series of exact inextensional bending displacements, it is concluded from numerical evidence that the criteria apply to finite element shapes in this representation when they are shallow, as is usually the case in practice. Criteria for homogeneous membrane actions follow from Gol'denveizer's static–geometric analogue.
Transformation of dependent variable in the finite element solution of some phase change problems
Authors: Borshukova Stefka , Konovski Petar 
Published: August 2005

AbstractThe approach of Cermak and Zlamal1 for solving quasilinear parabolic equations is modified and improved. The modified approach leads to a normal system of ODE, which may be solved with a standard program. The numerical solution of a specially selected example is compared with the exact solution. The method is applied on a system of quasilinear parabolic equations, which describes a real process—crystallization of a metal ingot.
A statically determinate truss model for thin shells: One‐surface analysis (membrane hypothesis)
Authors: Pavlović M. N. 
Published: August 2005

AbstractThis paper presents the modelling of open shells, such as those used in roof construction, by means of a single‐layered, pin‐jointed truss. The latter exhibits several advantages over existing framework models, such as, for example, statical determinacy and the capacity to cope with arbitrary material constants. In the present article, the truss model is developed for and applied to the numerical analysis of shells subject to the membrane hypothesis. However, the same statically determinate model forms the basis for a computational scheme for analysing shells according to the more formal, statically indeterminate bending theory; the latter application of the truss model will be presented in a subsequent paper.
A statically determinate truss model for thin shells: Two‐surface analysis (bending theory)
Authors: Pavlović M. N. 
Published: August 2005

AbstractThis paper presents a simple scheme for analysing shells subject to the Kirchhoff–Love hypothesis. The method combines a previously developed, statically determinate truss model with the static‐geometric analogy of elastic thin shell theory. In this way, both in‐plane and flexural mid‐surface actions are obtained by simply repeating the elementary computations performed on an essentially ‘membrane’ truss.
Some applications of numerical methods to the analysis of the compression of articular cartilage
Authors: Rombult P. A. , McC. Ettles C. M. 
Published: August 2005

AbstractThree different numerical formulations of the confined compression creep of cartilage have been developed to study the feasibility of applying numerical methods to dynamically loaded joints in biomechanics. The accuracy, convergence and stability of these numerical methods are assessed. Extensions of the analysis to include joint lubrication and non‐uniform properties are discussed, and an example is given of cartilage under dynamic load conditions. It is found that with the amplitude of loading maintained constant, the deflection of cartilage reduces as the frequency of load application is increased.
Analysis of microwave ovens loaded with lossy process materials using the transmission‐line‐matrix method
Authors: El‐Sayed El‐Deek M. , Morsy Mohamed N. 
Published: August 2005

AbstractThe transmission‐line‐matrix (t.l.m.) numerical analysis technique is used in this paper to evaluate resonant frequencies and field parameters of the generated modes in microwave ovens loaded with lossy process materials. Analysis is made for the variation of resonant frequencies with the loss factor of the loading material. Temperature rise profile through the load is predicted from the calculated results of field parameters of sustained modes. The demonstrated data are for the dimensional parameters of a rectangular cavity of a commercial microwave oven operating at the standard heating frequency 915 MHz.
A linearized analysis of buckling of thin rotational shells using the finite element method
Authors: Delpak R. 
Published: August 2005

AbstractAn isoparametric shell element has been developed capable of linear response to the imposed loads. The original formulation, which was written for static and dynamic analyses, was extended to embrace linear buckling problems. A variety of numerical examples were attempted in order to assess the adaptability of the element to different geometrical representations. Despite serious size limitations of the computer, the accuracy of the predicted buckling loads was found to be satisfactory.
Solution of the partial eigenproblem by iterative methods
Authors: Papadrakakis M. 
Published: August 2005

AbstractA combined iterative method is formulated for the partial solution of the eigenproblem Ax = λBx that arises from the application of the finite element method. The method is a combination of the conjugate gradient (CG) method and the symmetric successive co‐ordinate overrelaxation (SSCOR) method. Both of these methods belong to the same family of iterative methods which retain their vectorial form and approach the solution by seeking stationary points of the Rayleigh quotient. The formulation consists in splitting a characteristic matrix into the sum of two matrices, one of which corresponds to the SSCOR matrix, and then accelerating the associated iteration using the CG. The behaviour of the method is illustrated for five test cases and comparisons are made with other iterative methods. The influence of the relaxation parameter ω on the computational efficiency of the methods is also studied.
A solution method for planar and axisymmetric contact problems
Authors: Bathe Klaus‐Jurgen , Chaudhary Anil 
Published: August 2005

AbstractA solution procedure for the analysis of planar and axisymmetric‐contact‐ problems involving sticking, frictional sliding and separation under large deformations is presented. The contact conditions are imposed using the total potential of the contact forces with the geometric compatibility conditions, which leads to contact system matrices and force vectors. Some key aspects of the procedure are the contact matrices, the use of distributed tractions on the contact segments for deciding whether a node is sticking, sliding or releasing and the evaluation of the nodal point contact forces. The solutions to various sample problems are presented to demonstrate the applicability of the algorithm.
Equivalence between mixed models and displacement models sing reduced integration
Authors: Shimodaira Hisashi 
Published: August 2005

AbstractRelations between displacement models using reduced integration and hybrid mixed models based on the Hellinger–Reissner and the Herrmann principles have been investigated. Five different isoparametric elements are considered for the case of plane stress, plane strain and plate bending elasticity problems.It is proved that the following relations hold for both models, provided the number of terms of a polynomial expressing the stress or strain component in the formulation of the mixed models is equal to the number of integration points of the reduced integration. If the stiffness matrix of the mixed model is evaluated by the identical integration rule with the reduced integration, the stiffness matrices of both models are identical. Thus, both models are equivalent, if the stiffness matrix of the mixed model is integrated exactly by the identical integration rule with the reduced integration.The displacement models using uniform reduced integration and selective reduced integration are equivalent to the mixed models based on the Hellinger–Reissner and the Herrmann principles except for the 6‐node element, respectively.
A general matrix operator for linear boundary value problems in slip‐line field theory
Authors: Dewhurst P. 
Published: August 2005

AbstractA general matrix operator is established for solving linear boundary value problems in slip‐line field theory. The operator will enable a wider class of problems to be solved than were previously possible with the matrix slip‐line field technique. As an illustration, a range of solutions are generated involving the previously intractable Coulomb friction boundary condition.
The curved beam/deep arch/finite ring element revisited
Authors: Prathap Gangan 
Published: August 2005

AbstractIn this paper, an attempt is made to understand the errors arising in curved finite elements which undergo both flexural and membrane deformations. It is shown that with elements of finite size (i.e. a practical level of discretization at which reasonably accurate results can be expected), there can be errors of a special nature that arise because the membrane strain fields are not consistently interpolated with terms from the two independent field functions that characterize such a problem. These lead to errors, described here as of the ‘second kind’ and a physical phenomenon called ‘membrane locking’.The findings here emerge from recent research on the effect of reduced integration on shallow curved beam elements and on the use of coupled displacement fields in finite rings. The failures which have occurred in earlier attempts to use independent polynomial displacement fields for curved elements may not have been due to neglect of rigid body motions or failure to achieve constant strain states, but because of locking due to spurious constraints. These emerge in the penalty limits of extreme thinness (an inextensional regime), when exact integration of the energy functional of an element based on low order independent interpolations for the in‐plane and normal displacements is used.It seems possible to determine optimal integration rules that will allow the extensional deformation of a curved beam/deep arch/finite ring element to be modelled by independently chosen low order polynomial functions and which will recover the inextensional case in the penalty limit of extreme thinness without spurious locking constraints. The much maligned ‘cubic in w–lincar in u’ curved beam element is now reworked to show its excellent behaviour in all situations. What is emphasized is that the choice of shape functions, or subsequent operations to determine the discretized functionals, must consistently model the physical requirements the problem imposes on the field variables. In this manner, we can restore an old element to respectability and thereby indicate clearly the underlying principles. These are: the importance of ‘field consistency’ so that arch and shell problems can be modelled consistently by independent polynomial displacement fields, and the role that reduced integration or some equivalent construction can play to achieve this.
Skyline algorithms for multilevel substructure analysis
Authors: Elwi A. E. , Murray D. W. 
Published: August 2005

AbstractA matrix derivation of the method of partial decomposition for substructure equilibrium equations is given and algorithms and subroutines necessary for implementing a multi‐level substructuring scheme are presented. The algorithms are based upon partial decomposition of skyline matrices by the Cholesky method. Transformation of co‐ordinates and prediction of the skyline for higher level substructures are also discussed.
The mode‐amplitude technique and hierarchical stress elements—a simplified and natural approach
Authors: Robinson John 
Published: August 2005

AbstractThis paper reviews the derivation procedure of conventional stress‐based elements and then shows how the procedure can be simplified by using degrees‐of‐freedom which are amplitudes of the boundary loading modes (‘mode‐amplitude technique’). This gives one class of element based on stress assumptions and uses only one virtual principle. The natural formulation of hierarchical stress elements is shown.
Generalized finite element analysis with T‐complete boundary solution functions
Authors: Zielinski A. P. , Zienkiewicz O. C. 
Published: August 2005

AbstractThe use of a complete and nonsingular set of Trefftz functions in the solution of quasi‐harmonic equations is demonstrated and shown to be often superior to the more conventional singularity distribution in boundary‐type approximation. Procedures for coupling separate domains of such solution and indeed of deriving equivalent finite elements are demonstrated.
Finite prism analysis of plates and shells
Authors: Wong Carlos C. K. , Vardy Alan E. 
Published: August 2005

AbstractThe finite prism technique introduced by Zienkiewicz and Too4 is extended to include 12‐node prism elements and, more importantly, a novel offset beam element. The use of 12‐node prism elements enables parabolic strain distributions to be simulated, this being useful for structures which have strongly tapered cross‐sections. The offset beam element is used to simulate flexure and torsion of a beam whose centroid is offset from the main structure. The element is specified completely at the nodes of adjacent prism elements and so is not really an ‘element’ in the usual sense.The analysis is applied to thin and thick plates and to shells, with and without edge beams. It is shown to be more versatile than the finite strip method and it requires smaller computer resources than the finite element method. Experimental verification of the analysis is obtained by comparison with measurements for a double‐T bridge deck tested by Loo14.
On the Galerkin finite difference method: A multi‐bases approach
Authors: Prochnow Dieter 
Published: August 2005

AbstractAt present there are many general methods of approximating a possibly nonlinear operator equation by a finite equation system. The most commonly applied methods are the finite element and the finite difference. Numerous papers (e.g. References 9 and 10) have dealt with a comparison of these methods.In Reference 12 the Galerkin finite difference method (GFDM) is developed. The GFDM is a special finite element method designed t o solve nonlinear and possibly coupled partial differential equations numerically. It consists of a finite difference scheme derived from a Galerkin finite element method through the use of special local basis functions and a special grid.In this paper, we are concerned with extending the GFDM to derive ‘normal’ difference schemes. e.g. five‐point schemes on two‐dimensional domains for a general class of operators, even in nonlinear cases.Using GFDM or the finite element method on two‐dimensional regions generally leads to at least 7‐ or 9‐point schemes as well as expensive approximations of the nonlinear terms. Often, numerical integration is necessary. These computational costs are due to the non‐orthogonality of the continuous and differentiable local basis functions that are needed in this case.The basic idea of the multi‐bases approaches, which are the major concern in this paper11, is to reduce the smoothnessproperties ofthelocal basis functions in favour oftheir orthogonality. Thiscan beachieved with the help of so‐called transfer operators which map the non‐orthogonal and differentiable basis onto an only bounded but orthogonal basis.
INACOF—A computer program for the inelastic analysis of reinforced concrete framed structures
Authors: Gurujee C. S. , Agashe S. N. 
Published: August 2005

AbstractThe paper presents a general‐purpose computer program for the inelastic analysis of reinforced concrete frames based on the method of imposed rotations. The program is capable of calculating the response of the structure to a given loading and also capable of performing collapse load analysis of the given structure. The program has been tested for a variety of problems and has been found to be extremely efficient compared to the other existing routines with much more limited capabilities. Complete listing and information for using the program has been presented.