bluuebunny/crossref_metadata_2025 huggingface dataset:
Optimization of non‐unimodal systems
Authors: Wang Bi‐Chong , Luus Rein
Published: August 2005

Two direct search algorithms for the optimization of non‐unimodal systems are presented. One method is interior in nature by using boundary relaxation with pseudo one‐dimensional search in the feasible region; the other one is an exterior method which allows the violation of constraints followed by the use of a penalty function to drive the search back into the feasible region. These two methods are usually capable of leaving local optima to reach a better solution if such exists. The application of the proposed approaches to several non‐unimodal systems shows that they are better than the existing methods. The proposed methods are also attractive because of the ease of programming and the high probability of reaching the global optimum.
A hybrid stiffness matrix for orthotropic sandwich plates with thick faces
Authors: Kraus Hans Dieter
Published: August 2005

A stiffness matrix is derived for a rectangular orthotropic sandwich plate element with thick faces by the assumed stress hybrid approach.

It will be demonstrated that an independent polynomial can be used for the internal forces of the sandwich plate by the membrane theory (assumption of thin faces) and also for the additional moments and shear forces of the faces.

The boundary displacements are approached solutions of the homogeneous differential equation of a sandwich beam.
A simplified integral equation method for the calculation of the eigenvalues of Helmholtz equation
Authors: De Mey G.
Published: August 2005

An integral equation method is presented for the numerical calculation of the eigenvalues of the scalar Helmholtz equation. By using a particular solution instead of Green's function, the calculations could be simplified due to the elimination of complex numbers.
A simple and efficient finite element for plate bending
Authors: Hughes Thomas J. R. , Taylor Robert L. , Kanoknukulchai Worsak
Published: August 2005

A simple and efficient finite element is introduced for plate bending applications. Bilinear displacement and rotation functions are employed in conjunction with selective reduced integration. Numerical examples indicate that, despite its simplicity, the element is surprisingly accurate.
An unconditionally stable explicit algorithm for structural dynamics
Authors: Trujillo D. M.
Published: August 2005

This paper presents an unconditionally stable explicit algorithm for the direct integration of the structural dynamic equations of motion. The algorithm is restricted to a diagonal mass matrix and positive definite symmetric stiffness and damping matrices. The algorithm is based on splitting the stiffness and damping matrices into strictly lower and upper trangular form. Unconditional stability is proven, but only for the undamped case and a completely symmetric splitting of the stiffness matrix. An alternate splitting method is also presented and numerical examples indicate superior performance over the symmetric splitting, but only a conditional stability. A spring‐mass‐dashpot model is used to illustrate the algorithm.
Newtonian die swell evaluation for axisymmetric tube exits using a finite element method
Authors: Allan W.
Published: August 2005

Using a finite element method, a value of 13.2 per cent is obtained for the die swell of a highly‐viscous Newtonian fluid flowing at very low Reynolds number from a circular tube of constant radius. The same method is then used to obtain die swell values for a variety of axisymmetric tube exits. It is found that, in general, conical constrictions at or near the tube exit result in a decrease in die swell, while conical expansions increase the die swell.
A finite element Laplace transform solution technique for the wave equation
Authors: Aral Mustafa M. , Gülçat Ülgen
Published: August 2005

A technique is described for the solution of the wave equation with time dependent boundary conditions. The finite element solution accompanied by the numerical Laplace inversion process seems to be an efficient procedure to treat such problems. The programming involved is straightforward in the sense that numerical Laplace inversion routines can be directly used as a time integration procedure after obtaining standard finite element differential equation solutions in the transformed domain.

Some results are presented for one‐ and two‐ dimensional applications, such as wave propagation in longitudinal bars and wave propagation in harbours.
A data structure for finite element analysis
Authors: Bettess J. A.
Published: August 2005

The philosophy of a simple data structure for handling data for finite element analyses is described. The technique is advocated as an efficient way of handling finite element data and of communicating between programs using the data.
An investigation of the stability of numerical solutions of the equations of viscoelasticity
Authors: Booker J. R. , Small J. C.
Published: August 2005

In this paper the correspondence principle is used to reduce the equations of viscoelasticity to the equations of elasticity by means of a Laplace transform.

The finite element technique is used to approximate these equations in Laplace transform space. The approximating equations are then inverted to obtain a set of simultaneous Volterra integral equations. It is then shown how the introduction of certain auxiliary variables can be used to develop an integration scheme which considerably reduces computer storage requirements.

The conditions under which this integration scheme is conditionally stable and unconditionally stable are both investigated and illustrated by means of examples.
A finite element formulation for creep analysis
Authors: Kim Hong Ou , Kuhlemeyer Roger L.
Published: August 2005

As an alternative to the initial strain method, a variable stiffness method is presented for creep analysis. The method is developed by incorporating the change in stress state during a time interval in determining the creep strain increments concurrent with the change. It is shown by means of examples that this method provides solution stability for relatively large time intervals for which the initial strain method may fail to function properly.
Continuous elements in the finite element method
Authors: Rukos Eduardo A.
Published: August 2005

The discretization of the media at all spatial co‐ordinates but one is presented here. This partial discretization leads to continuous finite elements as opposed to fully discrete ones and the problem resolves, for the cases presented here, into a set of linear differential equations rather than algebraic equations. The general problem of first derivative functionals in elastostatics is considered and it is shown, in general, how the continuous finite elements required for the solution may be obtained. Plane states, axisymmetric and three‐dimensional continuous elements are obtained to illustrate application to particular cases.

Different methods of solution for the set of differential equations are discussed and it is shown that several existing and widely used finite element related techniques are particular cases of this local partial discretization. Three numerical examples are solved to demonstrate the good comparison obtained between the numerical and the exact solutions. The semi‐infinite examples included also illustrate the treatment of these types of problems without the use of fictitious boundaries.
A finite element for transition from a fine to a coarse grid
Authors: Gupta A. K.
Published: August 2005

Formulation of a transition element is presented. Such an element makes it possible to match one element with two elements side‐by‐side. A modified quadrature formula is used to numerically integrate discontinuous functions in the expression of the stiffness matrix. Numerical examples show the applicability of the element.
Discussion of a paper by E. O. Frind
Authors: Brockman R. A.
Published: August 2005

In a recent paper, Dr. Frind has formulated a two‐dimensional isoparametric finite element based upon the Hermite bicubic interpolation scheme. The present discussion focuses upon certain simplifications in the derivation which appear to have diminished the accuracy of the resulting element, and suggests a simpler approach to the element formulation. This author agrees strongly with Dr. Frind's recommendation of the Hermite parametric element as an efficient and useful tool for general field problems; the present comments are offered to point out that, in fact, the accuracy comparisons presented by Dr. Frind are biased against the Hermite finite element.
A hybrid element method for diffraction of water waves by three‐dimensional bodies
Authors: Yue Dick K. P. , Chen Hsuan S. , Mei Chiang C.
Published: August 2005

A hybrid element method developed recently for two‐dimensional problems of water waves in an infinite fluid is extended to three dimensions. In this method only a limited fluid domain close to irregular bodies is discretized into conventional finite elements, while the remaining infinite domain is treated as one element with analytical representations of high accuracy. Continuity at the junction surface is treated as natural boundary conditions in a variational principle. Computation experience and numerical results for several ocean structures are presented.
Cold rolling of a laminated composite sheet—A numerical solution
Authors: Batra R. C.
Published: August 2005

The problem of cold rolling of a composite sheet which consists of alternate layers of viscoelastic and elastic materials is studied by the finite element method. Results computed and presented graphically include the pressure distribution at the contact surface, the normal stress distribution at the middle surface and the asymmetric deformation of the surface of the sheet in contact with the roller.
The generalized problem of confined seepage
Authors: Cecchi M. M. , Mancino O. G.
Published: August 2005

The problem of confined seepage of water under a hydraulic structure, through a porous medium, is considered in an appropriate abstract space. Existence and uniqueness of the solution are proved. The numerical solution is derived by means of the finite element method. An error estimate is given. A sample problems in included.
A numerical method to obtain optimal quadrature formulas
Authors: Wang A. H. , Klein R. L.
Published: August 2005

This paper present a numerical method to obtain optimal quadrature formulas of Gauss type and Radau type in the sense of Sard. Using the relation between optimal quadrature formulas and nonospline functions, the optimal quadrature formula can be obtained by solving a set of no‐linear simultaneous algebraic equations induced from the interpolatory conditions of the monospline. In attempting to solve this set of non‐linear algebraic equations for numbers of knots and degrees of interpolution required in estimation problem applications insurmountable numerical errors were encountered. This paper solves the numerical problem by first reducing the number of unknowns and equations to approximately one half the original number. This is accomplished by showing and then using a symmetry property of the monospline. Second an iteration scheme which partitions the reduced order set of non‐linear algebraic equations into a linear subsystem and a non‐linear subsystem is developed to numerically solve the equations. This iteration algorithm provides the advantages of reducing the computational complexity, dynamically checking the convergence and explicitly evluating the resulting accuracy.
Application of dynamic programming to the general inverse problem
Authors: Trujillo D. M.
Published: August 2005

The general inverse problem is one for which measurements are made on some of the state variables and it is desired to find the forcing functions. This problem is a natural one for the method of dynamic programming. The formulation and solution of the problem are presented in matrix form, together with two illustrative examples of an inverse heat conduction problem and an inverse structural dynamics problem.
A non‐circular arc roll force model for gold rolling
Authors: Grimble M. J. , Fuller M. A. , Bryant G. F.
Published: August 2005

A long established approximation, normally invoked in the development of classical rolling theory, is that the work roll‐strip interface assumes a circular profile. Although valid for a wide range of practical rolling conditions, the approximation is definitely suspect for instance in the last and penultimate stand of a thin sheet tandem mill, and algorithms based on classical theory may fail to converge. This paper computing solutions. In deriving the algorithm it is convenient to employ the formalism of functional One notable feature is that the gradients have to be carefully defined with respect to the correct ‘space’, in order that physically inadmissible discontinuties are not introduced during the hill‐climbing. Computed roll gap solutions sometimes display elastic deformation regions embedded within the normal plastic deformation zone. It is thought that this is the first time this possibility has been allowed for in the formulation, or solutions obtained exhibiting this feature.
A split Band‐Cholesky equation solving strategy for finite element analysis of transisent field problems
Authors: Cooke Charlie H.
Published: August 2005

An efficient strategy is outlined for out‐of‐core solution of the large systems of equations which specify nodal point time derivatives in finite element models of transient flow problems. The positive definiteness, symmetry, and band structure of the finite element mass matrices, as well as the nature of the equation assemblage process, is exploited by the method. Computational results are indicated for systems on the order of several thousand unknowns in size.
A finite difference‐Galerkin finite element solution of compressible laminar boundary‐layer flows
Authors: Bismarck‐Nasr Maher N.
Published: August 2005

A finite difference‐Galerkinfinite element method is presented for the solution of the two‐dimensional compressible laminar boundary‐layer flow problem. The streamwise derivatives in the momentum and energy equations are approximated by finite differences. An iterative scheme, due to the non‐linearity of the problem, in conjunction with the Galerkin finite element method is then proposed for the solution of the problem through the boundary‐layer thickness. Numerical results are presented and these are compared with other numerical and analytical solutions in order to show the applicability and the effectiveness of the proposed formulation. In all the cases here examined, the results obtained attained the same accuracy of other numerical methods for a much smaller number of points in the boundary‐layer.
On a numerical solution of the plastic buckling problem of structures
Authors: Gupta K. K.
Published: August 2005

An automated digital computer procedure is presented for the accurate and efficient solution of the plastic buckling problem of structures. This is achieved by a Sturm sequence method employing a bisection strategy, which eliminates the need for having to solve the buckling eigenvalue problem at each incremental (decremental) loading stage that is associated with the usual solution techniques. The plastic bucking mode shape is determined by a simple inverse iteration process, once the buckling load has been established.

Numerical results are presented for plate problems with various edge conditions. The resulting computer program written in FORTRAN for the JPL UNIVAC 1108 machine proves to be most economical in comparison with other existing methods of such analysis.
Hierarchal finite elements and precomputed arrays
Authors: Rossow M. P. , Katz I. N.
Published: August 2005

Two‐dimensional C° finite elements of arbitrary polynomial order are developed for a general functional which includes a least squares or potential energy functional as special cases. The elements are ‘hierarchal’ in the sense that the nodal variables for polynomial order p constitute a subset of the nodal variables for order p+1. It is shown that the elemental arrays for high polynomial order may be efficiently computed by using hierarchal elements together with precomputed arrays—i.e., arrays which are computed once, stored on permanent file, and then re‐used in all subsequent applications of the program. A number of example problems are solved. Comparisons are made of the relative efficiency of finite element convergergence with mesh refinement (polynomial order held fixed) and with increasing polynomial order (mesh held fixed). The latter approach is found superior.
The finite element solution of rapid cycling creep problems
Authors: Ponter A. R. S. , Brown P. R.
Published: August 2005

The paper describes a simplified finite element method for high temperature creep problems involving cyclic load and temperature. The principal assumptions, that the cycle time is small compared with characteristic material time scales, is appropriate for the moderate load levels which occur when structures are designed for life times measured in years and decades. Because of the simplicity of the method, thermal loading problems may be studied in some detail. A parametric study of a plane stress problem is presented. Characteristic deformation rates are related to reference stress and timperature quantities, thereby reducing the main features of the solution to a few important structural and material parameters.
Numerical solutions for a class of multi‐part mixed boundary value problems
Authors: Aksogan O.
Published: August 2005

This paper proposes a procedure for the extension of a widely used numerical method1−4 for the solution of systems of singular integral equations, from mixed boundary value problems with two or three parts to those having many parts. The procedure is applied to three previously solved mixed boundary value problems and the result are presented in graphical form. The effectiveness of the given procedure is observed through the results for some limiting and special cases found in the literature.
A study of quadrilateral plate bending elements with ‘reduced’ integration
Authors: Pugh E. D. L. , Hinton E. , Zienkiewicz O. C.
Published: August 2005

The accuracy of certain thick plate elements when used in the context of thin plate problems can be improved by the use of reduced integration of the stiffness matrices. A series of numerical experiments on five different quadrilateral thick plate elements demonstrates the use of reduced integration and indicates the main reason for its success. This is the relaxation of a constraint on the shear strains. It is shown that the performance of a nine‐noded Lagrangian element is near optimal.
A finite difference‐element integration scheme for long‐period water wave propagation
Authors: Meissner Udo
Published: August 2005

An explicit formulation for the dynamic analysis of rivers is presented. The model is based on the finite element method but works like an explicit finite difference scheme. It includes the advantages of both methods: high flexibility and low computer costs.
Efficient implementation of anisotropic three dimensional boundary‐integral equation stress analysis
Authors: Wilson R. B. , Cruse T. A.
Published: August 2005

The boundary‐integral equation medthod is particularly well suited for solution of stress concentration and elastic fracture mechanics problems. The method was not previously applicable to anisotropic three dimensional problems because no efficient technique existed for calculation of the required point load solution for an infinite body. A technique has been developed to evaluate numerically the anisotropic point load soultions, and used to generate data bases for various materials. An intrpolation technique is used to evaluate the point load solutions efficiently within a higher order boundary‐intgral equation code. The effectiveness of the technique is verified by solution of problems involving both uniaxial stress states and stress concentrations.
Stability analysis of some finite difference schemes for the Navier‐Stokes equations
Authors: Rigal Alain , Aleix Georges
Published: August 2005

We study the stability of two standard finite differnce schemes for the unsteady Navier‐Stokes equations. We write a scheme for small values of Reynolds number, where teh diffusion is predominant, and another one for large values of Reynolds number, where convection is predominant. The purpose of this results may be extended to unsteady problems leading to mixed hyperbolic‐parabolic partia differenctial equations.
A numerical comparison of axisymmetric finite elements
Authors: Durocher Lawrence L. , Gasper Andrew , Rhoades Gene
Published: August 2005

The advantages and disadvantages of a variety of axisymmetric elements are examined by comparing various elements from accuracy, computer time, and stress interpretation viewpoints. In addition, various techniques of stress averaging and/or smoothing are discussed from an acuracy and a computational effort standpoint. Numerical results are presented for three problems having classical solutions.
A‐posteriori error estimates for the finite element method
Authors: Babuška I. , Rheinboldt W. C.
Published: August 2005

Computable a‐posteriori error estimates for finite element solutions are derived in an asymptotic form for h → 0 where h measures the size of the elements. The approach has similarity to the residual method but differs from it in the use of norms of negative Sobolev spaces corresponding to the given bilinear (energy) form. For clarity the presentation is restricted to one‐dimensional model problems. More specifically, the source, eigenvalue, and parabolic problems are considered involving a linear, self‐adjoint operator of the second order. Generalizations to more general one‐dimensional problems are straightforward, and the results also extend to higher space dimensions; but this involves some additional considerations. The estimates can be used for a practical a‐posteriori assessment of the accuracy of a computed finite element solution, and they provide a basis for the design of adaptive finite element solvers.
A systematic procedure for generating useful conformal mappings
Authors: Caughey D. A.
Published: August 2005

A Procedure is presented for generating a class of conformal mappings useful in the formulation of finite−difference problems involving curved boundaries. The method provides a systematic approach that is capable, in principle, of reducing the geometry to a nearly−rectangular domain for a wide variety of partical problems. The introduction of sheared co−ordinates in this computational domain then provides for solution of the problem in a nearly−orthogonal (in fact, nearly−conformal) co−ordinate system, with its boundaries corresponding to co−ordinate lines. The method is based upon the Schwarz−Christoffel transformation and is quite simple to apply. Several examples illustrating the types of geometries which can be treated in this manner are presented.
Upwinding of high order Galerkin methods in conduction−convection problems
Authors: Christie I. , Mitchell A. R.
Published: August 2005

Upwinded parabolic and cubic elements are derived on a uniform grid of size h for the finite element Galerkin method applied to the solution of the model conduction−convection problem εu″ — Ku′ = 0, ε, K > 0, subject to the boundary conditions u(0) = 1, u (1) = 0. Extension of the results to more complicated problems is indicated. Finally numerical results are given comparing some of the methods derived for a range of L(=Kh/2ε), the grid Peclet number.
An elasto‐viscoplastic thermal stress model with applications to the continuous casting of metals
Authors: Williams J. R. , Lewis R. W. , Morgan K.
Published: August 2005

A finite element model is presented for the analysis of the thermal stress development in a body with temperature dependent material properties. The thermal model allows a change of phase to occur within the body and an elasto‐viscoplastic constitutive relationship is used for the stress analysis. An example is given of the applicability of the technique to the analysis of continuous casting in metals.
A simply implemented two dimensional Shockley–Poisson solver with applications to CCD
Authors: Fortino Andres G. , Nandan Joseph S.
Published: August 2005

A numerical method for the solution of the two dimensional Shockley–Poisson equation is presented and applied to the analysis of MOS devices. This SOR–Newton method is compared to Gummel's algorithm in two dimensions and shown to be more easily implemented. Application of the resulting code to interelectrode effects in charge coupled devices is given as an example.
A quadrature rule for conforming quadratic crack tip elements
Authors: Dunham Robert S.
Published: August 2005

A simple quadrature rule that precisely integrates products of singular √r and quadratic shape function gradients for a two‐dimensional six node triangle and a three‐dimensional fifteen node prism is derived.
Restricted range adaptive curve fitting
Authors: Hull J. A. , Taylor G. D.
Published: August 2005

In this paper we present an algorithm for adaptively computing smooth piecewise polynomial approximations using restricted range uniform approximations on a finite point set. We also present several numerical examples and offer suggestions for the effective use of this algorithm. We have found the algorithm to be effective for approximating a wide class of functions, either with or without significant levels of noise. Furthermore, since the user of this algorithm actually defines tolerance bands within which the approximation will lie, the algorithm allows the user a great deal of flexibility and control over the shape of the resulting approximations.
On the use of the total scalar potential on the numerical solution of fields problems in electromagnetics
Authors: Simkin J. , Trowbridge C. W.
Published: August 2005

The paper summarizes the formulation of a set of computer algorithms for the solution of the three‐dimensional non‐linear Poisson field problem. Results are presented that were obtained by applying algorithms to the analysis of two‐dimensional magnetostatic fields. Scalar and vector potentials were used, and it is shown that the convenient single valued scalar potential associated with the induced sources gives severe accuracy problems in permeable regions. The results become as good as those obtained using vector potential if the scalar potential associated with the total field is used for permeable regions. The combination of two scalar potentials has a significant advantage for three‐dimensional problems.
An algorithm for automatically tracking ablating boundaries
Authors: Weeks George E. , Cost Thomas L.
Published: August 2005

An algorithm has been developed which automatically calculates the time‐dependent positions of points on the ablating boundaries of two‐dimensional continuum structures with geometrially complex shapes. The structural boundary may consist of ablating and non‐ablating parts. The initial ablating and non‐ablating boundaries are defined by the disjoint union of piecewise linear arcs passing through a finite set of nodal points on the boundary, each defined by a pair of rectangular Cartesian co‐ordinates. For a specified ablation rate, the algorithm calculates successive positions of the boundary points at times specifiec by the user. The algorithm is designed such that it may be easily incorporated, along with an automated mesh generation procedure, into existing finite element codes for transient thermal or stress analysis of structures with ablating boundaries. Two examples are presented from the field of solid rocket analysis.
An improved method for contouring on isoparametric surfaces
Authors: Gray W. H. , Akin J. E.
Published: August 2005

A general non‐linear interpolation procedure for contouring on any isoparametric surface was presented in a previous article. The method used standard isoparametric interpolation functions and a predictor method for tracing element contour lines. The method presented here extends the previous work by using a predictor‐corrector method to trace element contour lines, thereby making the contouring algorithm more accurate.
The thermal loads in the finite element analysis of elasto‐plastic stresses
Authors: Grill A. , Sorimachi K.
Published: August 2005

The method for the evaluation of the thermal loads used in the incremental finite element analysis of elasto‐plastic stress is presented. The stress distributions obtained by two apparently possible methods for evaluation of the thermal loads are compared.
Frequency analysis of thick orthotropic plates on elastic foundation using a high precision triangular plate bending element
Authors: Babu P. V. Thangam , Reddy D. V. , Sodhi D. S.
Published: August 2005

A high precision triangular thick orthotropic plate bending element on an elastic foundation is developed for the free vibration analysis of thick plates on elastic foundation. The element has three nodes with twelve degrees‐of‐freedom per node, and takes into account the shear deformation and rotatory inertia. The accuracy of the element is established by comparison of the natural frequencies of certain thick and thin plates, determined from a consistent mass matrix formulation, with available results.
The evaluation of improper integrals encountered in the use of conformal transformation
Authors: Binns K. J. , Rees G. R. , Kahan P.
Published: August 2005

Methods are described and reviewed for the accurate numerical evaluation of improper integrals encountered in conformal transformation solutions involving boundaries of relatively complicated shape. Four methods are reviewed for the solution of integrals containing end‐point singularities. Two new methods are discussed for the solution of integrals containing both end point singularities and simple poles within the range of integration. One method uses a combination of a simple recursive formula and the coefficients of a Chebyshev series and a second method involves subtracting out the singularity and the use of Gauss–Jacobi quadrature. Both methods can give results of high accuracy and an upper limit of the error is readily found. A numerical example is taken which is typical of the application to practical problems and this brings out a comparison of the two methods.
Finite elements for an optimal control problem governed by a parabolic equation
Authors: Meric R. A.
Published: August 2005

A stationary variational formulation of the necessary conditions for optimality is derived for an optimal control problem governed by a parabolic equation and mixed boundary conditions. Then a mixed finite element model with elements in space and time is utilized to solve a simple numerical example whose analytical and finite difference solutions are given elsewhere. Numerical results show that the proposed method with C° continuity elements constitutes a powerful numerical technique for solution of optimal control problems of distributed parameter systems.
Piecewise linear elastic–plastic analysis
Authors: Kaneko Ikuyo
Published: August 2005

The purpose of this paper is to show that a mathematical programming method, due to Maier and his co‐workers, of nonlinear structural analysis can be rerformulated so that greater computational efficiences are achived. The methods are designed for a class of elastic–plastic structures under ‘piecewise linear’ assumptions and solve among others the problem of determining the stresses and strains in the structure. The reformulation gives rise to a class of mathematical programming problems calles a ‘n by dn linear complementarity problem’, for which the author has developed an efficient algorithm. It will be explained why and by how much the proposed method (the reformulation and its solution by the author's algorithm) solves the structural problems more efficiently than the existing one. Results of a systematic computer experiment supporting the efficiency of the proposed method are also presented.
Representation and discretization of arbitrary surfaces for finite element shell analysis
Authors: Wu Sheng‐Chuan , Abel John F.
Published: August 2005

An interactive computer graphics system has been developed for generating the geometric description of an arbitrary shell surfface. The various difficulties facing the user of sophisticated, doubly‐curved shell finite elements and the inefficiency of preprocessing for shell analysis are discussed to explain the benefits of this system. The method is a synthesis of spline theory and algorithms, and an interactive means for man–machine communication. The basic technique employed is a modified lofting method in which cardinal splines. An inversion procedure is incorporated which increases significantly the efficiency of the B‐spline approximation process. Static and dynamic graphic displays greatly enhance visualization at any stage of the procedure. Two examples of practical interest are presented in some detail to demonstratge the flexibility and usefulness of this approach. Some natural extensions of this system for interactive mesh generation on the surface are also demonstrated.
Strees analysis of variable cross‐section indeterminate beams using reopeated integration
Authors: Wilson Howard B. , Farrior Donna S.
Published: August 2005

A simple computer method is presented for analysing statically indeterminate beams having sectionally constant EI values and loads consisting of any number of arbitrarily placed concentrated forces and couples as well as any number of uniform and ramp loads. Unknown reactions are treated as parameters which are determined by simulataneous imposition of end conditions and interior constraints. Support locations are specified independently of any discontinuites of load or cross‐section. A computer program implementing this method is described which has very concise data input considerably shorter than tupically required in programs based on the stiffness method.
Adaptive l1–l2 curve fitting
Authors: Avila P. G. , Taylor G. D.
Published: August 2005

In References 1 and 2, algorithms were introduced for adaptively computing smooth piecewise polynomial approximations using uniform, least‐squars (l2) and restricted‐range uniform approximations. This present paper introduces a FORTRAN program for computing smooth piecewise polynomial approximations to data and/or precise mathematical functions (in discrete form) which allows the user the option of using best l1 of best l2 approximations. (The l2 option of this newly developed l1–l2 adaptive curve‐fitting package supersedes the code listed in Reference 1 for the old least‐squares program.) In this paper, adaptive curve‐fitting algorithm used in this l1–l2 package is described in detail, the FORTRAN program is the given (in the Appendix) and discussed, the numerical results are presented in an effort to illustrate how the l1 and l2 versions of this algorithm may be used most effectively.
Errors arising from irregular boundaries in ADI solutions of the shallow‐water equations
Authors: Weare T. J.
Published: August 2005

Truncation errors introduced by operator splittingtechniques, such as the ADI scheme, are discussed in the contextof the two‐dimensional shallow‐water equations. Numericalexamples of flow along a uniform channel, with and withoutfriction, illustrate the practical significance of these errors when the boundary is not aligned with the computational gridaxes. With irregular boundaries the maximum time step aceptable ismore severely restricted than has been realized hitherto. The problem, which is shown to stem from the treatment of the boundary conditons, is inherent in any splitting scheme and is difficult to circumvent.
A new numerical method for transient thermal stress problems
Authors: Takeuti Y. , Tanigawa Y.
Published: August 2005

A new numerical method of calculating unsteady‐state heat conduction and thermal stresses by using improved coefficient matrix patterns on the nodal points of a structure is given. Good agreement is obtained between our results and the rigorous results, and this method seems to yield better accuracy than other well‐known approximate methods for two‐dimensional transient thermal stress problems.
A class of preconditioned conjugate gradient methods for the solution of a mixed finite element discretization of the biharmonic operator
Authors: Axelsson Owe , Munksgaard Niels
Published: August 2005

The homogeneous Dirichlet problem for the biharmonic operator is solved as the variational formulation of two coupled second‐order equations. The discretization by a mixed finite element model results in a set of linear equations whose coefficient matrix is sparse, symmetric but indefinite. We describe a class of preconditioned conjugate gradient methods for the numerical solution of this linear system. The precondition matrices correspond to incomplete factorizations of the coefficient matrix. The numerical results show a low computational complexity in both number of computer operations and demand of storage.
Description of a curved boundary shape without first derivative discontinuities
Authors: Redmer J. , Kuehne K. , Dahl W.
Published: August 2005

For the two‐dimensional isoparametric 8‐node element an additive condition is formulated, so that the function describing the domain boundary is continually differentiable at the common nodes on the boundary. This condition will be satisfied by moving the mid‐side nodes into a special position. The advantage in using this modified element will be shown by an example of the elasto‐plastic calculation of a double‐edge notched specimen.
On the approximation of incompressible materials in the displacement method
Authors: Debongnie J. F.
Published: August 2005

A mathematical description of the numerical approximation to incompressibility with nearly incompressible displacement finite elements is presented. By the way of functional analysis, it leads to a condition of convergence to the incompressible problem when v is increased up to 0.5, which can be identified with Fried's K1 criterion.
On modified incomplete cholesky factorization methods for the solution of problems with mixed boundary conditions and problems with discontinuous material conefficients
Authors: Gustafsson Ivar
Published: August 2005

In Reference 1 a class of first‐order factorization methods for the solution of large, sparse systems of equations, of which the coefficient matrix is a symmetric M‐matrix, was introduced. Asymptotic results for the computational complexity was proved in the case of systems arising from finite difference approximation of second‐order self‐adjoint elliptic partial differential equation problems in two dimensions with Dirichlet boundary conditions. In this paper the result is extended to cover even mixed boundary conditions and problems with discontinuous material coefficients. Results from numerical experiments with various finite difference and finite element approximations are presented and comparisons with direct and other interative methods are made.
Orthogonal base functions and consistent diagonal mass matrices for two‐dimensional elements
Authors: Schreyer Howard L. , Fedock Joseph J.
Published: August 2005

Orthogonal base functions that are complete first‐order polynomials but contain higher order terms are developed for normalized rectangular and triangular elements. To obtain exact expressions for kinetic energy under rigid body rotation, an internal node is introduced at the centroid of each element. Then the corresponding mass matrix is both diagonal and consistent. A mixed variational formulation is used in the derivation of spatially discretized field equations. Central Difference time integration is utilized to provide sample results which are compared with other numerical or analytical solutions.
Exterior flow with an isoparametric Hermite cubic element
Authors: Williams B. R. , Morton K. W.
Published: August 2005

An isoparametric Hermite cubic element is developed for calculating compressible flows past complex aerofoils in two dimensions. A simple intermediate transformation is used to derive an isoparametric transform whose Jacobian is always non‐zero and which attains very high accuracy on the boundary. Application of the method and assessment of the error is illustrated by flow past a circular cylinder.
The finite element method in problems of nonlinear optics
Authors: Chesnokov S. S. , Egorov K. D. , Kandidov V. P. , Vysloukh V. A.
Published: August 2005

The Possibility of the application of the finite element method to some problems of nonlinear optics is investigated in this paper. The self‐action of a light beam in a nonlinear medium is considered. The general approach to the cretion of conservative computation schemes is presented, based on varitional principles. Definite schemes, which are applicable for the problem of thermal self‐action, are described in detail both in the case of cylindrical and or rectangular co‐ordinates. The accuracy and convergence of the models are analysed. The results of computation of the self‐action problems in motionless and moving media are presented.
Weight functions from virtual crack extension
Authors: Parks D. M. , Kamenetzky E. M.
Published: August 2005

The stiffness‐derivative method of Parks1 for calculating the linear elastic crack tip stress intensity factor for any symmetric crack configuration and a particular loading is extended to calculate the weight function vector field2,3 which serves as a Green's function for the stress intensity factor. The method, which combines the observations of Rice3 on the weight function and of Zienkiewicz4 on the differential stiffness method, permits very efficient determination of the weight function, requiring only one additional back‐substitution on the already‐factored stiffness matrix. Thus, the stress intensity factor for arbitrary loading of this configuration can subsequently be determined by quadrature alone. The promising extension of the method to three‐dimensional configurations is outlined.

While this manuscript was under review, the authors became aware of the recent work of Vanderglas,21 in which the same approach as ours is used to extend the stiffness derivative method. The present work was then voluntarily revised in order to address further certain aspects of the topic of shape function perturbation, which Vanderglas noted.
Structural weight optimization by dual methods of convex programming
Authors: Fleury C.
Published: August 2005

This paper is mainly concerned with a new structural optimization method based upon the concept of duality in convex programming. This rigorous formulation permits justification of many intuitive procedures which are used in the classical optimality criteria approaches. Furthermore, the dual algorithms proposed in this paper do not suffer from the drawbacks inherent to the optimality criteria approach. The selection of the set of active constraints does not introduce any difficulty and is achieved correctly in all cases. The subdivision of the design variables in an active and passive group is intrinsically contained in the dual formulation. The efficiency of the dual algorithms is shown with reference to some problems for which the classical methods do not lead to satisfactory results.
Finite element and conjugate gradient methods for a nonlinear optimal heat transfer control problem
Authors: Meric R. A.
Published: August 2005

The boundary control problem of optimal heating of an infinitely long slab with tempertue‐dependent thermal conductivity, subjected to a convection and radiation boundary condition, is analysed by numerical methods.

In order to reformulate the optimal control problem of distributed parameter systems as a mathematical programming problem of finite dimension, a space, co‐ordinate is discretized by use of the finite element method, while the Runge–Kutta method is utilized for time integrations. Finally, the performance index of the optimal control problem is minimized by the conjugate gradient method of optimization.
On the analysis of accuracy for two‐equation transient problems
Authors: Lynch Daniel R. , Gray William G.
Published: August 2005

Fourier analysis of numerical accuracy has traditionally concentrated on the propagation behaviour of various methods. When systems of equations in more than one unknown are involved, analysis of propagation accuracy alone is shown to be incomplete. A distribution factor is introduced to complement the Fourier analysis in these cases, and application of the concept to two problems commonly encountered in the water resources field is demonstrated. The distribution factor is shown to provide important information which cannot be obtained from the customary analysis of propagation accuracy.
Improved boundary–integral equation method for time‐dependent inelastic deformation in metals
Authors: Morjaria Mahes , Mukherjee Subrata
Published: August 2005

Efficient solution of boundary value problems for time‐dependent inelastic deformation in metallic structures is of great practical importance. These problems are generally solved by finite element methods and separate descriptions for time‐independent plasticity and time‐dependent creep are normally used. The boundary–integral equation method was recently applied for the first time to such problems. This paper presents a very efficient numerical implementation of the method with a linear description of the relevant variables over each boundary element and a newly developed Euler‐type time‐integration scheme with automatic time‐step control for time integration. Numerical results for plates in plane stress with and without cutouts, under different loading histories, are presented. A combined creep–plasticity constitutive theory with state variables is used to model material behaviour. The results are more accurate and are obtained with much less computational effort compared to a previous attempt with an uniform description of variables over each boundary element and a predictor–corrector scheme for time integration. The computer program developed is quite general and can handle plane stress problems for plates of arbitrary shapes subjected to arbitrary time‐histories of loadings. The numerical results presented in the paper are for certain illustrative problems.
MAGGY2, a program package for two‐dimensional magnestostatic problems
Authors: Polak S. J. , De Beer A. , Wachters A. , Van Welij J. S.
Published: August 2005

This paper describes the essential features of the program package MAGGY2. With MAGGY2, magnetostatic problems in two dimensions can be analysed. The co‐ordinate system may be Cartesian, cylindrical or polar. A finite element method with bilinear isoparametric quadrilaterals is used. Input must be given in the problem‐oriented language MAGLAN. This language is based on the idea that a user of MAGGY2 wants to describe his problem rather than give commands for its solution. The algorithm and the problem‐oriented language are described. Some examples showing the use of the package are given.
Transient and pseudo‐transient analysis of Mindlin plates
Authors: Pica A. , Hinton E.
Published: August 2005

A unified approach is presented for the static and transient dynamic linear and geometrically nonlinear analysis of Mindlin plates including initial imperfections. The effects of transverse shear deformation and rotatory inertia are automatically taken into account. A finite element idealization is adopted and the quadratic Lagrangian Mindlin plate element is used together with selective integration. Several numerical examples are presented and compared with results from other sources.
Converged stress solutions in thin plates by the extended field method
Authors: Donaldson B. K. , Chander S. , Negm H. M.
Published: August 2005

This paper presents numerical results calculated by the extended field method for the problem of the forced harmonic vibration of two plates—one rectangular and one triangular. The numerical results demonstrate that the extended field method, which is a deflection‐based series solution method, is capable of producing converged stress solutions suitable for being bases of comparison for other approximate methods of analysis.