bluuebunny/crossref_metadata_2025 huggingface dataset:
Displacement discontinuity method applied to nondestructive testing related stress problems
Authors: Zachary L. W. , Skillings B. J.
Published: August 2005

A numerical stress analysis technique using the displacement discontinuity method (DDM) is used to evaluate surface breaking and near surface flaws. DDM is described briefly, with the main body of the work devoted to exploring the use of DDM in a nondestructive evaluation (NDE) program. DDM is a subset of boundary element method technique, and it requires that only the boundaries of the problem be described. Two smooth subsurface voids are investigated. Results for two‐dimensional circular and elliptical holes are presented. Comparisons with experimental and theoretical work are shown. The method of uneven element spacing is explored. The results are examined in the context of providing information for NDE inspection requirements and the definition of acceptable flaws. DDM is very well suited for examining the stress field around a surface crack. Surface cracks can be very dangerous and good NDE inspection techniques are required. A method of obtaining the stress intensity factors is developed and illustrated on angular surface breaking cracks. The results are compared with limited experimental and numerical results and interpreted in terms of NDE inspection requirements.
Plane intersections of a three‐dimensional mesh
Authors: Afzali M.
Published: August 2005

In order to detect geometric anomalies in 3D boundary element mesh or to obtain the contour plotting of stresses on a plane intersecting the 3D mesh, a computer program PP3D‐COUPE has been developed to generate the contours on the intersection plane. The automatic mesh M2D is used to discretize the surfaces bounded by the contours for further computations.
Damped second‐order Rayleigh‐Timoshenko beam vibration in space—an exact complex dynamic member stiffness matrix
Authors: Lundén Roger , Åkesson Bengt
Published: August 2005

A uniform linear beam in a uniform linear ambient medium is studied. The beam performs stationary harmonic damped nonsynchronous space vibration in simultaneous tension, torsion, bending and shear in the presence of a large static axial load. Hysteretic and viscous dampings of the beam material and ambient medium are considered. Generalized complex Koloušek functions are derived. A 12 × 12 complex symmetric stiffness matrix is established for a supported beam member excited at its ends by prescribed harmonic translations and rotations which have the same frequency but may be out of phase. This matrix allows for an exact analysis of nonproportionally damped built‐up beam structures, thus avoiding assumed mode shapes and lumped or consistent masses. A general notation is suggested. Numerical examples are given, including applications of the computer program SFVIBAT‐DAMP.
Solution of the Poisson equation by differential quadrature
Authors: Civan Faruk , Sliepcevich C. M.
Published: August 2005

The method of differential quadrature is demonstrated by solving the two‐dimensional Poisson equation. The results for three test problems are compared with the exact analytical solutions and the numerical solutions obtained by others for the Galerkin, the control‐volume and the five‐point finite difference methods. The method of differential quadrature leads to more accurate results for comparable levels of computational effort.
An accurate scalar potential finite element method for linear, two‐dimensional magnetostatics problems
Authors: McDaniel T. W. , Fernandez R. B. , Root R. R. , Anderson R. B.
Published: August 2005

We have assessed the accuracy of a commercially available computer software package for finite element method calculations of magnetostatic fields. The computer program, MSC/NASTRAN,

Available from the MacNeal‐Schwendler Corporation, Los Angeles, CA 90041, U.S.A.

is well known for its wide applicability in structural analysis and heat transfer problems. We exploit the fact that the differential equations of magnetostatics are identical to those for heat transfer if the magnetic field problem is formulated with the reduced scalar potential.1 Consequently, the powerful, optimized numerical routines of NASTRAN can immediately be applied to two‐ and three‐dimensional linear magneto‐statics problems. Application of the NASTRAN reduced scalar potential approach to a ‘worst case’ two‐dimensional problem for which an analytic solution is available has yielded much better accuracy than was recently reported2 for a reduced scalar potential calculation using a different finite element program. Furthermore, our method exhibits completely satisfactory performance with regard to computational expense and accuracy for a linear electromagnet with an air gap. Our analysis opens the way for large three‐dimensional magnetostatics calculations at far greater economy than is possible with the more commonly used vector potential and boundary integral methods.
Boundary element analysis of nonlinear water wave problems
Authors: Nakayama Tsukasa
Published: August 2005

A new boundary element technique based on Green's formula is applied to the analysis of nonlinear water wave problems. The problems are formulated mathematically as two‐dimensional nonlinear initial‐boundary value problems in terms of a velocity potential, assuming the fluid to be inviscid and incompressible, and the flow to be irrotational.

In the present paper, two kinds of wave‐making problems are analysed: (1) a tsunami generated by sea bed elevation; (2) generation, propagation and run‐up on a vertical wall of a solitary wave. Numerical results obtained by the present method are compared with available experimental data and analytical solutions. Excellent agreements are obtained.
Number of non‐zero blocks in the stiffness matrix of the finite element network
Authors: Feng Zhenxing
Published: August 2005

In Reference 1 a series of general formulae for evaluating the total number of non‐zero blocks in the stiffness matrix, both of two‐dimensional and three‐dimensional (arbitrary polygonal/polyhedral) finite element networks, was presented. In this paper, an alternative, more direct and efficient method for deriving such formulae is presented. In addition, this new method can be used for more complex situations. In fact, it may be used for almost all kinds of finite element networks.
A numerical analysis of time‐dependent two‐dimensional magnetic fields
Authors: Macbain John A.
Published: August 2005

The nonlinear diffusion equation as applied to two‐dimensional time‐dependent magnetic fields is solved with a finite element algorithm. This algorithm permits the analysis of problems possessing complex geometries, induced eddy currents, permanent magnets, and nonperiodic excitation currents. The numerical procedure utilizes implicit time stepping with an iterative scheme to solve the resulting set of equations. Two examples of applications of this program are presented.
Implementation of an improved bisection algorithm in buckling problems
Authors: Evans D. J. , Shanehchi J.
Published: August 2005

An improved bisection strategy is presented to determine the eigenvalues of a real symmetric tridiagonal matrix which occurs in a simple column buckling problem. The new strategy, which involves only a minor modification, utilizes incomplete Sturm sequences only as long as relevant information on the next and following eigenvalues is obtained resulting in a minimization of the computational work. The strategy is particularly effective if only a few eigenvalues are required. The technique can be used for a wider class of eigenvalue problems than the illustrative one presented here.
AGTHOM—automatic generation of triangular and higher order meshes
Authors: Moscardini A. O. , Lewis B. A. , Cross M.
Published: August 2005

The development and implementation of a comprehensive interactive computer package for the generation of finite element meshes for two‐dimensional problems is described. The package, AGTHOM, minimizes the user defined input and attempts to maximize the flexibility for the user with regard to modifying the mesh. An important feature of AGTHOM is its independence of expensive graphics hardware by using approximate terminal plots. Versions are available in both extended BASIC and FORTRAN.
An engineers' defence of the patch test
Authors: Irons Bruce , Loikkanen Matti
Published: August 2005

This convergence criterion is proved for any ‘legalizable’ finite element formulation, i.e. any model for which a conforming displacement version is possible, using the same nodal variables. Engineers may therefore take control of (and responsibility for) convergence, for most of the elements in service today. Stummel's counter‐example is explained as a technical misunderstanding, due to inadequate documentation of the patch test. It is suggested, without proof, that the test (properly applied) is universal, provided that it is always combined with an adequate test of stability.
Simplified finite element mesh for dynamic analysis of a nuclear reactor building
Authors: Bakeer Reda M. , Mandel James A.
Published: August 2005

The design of nuclear facilities requires dynamic analysis to evaluate their performance during an earthquake. In modal analysis, a method recommended for dynamic analysis by the Nuclear Regulatory Commission, the natural frequencies and mode shapes of the structure are commonly calculated using a stiffness matrix computed using the finite element method.

A primary goal of this study was to design a finite element mesh, capable of modelling a reactor structure, with a minimum number of nodes and elements. This is necessary since analysis using a mesh fine enough to include all of the structural elements is not feasible because of exorbitant computer time and storage requirements. It was found that for lateral motion, a representative reactor structure could be accurately modelled using a simplified mesh with only one isoparametric quadratic quadrilateral element per floor. In this mesh essentially infinite springs must be placed between the masses at each floor level to prevent internal movements of the lumped masses within the quadratic quadrilateral elements.

It was also found that a structure with rigid heavy bottom floors and a light top floor can be subjected to large displacements in the top floor during earthquakes. It was concluded that the properties of that light top floor (especially shear area) controls the value of the fundamental frequency of the building.
Unified finite element analysis
Authors: Mikhailov Mikhail Dimitrov
Published: August 2005

A special matrix is introduced, the elements of which are zero or first‐order differential operators. This matrix is used to define a boundary value problem which covers a wide class of engineering applications. An equivalent variational formulation is found using an extension of the Gauss theorem. From this variational principle the equations of the elements are derived. The unified formulae presented here can be useful for educational purposes and for the design of a finite element system for total analysis.
The consistency and accuracy of the TLM method for diffusion and its relationship to existing methods
Authors: Johns Peter , Butler Graham
Published: August 2005

This paper investigates the conditions under which a simple transmission‐line model for diffusion corresponds to the simple explicit finite difference method and to the method of Du Fort and Frankel. Consideration is also given to the consistency and accuracy of the methods.
Indentation of a half‐space with a rigid indentor
Authors: Voyiadjis George Z. , Buckner N. Ellis
Published: August 2005

In this work the problem of indentation of a half‐space by a spherical rigid indentor is investigated using the finite element method.

A system of constitutive equations applicable to elasto‐plastic materials subjected to large deformations is used to determine the deformations and stresses for the contact problems. These equations represent the simplest generalization for the large‐deformation conditions of the classical theory of plasticity of metals based on the von Mises yield condition and the associated flow rule. The material formulation of the kinematical and dynamical relations will be used. These equations combine the kinematic and the isotropic strain‐hardening models.

The results obtained from this work are compared with existing solutions for this problem that are confined to small strains and elastic, ideal‐plastic materials.
How upstream collocation works
Authors: Allen Myron B.
Published: August 2005

The smoothing effects of upstream collocation in convective problems are attributable to a dissipative error term analogous to that in upstream‐weighted finite differences.
Boundary integral equation solution of moving boundary phase change problems
Authors: O'Neill Kevin
Published: August 2005

Boundary integral equation methods are presented for the solution of some two‐dimensional phase change problems. Convection may enter through boundary conditions, but cannot be considered within phase boundaries. A general formulation based on space‐time Green's functions is developed using the complete heat equation, followed by a simpler formulation using the Laplace equation. The latter is pursued and applied in detail. An elementary, noniterative system is constructed, featuring linear interpolation over elements on a polygonal boundary. Nodal values of the temperature gradient normal to a phase change boundary are produced directly in the numerical solution. The system performs well against basic analytical solutions, using these values in the interphase jump condition, with the simplest formulation of the surface normal at boundary vertices. Because the discretized surface changes automatically to fit the scale of the problem, the method appears to offer many of the advantages of moving mesh finite element methods. However, it only requires the manipulation of a surface mesh and solution for surface variables. In some applications, coarse meshes and very large time steps may be used, relative to those which would be required by fixed grid domain methods. Computations are also compared to original lab data, describing two‐dimensional soil freezing with a time‐dependent boundary condition. Agreement between simulated and measured histories is good.
Optimum design sensitivity based on approximation concepts and dual methods
Authors: Schmit L. A. , Chang K. J.
Published: August 2005

An optimum design sensitivity analysis capability is reported which exploits the approximation concepts‐dual method formulation of the minimum weight structural sizing problem. An efficient iterative solution technique is used to facilitate determination of sensitivity derivatives for both primal and dual variables. Estimates on the useful range of parameter perturbations, over which the optimum design sensitivity projections can be expected to yield satisfactory revised optimum designs, are also obtained. Numerical results for several example problems will be presented to illustrate the effectiveness of the capability reported.
Numerical solutions to some free surface flows through nonhomogeneous media
Authors: Remar J. , Bruch J. C. , Sloss J. M.
Published: August 2005

Steady‐state, free surface seepage through a heterogeneous porous medium underlain by a drain at a finite depth is solved using a fixed domain solution technique. The problems investigated are axisymmetric seepage from a circular pond and plane seepage from a symmetric channel. These ponds and channels may have variable shaped bottoms. Since the Baiocchi transformation was used to define a new dependent variable, the form of the permeability function was restricted to a product of functions of the independent variables. Herein the permeability was chosen to be a function of the depth only. For certain forms of this function, namely those having negative gradients, part of the flowfield becomes unsaturated and this violates the assumed saturation of the flowfield in the flow theory. The governing differential equation, which holds in the sense of distributions, is derived for a fixed solution domain and a simple algorithm (a finite difference successive over‐relaxation scheme with projection) is given to obtain the solution to these free surface problems. Numerous comparisons are made with published results. Rigorous mathematical justification of the methods used herein can be found in the references cited.
Chebyshev filtering Lanczos' process in the subspace iteration method
Authors: Loh Chee Hoong
Published: August 2005

Bathe's basic algorithm of subspace iteration for the solution of the symmetric eigenvalue problem is improved by including a Chebyshev filtering mechanism. To obtain satisfactory convergence for the largest eigenvalues, a shifting strategy is adopted. The shift factor is approximately computed by the Lanczos process.
Finite elements with increased freedom in choosing shape functions
Authors: Bergan P. G. , Nygård M. K.
Published: August 2005

Starting with a mathematical statement of the convergence requirements for an element stiffness matrix, the paper discusses displacement shape functions that may be used in connection with the potential energy principle. In short, these functions must be force orthogonal and energy orthogonal, but they need not be conforming (satisfy interelement compatibility). It is shown that the requirements to the displacement functions may be greatly relaxed through slight modifications of the coupling stiffness between fundamental and higher order displacement modes. Several alternative formulations are examined. In particular, a new ‘free formulation’ is suggested. Using this form, which is very simple, the only requirement to the displacement patterns used is that they should contain the fundamental deformation modes and be linearly independent. Applications of the theory to triangular and rectangular plate bending elements are shown; the simple stiffness matrix for the latter is given explicitly. The numerical results compare favourably with other types of finite elements.
Scalar potentials in multiply connected regions
Authors: Brown M. L.
Published: August 2005

An algorithm, for use on a digital computer, is explained for cutting multiply connected regions in three‐dimensional space. The algorithm is suitable for complex electromagnetic field problems where a magnetic scalar potential, affected by current loops, is to be calculated in a multiply connected region. Problems in fluid dynamics with vorticity affecting a scalar potential, could also be attacked with this algorithm. Since finite element methods are ubiquitous in field calculations, the cuts of the space constructed by the algorithm should ideally correspond to the given discretization; this can be arranged by an application of the Lebesgue Covering Theorem, for which a second algorithm is provided.
Finite element approach to propagation in elliptical and parabolic waveguides
Authors: Daly P.
Published: August 2005

This paper deals with the application of the finite element method to the solution of propagation problems in elliptical and parabolic waveguides. Mode classification in empty waveguides is discussed, followed by extensions of the method to problems where metallic ridges lie along either major or minor axes.
The application of shape‐preserving splines for the solution of differential equations
Authors: Shoucri Magdi M. , Shoucri Rachad M.
Published: August 2005

This paper investigates the use of shape‐preserving interpolants based on Bernstein polynomials for the numerical solution of differential equations. A simple and accurate algorithm is presented for the integration of the initial value ordinary differential equation, as well as for the partial differential equation of the Burger type.
Minimum‐weight design of trusses by an optimality criteria method
Authors: Allwood R. J. , Chung Y. S.
Published: August 2005

This work presents an optimality criteria method which accurately and efficiently solves the structural optimization problem of trusses subject to deflection and stress constraints. The method is based upon the Newton–Raphson method and a first‐order approximation both for deflection and stress constraints using the method of virtual work. It solves the problem rigorously and no serious difficulties have yet been encountered in spite of the drawbacks inherent in the Newton–Raphson method. Worked examples show its superiority to other methods and its ability to cope with trusses with many members and subject to multiple constraints.
A memory‐economic frontwidth reduction algorithm
Authors: Silvester Peter P. , Auda Hesham A. , Stone Geoffrey D.
Published: August 2005

A simple element numbering algorithm is described which yields near‐minimal frontwidths for two‐ and three‐dimensional finite element assemblies. Renumbering of E elements requires an immediate‐access computer memory size which is proportional to the square root of E in two‐dimensional problems, and to the two‐thirds power of E in three dimensions. This very small memory requirement allows processing of large problems in minicomputers. When used in large computers, page‐swapping operations are minimized.
A recursive quadratic programming method with active set strategy for optimal design
Authors: Belegundu Ashok D. , Arora Jasbir S.
Published: August 2005

Recursive quadratic programming methods have become popular in the field of mathematical programming owing to their excellent convergence characteristics. There are two recursive quadratic programming methods that have been published in the literature. One is by Han and the other is by Pshenichny, published in 1977 and 1970, respectively. The algorithm of Pshenichny had been undiscovered until now, and is examined here for the first time. It is found that the proof of global convergence by Han requires computing sensitivity coefficients (derivatives) of all constraint functions of the problem at every iteration. This is prohibitively expensive for large‐scale applications in optimal design. In contrast, Pshenichny has proved global convergence of his algorithm using only an active‐set strategy. This is clearly preferable for large‐scale applications. The method of Pshenichny has been coded into a FORTRAN program. Applications of this method to four example problems are presented. The method is found to be very reliable. However, the method is found to be very sensitive to local minima, i.e. it converges to a local minimum nearest to the starting design. Thus, for optimal design problems (which usually possess multiple local minima) it is suggested that Pshenichny's method be used as part of a hybrid method.
A robust incomplete Choleski‐conjugate gradient algorithm
Authors: Ajiz M. A. , Jennings A.
Published: August 2005

When applied to large sparse sets of simultaneous equations, classical iterative methods may yield very poor convergence rates. This paper gives an incomplete Choleski‐conjugate gradient algorithm (ICCG) which has reliably good convergence rates at the expense of computing and using at each iteration an incomplete Choleski factor of the coefficient matrix. The method is applicable to any problems in which the coefficient matrix is symmetric positive definite and is likely to be advantageous with respect to elimination when it is not possible to represent the equations in a dense band form.
A discrete singularity formulation for solving steady, fully developed duct flows
Authors: Yano H. , Fukutani S. , Kieda A. , Oshima T.
Published: August 2005

A very effective numerical formulation is proposed to solve approximately the problem of steady, fully developed laminar flows of incompressible fluids in straight ducts of arbitrary, simply connected cross‐sections. The method is an application of the discrete singularity technique, with a finite number of singularities located outside the domain concerned. To illustrate the usefulness of the method, some examples of computations are also presented.
Finite layer analysis of layered elastic materials using a flexibility approach. Part 1—Strip loadings
Authors: Small J. C. , Booker J. R.
Published: August 2005

It is well known that the analysis of a horizontally layered elastic material can be considerably simplified by the introduction of a Fourier or Hankel transform and the application of the finite layer approach. The conventional finite layer (and finite element) stiffness approach breaks down when applied to incompressible materials. In this paper these difficulties are overcome by the introduction of an exact finite layer flexibility matrix. This flexibility matrix can be assembled in much the same way as the stiffness matrix and does not suffer from the disadvantage of becoming infinite for an incompressible material. The method is illustrated by a series of examples drawn from the geotechnical area, where it is observed that many natural and man‐made deposits are horizontally layered and where it is necessary to consider incompressible behaviour for undrained conditions.
The post‐processing approach in the finite element method—part 1: Calculation of displacements, stresses and other higher derivatives of the displacements
Authors: Babuška I. , Miller A.
Published: August 2005

This is the first in a series of three papers in which we discuss a method for ‘post‐processing’ a finite element solution to obtain high accuracy approximations for displacements, stresses, stress intensity factors, etc. Rather than take the values of these quantities ‘directly’ from the finite element solution, we evaluate certain weighted averages of the solution over the entire region. These yield approximations are of the same order of accuracy as the strain energy. We obtain error estimates, and also present some numerical examples to illustrate the practical effectiveness of the technique. In the third paper of this series we address the matters of adaptive mesh selection and a posteriori error estimation.
Incremental shakedown analysis in the case of thermal effects
Authors: Kleiber M. , König J. A.
Published: August 2005

A new method of performing the shakedown analysis of structures subjected to variable repeated loads and temperature fields is presented. The method employs the standard incremental elastic‐plastic finite element algorithm and is based upon a cyclic repetition of piecewise‐proportional paths that contain all the vertices of the load‐temperature variation domain. A numerical example illustrates the approach.
A partial‐boundary element approach to the elastic torsion problem of a prismatic beam with a cracked rectangular cross‐section
Authors: Shangchow Chang
Published: August 2005

Using the partial‐boundary element approach, in which only a part of the boundary in problem is discretized, the elastic torsion problem of a prismatic beam of a cracked rectangular cross‐section has been solved in this brief paper, together with a numerical example to show the accuracy and versatility of the approach.
The design of a variable‐step integrator for the simulation of gas transmission networks
Authors: Chua T. S. , Dew P. M.
Published: August 2005

The simulation of a large‐scale gas transmission network involves the numerical solution of a large system of initial valued, stiff algebraic/differential equations. Rapid changes in the solution are present due to the disturbances generated by the varying consumer demand and the operation of network controlling devices such as compressors. This paper discusses the design of an efficient variable‐step integrator for the solution of the problem. Two sets of strategies are presented for implementing the variable‐step integrator; one for the implicit numerical method such as the diagonally implicit Runge–Kutta methods, and the other for the linearly implicit Rosenbrock‐type method. The performance of the numerical methods implemented are compared with the British Gas simulation program PAN on a number of large, realistic transmission networks.
On the use of quarter‐point boundary elements for stress intensity factor computations
Authors: Martínez José , Domínguez José
Published: August 2005

This communication studies a procedure for stress intensity factor computations using traction singular quarter‐point boundary elements. Opening mode stress intensity factors are computed from the tractions' nodal values at the crack tip. A comparison is made between the factors calculated using this procedure and those obtained by previously recommended methods which made use of the nodal values of the displacements. The proposed procedure was seen to be less discretization sensitive than any other of the considered methods. Accurate results were obtained even in the case of coarse meshes.
Postbuckling resonance analysis of thin shells
Authors: Tesár Alexander
Published: August 2005

The present paper is concerned with the nonlinear finite solution of the postbuckling instability behaviour of thin shell structures in resonance regions of vibration. The development of reliable and efficient techniques for handling the dynamic postbuckling behaviour is emphasized. An illustrative solution associated with the postbuckling resonance response of thin shells is presented.
A unified set of single step algorithms. Part 2: Theory
Authors: Wood W. L.
Published: August 2005

Part 1 of this paper1 presents a very general single step algorithm SSpj for the numerical integration of first and second order time dependent differential equations. In Part 2 we present and discuss results of the accuracy and stability analysis for SS11, SS21, SS31, SS22 and SS32. There is also a detailed comparison of SS22 and the Newmark algorithm.
Accelerated ‘relaxation’ or direct solution? Future prospects for fem
Authors: Zienkiewicz O. C. , Löhner R.
Published: August 2005

‘Dynamic’ or ‘viscous’ relaxation procedures have not gained much popularity in finite element analysis in which the direct (Gaussian elimination) solution dominates. Reasons for this are various—the most important being the rather slow convergence generally achieved for such procedures. However, it is possible to accelerate this quite dramatically and a method of doing so is shown in this paper. With the use of such acceleration and the inherent advantages of greatly reduced storage requirements and simplicity of programming, relaxation procedures promise an exciting possibility for the solution of large two‐ and three‐dimensional problems in both linear and nonlinear ranges.
Sparse matrix factor modification in structural reanalysis
Authors: Law Kincho H.
Published: August 2005

Structural reanalysis problems, such as in nonlinear finite element analysis or optimum design, involve progressive changes in the global stiffness matrix and its matrix factors. Although many studies have been devoted to the subject of matrix factor modification, most investigations have dealt with the problem separately from sparse matrix methods. This paper introduces a graph‐theoretic model for the forward solution procedure which is applicable for identifying the modified entries of the matrix factors due to changes in the original matrix. Applications of this graph‐theoretic model to existing refactorization methods are presented. The relation between substructuring and sparse matrix ordering strategies, and their effects on reanalysis are discussed. Modification of a sparse matrix associated with an n × n finite element grid ordered by the nested dissection scheme is analysed.
A boundary integral equation method for radiation and scattering of elastic waves in three dimensions
Authors: Rizzo F. J. , Shippy D. J. , Rezayat M.
Published: August 2005

A vector boundary integral equation (BIE) formulation and numerical solution procedure is presented for problems of three‐dimensional elastic wave radiation and scattering from arbitrarily shaped obstacles. The formulation is explicitly in terms of surface traction and displacement, rather than wave potentials, and the BIE on which numerical work is based is written in a form entirely free of Cauchy principal value integrals. Indeed, the subsequent computational process, based on quadratic isoparametric boundary elements, renders all integrals free of singularities, so that ordinary Gaussian quadrature may be used. Numerical examples include scattering from spherical surfaces and radiation from a cube.
A six‐node finite element for plate bending
Authors: Lee S. W. , Zhang J. C.
Published: August 2005

A six‐node plate bending element has been developed by employing mixed formulation based on a modified Hellinger–Reissner principle and the Reissner–Mindlin plate bending theory. The numerical result indicates that, among the types of assumed independent transverse shear strains considered, a combination of 2α version with either 5α version or 6α version is free of spurious kinematic modes and leads to accurate and reliable solutions even for very thin plates.
A simple approach to bifurcation and limit point calculations
Authors: Fujikake Masahisa
Published: August 2005

A simple approach is proposed to calculate the bifurcation and limit points of structures, talcing into account the pre‐unstable behaviour, by the finite element method. The approach is as follows: at each load step, the triangular factorization of the tangent stiffness matrix is checked to determine if the matrix is positive definite or not. When the tangent stiffness matrix is positive definite at a certain load step and non‐positive definite at the next load step, the structure is considered to become unstable between the two load steps and an eigenproblem is constructed based on the difference of the tangent stiffness matrices at the two load steps. The critical load and corresponding mode of the structure are then derived from solving the eigenproblem. The proposed procedure is simple and economical, and it can be easily incorporated into a conventional geometric nonlinear analysis computer program. It is implemented in the ADINA program and some sample calculations are shown.
Finite element analysis of nonlinear oscillators
Authors: Krishnamurthy K. , Burton Thomas D. , Zeller Lavern D.
Published: August 2005

Presented in this paper is a finite element method for the analysis of nonlinear oscillations which exhibit periodic response. The basic idea of the method is to recast the initial value problem as a boundary value problem in which the domain (that is, period) may be unknown. We apply the method to study the free response of the conservative oscillator ü + mu + ϵf(u)=0, where m is either − 1, 0 or 1, f(u) is an odd nonlinear function, and ϵ need not be small. The harmonically forced case, ü + mu + ϵf(u) = Psin Ωt, is also considered, and it is shown that the superharmonic response can be efficiently calculated using this technique.
Multiple coplanar embedded elliptical cracks in an infinite solid subject to arbitrary crack face tractions
Authors: O'Donoghue P. E. , Nishioka T. , Atluri S. N.
Published: August 2005

This paper extends the earlier work by the present authors for a single embedded crack in an infinite solid and presents a solution to the problem of multiple coplanar cracks in an infinite medium. An alternating method in conjunction with an analytical solution for a single crack is used to determine the stress intensity factors for interacting multiple coplanar embedded cracks in an infinite body. The alternating method, as implemented here, leads to a highly accurate evaluation of the appropriate stress intensity factors.
Theorems of structural variation: A simplification
Authors: Atrek Erdal
Published: August 2005

An equation related to the ‘first theorem of structural variation’ is simplified for computational purposes.
An isoparametric joint/interface element for finite element analysis
Authors: Bfer G.
Published: August 2005

A generally applicable and simple joint/interface element for three‐ and two‐dimensional finite element analysis is presented. The proposed element can model joints/interfaces between solid finite elements and shell finite elements. The derivation of the joint element stiffness is presented and algorithms for the treatment of nonlinear joint behaviour discussed. The performance of the element is tested on typical problems involving shell‐to‐shell and shell‐to‐solid interfaces.
Variational approach to first‐ and second‐order sensitivity analysis of elastic structures
Authors: Dems K. , Mróz Z.
Published: August 2005

For a linear elastic structure, the first variations of arbitrary stress, strain and displacement functionals were explicitly expressed in terms of variations of material stiffness parameters within specified domain, in References 1 and 2, by using the solutions for primary and adjoint systems. In this paper, explicit expressions for second variations are derived for the case when the material stiffness or compliance variations depend on a set of parameters. These expressions arc obtained in terms of variations of stiffness or compliance parameters by using the solutions of two additional sets of adjoint systems. Furthermore, the variation of local stress, strain or displacement is considered. Several illustrative examples are provided for the first‐ and second‐order sensitivity analysis of beams.
The gradient of the finite element variational indicator with respect to nodal and applications in fracture mechanics and mesh optimization
Authors: Sussman Theodore , Bathe Klaus‐Jurgen
Published: August 2005

We derive a closed‐form expression for the change in the variational indicator of a finite element mesh with respect to perturbations in nodal point co‐ordinates. The expression is evaluated very effectively from standard finite element data obtained in one solution, and may be easily programmed as part of a general finite element code. We present the derivation for two‐ and three‐dimensional isoparametric elements used in linear and nonlincar elasticity. The expression has practical applications in the computation of stress intensity factors in fracture mechanics and in the determination of the ‘optimal’ mesh with a given element‐node connectivity. We demonstrate both applications by accurately determining the stress intensity factor of a Mode I crack using a finite element mesh which was improved using mesh optimization.
On body‐fitted co‐ordinates for separated laminar flows past wall‐mounted obstacles
Authors: Yeung P. K. , Kot S. C.
Published: August 2005

A body‐fitted curvilinear co‐ordinate system is used to solve the equations of two‐dimensional incompressible laminar flow over bluff obstructions by finite differences. Arbitrary conditions at the corner are removed by this method. Results for a backward‐facing step are in reasonable agreement with those obtained with conventional mesh systems, and the differences are explained. A treatment of a channel expansion, in comparison with empirical data, is also included. The capability of the present method to handle arbitrary two‐dimensional geometries is stressed and demonstrated, using a triangle and a semi‐circle as examples.
A method for solving algebraic systems consisting of linear and nonlinear equations
Authors: Tewarson R. P. , Chen D. Q.
Published: August 2005

An efficient method for solving algebraic equations is given. The linear equations are solved only once and iterations are performed on the non linear equations. If an initial approximation to a desired root is available, then it is utilized in the solution process. Results of some computational experiments are given.
An algorithm based on the boundary element method for problems in engineering mechanics
Authors: Vable Madhukar
Published: August 2005

The solution to a two‐dimensional problem using the boundary element method requires the evaluation of a line integral over the boundary. The integrand ot this line integral is a product of a known Green's function and an unknown function. A large number of Green's functions for two‐dimensional problems can be represented by a linear combination of four singular functions. By approximating the unknown function by a linear combination of known polynomials, integrals are generated whose integrand is a product of the polynomiais and one of the four singular functions. To evaluate these integrals analytically, the boundary is approximated by a sum of straight‐line segments. Recursive formulae are established which reduce the generality and the complexity of the integrands to simple expressions. Analytical forms for these simple expressions are found and are used for initiating the algorithm.
Transmission line interpretation of the finite element mesh for a wave propagation problem
Authors: Mason John L. , Anderson William J.
Published: August 2005

A one‐dimensional exterior electromagnetic scattering problem is formulated using a differential equation approach followed by a finite element discretization. By interpreting the resulting linear algebraic equations as node voltage equations for a transmission line, a boundary element is obtained which satisfies the requirement of no wave reflection at the edge of the finite element region. Numerical results which show the elimination of non‐physical standing waves from the scattered field are presented and discussed.
Projection and iteration in adaptive finite element refinement
Authors: Carey G. F. , Seager M.
Published: August 2005

A local elliptic projection is introduced to provide improved local approximations to the finite element solution of boundary‐value problems. The approach yields a composite global approximation that is more accurate and provides a good starting value for iterative solution methods. The procedure is particularly effective when used in conjunction with adaptive mesh refinement, as illustrated in numerical studies involving two‐point problems of boundary‐layer and interior‐layer type.
Finite element formulations for non‐steady‐state large viscoplastic deformation
Authors: Bohatier Claude , Chenot Jean‐Loup
Published: August 2005

Different mechanical formulations are employed for calculation of the large deformations occurring in metal forming processes. Eulerian and updated Lagrangian descriptions, valid for viscoplastic materials, are presented. In view of the numerical tests which were carried out, the Eulerian formulation, associated with an implicit integration scheme which proved to be numerically accurate and reliable, is shown to be preferable.
Finite layer analysis of layered viscoelastic materials under three‐dimensional loading conditions
Authors: Booker J. R. , Small J. C.
Published: August 2005

A method is presented which enables the calculation of the settlement behaviour of circular or general loadings on horizontally layered soils which undergo secondary or ‘creep’ consolidation. The method of analysis involves the use of Hankel or double Fourier transforms to simplify the equations governing the consolidation process. This leads to great savings in the preparation of data and the amount of computer storage needed to solve problems involving three‐dimensional loadings since such problems are essentially reduced to that of one spatial dimension: Solutions are then obtained by a ‘forward marching’ process where solutions at a particular time are found from those at a previous time. A method is presented which eliminates the need to store the solutions at all previous time steps, and is therefore very efficient. The theory is illustrated by examples of the behaviour of rectangular and circular loadings on layered soil profiles.
Eigenvalues and stable time steps for the bilinear Mindlin plate element
Authors: Belytschko Ted , Lin Jerry I.
Published: August 2005

Eigenvalues are obtained for the 4‐node Mindlin plate element with one‐point quadrature. Both isotropic and some anisotropic matenals are considered, but for the latter only bounds are obtained on the eigenvalues. These eigenvalues provide stable time steps for explicit time integration algorithms.
Analysis of heat conduction in solids by space‐time finite element method
Authors: Yu J. R. , Hsu T. R.
Published: August 2005

A functional in the form of a convolution of the temperature variation in the space–time domain has been derived. It has been used as the basis for a finite element formulation of heat conduction in solids. Numerical illustrations have indicated that the space–time finite element algorithm provides a more rapid convergence to the exact solutions than the usual finite element analysis with discretization in space only.
Fixed‐point iteration to nonlinear finite element analysis. Part I: Mathematical theory and background
Authors: Zeid Ibrahim
Published: August 2005

This paper sets the stage for the implementation of the Fixed‐Point Iteration (FPI) to nonlinear finite element analysis as an alternative to the existing Newton‐Raphson Method (NRM) or its derivatives. The superiority of the former method over the latter one is such that it enables one to obtain nonlinear structural static or dynamic responses without inverting the structural stiffness matrix.

In the first part of the paper, a new convergence correction/acceleration factor has been developed for the FPI when applied to a single nonlinear algebraic equation. This new factor causes the iteration function of the equation under consideration to rotate about an axis that passes through one of its fixed points or roots. Using this observation, the slope of the iteration function can be adjusted in the neighbourhood of a specific root to ensure the convergence of the FPI. It is found that the optimum choice of the new factor corresponds to a zero slope, evaluated at the root, of the iteration function. The rate of convergence and the error estimate of this form of the FPI is developed and compared with the NRM. The equilibrium positions of a nonlinear loaded softening spring have been obtained by both methods as an illustrative numerical example to measure the effect of the new factor on the convergence rate.

The second part of the paper extends the above concept to find the solution of a linear system of algebraic equations using the FPI. This leads to a better diagonal approximate inverse for the Jacobi iteration, or method of simultaneous displacements. If the elements of the solution vector of a specific system are all equal, the new Jacobi iteration becomes an exact method and the solution is obtained in one iteration. The concept is also extended to the Gauss‐Seidel iteration, or method of successive displacements. Systems involving symmetric as well as nonsymmetric coefficient matrices have been used as numerical examples and are presented. For future implementation to nonlinear finite element analysis, the active column or the skyline (or the non‐zero profile) FPI algorithms are developed for programming considerations.
A new method for evaluating singular integrals in stress analysis of solids by the direct boundary element method
Authors: Li Hong‐Bao , Han Guo‐Ming , Mang Herbert A.
Published: August 2005

The purpose of this paper is to report on a new and efficient method for the evaluation of singular integrals in stress analysis of elastic and elasto‐plastic solids, respectively, by the direct boundary element method (BEM). Triangle polar co‐ordinates are used to reduce the order of singularity of the boundary integrals by one degree and to carry out the integration over mappings of the boundary elements onto plane squares. The method was subsequently extended to the cubature of singular integrals over three‐dimensional internal cells as occur in applications of the BEM to three‐dimensional elasto‐plasticity. For this purpose so‐called tetrahedron polar co‐ordinates were introduced. Singular boundary integrals stretching over either linear, triangular, or quadratic quadilateral, isoparametric boundry elements and singular volume integrals extending over either linear, tetrahedral, or quadratic, hexahedral, isoparametric internal cells are treated. In case of higher order isoparametric boundary elements and internal cells, division into a number of subelements and subcells, respectively, is necessary. The analytical investigation is followed by a numerical study restricted to the use of quadratic, quadrilateral, isoparametric boundary elements. This is justified by the fact that such elements, as opposed to linear elements, yield singular boundary integrals which cannot be integrated analytically. The results of the numerical investigation demonstrate the potential of the developed concept.