bluuebunny/crossref_metadata_2025 huggingface dataset:
Finite element analysis of non‐stationary one‐dimensional random diffusion problems
Authors: Tasaka Seiichi , Matsuoka Osamu
Published: August 2005

A finite element analysis of a class of non‐stationary random diffusion problems is considered. By using the one‐dimensional heat equation with random initial condition and random external excitation, the statistical numerical formulation is presented. Two typical numerical examples are given for somewhat simplified problems by which the validity of the finite element scheme is discussed. The results obtained by the finite difference scheme are also shown.
Universal finite element matrices for tetrahedra
Authors: Silvester Peter P.
Published: August 2005

Methods are described for forming element matrices for a wide variety of operators on tetrahedral finite elements, in a manner similar to that previously employed for line segments and triangles. This technique models the differentiation and product‐embedding operators as rectangular matrices, and produces finite element matrices by replacing all required analytic operations by their finite matrix analogues. The method is illustrated by deriving the conventional matrix representation for Laplace's equation. Computer programs are available, which generate universal finite element matrices for use in various applications.
Invariant 8‐node hybrid‐stress elements for thin and moderately thick plates
Authors: Spilker R. L.
Published: August 2005

Eight‐node hybrid‐stress elements are developed for the analysis of plates ranging from arbitrarily thin to moderately thick. The displacement behaviour is characterized by a transverse displacement and independent cross‐section rotations, which are interpolated using the 8‐node Serendipity shape functions. All components of stress are included; alternative elements are developed which differe in the form of the inplane distribution of the stresses. Elements are sought for whic the stiffiness is invariant and of correct rank, and whic show on signs of deterioration in the thin‐plate limit. A discussion of the prospects for developing a 4‐node element with these characteristics is also presented. Example problems are used to compare the performance of the 8‐node elements including convergence behaviour, intraelement stress distributions and optimal sampling locations, and range of applicability in terms of plate thickness ratio.
A qualitative accuracy consideration on arch elements
Authors: Yamamoto Yoshiyuki , Ohtsubo Hideomi
Published: August 2005

In the present paper, discretization errors in the finite element analysis of arches are investigated quantitatively. So far they have been estimated as an order, such as a power of the element size by means of functional analysis; however, it is insufficient for practical applications, because they depend to a great extent upon the constant of proportionality, which is investigated herein. As a result, it is shown that the constant is affected largely by the arch's stiffness. Errors for displacements are also evaluated with the aid of the energy principle. A formula for a posteriori estimating errors is proposed, which can be evaluated only from the finite element solutions calculated. The validity of the present theory is verified by numerical examples.
Band algorithm for unsymmetric matrices in finite element and semi‐discrete methods
Authors: Gopalakrishnan T. C. , Palaniappan A. B.
Published: August 2005

A compact FORTRAN subroutine for reducing unsymmetric band matrices (in‐core solution) is presented. As usual, the zeros inside the band are skipped during the Gauss elimination. However, the theme of the paper is centred on a new approach in applying the above‐mentioned band solver to transient problems. The approach results in considerable saving of computational time while also achieving reduction in memory space. This double advantage makes it particularly useful in handling dynamic real world problems. Extension of the use of the algorithm to moving boundary problems is indicated.
Permutation rules for simplex finite elements
Authors: Silvester Peter P.
Published: August 2005

Simplicial finite elements have many symmetries, which are commonly exploited in programs to save computing time and storage. All possible permutations of the interpolation functions of an N‐simplex can be expressed in terms of N basic permutation operations. The relevant permutation matrices are given for triangles up to order 20 and tetrahedra up to order 10.
Solution of a free boundary problem by finite elements: Numerical considerations and results
Authors: Caprili M.
Published: August 2005

This paper contains numerical considerations on, and the results of the problem of a fluid filtering through a porous, isotropic, homogeneous, three‐dimensional dam with variable cross‐section. The numerical solution is obtained by the finite element method using cylindrical elements that exactly match the curved part of the boundary.

Furthermore, a lower and an upper numerical enclosure of the free boundary are considered, together with a description of the procedure of calculations performed by an IBM 370/158 computer.
A novel boundary infinite element
Authors: Zienkiewicz O. C. , Emson C. , Bettess P.
Published: August 2005

A new, improved infinite element based on mapping is proposed for modelling unbounded domain problems. Mapping has previously been used in such problems, not only for the entire domain, but also for the infinite element itself. The novelty of the present approach is the simplicity of the mapping, and the retention of standard integration abscissae and weights. The implementation of these elements is very straightforward, and they are ideally suited for the analysis of infinite domain static problems in two and three dimensions.
A stabilization procedure for the quadrilateral plate element with one‐point quadrature
Authors: Belytschko Ted , Tsay Chen‐Shyh
Published: August 2005

A stabilization procedure is developed for controlling the kinematic modes of the four‐node, bilinear quadrilateral element when single‐point quadrature is used. These kinematic modes manifest themselves by spatial oscillations or singularity of the total stiffness. In this stabilization procedure, additional generalized strains are defined which are activated by the kinematic modes; these generalized modes are furthermore not activated by rigid body motions regardless of the shape of the quadrilateral. By using a scaling law developed in an earlier paper, the stabilization parameters are defined so they do not adversely affect the element's performance. Several problems which are subject to kinematic modes are presented to illustrate the performance of this stabilization procedure for linear problems.
Fortran computer program for inextensional bending of a doubly curved shell triangular element
Authors: Morley L. S. D.
Published: August 2005

A Fortran computer program is described which calculates physical quantities for a class of shell triangular elements undergoing inextensional bending. These elements are in quadratic parametric representation and may have positive, zero or negative Gaussian curvature.

The exact inextensional bending solutions for the rectangular displacement components are cubic in the surface co‐ordinates and the curvature changes are relatively slowly varying.
Performance evaluation of algorithms for mildly nonlinear elliptic problems
Authors: Houstis E. N. , Mitchell W. F. , Papatheodorou T. S.
Published: August 2005

A number of numerical methods for mildly nonlinear elliptic boundary value problems on general domains is presented. The discretization procedures considered are: a fourth‐order FFT‐type method, collocation using Hermite bicubic splines and Galerkin with linear triangular as well as quadratic quadrilateral isoparametric elements. The linearized collocation and Galerkin equations are solved by various direct methods available in the ELLPACK system. A comparative study of the above equation solvers is presented for different domain geometries and compilers. The evaluation of software for the general mildly nonlinear elliptic equations is performed over 36 instances from a population of 16 parametrized problems with ‘real world’ and ‘mathematical’ behaviour. The performance data suggests that collocation is an effective method for such general problems, while Galerkin with quadratic quadrilateral isoparametric elements is uniformly superior to the one with linear elements.
Nonlinear programming on a microcomputer
Authors: Rangaiah V. P. , Sadasivan S.
Published: August 2005

The Davidon‐Fletcher‐Powell (DFP) algorithm for multivariable unconstrained nonlinear function minimization is implemented on a desk microcomputer—the Hindustan Computers MICRO‐2200—with a floppy disk memory extension peripheral. The program is developed using the programming keys of the system. The program is closely based on FMFP, a well‐known FORTRAN subroutine of the algorithm. Among the exercises performed are two standard nonlinear programming (NLP) test problems, namely the Rosenbrock and Wood function minimization and two SUMT (Sequential Unconstrained Minimization Technique) illustration problems in structural optimization, i.e. two‐bar and three‐bar truss weight minimization examples. Experience bears out the potential of desk calculating systems as tools in nonlinear programming algorithm research. Also, the small‐scale structural optimization capability afforded by such systems is expected to be of significance in teaching and preliminary design contexts.
A predictor‐corrector contouring algorithm for isoparametric 3D elements
Authors: Kontopidis George D. , Limbert David E.
Published: August 2005

This paper describes a new contouring algorithm for isoparametric elements which can be used to map three‐dimensional scalar fields. The contours are generated on arbitrary planes intersecting finite element structures. Tracing element contour lines is accomplished by an accurate predictor‐corrector technique. A method of finding starting points for the algorithm on the boundary of the elements is also given.
An arc‐length method including line searches and accelerations
Authors: Crisfield M. A.
Published: August 2005

This paper describes a method for introducing line searches into the arc‐length solution procedure. Such line searches may be used at each iteration to calculate an optimum scalar step‐length which scales the normal iterative vector. In practice, a loose tolerance is provided so that on many iterations the line searches are avoided. However on ‘difficult iterations’, the line searches are shown to lead to a substantial improvement in the convergence characteristics. A simple single‐parameter acceleration is also developed using line search concepts. The new arc‐length method is applied to both the geometrically nonlinear analysis of shallow shells and the materially nonlinear analysis of reinforced concrete beams and slabs. Significant improvements are demonstrated in relation to the standard arc‐length method.
A solution to the C1 continuity problem in plate bending
Authors: Caramanlian C.
Published: August 2005

A family of high‐order, conforming triangles for the finite element analysis of plate bending problems is developed, using the displacement method of formulation.

The development proceeds in two steps. A family of non‐conforming triangles, based on polynomial expansions of order >4 is first generated, and its performance found to be unacceptable. Nodal variables for the non‐conforming family are selected from the set w, wx, wy, wn. The elements are then made to conform, by adding a twist nodal variable wnt at the mid‐side nodes. Rational functions define the three additional degrees‐of‐freedom. Simple and very accurate procedures solve the problems associated with the use of such functions.

Numerical results are presented for the conforming triangles of order 4 and 7, following a brief description of the two elements. A listing of the explicit shape functions for the quartic triangle is included.

The numerical results are very good. In particular, they are superior per degree‐of‐freedom to the results predicted by the various non‐conforming and conforming, cubic and related elements at present used in computer packages. Together with a similar performance by the quintic member10 of the family, they validate the proposed theoretical solution.
Minimum weight design using finite elements
Authors: Kark S. K. , Scholes A.
Published: August 2005

The authors' aim was the development of a suitable procedure for the structural design of railway vehicles within an existing general purpose finite element package. A previous application to railway vehicles was based on the use of a sequence of linear programming steps incorporating move limits on the design variables. This approach was slow and in other fields mathematical programming techniques tended to give way to methods based on optimality criteria.

Nevertheless because of its simplicity of concept, and because some apparently successful alternatives to the move limit idea were available, the use of linear programming was returned to and the method is now incorporated in the British Rail finite element program NEWPAC. Couched in terms of inverse variables and using linearized forms of the stress constraints, the linear programming approach converges with the optimality criteria method. Details of the implementation and of some standard examples are given.
Analysis of steel frames under fire environment
Authors: Jain P. C. , Rao M. N. G.
Published: August 2005

A numerical technique is developed using an implicit time‐marching scheme to study the deformation history of steel building frames in fire, by considering the change in the material properties due to rise of temperature, effect of creep and large deformations. A computer program has been developed for the analysis of plane frames based on the above algorithm using incremental and iterative procedures. Based on such a study, the length of time for which the structure can perform its function without either local or overall failure can be predicted.
A static infinite element
Authors: Curnier Alain
Published: August 2005

This paper describes a simple procedure to derive a static infinite element from a linear isoparametric finite element.
Asymptotic rates of convergence of iterative methods applied to finite difference calculations on non‐uniform grids
Authors: Jones I. P.
Published: August 2005

In this paper the use of strongly stretched finite difference grids is examined in detail for a simple model equation. Numerical solutions of this equation demonstrate the overall second‐order accuracy of the difference approximations. The behaviour of two simple iterative methods, S.O.R. and stationary A.D.I. is discussed for several cases with strong grid stretching and with variable diffusion coefficients. The results show that grid compression near to boundaries can greatly enhance the rates of convergence of these iterative methods, whereas with grid compression in the centre the rate of convergence can be extremely slow. The case of a diffusion coefficient which increases away from the boundaries of a region is analogous to grid compression in the centre and again the convergence rates can degrade considerably.
On computing the inverse of a sparse matrix
Authors: Niessner H. , Reichert K.
Published: August 2005

The Gauss‐Jordan inversion algorithm requires 0(n3) arithmetic operations. In some practical applications, like state estimation or short‐circuit calculation in power systems, the given matrix is sparse and only part of the inverse is needed. Most frequently in the diagonal dominant case this is the diagonal. There are two ways to exploit sparsity to determine elements of the inverse:

Columnwise inversion via the solution of sparse linear systems with columns of the unit matrix as right‐hand sides.

Application of the algorithm of Takahashi et al6

.

The latter algorithm arises very naturally from multiplying the left‐ and right‐hand factors of the Zollenkopf bifactorization in reverse order. We indicate how computing time can be gained in the important symmetric diagonal dominant case if only part of the diagonal is needed and compare computing times of the method of Takahasi et al.6 with several variants of columnwise inversion. Whereas most of the theory holds for general matrices, experiments are performed on the symmetric diagonal dominant case. For band matrices the operation count is 0(n) both for computing a column of the inverse by columnwise inversion and the diagonal by the algorithm of Takahashi et al6.
On the suppression of zero energy deformation modes
Authors: Pian Theodore H. H. , Chen Dapeng
Published: August 2005

Based on the Hellinger‐Reissner principle and the deformation energy due to assumed stresses and displacements, the problem of the kinematic deformation modes in assumed stress hybrid/mixed finite elements has been examined. Basic schemes are developed for the choice of assumed stress terms that will suppress all kinematic deformation modes. Quadrilateral membrane and axisymmetric elements, and three‐dimensional hexahedral elements, are used to illustrate the suggested procedure.
Multiple‐parameter reduced basis technique for bifurcation and post‐buckling analyses of composite plates
Authors: Noor Ahmed K. , Peters Jeanne M.
Published: August 2005

A multiple‐parameter reduced basis technique and a problem‐adaptive computational algorithm are presented for the bifurcation and post‐buckling analyses of composite plates subjected to combined loadings. The computational algorithm can be conveniently divided into three distinct stages. The first stage is that of determining the stability boundary. The plate is discretized by using displacement finite element models and the analysis region is reduced by exploiting the special symmetries exhibited by the response of the plate. The vector of unknown nodal displacements is expressed as a linear combination of a small number of path derivatives (derivatives of the nodal displacements with respect to path parameters), and a Rayleigh‐Ritz technique is used to approximate the finite element equations by a small system of algebraic equations. The reduced equations are used to determine the stability boundary of the plate.

In the second stage, a nonllnear solution in the vicinity of the stability boundary is obtained by using a bifurcation buckling mode as a predictor, and a set of reduced equations is generated. In the third stage, the reduced equations are used to trace post‐buckling paths corresponding to various combinations of the load parameters.

The potential of the proposed approach is discussed and its effectiveness is demonstrated by means of a numerical example of laminated composite plate subjected to combined compressive and shear loadings.
A posteriori error indicators for the p‐version of the finite element method
Authors: Dunavant David A. , Szabo Barna A.
Published: August 2005

The existence of local a posteriori error indicators for the p‐version of the finite element method is demonstrated through numerical examples. The optimal sequence of p‐distributions can be closely followed on the basis of the indicators.
Heat diffusion with time‐dependent convective boundary conditions
Authors: Becker N. M. , Bivins R. L. , Hsu Y. C. , Murphy H. D. , White A. B. , Wing G. M.
Published: August 2005

The heating (or cooling) of the rock adjacent to water flowing through a crevice is of interest in certain geothermal studies. For many purposes, only the rock temperature at the rock‐water interface is needed. The fact that the convective heat transfer coefficient is a function of time in the case of unsteady flow takes this problem out of the strictly classical domain.

Several methods of solution are described. An approach in which the heat equation is solved, under appropriate side conditions, by standard finite difference techniques is shown to be satisfactory but rather wasteful because much unneeded information concerning internal rock temperatures must be obtained. Several integral equations of Volterra type are derived that provide the temperature only at the interface. Two numerical approaches to their solution are described: one quite classical and only partially effective; the other an apparently new algorithm that is fast and efficient. Analytical upper and lower bounds on the temperature are obtained and serve to demonstrate that this numerical device is also very accurate.

The algorithm is applicable to a wide class of Volterra integral equations of the second kind. A brief discussion of the possible future uses of this scheme and the need for additional research is given.
Numerical evaluation of stress intensity factor and J integral in three‐point bend specimen
Authors: Pratap C. R. , Pandey R. K. , Natarajan R. , Gupta K. N.
Published: August 2005

The present paper attempts to evaluate the fracture mechanics parameters, the stress intensity factor (K) and Rice's energy integral (J) in plane strain conditions for three‐point bend specimens. Both the parameters have been evaluated by the FEM using higher order isoparametric elements (i.e. quadratic elements). The crack tip elastic singularity (1/√r) has been taken into account by the use of the special crack tip elements of degenerate triangular element type as well as the fine eight‐noded isoparametric plane elements. The stress distribution has been compared with the Westergaard solution in the vicinity of the crack. The K and J values have also been‐compared with the theoretical results.
A Taylor–Galerkin method for convective transport problems
Authors: Donea Jean
Published: August 2005

A method is described to derive finite element schemes for the scalar convection equation in one or more space dimensions. To produce accurate temporal differencing, the method employs forward‐time Taylor series expansions including time derivatives of second‐ and third‐order which are evaluated from the governing partial differential equation. This yields a generalized time‐discretized equation which is successively discretized in space by means of the standard Bubnov–Galerkin finite element method. The technique is illustrated first in one space dimension. With linear elements and Euler, leap‐frog and Crank–Nicolson time stepping, several interesting relations with standard Galerkin and recently developed Petrov–Galerkin methods emerge and the new Taylor–Galerkin schemes are found to exhibit particularly high phase‐accuracy with minimal numerical damping. The method is successively extended to deal with variable coefficient problems and multi‐dimensional situations.
An integral equation method for non‐self‐adjoint eigenvalue problems and its applications to non‐conservative stability problems
Authors: Tosaka Nobuyoshi , Kakuda Kazuhiko
Published: August 2005

The aim of the work reported in this paper is to present the new formulation of the integral equation method for non‐self‐adjoint problems and to apply the method to stability problems of elastic continua subjected to non‐conservative loadings. A general non‐self‐adjoint eigenvalue problem stated in terms of differential operators is transformed into a set of coupled integral equations. Our derivation of integral equations is based on an inverse formulation of a canonical form for the original problem and the corresponding fundamental solution pair. Three well‐known non‐conservative stability problems in elasticity are examined by this integral equation method as illustrative examples. The approximate values of the critical parameters of sample problems demonstrate a sufficient accuracy through a comparison of other values.
Asymmetric bending of axisymmetric shells
Authors: Vykutil Josef
Published: August 2005

A two‐noded, straight element with one‐point quadrature is introduced for the unsymmetrical bending of orthotropic axisymmetric shells. The numerical results indicate that the present simple element performs accurately for both thick and thin shell applications.
Comparative study of six explicit and two implicit finite difference schemes for solving one‐dimensional parabolic partial differential equations
Authors: Roberts David L. , Selim M. Sami
Published: August 2005

Eight finite difference schemes used in solving parabolic partial differential equations are compared with respect to accuracy, execution time and programming effort. The analysis presented is useful in selecting the appropriate numerical scheme depending on the emphasis placed upon accuracy, execution time or programming effort.
Two high‐order numerical methods for solving boundary‐value nonlinear ordinary differential equations
Authors: Tewarson R. P.
Published: August 2005

Two numerical methods for solving two‐point boundary‐value problems associated with systems of first‐order nonlinear ordinary differential equations are described. The first method, which is based on Lobatto quadrature, requires four internal function evaluations for each subinterval. It does not need derivatives and is of order h7, where h is the space chop. The second method, which is similar to the first but is based on Lobatto–Hermite quadrature, makes the additional use of derivatives to achieve O(h9) accuracy. Results of computational experiments comparing these methods with other known methods are given.
A simple element for static and dynamic response of beams with material and geometric nonlinearities
Authors: Yang T. Y. , Saigal Sunil
Published: August 2005

A unified simple 6 degrees‐of‐freedom beam finite element and the associated computational procedures have been developed for the fast and efficient solution of a wide class of static and dynamic response problems of the beam type with material and/or geometrical nonlinearities.

The material nonlinearity is treated by including its effect in the governing equations by forming the stiffness matrix of each element using a two‐dimensional grid of Gauss points and using the material properties at each point corresponding to the uniaxial strain at that point. Examples are provided for metal and reinforced concrete beams.

A powerful yet straightforward method for the solution of elastica problems of beams and frames, using the beam element developed by the senior author, has been extended for determining the dynamic response of beams undergoing large displacements, including large rotations.

The solution procedure involves piecewise linearization of response equations and iterations at each incremental step to achieve equilibrium. The solution procedure is simple and easy to apply. A variety of problems is solved to determine the applicability of the proposed simple formulations. Excellent agreement with existing analytical solutions which employ higher order elements demonstrates the efficiency and versatility of the present simple beam element in nonlinear analysis.
Formulation methods of geometric and material nonlinearity problems
Authors: Gadala M. S. , Dokainish M. A. , Oravas G. Ae
Published: August 2005

A concise survey of formulation methods of geometric and material nonlinearity problems is given. Differences between existing formulations in the literature are discussed. A consistent Lagrangian and updated Lagrangian formulations are derived from the energy balance equation transformed to the proper reference configuration. Differences between the existing formulations and similar ones in the literature are found to be in specific geometric nonlinear terms in the final incremental equation as well as in the definition of the load increment vector. Specific forms of constitutive equations for elastic and elastoplastic materials are presented. Some of the forms used by other authors in application to elastoplastic materials are shown to be inconsistent. Sample numerical examples intended for checking some particular points in the formulation are presented.
Efficient linear and nonlinear heat conduction with a quadrilateral element
Authors: Liu Wing Kam , Belytschko Ted
Published: August 2005

A method is presented for performing efficient and stable finite element calculations of heat conduction with quadrilaterals using one‐point quadrature. The stability in space is obtained by using a stabilization matrix which is orthogonal to all linear fields and its magnitude is determined by a stabilization parameter. It is shown that the accuracy is almost independent of the value of the stabilization parameter over a wide range of values; in fact, the values 3, 2 and 1 for the normalized stabilization parameter lead to the 5‐point finite difference, 9‐point finite difference and fully integrated finite element operators, respectively, for rectangular meshes; numerical experiments reported here show that the three have identical rates of convergence in the L2 norm. Eigenvalues of the element matrices, which are needed for stability limits, are also given. Numerical applications are used to show that the method yields accurate solutions with large increases in efficiency, particularly in nonlinear problems.
A further look at Newmark, Houbolt, etc., time‐stepping formulae
Authors: Wood W. L.
Published: August 2005

This 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

In 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

Rigid‐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

Exact 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

Least 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

The 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

A 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

A 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

In 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

Simple 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.
Animating structure plots: Experiments with a PERQ
Authors: Colyer Bryan
Published: August 2005

A PERQ single user computer can be used to animate structure plots, which is of great assistance when interpreting the results from finite element programs. Excellent appreciation may be obtained of a structure oscillating in complicated natural modes. The technique is also useful for studying deformations due to static forces.
Transformation of dependent variable in the finite element solution of some phase change problems
Authors: Borshukova Stefka , Konovski Petar
Published: August 2005

The 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

This 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

This 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

Three 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

The 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

An 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

A 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

A 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

Relations 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

A 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

In 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

A 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

This 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.