bluuebunny/crossref_metadata_2025 huggingface dataset:
Anisotropic elasto‐plastic finite element analysis of thick and thin plates and shells
Authors: Owen D. R. J. , Figueiras J. A.
Published: August 2005

An elasto‐plastic analysis of anisotropic plates and shells is undertaken by means of the finite element displacement method. A thick shell formulation accounting for shear deformation is considered, which is based on a degenerate three‐dimensional continuum element. The accommodation of variable material properties, not only along the surface of the structure but also through the thickness, is made possible by a discrete layered approach. Although isoparametric elements of the Serendipity family give satisfactory solutions for thick and moderately thin shells the results exhibit ‘locking’ for an increasing ratio of span to thickness. To develop a numerical model which is applicable to thick or thin plates and shells, the nine‐node Lagrangian element and the Heterosis element are also introduced into the present model. Plastic yielding is based on the Huber‐Mises yield surface extended by Hill for anisotropic materials. The yield function is generalized by introducing anisotropic parameters of plasticity which are updated during the material strain hardening history. Numerical examples are presented and compared with available solutions. The effects of anisotropy on these solutions are also discussed.
Finite element, boundary element and coupled analysis of unbounded problems in elastostatics
Authors: Beer G.
Published: August 2005

The implementation of a combined boundary element‐finite element analysis capability is discussed. A comparison is then made between the finite element, boundary element and coupled method as applied to unbounded problems in elasticity and plasticity.
Algorithms for determining invertible two‐ and three‐dimensional quadratic isoparametric finite element transformations
Authors: Field David A.
Published: August 2005

This paper presents an algorithm which determines the invertibility of any planar, triangular quadratic isoparametric finite element transformation. Extensions of the algorithm to three‐dimensional isoparametric finite element transformations yield conditions which guarantee invertibility of 10‐node tetrahedra and 8‐node bricks. The mathematical basis for the algorithm focuses on the Jacobian as a continuous function defined over a compact set where the Jacobian attains a maximum and a minimum value. The algorithm then determines whether these values are of opposite sign.
An iterative algorithm for solving inverse problems in structural dynamics
Authors: Chen Y. M. , Lin Yi
Published: August 2005

The pulse‐spectrum technique (PST), an iterative numerical algorithm, is presented and extended to solve the inverse problems arising from the dynamic structural identification and structural design problems. A simple one‐dimensional shear beam model is used to demonstrate the applicability of PST. Numerical simulations are carried out to test the feasibility and to study the general characteristics of this technique without the real measurement and design data. It is found that the PST is not only quite robust in providing accurate results but also an excellent numerical method according to the four practical criteria for evaluating numerical methods.
An optimally integrated four‐node quadrilateral plate bending element
Authors: Prathap G. , Viswanath S.
Published: August 2005

A clearer understanding of the problems associated with reduced integration and optimum integration schemes for the development of Mindlin plate elements is presented. It is shown that an optimal selective integration rule can be found for the 4‐node quadrilateral plate bending element which requires 2 × 2 Gaussian integration for bending energy and 1 × 2 and 2 × 1 rules for the shear energy terms from (θx − w,x) and (θy − w,y), respectively. This will give an element of correct rank, without any zero energy mechanisms and without shear locking in the thin plate limit, and better performance in moderately thick situations than the currently available 4‐node quadrilaterals using one‐point shear integration or modified one‐point shear integration due to Hughes et al. The effects of arbitrary orientation of the grid and the non‐rectangular form of element are discussed.
Lanczos versus subspace iteration for solution of eigenvalue problems
Authors: Nour‐Omid Bahram , Parlett Beresford N. , Taylor Robert L.
Published: August 2005

In this paper we consider solution of the eigen problem in structural analysis using a recent version of the Lanczos method and the subspace method. The two methods are applied to examples and we conclude that the Lanczos method has advantages which are too good to overlook.
A two‐step approach to finite element ordering
Authors: Fenves Steven J. , Law Kincho H.
Published: August 2005

A two‐step approach to finite element ordering is introduced. The scheme involves ordering of the finite elements first, based on their adjacency, followed by a local numbering of the nodal variables. The ordering of the elements is performed by the Cuthill‐McKee algorithm. This approach takes into consideration the underlying structure of the finite element mesh, and may be regarded as a ‘natural’ finite element ordering scheme. The experimental results show that this two‐step scheme is more efficient than the reverse Cuthill‐McKee algorithm applied directly to the nodes, in terms of both execution time and the number of fill‐in entries, particularly when higher order finite elements are used. In addition to its efficiency, the two‐step approach increases modularity and flexibility in finite element programs, and possesses potential application to a number of finite element solution methods.
Finite element triangular meshing optimization for pure torsion
Authors: Liniecki Alexander , Yun Jixia
Published: August 2005

This paper presents a new approach to the mesh generation for torsional problems in the finite element discretization using quadratic triangular elements. A nonlinear constrained optimization program is used as a tool.

As a criterion for the optimum meshing, the minimum error of second‐order differential operator is adopted.

An example problem is included to demonstrate the applicability of the method. Final results of the mesh distribution show significant improvements in meeting the criterion's objectives.
A method for eigenvalues of sparse λ‐matrices
Authors: Yang Wei H.
Published: August 2005

The matrix N(λ) whose elements are functions of a parameter λ is called the λ‐matrix. Those values of λ that make the matrix singular are of great interest in many applied fields. An efficient method for those eigenvalues of a λ‐matrix is presented. A simple explicit convergence criterion is given, as well as the algorithm and two numerical examples.
A new approach to the dynamic analysis of structures using fixed frequency dynamic stiffness matrices
Authors: Fricker A. J.
Published: August 2005

The dynamic analysis of structures by the standard finite element method introduces additional inaccuracies into the solution which are not present when the method is used for static analyses. These inaccuracies can arise from two sources: (i) the element formulation and (ii) the reduction of the size of the matrices by a static condensation (i.e. using the Guyan method1,2). The errors in both cases are caused by neglecting frequency‐dependent terms in the functions relating the displacements at any point in the structure to the displacements at certain fixed points (i.e. nodes in the element formulation and ‘masters’ in the condensation). A new method of solution is proposed in this paper in which the frequency‐dependent terms are retained implicitly by using dynamic stiffness matrices defined at a number of fixed frequencies. The dynamic stiffness matrices may be condensed efficiently to a relatively small number of master degrees‐of‐freedom using a front solution algorithm. The final stage in the solution uses these matrices to synthesize a high‐order eigenvalue problem. A method of solving such an eigenvalue problem, of arbitrary order, is described in a separate paper.3 Numerical examples are given to show the accuracy and efficiency of the proposed method compared with conventional methods of solution.
A method for solving high‐order real symmetric eigenvalue problems
Authors: Fricker A. J.
Published: August 2005

A new method for solving structural dynamics problems has been proposed by the author in a separate paper.1 This method of solution produces a high order real symmetric eigenvalue problem of the form (A − λ B − λ2C − λ3D…)U = 0. An algorithm for solving such an eigenvalue problem using simultaneous iteration is presented in this paper. Methods of accelerating the convergence and reducing the amount of computation are also described. A numerical example is given in which the algorithm is used to calculate the eigenvalues and eigenvectors of a framed structure.
Simple and effective bandwidth reduction algorithm
Authors: Puttonen Jari
Published: August 2005

An automatic algorithm is presented for reducing the bandwidth of symmetric interconnectivity matrices. The technique takes an arbitrary input scheme and reorders the nodes so as to reduce the bandwidth. A large number of examples is presented to illustrate the reliability and cost‐effectiveness of the method.
Automatic element reordering for finite element analysis with frontal solution schemes
Authors: Sloan S. W. , Randolph M. F.
Published: August 2005

This paper describes an element reordering algorithm which is suitable for use with a frontal solution package. The procedure is shown to generate efficient element numberings for a wide variety of test examples. In an effort to obtain an optimum elimination order, the algorithm first renumbers the nodes, and then uses this result to resequence the elements. This intermediate step is necessary because of the nature of the frontal solution procedure, which assembles variables on an element‐by‐element basis but eliminates them node by node. To renumber the nodes, a modified version of the King1 algorithm is used. In order to minimize the number of nodal numbering schemes that need to be considered, the starting nodes are selected automatically by using some concepts from graph theory. Once the optimum numbering sequence has been ascertained, the elements are then reordered in an ascending sequence of their lowest‐numbered nodes. This ensures that the new elimination order is preserved as closely as possible.

For meshes that are composed of a single type of high‐order element, it is only necessary to consider the vertex nodes in the renumbering process. This follows from the fact that mesh numberings which are optimal for low‐order elements are also optimal for high‐order elements. Significant economies in the reordering strategy may thus be achieved. A computer implementation of the algorithm, written in FORTRAN IV, is given.
Finite element techniques for problems of unbounded domains
Authors: Medina Francisco , Taylor Robert L.
Published: August 2005

A general approach for using infinite elements within the context of the finite element method is presented. Based upon Gauss‐Laguerre quadrature, a scheme for numerically computing the infinite element characteristic matrices is proposed. The general formulation of the element shape functions is outlined, including that for infinite elements that model the far field of hyperbolic systems. The technique is illustrated with a classical example in elasticity: a vertically loaded circular rigid plate.
Subdivision of the Bézier curve
Authors: Chang Gengzhe
Published: August 2005

Any segment between two points on a Bézier curve is itself a Bézier curve whose Bézier polygon is expressed explicitly in terms of the sides of the Bézier polygon associated with the original curve.
Control of spurious oscillations in the salt water intrusion problem
Authors: Wikramaratna R. S. , Wood W. L.
Published: August 2005

This paper shows that the ‘streamline upwinding’ proposed by Hughes and Brooks1 is particularly simple to implement with the coupled nonlinear equations of the problem of salt water intrusion in a coastal aquifer. Because the mechanical dispersion effect is far larger than the molecular diffusion, the notorious spurious oscillations can be controlled by limiting the ratio of grid size to the streamline mixing length. The method is demonstrated on an example of a typical aquifer by giving the diagnostic variation of concentration and various salt profiles for different values of the key parameter.
A posteriori error analysis and adaptive processes in the finite element method: Part I—error analysis
Authors: Kelly D. W. , De S. R. Gago J. P. , Zienkiewicz O. C. , Babuska I.
Published: August 2005

This is a paper presented in two parts dealing respectively with error analysis and adaptive processes applied to finite element calculations. Part I contains the basic theory and methods of deriving error estimates for second‐order problems. Part II of the paper deals with the strategy for adaptive refinement and concentrates on the p‐convergent methods. It is shown that an extremely high rate of convergence is reached in practical problems using such procedures. Applications to realistic stress analysis and potential problems are presented.
Two bracketing theorems characterizing the eigensolution for the h‐version of the finite element method
Authors: Meirovitch L. , Silverberg L. M.
Published: August 2005

This paper demonstrates that the classical inclusion principle is in general not valid for the h‐version of the finite element method. Whereas the inclusion principle is valid for second‐order systems discretized by the h‐version of the finite element method, provided linear interpolation functions are used as admissible functions, the principle is not valid for fourth‐order systems. To characterize the computed eigenvalues for fourth‐order systems discretized by the h‐version of the finite element method, this paper formulates two bracketing theorems.
A contribution to the computation of rotor moments of inertia suitable for computer processing
Authors: Witfeld H.
Published: August 2005

For the two most common rotor types–the cylindrical rotor with an arbitrarily shaped cross‐section and the axially symmetrical rotor with an arbitrary contour of the longitudinal section–algorithms for the computation of the moments of inertia with respect to the major axes are developed, which are particularly suitable for digital computer programming. In both cases the volume integrals can be reduced to area integrals which in turn can be reduced to contour integrals along the boundary of the generating area. The boundary can be approximated as accurately as desired by a polygonal course. For the area moments of any order of the resulting polygonal bounded domain, an analytical solution is presented, for whose numerical calculation only the co‐ordinates of the corner points are required. Hence the preparations for data processing are reduced to the absolutely necessary minimum.
A new class of transitional blended finite elements for the analysis of solid structures
Authors: Cavendish James C. , Hall Charles A.
Published: August 2005

Recently developed computer aided design systems for the design and modification of complex physical solids using interactive computer graphics offer the exciting possibility of an integrated design/analysis system. Called geometric modellers, these systems build complex solids from primitive solids (cubes, cylinders, spheres, etc.) and macro solids (combinations of primitives). To provide an effective finite element analysis capability for these systems, methods must be devised to ease the burden of discretizing the solid geometry into a user controlled finite element mesh. In this paper we describe a new class of transitional blended finite elements which make substantially simpler the task of finite element mesh generation and local mesh refinement. Computational experience indicates that numerical accuracy is not compromised by use of these flexible elements.
Shells of revolution with local deviations
Authors: Han Kye J. , Gould Phillip L.
Published: August 2005

A finite element model that is suitable for the analysis of shells of revolution with arbitrary local deviations is presented. The model employs three types of shell elements: rotational, general and transitional. The rotational shell elements, which are most efficient, are used in the region where the shell is axisymmetric. The general shell elements, which can simulate almost any shell geometry, are used in the local region of the deviation. The transitional shell elements connect these two distinctively different types of elements and make it possible to combine them in a single analysis.

The form of the global stiffness matrix is somewhat unique in the new model. Non‐zero terms are not confined to a narrow band along the diagonal, but occur throughout the matrix. This is due to the following: (1) two different types of nodes, ring nodes and point nodes, are combined in a single analysis; and (2) a locally non‐axisymmetric geometry creates a coupling of the Fourier harmonic coefficients of the rotational elements. Yet, the matrix still contains many scattered zero terms that should be considered for numerical efficiency. In this paper an efficient solution procedure that is effective for this situation is developed. The steps include the use of a substructuring technique and separate partial harmonic analysis. A numerical example is presented and compared with existing solutions to demonstrate the capabilities and the efficiency of the new model.
Explicit forms for the tangent modulus tensor in viscoplastic stress analysis
Authors: Brockman R. A.
Published: August 2005

Viscoplastic constitutive models typically lead to compliance (strain–stress) relationships, which must be inverted for use in the finite element displacement method. Computational requirements can be increased significantly for models of practical size due to the large number of matrix inversions which are necessary. This paper describes a method of obtaining the required stress–strain relations analytically, thus eliminating the need for numerous matrix inversions in the solution. The technique is applicable to a number of commonly‐used viscoplastic models, as demonstrated in the examples.
Adaptive Eulerian–Lagrangian finite element method for advection–dispersion
Authors: Neuman Shlomo P.
Published: August 2005

A new adaptive finite element method is proposed for the advection–dispersion equation using an Eulerian–Lagrangian formulation. The method is based on a decomposition of the concentration field into two parts, one advective and one dispersive, in a rigorous manner that does not leave room for ambiguity. The advective component of steep concentration fronts is tracked forward with the aid of moving particles clustered around each front. Away from such fronts the advection problem is handled by an efficient modified method of characteristics called single‐step reverse particle tracking. When a front dissipates with time, its forward tracking stops automatically and the corresponding cloud of particles is eliminated. The dispersion problem is solved by an unconventional Lagrangian finite element formulation on a fixed grid which involves only symmetric and diagonal matrices. Preliminary tests against analytical solutions of one‐ and two‐dimensional dispersion in a uniform steady‐state velocity field suggest that the proposed adaptive method can handle the entire range of Péclet numbers from 0 to ∞, with Courant numbers well in excess of 1.
The solution of higher order integration formulae for dynamic response equations by the conjugate gradient method
Authors: Carter A. L. , Shiflett G. R. , Laub A. J.
Published: August 2005

Higher order implicit integration techniques for solving dynamic response equations are derived utilizing Padé approximations. In an effort to minimize the disadvantages of using these higher order formulae to obtain solutions to systems with large numbers of degrees‐of‐freedom, the conjugate gradient method is employed to solve for the displacements. The accuracy and efficiency of the techniques are evaluated by making comparisons between known analytical and calculated results.
Ritz finite element approach to nonlinear vibrations of beams
Authors: Sarma B. S. , Varadan T. K.
Published: August 2005

A Ritz finite element approach is used here to study the large amplitude free flexural vibrations of beams with immovable ends. The formulation is based on Lagrange's equation of motion with the definition of the time function at an instant corresponding to the point of reversal. The element displacement vector is chosen as a combination of inplane and transverse displacements. The nonlinear stiffness is written as a combination of the bending–membrane interaction and bending stiffness. The solution for nonlinear equations is sought by using an algorithm—the direct iteration technique—suitably modified for eigenvalue problems. Convergence is checked using the displacement norms on eigen‐modes, and frequency norms for eigenvalues.

The nonlinear frequencies, and modeshapes for transverse and longitudinal displacements, are determined for the simply‐supported, clamped–clamped and simply‐supported–clamped beams. Results are presented in the form of tables. In almost all the cases the nonlinear frequency values are found to be the lower bound like the earlier Galerkin finite element method.
An 8‐node brick finite element
Authors: Loikkanen M. J. , Irons B. M.
Published: August 2005

An 8‐node brick element based on the assumed stress hybrid formulation is described. With three additional stress fields, the element stiffness matrix now has the required rank of 18, and the ‘bending’ response is exact with rectangular elements. Surprisingly, the 2 × 2 × 2 Gauss rule suffices for all numerical integrations, to satisfy the constant stress patch test.
An assumed stress hybrid curvilinear triangular finite element for plate bending
Authors: Morley L. S. D.
Published: August 2005

An assumed stress hybrid curvilinear triangular finite element is described which is based upon the Kirchhoff theory of plate bending. The derivation extends the assumed stress hybrid technique to curvilinear boundaries where the twelve connectors are related to those of an equilibrium rectilinear element and to Semiloof. The solution process demands only first derivatives of the shape functions.

The element is subjected to various patch tests for constant bending, e.g. where the central element is in close approximation to a circle. All tests are passed for stress couples and vertex displacements, but values of the remaining connectors do not resemble exact results. Patch tests for rigid‐body movements are passed exactly in every respect.
The maximum principle for bilinear elements
Authors: Christie I. , Hall C.
Published: August 2005

It is demonstrated that finite element discretizations may not, in general, satisfy the maximum principle; and sufficient conditions are presented to guarantee that solutions based on bilinear elements do satisfy the maximum principle.
Economy and convergence of notch stress analysis using boundary and finite element methods
Authors: Radaj D. , Möhrmann W. , Schilberth G.
Published: August 2005

The BEM is shown to be superior to FEM with respect to economy (man hour and data processing) and convergence (with increasing number of boundary nodes) in the elasic notch stress analysis of compact components.
The accelerated power method
Authors: Roberti Paolo
Published: August 2005

An algorithm is presented to accelerate the convergence of the inverse iteration method for the solution of algebraic symmetric eigensystems. The algorithm is based on the use of the Ritz analysis during inverse iteration to generate improved trial vectors at virtually no extra cost. Examples are shown to illustrate the computational advantages of the method. The results are compared with those obtained using the subspace iteration method, the determinant search method and the accelerated subspace iteration method.
An explicit analysis of Stummel's patch test examples
Authors: Shi Zhong‐Ci
Published: August 2005

A constructive approach for the treatment of Stummel's examples to the patch test is presented, together with generalizations of these examples. The strange convergence phenomenon of nonconforming approximations is discussed in detail, and a kind of modified variational equation for remedying these defects is introduced. Our variational equation uses a combination of hybrid and penalty methods that define a convergent procedure with optimal order of convergence to the exact solution with respect to a mesh‐dependent norm.
A finite difference calculation procedure for three‐dimensional turbulent separated flows
Authors: Nakayama Akira
Published: August 2005

A general finite difference scheme has been proposed along with a three‐dimensional co‐ordinate transformation procedure for the prediction of three‐dimensional fully elliptic flows. This numerical scheme has been successfully employed for the calculations of the three‐dimensional turbulent separated flow in a rectangular diffuser. The complexity of the phenomena is seen to increase tremendously for the three‐dimensional flows of this class.
Generalized Petrov–Galerkin methods for the numerical solution of Burgers' equation
Authors: Herbst B. M. , Schoombie S. W. , Griffiths D. F. , Mitchell A. R.
Published: August 2005

Generalized Petrov–Galerkin methods are applied in two different ways for the numerical solution of Burgers' equation. In the first place, it is used to produce upwinding in the way described by Mitchell and Griffiths.9,10 The main objective of this paper is in the second place to use it as a moving finite element method. In particular, it is shown that the methods of Miller and co‐workers4–6 and Herbst et al.7,8 can be incorporated in the more general approach presented in this paper. Several choices for the test functions are discussed and numerical results are given.
Boundary element methods for optimization of distributed parameter systems
Authors: Meric R. A.
Published: August 2005

A numerical method of solution is proposed for optimization problems of distributed parameter systems. Two model problems from continuum mechanics are investigated by means of constructing the problems as the steady‐state optimal control problems governed by elliptic partial differential equations.

The basis of the suggested method of solution lies in the space discretization of the necessary conditions for optimality by the boundary element method, and the minimization of the performance indices by the conjugate gradient method of optimization.
A procedure for analysing space frames with partial warping restraint
Authors: Yang Yeong‐Bin , McGuire William
Published: August 2005

Stiffness matrices for three‐dimensional beam elements that include the effect of warping restraint on elastic torsional response have been derived by various investigators. Using one of the available stiffness matrices and assuming that the warping boundary conditions can be specified on a member‐by‐member basis, an elastic ‘warping’ support is introduced to represent conditions of partial warping restraint at the member ends. The concept of a ‘warping indicator’ is then introduced to facilitate use of warping springs. Following this, static condensation is used to eliminate the restrained warping degrees‐of‐freedom. The condensed stiffness matrices for the elements can then be assembled to yield a global stiffness matrix. In the global matrix, continuous warping degrees‐of‐freedom, that is, those internal to a member represented by several elements, are expressed in local co‐ordinates. The remainder are expressed in global co‐ordinates. In the force recovery phase, it is shown that an ‘indirect’ method yields most accurate results for the bimoment and warping torsion when the twist function is represented by a cubic polynomial. Solutions to examples of linear elastic analysis are compared with well‐known analytical solutions to demonstrate the application of the method.
Numerical formulation for a higher order plane finite dynamic element
Authors: Gupta K. K.
Published: August 2005

The paper describes the development of an eight‐node plane rectangular finite dynamic element and presents detailed descriptions of the associated numerical formulation involving the higher order dynamic correction terms pertaining to the related stiffness and inertia matrices. Numerical test results of free vibration analyses are presented in detail for the newly developed eight‐node element and also the corresponding four‐node element in order to make a clear comparison of the relative efficiencies of the corresponding finite element and dynamic element procedures. Such results indicate a superior pattern of solution convergence of the presently developed dynamic element.
A consistent and accurate procedure for obtaining difference equations from differential equations
Authors: Lick Wilbert , Gaskins Tom
Published: August 2005

A general, consistent and accurate procedure for obtaining difference equations from differential equations is presented and illustrated by several examples. The procedure is an extension of the integral method and incorporates what is known of the solution to the differential equation in the formation of the corresponding difference equation. For the same accuracy, large increases in grid size over that obtained by standard Taylor's series approximations are possible. Both boundary‐value and initial‐value problems are treated.
The self‐equilibration of residuals and complementary a posteriori error estimates in the finite element method
Authors: Kelly D. W.
Published: August 2005

It is demonstrated that the residual in a compatible (displacement) finite element solution can be partitioned into local self‐equilibrating systems on each element. An a posteriori error analysis is then based on a complementary approach and examples indicate that the guaranteed upper bound on the energy of the error is preserved.
Numerical laplace transformation and inversion in the analysis of physical systems
Authors: Wilcox D. J. , Gibson I. S.
Published: August 2005

The paper develops a new discrete transform pair which economizes on the number of samples of F(s) and f(t) compared with the standard pair. Whereas the standard pair used uniform sampling along the Bromwich contour, the new method allows a progressive increase in the sampling interval, thereby reducing the number of samples required to meet a specified bandwidth requirement. In the case of the computation of transient responses of physical systems, a reduction by a factor of 10 is not unrealistic. The new transform pair is based on the generalization of fundamental sampling principles. In particular, this leads to an integration contour different from the Bromwich contour.
Evaluation of a new method for numerical laplace transformation and inversion
Authors: Wilcox D. J. , Gibson I. S.
Published: August 2005

The paper presents results obtained by the implementation of a new method of Laplace transformation and inversion developed by the authors. Test functions are used to show that basic accuracy is comparable to that obtainable by uniform sampling along the Bromwich contour. The advantage of the new method is seen to be that it generally requires far fewer samples of F(s). It is clarified that the new method does have certain limitations so far as general application is concerned. However, given results indicate that very satisfactory performance may be expected whenever the method is specifically applied to the calculation of transient responses of damped physical systems.
A solution technique for indefinite systems of mixed finite elements
Authors: Mirza F. A.
Published: August 2005

A solution technique for indefinite systems of symmetric linear, simultaneous equations, via the Hellinger–Reissner variational principle, is presented. The method utilizes symmetry of the global matrix and its expected real eigenvalues. Premultiplication of the global matrix with itself renders a positive definite matrix, hence enabling the use of any standard equation solver for a positive definite system and requiring only about twice the memory requirement for the original set of equations. Two subroutines, MULT and MULTIP, which are compatible with the sky‐line technique, are also listed.
Automatic three‐dimensional mesh generation by the modified‐octree technique
Authors: Yerry Mark A. , Shephard Mark S.
Published: August 2005

An approach for the fully automatic generation of three‐dimensional finite element meshes is presented. The method is specifically designed for use with solid modelling systems which provide a complete and unique definition of the geometry of a part. The method follows from the basic concepts of the octree encoding technique with specific modifications made to produce valid, user controllable finite element meshes. Example problems are included to demonstrate the technique.
On the convergence rate of the boundary penalty method
Authors: Shi Zhong‐Ci
Published: August 2005

The convergence rate of the boundary penalty finite element method is discussed for the Poisson equation with inhomogeneous Dirichlet boundary conditions on a polygonal domain. It is proved that, under certain circumstances, an optimal convergence rate may be achieved which agrees with the rate obtained recently in the numerical experiments by Utku and Carey.
Plastic straining, unstressing and branching in large displacement perturbation analysis
Authors: de Freitas J. A. Teixeira , Smith David Lloyd
Published: August 2005

The nonlinear system of equations and inequalities relating to the large displacement behaviour of elasto‐plastic structures can be transformed by the method of perturbations into an infinite sequence of recursive linear complementarity problems (LCP). Each such LCP can be solved by a simple variant of the simplex algorithm of linear programming. Special consideration is given to describing those steps of the algorithm that are needed for detecting and controlling the phenomena of plastic straining, unstressing and branching.
A new 48 d.o.f. quadrilateral shell element with variable‐order polynomial and rational B‐spline geometries with rigid body modes
Authors: Moore Carleton J. , Yang T. Y. , Anderson David C.
Published: August 2005

A 48 degrees‐of‐freedom (d.o.f.) quadrilateral thin elastic shell finite element using variable‐order polynomial functions, B‐spline functions and rational B‐spline functions to model the shell surface is developed. This development may allow the stiffness formulation of the shell element to be linked to the geometry data bases created by computer aided design systems. The displacement functions are that of bicubic Hermitian polynomials. The displacement functions and d.o.f. are expressed and investigated in both the curvilinear and Cartesian forms. The cuivilinear form is simpler and can provide the proper solution for a certain class of shell problems. For certain highly curved shells such as bellows, however, the curvilinear form fails to properly model some rigid body modes even with either the explicit inclusion of rigid body terms or the high order displacement functions. It is suggested in this study that such difficulty can be circumvented and the rigid body modes can be properly included if a Cartesian form is used for displacement functions. The strain–displacement equations are expressed in curvilinear co‐ordinates. Thus, the Cartesian displacement functions require a transformation to curvilinear displacement at each numerical integration point. Examples include a pinched cylinder, a translational shell under central load, a uniformly loaded hypar shell, a pressurized ovel shell, a semi‐toroidal bellows and a U‐shaped bellows. For the first four examples, geometric modellings consist of polynomials of second‐order (subparametric), third‐order (isoparametric), and fourth and fifth‐order (both superparametric) as well as B‐spline functions of fourth‐ and fifth‐order. The geometries of the pinched cylinder, the semi‐toroidal bellows, and the U‐shaped bellows were modelled exactly using rational B‐spline functions. All the results obtained are in good agreement with alternative existing solutions.
Development of a solid hexahedron finite dynamic element
Authors: Gupta K. K.
Published: August 2005

This paper presents the pertinent details of a newly developed solid rectangular hexahedron finite dynamic element, involving the derivation of the higher order stiffness and inertia dynamic correction matrices. Numerical results of a test case are also presented which indicate that adoption of the dynamic elements significantly improves the solution convergence, when compared with the related performance of the corresponding finite elements.
Potential integrals associated with quadratic distributions in a triangular domain
Authors: Okon E. E.
Published: August 2005

Exact expressions are presented for the potentials, at an arbitrary point in space, due to two quadratic distributions in a triangular disc. These expressions are obtained by means of extensions of the analytical techniques previously developed for evaluating the potential integrals for constant and linear distributions. It is shown that the potential due to any quadratic distribution in a triangle may be obtained by using the two expressions derived here, together with an expression for the potential corresponding to a linear distribution. This latter expression was presented in an earlier paper.1 Numerical values obtained through the use of the two expressions are compared with those which result from the numerical evaluation of the potential integrals by triangle quadratures.
Accurate numerical integration of singular boundary element kernels over boundaries with curvature
Authors: Lean Meng H. , Wexler A.
Published: August 2005

Use of the Green function, for the solution of boundary‐value problems, frequently results in singular integral equations. Algorithms are presented for the accurate and efficient treatment of singular kernels frequently encountered in the boundary element method (BEM). They are based upon the use of appropriately weighted Gaussian quadrature formulae, together with numerical geometrical transformations of the region of integration. The use of high‐order subdomain expansion functions, for interpolation over nonplanar elements, allows boundary curvature to be accommodated. In particular, the handling of Green functions with logarithmic and r−1 behaviour are detailed. Volume integrals, with r−2 singularity, are outlined. Operations are performed on a simplex, thus resulting in generality and ease of automation. This scheme has been incorporated into boundary element method software and successfully applied to a variety of problems.
Analysis of laminated bimodulus composite thin shells of revolution using a doubly curved quadrilateral finite element
Authors: Murthy P. V. Ramana , Rao K. P.
Published: August 2005

This paper presents a finite element analysis of laminated bimodulus composite thin shells of revolution using a 48 d.o.f. doubly curved quadrilateral finite element. All the three displacements of the shell element reference surface are expressed as products of one‐dimensional first‐order Hermite interpolation polynomials. The constitutive relationship for a bimodulus composite is assumed to depend on the fibre‐direction strain experienced by each orthotropic layer. Consequently the true state of strain and the corresponding constitutive relationship in a bimodulus composite structure are to be determined iteratively. The true state of stress/strain is obtained by specifying a maximum error in the locations of the two neutral surfaces (one along each of the orthogonal reference axes) in the shell. The use of the quadrilateral shell finite element is validated by solving the problem of (i) a freely supported single layer (0°) bimodulus composite square plate and (ii) a freely supported single layer (0°) cylindrical panel, which are subjected to sinusoidal transverse loading and for which analytical solutions are available. Next, the problems of a single layer (90°) pinched cylindrical shell and a single layer (0°) open crown hemispherical shell are solved to show the ability of the present program.
Geometrically nonlinear formulation of a 48 D.O.F. quadrilateral shell element with rational B‐spline geometry
Authors: Yang T. Y. , Moore Carleton J. , Anderson David C.
Published: August 2005

A geometrically nonlinear formulation for a 48 degrees‐of‐freedom (d.o.f.) quadrilateral shell element is presented. Each of the three displacement functions of u, v and w is based on the bicubic Hermitian polynomial. The surface of the element is modelled using linearized ratronal B‐spline functions which may be linked to the geometric data bases generated by the computer‐aided design system. The displacement functions and the 48 d.o.f. are expressed in both curvilinear and Cartesian forms, whereas the strain‐displacement equations are expressed in curvilinear co‐ordinates. The use of Cartesian displacement functions and degrees‐of‐freedom allow for the proper representation of the six rigid body motions even for the element with nonzero Gaussian curvature, such as a bellows. Two examples are demonstrated: snap‐through buckling of a spherical cap and large deflection of a semi‐toroidal bellows shell. Results compare well with alternative solutions.
Numerical solution to a two‐dimensional inverse heat conduction problem
Authors: Busby H. R. , Trujillo D. M.
Published: August 2005

The two‐dimensional inverse heat conduction problem is solved using the method of dynamic programming. One problem involves determining two unknown heat flux histories imposed on two faces of a slab. Several numerical experiments were performed to ascertain the effects of noise and the weighting parameters.
Stability and convergence of some finite element algorithms for nonlinear elastodynamics
Authors: Hamdan S. M. , Patamapongs N.
Published: August 2005

A series of direct‐integration and model‐expansion finite element algorithms for a geometrically and materially nonlinear elastodynamic problem are constructed and analysed. The algorithms are constructed by temporally approximating the individual nonlinear stiffness terms such that discrete conservation laws are obtained. This conservative property has a positive effect in providing a stable appromixation, and in addition allows the stability properties of the algorithms to be easily assessed. Stability and convergence criteria for the algorithms are rigorously established using an energy method.
A procedure to debug computer programs
Authors: Shih T. M.
Published: August 2005

This analysis presents a procedure that can reliably debug computer programs. The central idea lies in creating a fictitious problem whose exact solution exists and is known, and in obtaining the numerical solution for comparison with the exact solution. If the two solutions are found identical, it is safe to assume that the computer program computing the fictitious problem is free of bugs. Then, conversion of the program computing the ficititious problem to that computing the real problem generally involves changing only one single statement. This procedure may be jointly used with all the existing numerical schemes.
Finite element hourglassing control
Authors: Schulz J. C.
Published: August 2005

A new hourglassing control technique for quadrilateral and hexahedral elements used in dynamic finite element codes is presented. Based on expansion of the strees in a Taylor series and retention of additional terms beyond the usual constant stress term, this technique has the advantage that actual rather than artificial material properties are used. Simplifications that render this technique competitive with artificial viscosity and stiffness procedures in terms of additional storage and computation requirements are described.
A CAD approach to the minimum weight design problem
Authors: Esping Björn J. D.
Published: August 2005

A structure is defined by a set of governing points. These points can be used to define lines, surfaces and solids. A governing point can be connected to a design variable. The values of the design variables are determined in order to minimize the weight of the structure subject to a number of stress constraints. Three simple structures are then designed.
High degree efficient symmetrical Gaussian quadrature rules for the triangle
Authors: Dunavant D. A.
Published: August 2005

Gaussian quadrature is required for the computation of matrices based on the isoparametric formulztion of the finite element method. A brief review of existing quadrature rules for the triangle is given, and the method for the determination of high degree efficient symmetrical rules for the triangle is discussed. New quadrature rules of degree 12–20 are presented, and a short FORTRAN program is included.
A simple plate/shell triangle
Authors: Prathap G.
Published: August 2005

A simple shear flexible triangular plate/shell element with three/five displacement degrees‐of‐freedom at the three corner nodes only, is identified. It does not lock or have zero‐energy mechanisms. The specific geometrical configurations in which this is possible are derived through field consistency patch tests.
Evaluation of added mass by a cloning algorithm
Authors: Dasgupta Gautam
Published: August 2005

In problems of structure interaction with infinite surrounding of incompressible, inviscid fluid media, added mass matrices on wet surfaces have been considered for modelling the effects of outgoing waves. For an arbitrary geometry of the wet surface, an expression for the added mass matrix is derived according to a finite element procedure which utilizes the force‐displacement relations of representative elements on the boundary. In the element mass matrix a certain symmetry, which characterizes interactions between the interior and exterior surfaces, helps reduce the quadratic matrix equation of the cloning algorithm to a linear eigenvalue problem. A benchmark example is included to establish the numerical accuracy of the proposed formulation.
Numerical differentiation of tabulated functions with automatic choice of step‐size
Authors: McNamee John Michael
Published: August 2005

A method for determining the optimum step‐size in numerical differentiation of a tabulated function is described. In test cases it gives an average error of about four times the error in the data; thus, it is more than twice as accurate as previously published methods. A Fortran program is presented.
Beam element matrices derived from Vlasov's theory of open thin‐walled elastic beams
Authors: Friberg P. O.
Published: August 2005

A uniform beam element of open thin‐walled cross‐section is studied under stationary harmonic end excitation. An exact dynamic (transcendentally frequency‐dependent) 14 × 14 element stiffness matrix is derived from Vlasov's coupled differential equations. Special attention is paid to the computational problems arising when coefficients vanish in these equations because of symmetric cross‐section, zero warping stiffness, etc. The dynamic element stiffness matrix is established via a generalized linear eigenvalue problem and a system of linear algebraic equations with complex matrices. A static stiffness matrix is also derived and the associated consistent mass and geometric stiffness matrices are given. Modal masses are evaluated. A FORTRAN program and a numerical example are included.
Mapped infinite elements for exterior wave problems
Authors: Zienkiewicz O. C. , Bando K. , Bettess P. , Emson C. , Chiam T. C.
Published: August 2005

Recently, a new type of infinite elements which uses r−1 decay was proposed. They were applied to exterior wave problems and good results were obtained. In two‐dimensional problems, however, it was necessary to move the origin of the r−1 decay in order to model the outgoing wave more accurately, because it decays roughly as r−1/2. In this paper, the mapped infinite elements with r−1/2 decay and the necessary numerical integration procedure are presented. These elements do not require any artificial movement of the origin. Several example problems are solved. The results show that the infinite elements with r−1/2 decay here give much more accurate values than the infinite elements with exponential decay and any damper elements.