bluuebunny/crossref_metadata_2025 huggingface dataset:
Discrete numerical solution of the generalized boussinesq problem
Authors: Gellert M.
Published: August 2005

A family of stable algorithms for integration in time of the spatially discretized generalized Boussinesq equation is presented. In space, the finite element approximation is employed enabling arbitrary layout and variable physical properties. Furthermore, the proposed spatial–temporal discretization neither involves inversion of non‐diagonal matrices of large scale nor even their storage. The method is theoretically investigated and numerically tested. Comparison is made with known results.
Taylor expansions for singular kernels in the boundary element method
Authors: Aliabadi M. H. , Hall W. S. , Phemister T. G.
Published: August 2005

The problem treated is the integration of singular functions which arise in three‐dimensional isoparametric formulations of boundary integral equations. A Taylor expansion in the local parametric co‐ordinates is developed for the singular integrand, so allowing singular terms to be integrated in closed form, even for curved surface elements. The remainder integral obtained by subtracting out the worst singularities is integrated by repeated Gaussian quadrature.

Two groups of tests are presented. First, the accuracy of the integrations has been checked for plane parallelograms (for which exact solutions have been developed) and for curved elements on a sphere. Secondly, results from complete boundary element calculations based on point collocation have been compared with known analytical solutions to two problems; zonal surface harmonics on a sphere and the capacitance of an ellipsoid. The agreement obtained with few degrees‐of‐freedom suggests that errors which have previously been attributed to point collocation might have arisen in the numerical integration.
The patch test—a condition for assessing FEM convergence
Authors: Taylor R. L. , Simo J. C. , Zienkiewicz O. C. , Chan A. C. H.
Published: August 2005

This paper discusses various forms of the Irons patch test and shows again that its satisfaction is a necessary convergence condition being equivalent to consistency, Further, it is shown that the test can be applied for verification of stability requirements, thus providing also a sufficient condition of convergence. The patch test is useful in testing the order of asymptotic convergence and the satisfaction of the test gives a guide for development of certain incompatible element forms.
A new nine node degenerated shell element with enhanced membrane and shear interpolation
Authors: Huang H. C. , Hinton E.
Published: August 2005

A new nine node degenerated shell element is presented in this paper. In the formulation of the new element, an enhanced interpolation of the transverse shear strains in the natural co‐ordinate system is used to overcome the shear locking problem, and an enhanced interpolation of the membrane strains in the local Cartesian co‐ordinate system is applied to avoid membrane locking behaviour. It is shown that the resulting element has the requisite number of zero eigenvalues and associated rigid body modes. The element does not exhibit membrane or shear locking for large span/thickness ratios. To illustrate the good performance of the new element some examples are presented including comparisons with the behaviour of the selectively integrated Lagrangian degenerated shell elements.
Program structure and architecture for a finite element machine
Authors: Norrie D. H. , Norrie C. I. W.
Published: August 2005

Superproblems in finite elements require either general‐purpose or special‐purpose computing machines whose capabilities are very much greater than those currently existing. The advantage of the latter type of machine is that it can be highly optimized for the particular class of problem for which it is designed and can, in principle, for a given generation of hardware, be designed to operate at a higher speed than a corresponding general‐purpose computer. The Parallel Finite Element Machine (PARFEM) investigated at the University of Calgary has an architecture based on the finite element computational algorithms and employs a combination of parallel and vector processing. The overall architecture and program structure is described and the major design considerations outlined.
Improved strain interpolation for curved C° elements
Authors: Park K. C.
Published: August 2005

The strain energy of straight beam members derived from the isoparametric shape functions is known to be invariant with respect to the number of integration points as long as they exceed a minimum number. However, this invariant property is generally lost for curved members. For example, the two‐point integrated, membrane strain energy of curved beams by employing the quadratic shape functions is different from the three‐point integrated one. This paper presents an invariant strain interpolation scheme for quadratic curved beam elements, which can lead to improved membrane representations in curved shell elements, thus resolving the perplexing membrane‐bending coupling difficulties in thin shell analysis.
An inverse method for the design of axisymmetric optimal diffusers
Authors: Ahmed N. M. A. , Myring D. F.
Published: August 2005

An inverse inviscid–boundary‐layer interaction scheme is presented for the optimal design of axisymmetric ducts for subsonic, rotational flows. Distribution of the shape factor H on the duct wall, giving minimum total pressure loss and maximum static pressure rise, is used as boundary condition for the inverse integral boundary‐layer solution, to obtain the velocity and displacement thickness distributions on the wall. Vector addition of the inviscid core radius, derived from the solution of the inverse inviscid flow equations, and the displacement thickness produces the desired duct shape.
A new method for solving aerodynamic hybrid problem of profile cascade on S1 stream surface of revolution by employing stream‐function equation expressed with non‐orthogonal co‐ordinate system
Authors: Naixing Chen , Weihong Li
Published: August 2005

A new method is developed in this paper for solving an aerodynamic hybrid problem of profile cascade on the S1 stream surface of revolution by employing a stream‐function equation on the non‐orthogonal co‐ordinate system. For this kind of problem, the shape of a portion of the blade profile is unknown. The remainder is determined by a given prescribed velocity distribution. Three examples, including two turbine cascades and a compressor cascade, have been carried out to examine this method. It is shown that the calculation method presented herein can be used as a powerful tool, together with the aerodynamic optimization method, for blade cascade design.
Thickness effects of CCT specimens
Authors: Miyamoto Hiroshi , Machida Kenji , Kikuchi Masanori
Published: August 2005

First, the three‐dimensional elasto‐plastic analyses of 1CT and 18 mm thick CCT specimens are carried out by using the finite element method, and the thickness effects of both specimens are studied. In elastic states, there is no significant difference between the CT and CCT specimen in the distribution of theJ‐integral along the straight or curved crack front. However, in elasto‐plastic states, quite the contrary tendency is obtained in the distributions ofJ xand COD along the curved crack front for both specimens. Secondly, elasto‐plastic analyses are carried out for CCT specimens of four kinds of thickness (B= 200, 18, 6 and 4 mm). The distributions of theJ‐integral along the crack front are obtained and compared. Finally, the availability of theJRvalue is examined, which is evaluated from the load versus displacement curve by using Rice's formula.
A formulation of general shell elements—the use of mixed interpolation of tensorial components
Authors: Bathe Klaus‐Jürgen , Dvorkin Eduardo N.
Published: August 2005

We briefly discuss the requirements on general shell elements for linear and nonlinear analysis in practical engineering environments, and present our approach to meet these needs. We summarize and give further insight into our formulation of a 4‐node shell element using a mixed interpolation of tensorial components, and present a new 8‐node element using this approach. Specific attention is given to the general applicability of the elements and their efficient use in practice.
Numerical technique in plasticity including solution advancement control
Authors: Runesson Kenneth , Samuelsson Alf , Bernspång Lars
Published: August 2005

Numerical techniques applied to the consistent formulation of plasticity, which is based on convex analysis, are investigated. For each time step the stress is found as the projection in complementary energy of the elastic stress onto the set of plastically admissible stresses, while the velocity field is the extremal of a non‐quadratic functional. Explicit formulas for von Mises' yield criterion with mixed hardening are developed and the nonlinear equations arising from finite element discretization are solved, for comparison, by a number of Newton‐type iteration procedures with line search and are‐length control. A few numerical examples with proportional and non‐proportional loading are analyzed.
Hybrid finite difference/finite element solution method development for non‐linear superconducting magnet and electrical circuit breakdown transient analysis
Authors: Kraus H. G. , Jones J. L.
Published: August 2005

The problem of non‐linear superconducting magnet and electrical protection circuit system transients is formulated. To enable studying the effects of coil normalization transients, coil distortion (due to imbalanced magnetic forces), internal coil arcs and shorts, and other normal and off‐normal circuit element responses, the following capabilities are included: temporal, voltage and current‐dependent voltage sources, current sources, resistors, capacitors and inductors. The concept of self‐mutual inductance, and the form of the associated inductance matrix, is discussed for internally shorted coils. This is a Kirchhoff's voltage loop law and Kirchhoff's current node law formulation. The non‐linear integrodifferential equation set is solved via a unique hybrid finite difference/integral finite element technique.
Incomplete factorization for finite element methods
Authors: Zyvoloski George
Published: August 2005

An incomplete factorization iterative scheme with ORTHOMIN acceleration is evaluated for three‐dimensional finite element applications. Both heat conduction and combined heat and fluid flow are investigated. Computational efficiency is investigated for both linear (8 node) and quadratic (27 node) elements as well as for various degrees of LU Decomposition. The factorization schemes worked well with both types of elements, and a variable factorization scheme, which distributes the level of factorization, performed well on difficult heat and fluid flow problems.
An efficient algorithm for the optimum design of trusses with discrete variables
Authors: Sepúlveda A. , Cassis J. H.
Published: August 2005

A method to efficiently solve the problem of minimum weight design of plane and space trusses with discrete or mixed variables is developed. The method can also be applied to continuous variables. The original formulation leads to a non‐linear constrained minimization problem with inequality constraints, which is solved by means of a sequence of approximate problems using dual techniques. In the dual space, the objective function is to be maximized, depends on continuous variables, is concave and has first and second order discontinuities. In addition, the constraints deal simply with restricting the dual variables to be non‐negative. To solve the problem an ad hoc algorithm from mathematical programming has been adapted.

Some examples have been developed to show the effectiveness of the method.
A ‘characteristic’ finite element scheme for convective‐dispersive transport with non‐equilibrium reaction
Authors: Fujinawa K.
Published: August 2005

A finite element method coupled with the method of characteristics is applied to the problem of convective‐dispersive transport with non‐equilibrium reaction. Convective terms are calculated using moving particles together with influence element meshes for particle tracking, whereas dispersion terms are calculated by means of finite element techniques. The contribution from the term of non‐equilibrium reaction is incorporated into the algebraic equations by the use of analytical solutions to the equation of non‐equilibrium reaction for each time step and extended Simpson's numerical integrations.

Comparison of the numerical results from the proposed procedure with analytical solutions to the simultaneous partial differential equations shows good agreement for the wide spectrum ranging from dispersion‐ to convection‐dominated transport with various reaction parameters.
Three‐dimensional analysis of magnetic field distortion of ferromagnetic beam‐plates by the boundary element method
Authors: Minato A. , Tone T. , Miya K.
Published: August 2005

Magnetoelastic buckling of a ferromagnetic beam‐plate has been experimentally and theoretically studied by many investigators. A great discrepancy between the experimental results and the theoretical predictions has stimulated related studies. It has been supposed that the discrepancy could be attributed to the finite size of the test piece; this case has not yet been solved exactly, or even numerically.

In this study the boundary element method is applied to solve for the magnetic field distribution around the finite specimen.
An adaptive finite element approach for the free surface seepage problem
Authors: Rank Ernst , Werner Heinrich
Published: August 2005

A posteriori error estimates and adaptive mesh refinements are now on a rigorous mathematical foundation for linear, elliptic boundary‐value problems of second order. Yet, for non‐linear problems only a few results have been obtained till now. In this paper we consider as a non‐linear model problem the two‐dimensional fluid flow with free surface and show how results from linear a posteriori theory can be used to control the non‐linear iteration and to refine the mesh adaptively. A numerical example shows that, similar to linear problems, considerable improvement of the accuracy is obtained by an adaptive mesh refinement and that the influence of singularities on the order of convergence disappears.
A simple method for including shear deformations in thin plate elements
Authors: Fricker A. J.
Published: August 2005

A method is described for including the effect of shear deformations in existing thin plate finite elements, and thereby extending their range of application to include moderately thick plates. The method does not add extra degrees of freedom to the final element, so the thick and thin plate elements can be used interchangeably, and the thick plate solution is not appreciably more expensive than the thin plate solution.

It is assumed that the shear deformations are constant over the element and, to account for this, two extra internal shear strain variables are added to the element. Various methods for eliminating these internal variables are examined but it is shown to be impossible to simultaneously satisfy both the constant bending moment and constant shear patch tests, except for parallelograms. However, one method gives elements which pass the constant shear patch test and, although failing the constant bending moment patch test for arbitrary geometries, gives errors which are small enough to be neglected in most engineering applications.

This method has been applied to a triangular plate element and it is shown that the results obtained with this element converge (for all practical purposes) to the correct thick plate results.
The method of lines and exponential fitting
Authors: van der Houwen P. J. , Wubs F. W.
Published: August 2005

When the method of lines is used for solving time‐dependent partial differential equations, finite differences are commonly employed to obtain the semidiscrete equations. Usually, if the solution is expected to be smooth, symmetric difference formulae are chosen for approximating the spatial derivatives. These difference formulae are almost invariably based on Lagrange type differentiation formulae. However, if it is known in advance that periodic components of given frequency are dominating in the solution, more accurate difference formulae, based on exponentials with imaginary exponent, are available. This paper derives such formulae and presents numerical results which clearly indicate that the accuracy can be improved considerably by exploiting additional knowledge on the frequencies of the solution.
Transient analysis of three‐dimensional wave propagation using the boundary element method
Authors: Dohner Jeffrey L. , Shoureshi Rahmatallah , Bernhard Robert J.
Published: August 2005

In the past the time domain solution of the wave equation has been limited to simplified problems. This was due to the limitations of analytical methods and the capacity of computers to manipulate and store ‘large’ blocks of spatial information. With the advent of ‘super computers’ the ability to solve such problems has significantly increased. This paper outlines a method for transient analysis of wave propagation in arbitrary domains using a boundary element method. The technique presented will allow the definition of a domain, the input of impedance conditions on the domain's surface, the specification of inputs on the surface, and the specification of initial conditions within the domain. It will produce a complete solution of the wave equation inside the domain. The techniques are demonstrated using a program with a boundary element formulation of Kirchhoff's equation. The elements used are triangular and compatible.
A finite‐element–alternating technique for evaluating mixed mode stress intensity factors for part‐elliptical surface flaws
Authors: Simon H. L. , O'Donoghue P. E. , Atluri S. N.
Published: August 2005

An alternating method, in conjunction with the finite element method and an analytical solution for an elliptical flaw in an infinite solid, is used to determine the mixed mode stress intensity factors for surface flaws. This finite element alternating method leads to an inexpensive procedure for routine evaluation of accurate stress intensity factors in complex structural components containing surface flaws and subject to mixed‐mode loading. A variety of numerical examples is presented.
Numerical simulation of confined unsteady aerodynamical flows
Authors: Frey A. , Hall C. , Porsching T.
Published: August 2005

A system of algorithms is presented for the computer simulation of confined unsteady flows of a compressible fluid. The methods are valid for a wide range of time scales and are applied to simulate wind tunnel acoustics, flow over a ramp and flow past aircraft cavities.
A new boundary finite element method for fluid–structure interaction problems
Authors: Mariem J. Ben , Hamdi M. A.
Published: August 2005

In order to study problems on fluid–structure interaction, we have used a mixed formulation which couples the classical functional of the structure with a new variational formulation by integral equations for the fluid. This formulation has the advantage over the finite element methods of avoiding the discretization of the fluid domain. Furthermore, unlike collocation methods, the explicit calculation of the Hadamard finite part of the singular integrals is avoided. This leads after discretization by boundary finite elements to a small and symmetrical algebraic system.

Typical examples are presented that demonstrate the efficiency of this variational formulation by studying the sound transmission through a baffled plane structure and through a flexible panel backed by a rigid cavity. These include the calculation of the transmission loss factor and the determination of which modes dominate the noise transmission. Good agreement is obtained between numerical results and analytical results found in the literature.
A basis change strategy for the reduced gradient method and the optimum design of large structures
Authors: Joseph K. T.
Published: August 2005

This paper proposes a basis change strategy within the reduced gradient method for optimization under linear constraints. It ensures a non‐singular basis matrix at every iteration. The same strategy can reliably be used within the generalized reduced gradient method for optimization under non‐linear constraints. This method is applied to the minimum weight design of large structures under displacement and stress constraints, exploiting the sparsity of the constraint Jacobian matrix.
The comparative performance of some finite difference equations for transient heat conduction
Authors: Bhattacharya M. C. , Davies M. G.
Published: August 2005

The established finite difference equations to estimate one‐dimensional transient heat flow in solids are the ‘classical’ form (explicit), and the Crank–Nicolson and ‘pure‐implicit’ forms (both implicit). They are all based on finite difference approximation to the Fourier continuity equation. To these are now added three more explicit forms: exponential linear, exponential inverse cosine and polynomial, which are based on exact solutions to the Fourier equation. The performance of each of the six equations is tested against the exact results of a well known step excitations problem (the Groeber model). The tests consist of examining (i) finite difference errors arising from a single implementation of each form at different stages in the transient cooling process, (ii) the errors that accumulate during part or all of the cooling process (both as regards any bias that is introduced, and also a measure of variance) and (iii) the run times in executing the various forms. The nondimensional time step r was treated as the independent variable, and can be made arbitrarily large, by use of a simple time‐division procedure (otherwise r < ½ for use with the classical form). It is shown that having regard to both error and run time, the polynomial form appears to be the most efficient estimator.
An analysis of solidification problems by the boundary element method
Authors: Zabaras Nicholas , Mukherjee Subrata
Published: August 2005

The problem of interest in this paper is the calculation of the motion of the solid–liquid interface and the time‐dependent temperature field during solidification of a pure metal. An iterative implicit algorithm has been developed for this purpose using the boundary element method (BEM) with time‐dependent Green's functions and convolution integrals.

The BEM approach requires discretization of only the surface of the solidifying body. Thus, the numerical method closely follows the physics of the problems and is intuitively very appealing.

The formulation and the numerical scheme presented here are general and can be applied to a broad range of moving boundary problems. Emphasis is given to two‐dimensional problems. Comparison with existing semi‐analytical solutions and other numerical solutions from the literature reveals that the method is fast, accurate and without major time step limitations.
A finite element for edge‐cracked beam columns
Authors: Tharp Thomas M.
Published: August 2005

The stiffness matrix is derived for a finite element representing a beam column with rectangular cross section and a single edge crack. The element has zero length, and the standard nodal degrees of freedom associated with beam‐column elements. To illustrate its capabilities, the element is used to model propagation of multiple cracks in a self‐loaded fixed beam.
A finite element model for column‐supported shells of revolution
Authors: Han Kye J. , Tu Wen W.
Published: August 2005

A finite element model suitable for the analysis of column‐supported shells of revolution is presented. This model combines in a single analysis axisymmetric shell elements with nodal circles and column elements with nodal points. Thus, it takes advantage of the axisymmetry of the shell, while the non‐axisymmetric nature of individual columns is fully accounted for. The compatibility between the two different types of elements is achieved through the use of a co‐ordinate transformation. The accuracy of the solutions is demonstrated through numerical examples. When a shell of revolution supported on equispaced columns of the same stiffness is subjected to a harmonically varying load in the circumferential angle, it is found that the resulting displacements are associated with selective harmonic terms. An equation which precisely defines this coupling mechanism is also derived.
Self‐adaptive stress analysis based on stress convergence
Authors: Roberti Paolo , Melkanoff Michel A.
Published: August 2005

A new algorithm for self‐adaptive stress analysis is presented. The algorithm is based on h‐convergence and uses the measured stress convergence rate as an error indicator. A theoretical relation between stress convergence rate and pointwise error of stresses is derived for both the 1‐D and 2‐D case. Some examples are presented to illustrate the behaviour of the algorithm.
Equilibrium considerations of the updated Lagrangian formulation of beam‐columns with natural concepts
Authors: Gattass Marcelo , Abel John F.
Published: August 2005

Bathe and co‐workers'1,2 updated Lagrangian formulation is reviewed for a two‐dimensional beam‐column element. From this review a physical interpretation and properties are derived for the matrices of the method. A variant of Argyris and co‐workers'4,5 natural concept is introduced in the updated Lagrangian formulation, and a new method to derive element matrices arises. A detailed derivation of the matrices of the twodimensional beam‐column element is presented to clarify further the UL formulations. Explicit expressions for these matrices, computed with the use of symbolic manipulation,17 are also presented to illustrate the concepts discussed. Finally, numerical results are shown to compare and evaluate different methods and matrices.
A Legendre spectral element method for the Stefan problem
Authors: Rønquist Einar M. , Patera Anthony T.
Published: August 2005

In this paper we present a Legendre spectral element method for solution of multi‐dimensional unsteady change‐of‐phase Stefan problems. The spectral element method is a high‐order (p‐type) finite element technique, in which the computational domain is broken up into general (curved) quadrilateral macroelements, and the solution, data and geometry are expanded within each element in terms of tensor‐product Lagrangian interpolants. The discrete equations are generated by a Galerkin formulation followed by Gauss–Lobatto Legendre quadrature, for which it is shown that exponential convergence to smooth solutions is obtained as the polynomial order of fixed elements is increased. The spectral element equations are inverted by conjugate gradient iteration, in which the matrix‐vector products are calculated efficiently using tensor‐product sum‐factorization.

To solve the Stefan problem numerically, the heat equations in the liquid and solid phases are transformed to fixed domains applying an interface‐local time‐dependent immobilization transformation technique. The modified heat equations are discretized using finite differences in time, resulting at each time step in a Helmholtz equation in space that is solved using Legendre spectral element elliptic discretizations. The new interface position is then computed using a variationally consistent flux treatment along the phase boundary, and the solution is projected upon the corresponding updated mesh. The rapid convergence rate and stability of the method are discussed, and numerical results are presented for a one‐dimensional Stefan problem using both a semi‐implicit and a fully implicit time‐stepping scheme. Finally, a two‐dimensional Stefan problem with a complex phase boundary is solved using the semi‐implicit scheme.
Adaptive mesh redistribution for a boundary element (panel) method
Authors: Carey G. F. , Kennon S.
Published: August 2005

In this paper, we extend the concept of a grading function, as introduced by Carey and Dinh2 in a one‐dimensional context, to curved contours. We then apply the idea to adaptive grid redistribution for a boundary element method to solve a model boundary value problem. Numerical results are included for a potential problem to demonstrate the effect of the redistribution scheme on the solution and the geometry of the domain.
Arch dam–fluid interactions: By fem–bem and substructure concept
Authors: Tsai Chong‐Shien , Lee George C.
Published: August 2005

Arch dams can be conveniently analysed by the finite element method. For dam–fluid interaction problems, the fluid domain may be more conveniently handled by the boundary element method as a substructure first before connecting to the dam substructure. The added‐mass matrix calculated from the fluid domain is symmetrized and lumped first so that the banded and symmetrical characteristics of the finite element method are retained. In the boundary element formulation, a mirror image method and quadratic elements are used for computational efficiency and accuracy. The strong singular terms are handled by using a solution which satisfies the governing equation and the free surface boundary condition. Infinite boundary conditions at the upstream of the reservoir can be reasonably approximated from the fundamental solution with accurate results, if the interior pressure distribution in the fluid domain is neglected. Numerical solutions on hydrodynamic pressure distribution and the natural frequencies of the dam–reservoir system with various water levels are obtained and compared with available analytical and experiment results.
Generalized hybrid‐combined methods for the singularity problems of homogeneous elliptic equations
Authors: Li Z. C. , Bui T. D.
Published: August 2005

Combinations of the Ritz–Galerkin and finite element methods are applied to solving singularity problems of homogeneous, elliptic equations. The Ritz‐Galerkin method is used in the subdomains where there exist singular points; and the finite element method is still used in the rest of the solution domains. More general coupling techniques than those of Reference 6 along the common boundary of subdomains are discussed. Numerical experiments using these kinds of coupling techniques are provided for the first time. It is interesting that the calculated results of Motz's problem have shown the simplified hybrid strategy in Reference 6 to be optimal for both error bounds and stability of numerical solutions, among all general coupling techniques.
Spectral collocation methods for the primary two‐point boundary value problem in modelling viscoelastic flows
Authors: Karageorghis A. , Phillips T. N. , Davies A. R.
Published: August 2005

Expansions in terms of beam functions and Chebyshev polynomials are used to compute solutions to the primary two‐point boundary value problem within a spectral collocation formulation. The performance of the methods is analysed in terms of accuracy and robustness relative to the level of non‐linearity. Accurate results are obtained with Chebyshev polynomials and the performance of these trial functions is insensitive to the level of non‐linearity whereas the behaviour of the beam functions shows great sensitivity to the level of non‐linearity. The use of Newton's method to solve the mixed linear‐non‐linear system for the Chebyshev coefficients is successful for highly non‐linear problems without the need for parameter continuation.
Monte Carlo structural optimization in discrete variables with annealing algorithm
Authors: Elperin T.
Published: August 2005

The paper describes the basic ideas of Monte Carlo annealing algorithms for structural optimization with discrete design parameters. The algorithm generates randomly a set of design parameters, with probability depending on the objective function and given by the Boltzmann–Gibbs distribution. In this model the search for the global minimum is simulated by a relaxation process of the statistical mechanical system with the Hamiltonian proportional to the objective function. The rate of the convergence of the method and its dependence upon the annealing probability are discussed. Numerical implementation of the method for the weight optimization of the ten‐bar planar cantilever truss is presented. The results of numerical simulation are compared with those obtained by the dual methods. The principal conjecture is that the method is fairly efficient and has great potential for applicaton in engineering design.
Multi‐domain BEM for two‐dimensional problems of elastodynamics
Authors: Ahmad Shahid , Banerjee Prasanta K.
Published: August 2005

An advanced implementation of the boundary element technique for the periodic and transient dynamic analyses of two‐dimensional elastic or visco elastic solids of arbitrary shape and connectivity is presented. For transient dynamic analysis the problem is first solved in the Laplace transform space and then the time domain solutions are obtained by numerical inversion of transformed domain solutions.

The present analysis is capable of treating very large, multi‐domain problems by substructuring and satisfying the equilibrium and compatibilities at the interfaces. With the help of this substructuring capability, problems related to the layered media and soil–structure interaction can all be analysed. This paper also introduces a new type of element called ‘Enclosing Element’, which has been developed and used to model the infinitely extending boundaries of a half‐space or a layered medium. A number of numerical examples are presented, and through comparisons with available analytical and numerical results, the accuracy, stability and efficiency of the present analysis are established.
Thin plate elements with relaxed Kirchhoff constraints
Authors: Stolarski Henryk K. , Chiang Martin Y. M.
Published: August 2005

An analysis of thin plates by C0 elements is presented. The fundamental part of it is the formulation of a set of constraints that relate the rotational degrees of freedom to the translational degrees of freedom and which are weaker than the usual Kirchhoff constraints. A penalty term associated with these constraints is then introduced instead of the usual expression for the shear strain energy. It is shown that the approach is effective for both quadrilateral and triangular elements.
A three dimensional calculation of elastic equilibrium for composite materials
Authors: Lustman Liviu R. , Rose Milton E.
Published: August 2005

A compact scheme is applied to three dimensional elasticity problems for composite materials, involving simple geometries. The mathematical aspects of this approach are discussed, in particular its solution by iteration methods. A vector processor code implementing the compact scheme is presented, and several numerical experiments are summarized.
A full range analysis of reinforced concrete slabs using finite elements
Authors: May I. M. , Ganaba T. H.
Published: August 2005

This paper describes a full range analysis of reinforced concrete slabs, which includes the effects of both geometric and material non‐linearities, using the finite element method. A computer program is described which has been used to analyse slabs previously tested by a number of investigators. The comparisons between the test results and the computer program are considered to be good.
A mixed formulation of C0‐linear triangular plate/shell element—the role of edge shear constraints
Authors: Saleeb A. F. , Chang T. Y. , Yingyeunyong S.
Published: August 2005

A simple and effective linear C0‐triangular element for plates and shells is developed on the basis of the Hellinger‐Reissner mixed variational principle with independently assumed stress and displacement fields. Two main features are emphasized in this development concerning the assumed transverse shear stress field. Firstly, this assumption results in edge‐type penalty constraints in the thin plate/shell regimes. Secondly, the element is used in the form of a four‐triangle, cross‐diagonal macroelement mesh. As a result, the element is shown to be free from shear locking in thin plate/shell applications, and it satisfied all the appropriate patch tests required for Kirchhoff plate models. In addition, the element exhibits good overall convergence properties in a variety of test problems for plates and shells. Finally, from the computational standpoint, the element is very efficient since all stiffness component matrices are derived in explicit forms.
Sensitivity analysis with plate and shell finite elements
Authors: Brockman R. A. , Lung F. Y.
Published: August 2005

This paper addresses the problem of calculating sensitivity data by direct methods for isoparametric plate or shell elements. Sensitivity parameters of interest include intrinsic properties such as material modulus and plate thickness, as well as geometry variables which influence the size and shape of a structure. The sensitivity calculation therefore must consider the parametric mapping within an element, as well as the influence of geometric variables on the orientation of an element in space. The methods presented specialize directly to continuum elements, in which the co‐ordinate transformation is omitted, or to simple structural members situated arbitrarily in space. Numerical examples are presented which illustrate the accuracy of the proposed techniques, and the effect of discretization error on computed sensitivities.
A robust triangular plate bending element of the Reissner–Mindlin type
Authors: Zienkiewicz O. C. , Lefebvre D.
Published: August 2005

A new triangular plate element is presented. This new element is based on independent interpolations for slopes, displacement and shear forces, and it is shown that it does not suffer from any defect common to other Mindlin plate elements. Several examples are presented to illustrate the behaviour of this new element.
A new method for derivation of locking‐free plate bending finite elements via mixed/hybrid formulation
Authors: Gellert M.
Published: August 2005

The shear‐locking phenomenon in discrete bending analysis of Mindlin/Reissner plates is investigated. Mixed/hybrid variational principles are introduced which, unlike the rigorous displacement model, allow systematic derivation of locking‐free finite elements. This is achieved by satisfaction of an auxiliary condition, having the clear physical interpretation of shear‐force elimination on account of equilibrium. An example, using competitive techniques, demonstrates the applicability of the idea.
Curved composite boundary elements for Kirchhoff plate‐bending problems
Authors: Silva Paul J. , Mote C. D.
Published: August 2005

Composite boundary elements are formed for plate‐bending problems by attaching a circular sector to a triangle. Elements utilizing cubic and quintic interpolation are developed for convex and concave boundaries.

Smaller error and less numerical effort result when triangular elements are replaced by the composite boundary elements on clamped and most simply supported convex, boundaries. For domains with concave boundaries, greater accuracy is obtained when the quintic composite boundary element replaces the triangular element in fine mesh configurations.
A new finite‐volume approach with adaptive upwind convection
Authors: Kinney Robert B. , Mahdi Hashim S.
Published: August 2005

A new finite‐volume approach is developed and applied to the two‐dimensional continuity and convective‐diffusive energy equations. The variation of the field variables is approximated by bi‐quadratic interpolation formulae over the space occupied by the finite volume and the region surrounding it. These are used in the integral conservation laws for energy and mass. The convective transport is modelled using a new upstream‐weighting approach which uses volume averages for the energy transported across the boundaries of the finite volume. The weighting is dependent on the skewness of the velocity field to the surfaces of the finite volume as well as its strength. It is adaptive to local flow conditions. Two test cases are treated which have exact solutions. The first is not new and involves a rotating shaft. The errors are less than 0.06 per cent for this case. The second case is new and involves convection past a source and sink. In contrast to the first case, the global Peclet number is a strong parameter, and cell Peclet numbers (Peh) range from 0 to 20. The maximum error is 2.3 per cent for Peh = 4, and there is no evidence of numerical diffusion for even the largest value of Peh. For both test cases, the maximum error occurs at moderate values of Peh and diminishes at the extreme low and high values.
Buckling of multi‐lamellae compression flanges of welded I‐beams: A unilateral elasto‐plastic plate‐stability problem
Authors: Chen Zhen‐Sheng , Mang Herbert A.
Published: August 2005

Buckling of compression flanges of welded I‐beams consisting of more than one lamella is characterized by partial loss of contact between the lamella welded to the web and the neighbouring lamella. The boundaries of the contact regions of the buckling modes of the two lamellae are originally unknown. Thus, the present elasto‐plastic plate‐stability problem is coupled with a contact problem. It represents a unilateral problem because eigenforms with penetrations of lamellae are physically impossible. This problem is solved first for the elastic material domain. The Rayleigh‐Ritz method is used for determining symmetric eigenforms. A finite‐strip technique is employed for determining unsymmetric eigenforms. The solution of the unilateral elastic plate‐buckling problems serves as the starting point for the iterative solution of the corresponding elasto‐plastic plate‐stability problem. The buckling pressures obtained are compared with corresponding buckling stresses resulting from a classical design procedure disregarding the interaction of the lamellae at buckling.
A numerical study of holonomic approximations to problems in plasticity
Authors: Griffin T. B. , Reddy B. D. , Martin J. B.
Published: August 2005

The incremental holonomic boundary‐value problem in elastoplasticity has been shown to be characterized by a variational inequality. The problem may be approximated, however, by a perturbed minimization problem, characterized by a variational equality. This formulation is used as the basis for constructing finite element approximations of the original boundary‐value problem, leading to a system of non‐linear algebraic equations. Procedures for solving these equations are described and numerical results are presented and compared with those obtained using a conventional approach.
A parallel element‐by‐element solution scheme
Authors: Barragy E. , Carey Graham F.
Published: August 2005

A parallel element‐by‐element scheme is developed for finite‐element solution of elliptic boundary‐value problems. It is shown that, for a broad class of computational grids, the solution algorithm is totally parallelizable. Moreover, the conversion of an existing serial EBE code to a parallel code is seen to be quite simple. The method is implemented on the Alliant FX/8 and Sequent Balance parallel computers and ‘speedup’ performance studies are conducted for a representative elliptic PDE in two dimensions. The present procedure can be applied quite generally to other finite‐element applications, and the associated programs can be modified in a straightforward way to implement the method.
Geometry‐based fully automatic mesh generation and the delaunay triangulation
Authors: Schroeder W. J. , Shephard M. S.
Published: August 2005

One approach to fully automatic mesh generation in two and three dimensions is to generate and triangulate a set of points within and on the boundary of a geometry using the properties of the Delaunay triangulation. Because the point data generate mesh topology of greater dimension, it is necessary to insure topological compatibility and perform classification of the resulting mesh with respect to the original geometry. Necessary and sufficient conditions for classification of mesh topology on three‐dimensional planar geometry are given, as well as a discussion of the more complex case of curved geometry. This paper also presents conditions to insure topological compatibility along with techniques for identifying and resolving cases of incompatibility.
Description of some numerical tools for solving incompressible turbulent and free surface flows
Authors: Daubert O. , Hervouet J. M. , Jami A.
Published: August 2005

During the past ten years various methods have been devised to deal with the solution of the Navier–Stokes equations. In the meantime, different models have been worked out to represent turbulent incompressible flows. At LNH, deep participation in this enthusiastic research is still going on, together with a closely related development of physical modelling and metrology. In this paper, we will give an insight into a set of numerical codes which are now currently in use at our laboratory and some of their main applications to coastal engineering. This will include thermohydraulic internal flows and free surface flows. For each code a short presentation of the algorithm of solution is described.
Wind waves evaluation in the Adriatic and Mediterranean seas
Authors: Cavaleri Luigi , Bertotti Luciana , Lionello Piero
Published: August 2005

We present the results of the implementation of an advanced wave model in the Adriatic and in the Mediterranean Sea. With respect to the first and second generation models, the new approach does not accept any a priori assumption on the spectral shape of the wind waves, this being determined uniquely by the dynamical equilibrium of the various source functions. These include the generation by wind, non‐linear interactions and the dissipation due to whitecapping and to bottom friction.

The Adriatic is characterized by highly variable wind regimes. Several storms have been hindcasted, testing the model in the various possible meteorological conditions. In this paper we focus our attention on a particular storm that allowed us to verify the shallow water behaviour of the model. For the Mediterranean we concentrate on a heavy storm that occurred in February‐March 1986 in the Sicily Channel. The very good results obtained in these two highly different conditions prove the effectiveness of the physical approach to the numerical description of the wind waves evolution.
Wave plan computation method in study of the Calvi Bay erosion in Corsica, France
Authors: Lejeune A. , Lejeune M. , Sahloul M.
Published: August 2005

A study of linear monochromatic wave propagation is presented, based on a theory of potentials. The usual Berkhoff equation has been extended by the addition of partially pervious solid boundary effects and the bed friction.

The problem has been solved by a hybrid finite element method including the effect of singular local elements such as the end of breakwaters or wharfs. This numerical method confirms the interest in quadratic Lagrangian finite elements.

The comparisons with analytical solutions and existing numerical results show the validity of the method. Some original examples also prove the good performance of the proposed computation method.

As an example, the study of the erosion of the beach of Calvi Bay in Corsica, France is presented. The phenomenon had started already in 1960, but the problem began to be very severe four years ago, after the implementation of a new harbour in 1982 and buildings, hotels, restaurants, and a main sewer on the beach. To consider the impact of these constructions and other factors like waves, currents and geomorphological aspects, the studies were divided into four parts: sedimentological, currents, wave propagation and geomorphological.

This paper will describe the results of a complete two years study on the site, from February 1986 to December 1987.

Findings show that the erosion process is due to the rise of the relative sea level with, as a catalyst, tourist behaviour and the implementation of the new constructions.