bluuebunny/crossref_metadata_2025 huggingface dataset:
An efficient quadrilateral element for plate bending analysis
Authors: Saleeb A. F. , Chang T. Y.
Published: August 2005

A simple, shear flexible, quadrilateral plate element is developed based on the Hellinger/Reissner mixed variational principle with independently assumed displacement and stress fields. The crucial point of the selection of appropriate stress parameters is emphasized in the formulation. For this purpose, a set of guidelines is formulated based on the following considerations: (i) suppression of all kinematic deformation modes, (ii) the element has a favourable value for the constraint index in the thin plate limit, (iii) element properties are frame‐invariant. For computer implementation the components of the element stiffness matrix are evaluated analytically using the symbolic manipulation package MACSYMA. The effectiveness and practical usefulness of the proposed element are demonstrated by the numerical results of a variety of problems involving thin and moderately thick plates under different loading and support conditions.
Multi‐objective optimization of fuzzy structural systems
Authors: Rao S. S.
Published: August 2005

It is recognized that there exists a vast amount of fuzzy information in both the objective and constraint functions of the optimum design of structures. Since most practical structural design problems involve several, often conflicting, objectives to be considered, a multi‐objective fuzzy programming method is outlined in this work. The fuzzy constraints define a fuzzy feasible domain in the design space and each of the fuzzy objective functions defines the optimum solution by a fuzzy set of points. A method of solving a fuzzy multi‐objective structural optimization problem using ordinary single‐objective programming techniques is presented. The computational approach is illustrated with two numerical examples.
Stability convergence and accuracy of the DuFort and Frankel difference diagram approximating a class of non‐linear parabolic field equations
Authors: Wiak Sławomir
Published: August 2005

The paper presents a method of calculation for the transient electromagnetic field in a steel rotor screen of a superconducting generator. Using the difference method, the spatial–temporal distributions of the electromagnetic field have been calculated as a result of solving the non‐linear partial differential equation for the vector potential A (in space Ω(r, θ,t)). For the difference diagram the conditions of stability and convergence have been determined.
Residual flow procedure for sea water intrusion in unconfined aquifers
Authors: Sugio S. , Desai C. S.
Published: August 2005

A simplified procedure is presented for the analysis of sea water intrusion in unconfined aquifers. It involves the finite element method with a residual flow procedure which combines transformation of the salt water zone into the fresh water zone that has the same pressure distribution as that of the salt water. This procedure avoids simultaneous solutions of governing differential equations for both flow and mass transport. Numerical results are compared with laboratory observations.
Finite element analysis of quasi‐prismatic bodies using Chebyshev polynomials
Authors: Vijayakar Sandeep M. , Busby Henry R. , Houser Donald R.
Published: August 2005

A new kind of finite element is presented in this paper which is designed to work efficiently for bodies that are either prismatic or ‘quasi‐prismatic’ in shape. Quasi‐prismatic shapes are those which can be obtained from prismatic shapes by mere distortion. The element which is formulated in this paper may be coupled with other types of three‐dimensional elements to allow the modelling of structures which are only partially prismatic or which have prismatic shapes within them. The element allows for a variety of boundary conditions, yet yields meshes which are easy to generate. The performance of this element is evaluated by numerical experiments that compare its results with analytical solutions for a thick cylinder problem and a curved beam problem. The element has also been demonstrated on a turbine blade model.
A plane hybrid element with rotational d.o.f. and adjustable stiffness
Authors: Cook Robert D.
Published: August 2005

A simple formulation of a nine d.o.f plane triangle is achieved by the assumed‐stress hybrid approach. The element has two translations and the rotation about a normal to the plane as d.o.f. at each node. Performance of the element is shown to be good. A device for softening overly‐stiff elements is found to be effective and is suggested as a widely applicable method of improving the behaviour of hybrid elements. A particularly simple form of the element, herein called the CST Hybrid, appears to be the best performer.
An integral equation method for the solution of 3‐dimensional, non‐linear, magnetostatic problems
Authors: Loines Janet , Bernal Michael J. M.
Published: August 2005

A finite element method for computing the resultant magnetic field arising from a given source field in the presence of a magnetic material of variable permeability is described; in this method finite element approximations to the scalar potential of the resulting field and the magnetic susceptibility, in the region occupied by the magnetic material, are determined from the non‐linear integral equation for the scalar potential and the constitutive susceptibility relation, using a collocation scheme.

The method is used to compute the shielding effect of a thin rectangular plate of variable permeability on a given source field. The plate is subdivided uniformly into brick elements; the resulting translational invariance of the integrals required in the calculations is exploited to achieve major computational savings.

A consequence of the thinness of the plate is that the calculation of the requisite integrals by analytic methods leads to considerable loss of accuracy by differencing; this difficulty is overcome by using a scheme which combines both analytic and quadrature techniques.

The resulting system of non‐linear algebraic equations is solved by Powell's hybrid method; an efficient scheme for calculating an initial approximation to the Jacobian, which utilizes the structure of the equations, is presented.

The results of the calculations are discussed.
Application of the finite element–difference method to vibration problems
Authors: Huang Xianrui , Cook Robert D.
Published: August 2005

The so‐called finite element–difference method introduced in References 1 and 2 yields a continuous stress field by finite difference operations and finite element interpolations. In the present paper, applications of the method to vibration problems are discussed. The inverse iteration procedure is modified for this method. Numerical results show that the accuracy of solutions depends strongly on the type of finite difference operator chosen: for reliable and accurate solutions in modal analysis problems, element internal strains must be included in the strain field used to compute nodal forces associated with element deformations.
Discrete Green functions for layered strata
Authors: Lin Hong‐Tsung , Tassoulas John L.
Published: August 2005

A finite‐element discretization of a layered stratum is considered. The response to a time‐harmonic load at a single node is calculated. For all practical purposes, the result is obtained in closed form in the case of two dimensions (line load) while the Fast Fourier Transform is employed in the three‐dimensional problem (point load).
Notes on the stability of non‐rectangular space–time finite elements
Authors: Bajer Czesław I.
Published: August 2005

The method of space–time finite elements enables the simple solution of quite new problems. It is possible to assume the arbitrary partition of the structure area in each moment of integration of the motion equation. Instability is caused by a too large time step and too great changes of joint locations in successive time steps. A changeable spatial partition is useful in contact dynamic problems, in the case of a travelling support, generally in problems with movable edges. In this paper a stability problem is described and some investigations for chosen types of non‐rectangular space–time finite elements are carried out. Linear and surface elements which in time space gain an additional time dimension are presented. Some numerical examples prove the efficiency of the described method under determined limitations.
Finite elements in CFD: What lies ahead
Authors: Löhner R.
Published: August 2005

The current state of the art of Finite Element Methods in Computational Fluid Dynamics is reviewed. The aim of this review is to point out what appear currently as the main shortcomings of Finite Element Methods, so as to concentrate the efforts to remove them. The analysis of flows using Finite Elements will only be successful if all steps involved in it are optimized. Therefore, I deem it necessary to describe explicit and implicit flow solvers, unstructured multigrid methods, adaptive refinement schemes, grid generation and graphics in 3‐D, the effective use of supercomputer hardware and memory, as well as the combination of structured and unstructured grids.
A new finite element concurrent computer program architecture
Authors: Farhat Charbel , Wilson Edward
Published: August 2005

A new computer program architecture for the solution of finite elemet systems using concurrent processing is presented. The basic approach involves the automatic splitting of an arbitrary spatial domain. Processors are dynamically re‐assigned during the several phases of an analysis. Direct and iterative solution strategies are considered. Computational algorithms for finite element dynamic analysis of large‐scale structural problems that exploit concurrent features of MIMD computers are implemented in modules around the basic architecture. Also, problems with localized non‐linearities are treated. A first implementation on a 32‐processor hypercube achieves efficiency rates of up to 90 per cent.
Calculation of fracture mechanics parameters for an arbitrary three‐dimensional crack, by the ‘equivalent domain integral’ method
Authors: Nikishkov G. P. , Atluri S. N.
Published: August 2005

In this paper, an equivalent domain integral (EDI) method and the attendant numerical algorithms are presented for the computation of a near‐crack‐tip field parameter, the vector Jϵ‐integral, and its variation along the front of an arbitrary three‐dimensional crack in a structural component. Account is taken of possible non‐elastic strains present in the structure; in this case the near‐tip Jϵ‐values may be significantly different from the far‐field values Jf, especially under non‐proportional loading.
Analyses of steady‐state visco‐elastic fluids using the penalty function method
Authors: Shiojima Takeo , Shimazaki Yoji
Published: August 2005

The application of the penalty‐function formulation of the finite element method is made possible for analysing visco‐elastic fluid flows by the method which decouples the momentum and continuity equations from the constitutive equation. An upwind finite element scheme is combined with the method in order to solve the constitutive equation. As visco‐elastic fluid models, Jaumann derivative, upper and lower convected derivatives are considered. The Poiseuille flow and the flow through a plane converging channel are analysed.
Three‐dimensional finite element analysis of open‐die forging
Authors: Shiau Y. C. , Kobayashi S.
Published: August 2005

Three‐dimensional finite element analysis is applied to operation sequences in open‐die forging. Flat tools with rounded edges for open‐die forging are geometrically modelled using Bézier curves. With this technique, the problems at the die‐workpiece interface, such as the integration of frictional stress, node touching on dies and node separating from dies, can be handled effectively. It is shown that in solving general symmetric problems computation time can be saved by reducing variables and rearranging them in the stiffness matrix. One‐bite operations and operation sequences for producing two‐size bars and two‐size pipes in several bites are investigated in regard to geometry, load, energy and deformation distribution.
The structure of constitutive equations for finite deformation of elastic–plastic materials involving strain‐induced anisotropy with applications
Authors: Lee E. H. , Agah‐Tehrani A.
Published: August 2005

Constitutive relations based on finite‐deformation‐valid analysis require the formulation of coupling effects that were not needed in earlier developments which included small deformation restrictions. However, the feasibility to introduce such coupling effects mathematically requires that the new terms introduced must be in accord with physically based concepts of the phenomena involved. An example came to light in which objectivity of a constitutive relation, considered to be generalized for finite deformation applications involving strain‐induced plastic anisotropy, had been achieved by use of the Jaumann derivative in place of the material derivative for the growth of a tensor variable which expressed the anisotropic characteristics. The spin terms thus added to the infinitesimal displacement analogue were not in accord with a physically based assessment of the underlying micro‐mechanical phenomena and in fact led to the prediction of anomalous stress response. This paper comprises comments on the subsequent development of the theory, including a tensor equation for the evolution of the anisotropy. By solving a sample test problem with different initial conditions both the numerical implementation of the constitutive relation and the response according to the proposed growth law of the anisotropy are described and discussed.
Finite element computation of bulging in continuously cast steel with a viscoplastic model
Authors: Dalin J. B. , Chenot J. L.
Published: August 2005

The bulging of continuously cast steel between the support rolls has been computed using a viscoplastic finite element model. Both two‐dimensional and three‐dimensional models are based on the minimization of the functional associated with the Norton–Hoff law and use the streamlines integration to calculate the bulging. By using industrial data, the influence of both numerical parameters and process parameters on the extent of the calculated bulging values has been investigated. The comparison of our results with experimental measurements confirms the relevance of the hypothesis of viscoplastic behaviour.
Transient analysis of forging operations by the pseudo‐concentration method
Authors: Thompson Erik , Smelser R. E.
Published: August 2005

The pseudo‐concentration method is used to follow the flow of metal during the transient analysis of an axisymmetric forging problem. The technique requires a minimum of user interaction and appears to be ideal for computer aided design of dies. An analysis of an engine disc blocker die is presented and compared with experimental results. The same problem is analysed using a Newtonian fluid which is shown to give good qualitative results which would be acceptable in the initial stages of die design.
Plastic and viscoplastic flow of void‐containing metals. Applications to axisymmetric sheet forming problems
Authors: Oñate E. , Kleiber M. , De Saracibar C. Agelet
Published: August 2005

A formal analogy between the equations of pure plastic and viscoplastic flow theory for void‐containing metals and those of standard non‐linear elasticity is presented. The formulation is particularized for the analysis of axisymmetric sheet metal forming problems using simple two node linear finite elements. Details of the treatment of friction and strain hardening phenomena, time increment computation and elastic effects are also given. Examples of the effect of void porosity on the hemispherical stretching of a circular sheet are presented.
A finite element simulation of the sheet metal forming process
Authors: Nakamachi Eiji
Published: August 2005

A finite element simulation code of the sheet metal forming process has been developed. This simulation code plays an important role in the computer aided engineering (CAE) system for an automobile parts forming process, which includes the pre‐ and post‐processes. The paper presents the development of an updated Lagrangian type finite element modelling, based on the elastic–plastic (J2 flow law) membrane shell theory. An attempt is made to calculate the strain distribution incurred by peripherally clamped or non‐clamped square plates when impressed by rigid punches. These are the cases of square box‐shape punch drawing and arbitrary shaped panel stretch forming.
Computation of low‐speed compressible flows with time‐marching procedures
Authors: Merkle Charles L. , Choi Yun‐Ho
Published: August 2005

The extension of time‐marching procedures to low Mach number and low Reynolds number conditions is considered. It is shown that the disparate speeds of the acoustic and particle waves prevent convergence at high Reynolds numbers, while the requirement that both the Courant and the von Neumann numbers be of order one prevents convergence in very viscous flows. A perturbation expansion is used to introduce pseudo‐acoustic waves that propagate at speeds similar to the particle speed at high Reynolds numbers and that allows both the inviscid and viscous time step parameters to be of order one at low Reynolds numbers. The resulting algorithm is shown to give convergence rates that are independent of either Mach number or Reynolds number over a range of five orders of magnitude in both parameters. Results are shown for strong heat addition in low‐speed flow encompassing this broad range of variables.
Finite element analysis of turbulent forced convection in lid‐driven rectangular cavities
Authors: Nonino C. , Del Giudice S.
Published: August 2005

Turbulent fluid flow and heat transfer in lid‐driven rectangular cavities are analysed by a finite element procedure for the prediction of the turbulent forced convection in two‐dimensional recirculating flows. The (k–ε) model is used to compute effective viscosities and thermal conductivities. The fluid flow and turbulence model parabolic equations are solved sequentially, one after the other. Then, the calculated velocity distribution is used in the solution of the steady state energy equation to yield the temperature field. Aspect ratios e=0·75, 1·0 and 1·5 and Reynolds numbers ranging from 5 × 104 to 4 × 105 are considered in the numerical examples.
Buoyant flow calculations with non‐orthogonal curvilinear co‐ordinates for vertical and horizontal parallelepiped enclosures
Authors: Yang H. Q. , Yang K. T. , Lloyd J. R.
Published: August 2005

A control‐volume‐based finite‐difference formulation is developed for heat transfer and fluid flow in arbitrary three‐dimensional parallelepiped enclosures. The governing equations in Cartesian co‐ordinates are first transformed to those in non‐orthogonal curvilinear co‐ordinates by tensor transformations. After introducing the properties of the parallelepiped geometry, equations are obtained in the primitive variables for which all vectors and tensors are based on the curvilinear co‐ordinates. With proper treatment of the heat flux and stress tensor terms, the finite‐difference equations, analogous to those in the Cartesian coordinates, are formed. Examples are utilized to show the validity of the methodology and the results are found to compare well with existing experimental data. The differences in heat transfer and fluid flow inside parallelepiped enclosures and rectangular enclosures are delineated and discussed from a physical point of view.
Coarse‐fine mesh method for heat and mass transfer in locally complex flows
Authors: Kotake Susumu , Kodama Takeshi
Published: August 2005

Combined forced and free convective flows having locally complicated geometries or boundary conditions were numerically studied with a finite difference method of coarse and fine meshes. The coarse‐and‐fine mesh method developed can be used for numerical calculations of both unsteady and steady processes of heat and mass transfer in convective and diffusion flows which are strongly influenced by locally fine flows. The method was applied to a numerical calculation of the steady flow field of a CVD (chemical vapour deposition) reactor which has locally complicated flows caused by small inlet nozzles. The results of the calculation showed a considerable contribution of locally fine flows to the overall flow field, which is well predicted with the present method.
Ignition phase transition of a polymer: Convective exposure
Authors: Durbetaki P. , Phuoc T. X.
Published: August 2005

The ignition of a semi‐infinite solid polymer under convective exposure is investigated. A quasi‐steady approximation is used for the gas phase and the transient effect is accounted for in the solid phase only. Both surface and gas phase chemical reactions are included simultaneously. The ignition mechanism is studied in terms of the concurrent heat transfer, mass transfer, mass transfer and chemical processes at the surface as well as in the gas phase. The gas phase governing equations are integrated independently from the solid phase energy equation using the Adams‐Moulton subroutine. Corrections to the iterative procedure are carried out by establishing a set of perturbation equations and using the Newton‐Raphson and least‐squares methods. The results indicate that ignition occurs in the heterogeneous mode within a narrow range of low flow velocities and high temperatures. An ignition phase transition point exists, and within a wide range of high flow velocities, ignition switches to the homogeneous mode.
Non‐linear simulation of dendritic solidification of an undercooled melt
Authors: Sullivan John M. , Lynch Daniel R.
Published: August 2005

Two‐dimensional finite element simulations of solidification for quiescent undercooled pure metals are presented. The full non‐linear, transient heat equation is used with phase front tracking which is subject to local curvature and interfacial kinetics. During early stages of the waveform instability the simulated solutions match the linear stability analysis with fidelity. Beyond the valid range of that analysis the numerical solution continues to demonstrate the physically observed exponential growth behaviour and characteristic spacing between fingers. Whereas the simulations show the sensitivity of dendritic growth to initial conditions, as expected for an unstable process, the overall pattern formation preserves the characteristic spacing. The simulations are terminated after the onset of bifurcation. Thereafter, the numerical model is inappropriate for physical comparison owing to the planar, two‐dimensional limitation.
Transfinite element methodology for non‐liner/linear transient thermal modelling/analysis: Progress and recent advances
Authors: Tamma Kumar K. , Railkar Sudhir B.
Published: August 2005

Recent progress and advances in the development and applicability of a novel ‘transfinite element’ computational methodology is presented for general non‐linear/linear transient thermal problems. The proposed methodology and concepts are new and unique, and demonstrate the applicability to general transient non‐linear/linear thermal analysis situations by combining classical Galerkin schemes and transform approaches with contemporary finite element methods to preserve the modelling versatility and numerical features–thereby, a hybrid computational methodology is proposed. Characteristic features and pertinent details of the approach are described for non‐linear/linear transient thermal problems, wherein non‐linearities due temperature dependence of thermophysical properties and/or general non‐linear bound ary conditions to include radiation, effects due to phase change, etc., are considered. In addition, the use of high‐continuity formulations in conjuction with the proposed methodology to furnish accurate temperature distributions and temperature gradients making use of a relatively smaller number of degrees of freedom is also demonstrated. Numerical test cases are presented for a variety of problems to demonstrate the fundamental features and applicability of the proposed formulations. The proposed hybrid transfinite element methodology and concepts offer significant potential for extension to several areas of mathematical physics and engineering and to interdisciplinary research areas.
Monte Carlo method for radiative heat transfer analysis of general gas‐particle enclosures
Authors: Taniguchi Hiroshi , Yang Wen‐Jei , Kudo Kazuhiko , Hayasaka Hiroshi , Fukuchi Takeru , Nakamachi Ichiro
Published: August 2005

A new Monte Carlo method is developed to analyse multi‐dimensional radiative heat transfer in an enclosure containing grey gas with anisotropically scattering grey particles. One set of variables, called READ (Radiative Energy Absorption Distribution), is introduced to represent radiative transfer, thus appreciably reducing repeated computations required by the conventional Monte Carlo technique. A 1 m × 1 m square duct is used as the enclosure with the upper and lower walls at different temperatures in the one‐dimensional case and with adiabatic specular or diffuse side walls in the two‐dimensional case. Results agree well with the existing analytical solutions for one‐dimensional, non‐scattering cases. It is concluded that, with anisotropic scattering, an increase in the absorption coefficient and/or single scattering albedo produces adverse effects on radiative heat transfer. Anisotropic scattering effects cannot be simulated by the use of the effective absorption coefficient.
Some novel techniques for the finite element analysis of heat and mass transfer problems
Authors: Lewis R. W. , Sze W. K. , Huang H. C.
Published: August 2005

The coupled heat and mass transfer partial differential equations as derived by Luikov are used to analyse freezing problems in porous media. A numerical model is subsequently developed to depict the frost heave mechanism in a freezing soil system. An example is given of the application of the model and the results are compared with those achieved from field experiments.

Also, a novel application of the coincident node technique is presented for the coupled heat and mass transfer problem. This circumvents the numerical problems usually associated with flow through thin layers, in this case a vapour barrier, sandwiched between materials of greater thickness.
Theoretical basis of the finite element iterative method for the eigenvalue problem in stationary cracks
Authors: Barsoum Roshdy S.
Published: August 2005

In a recently published paper a finite element based iterative method was introduced for the solution of the eigenvalue problem of stationary cracks.1 In this paper we give the theoretical basis of this iterative method and we show why it converges and how it could be extended to more complex fracture problems. The cases of cracks at interfaces are illustrated.
Numerical analysis of a generalized plane ‘elastica’ with non‐linear material behaviour
Authors: Coulter Brett A. , Miller Robert E.
Published: August 2005

This article presents a numerical procedure for the analysis of a planar, continuous, flexible member. Large displacements and rotations, non‐linear material behaviour and general cross sections are admitted. A shooting method is utilized along with Newton‐type iteration for improved estimates. The resulting computer program is used to compare with numerical and analytical solutions of problems solved by others, and to present the solution to a problem which brings out very clearly the effects of both geometric and material non‐linearities.
Multi‐grid solutions to the elastic plastic torsion problem in multiply connected domains
Authors: Hoppe Ronald H. W.
Published: August 2005

The elastic plastic torsion problem for an elastic, perfectly plastic cylinder with multiply connected cross section twisted around its longitudinal axis is formulated as an obstacle problem for an associated stress potential, the obstacle being defined in terms of a generalized distance function. Based upon the reformulation of the obstacle problem as an equivalent linear complementarity problem, the latter is discretized by means of finite difference techniques, and a monotonically convergent iterative scheme for its numerical solution is developed. At each step of the iteration the solution of a reduced system of discrete Poisson equations is required which is done by applying multi‐grid techniques with respect to a hierarchy of grid‐point sets. Combined with a suitably chosen nested iteration process this results in a computationally very efficient algorithm for the approximate solution of the elastic plastic torsion problem.
Spectral Galerkin methods for the primary two‐point boundary value problem in modelling viscoelastic flows
Authors: Davies A. R. , Karageorghis A. , Phillips T. N.
Published: August 2005

The essential character of the primary elliptic‐hyperbolic operator encountered in the modelling of viscoelastic flows is encaptured in a non‐linear fifth‐order two‐point boundary value problem in one dimension. 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 Galerkin formulation. An investigation of the performance of the methods with respect to the level of non‐linearity is carried out. Accurate results are obtained with Chebyshev polynomials for high levels of non‐linearity, whereas the behaviour of beam function expansions proves far more sensitive to the level of non‐linearity.
Application of spline strip method to analyse vibration of open cylindrical shells
Authors: Mizusawa Tomisaku
Published: August 2005

This paper deals with the vibration of open cylindrical shells by the spline strip method based on Novozhilov's shell theory. Convergence of the solutions is investigated in a few examples and is found to be satisfactory. The accuracy of the results is compared with those calculated by other numerical methods and found to be in good agreement.

The effect of inlcuded angles and inplane constraints on vibrating characteristics of simply supported cylindrical shells is shown.
Isoparametric hybrid hexahedral elements for three dimensional stress analysis
Authors: Cheung Y. K. , Wanji Chen
Published: August 2005

Based on a new functional in which displacements, strains and stresses are taken as independent variables, a set of three 8‐node hexahedral hybrid elements QS11‐1, QS11‐2 and QS11‐3 is developed. The adoption of separated stress and displacement variables proves to be effective in improving the accuracy of the elements.

The new elements are all capable of yielding converging results, and they all possess the properties of having no zero energy deformation modes and of being co‐ordinate invariant. From the numerical example of a beam under bending it is concluded that exact solutions can be obtained for right prism elements, while good results are still attainable for severely distorted elements.

The relationship between the new hybrid elements and the conventional displacement elements is also explored in this paper.
Perspective projection of non‐convex polyhedra
Authors: Lo S. H.
Published: August 2005

An algorithm is presented for removing hidden lines for isometric and perspective projections of three‐dimensional objects. An object can be regarded as being made up of a number of planes, and the whole picture can therefore be visualized as only a collection of planes. Considering planes as the basic element of a picture, non‐convex polyhedra can be displayed directly without prior subdivisions into convex ones. Lines connecting nodal points are first retrieved from the model to be plotted by a simple but efficient technique. On the picture planes, each unique line is examined in turn to see if it is totally or partially hidden. The intersections between a unique line and a projected plane (with or without openings) are determined by a new method which, even in the presence of numerical errors, will always give correct intersection information. Unlike many classical algorithms, intersections are determined by a single formula without tedious case subdivisions. With little additional calculations, object penetrations can also be tackled.
Boundary integral equation method for shape optimization of elastic structures
Authors: Choi Joo Ho , Kwak Byung Man
Published: August 2005

A general method for shape design sensitivity analysis as applied to plane elasticity problems is developed with a direct boundary integral equation formulation, using the material derivative concept and adjoint variable method. The problem formulation is very general and a complete consideration is given to describing the boundary variation by including the tangential component of the velocity field. The method is then applied to obtain the sensitivity formula for a general stress constraint imposed over a small part of the boundary. The accuracy of the design sensitivity analysis is studied with a fillet and an elastic ring design problem. Among the several numerical implementations tested, the second order boundary elements with a cubic spline representation of the moving boundary have shown the best accuracy. A smooth characteristic function is found to be better than a plateau function for localization of the stress constraint. Optimal shapes for the two problems are presented to show numerical applications.
A third‐order semi‐implicit finite difference method for solving the one‐dimensional convection‐diffusion equation
Authors: Noye B. J. , Tan H. H.
Published: August 2005

A third‐order semi‐implicit five‐point finite difference method is developed to solve the one‐dimensional convection‐diffusion equation, using the ‘weighted’ modified equation method. It is shown to have a large stability region, to be very accurate and computationally fast.
The Almansi method of fundamental solutions for solving biharmonic problems
Authors: Karageorghis Andreas , Fairweather Graeme
Published: August 2005

A new fundamental solutions method for the numerical solution of two‐dimensional biharmonic problems is described. In this method, which is based on the Almansi representation of a biharmonic function in the plane, the approximate solution is expressed in terms of fundamental solutions of Laplace's equation, and is determined by a least squares fit of the boundary conditions. The results of numerical experiments which demonstrate the efficacy of the method are presented.
On some path‐related measures for nonlinear structural F. E. problems
Authors: Eriksson Anders
Published: August 2005

In the paper, the solution of a non‐linear structural mechanical problem is seen as a set of points along a curve in the displacement space, resulting from a continuous variation of a load parameter. The state of the structure at a specified point on the path is described by a tangent vector describing the response to a small load factor increment. For a completed, finite step, the deviation from this tangent response is described by a suggested measure. From this measure, some conclusions can be drawn concerning the iteration behaviour, guiding the iteration strategy in coming steps. Two path‐related stiffness measures are derived, giving information concerning the behaviour of the structure. Some conclusions concerning limit load points, bifurcations, etc. can be drawn from these measures.
Non‐local yield limit degradation
Authors: Bažant Zdeněk. P. , Lin Feng‐Bao
Published: August 2005

Presented is a new type of a non‐local continuum model which avoids problems of convergence at mesh refinement and spurious mesh sensitivity in a softening continuum characterized by degradation of the yield limit. The key idea, which has recently been proposed in a general context and has already been applied to softening damage due to stiffness degradation, is to apply the non‐local concept only to those parameters which cause the degradation while keeping the definition of the strains local. Compared to the previously advanced fully non‐local continuum formulation, the new approach has the advantage that the stresses are subjected to the standard differential equations of equilibrium and standard boundary or interface conditions. The new formulation exhibits no zero‐energy periodic modes, imbrication of finite elements is unnecessary and finite elements with standard continuity requirements are sufficient. Two‐dimensional finite element solutions with up to 3248 degrees of freedom are presented to document convergence and efficacy. The formulation is applied to tunnel excavation in a soil stabilized by cement grouting, with the objective of preventing cave‐in (burst) of the tunnel sides due to compression softening.
A solid‐shell transition element for geometrically non‐linear analysis of laminated composite structures
Authors: Liao C. L. , Reddy J. N. , Engelstad S. P.
Published: August 2005

Using the incremental equations of motion of a continuous medium and the total Lagrangian description, three different elements, i.e. degenerated shell element, 3‐D continuum element and solid‐shell transition element, are developed for the geometrically non‐linear analysis of laminated composite structures. Compatibility and completeness requirements are stressed in modelling shell‐type structures in order to assure the convergence of the finite element analysis. A number of laminated plate and shell examples are presented to demonstrate the validity and efficiency of various elements.
A least squares finite element formulation for elastodynamic problems
Authors: Pratap Rudra , Kundu Tribikram
Published: August 2005

A residual finite element formulation is developed in this paper to solve elastodynamic problems in which body wave potentials are primary unknowns. The formulation is based on minimizing the square of the residuals of governing equations as well as all boundary conditions. Since the boundary conditions in terms of wave potentials are neither Dirichlet nor Neumann type it is difficult to construct a functional to satisfy all governing equations and boundary conditions following the variational principle designed for conventional finite element formulation. That is why the least squares technique is sought. All boundary conditions are included in the functional expression so that the satisfaction of any boundary condition does not become a requirement of the trial functions, but they should satisfy some continuity conditions across the interelement boundary to guarantee proper convergence. In this paper it is demonstrated that the technique works well for elastodynamic problems; however, it is equally applicable to any other field problem.
A nine node finite element for analysis of geometrically non‐linear shells
Authors: Rhiu J. J. , Lee S. W.
Published: August 2005

A nine node finite element is presented for the analysis of thin shell structures undergoing large deflection. The finite element formulation is based on the concept of degenerate solid shell element and the Hellinger‐Reissner principle with independent strain. Three versions of assumed independent strain are selected to suppress spurious kinematic modes. One version leads to a finite element model which is kinematically stable at element level while the other two give globally stable models. Numerical tests indicate that the finite element model which is stable at element level may reveal the locking effect in certain cases. However, the other two models are free of locking.
Finite element approximations of singular parabolic problems
Authors: Paolini M. , Sacchi G. , Verdi C.
Published: August 2005

An efficient implementation of finite element methods for free boundary parabolic problems in general two dimensional space domains is presented. The Stefan problem, the Hele‐Shaw problem and the porous medium equation are included. Backward differences or linearization techniques are used for the time discretization of the problem. The performances of these schemes are discussed with several numerical tests.
Formulations in rates and increments for elastic‐plastic analysis
Authors: Feijoo R. A. , Zouain N.
Published: August 2005

Minimum principles in velocities, stress rates and plastic strain rates are extended in order to derive formulations for finite increments of displacement, stress and plastic strain fields defining complete numerical methods. Kinematical, statical and mixed principles are developed from a new variational formulation of the elastic‐plastic work‐hardening constitutive relation.

The consequences of this time discretization are discussed independently of any discretization of the continuum. In particular, the incremental formulations derived from extended rate principles account for local elastic unloading and produce stress field approximations complying with equilibrium and plastic admissibility without any additional procedure, at least for piecewise linear yield functions. These properties are not fulfilled when the incremental analysis is based on direct discrete versions of classical rate principles.

Finally, FEM approximations are formally introduced and the solution of the resulting finite dimensional quadratic optimization problem is considered.
A simple discrete element method for the initial postbuckling of elastic structures
Authors: El‐Naschie M. S. , Wu C. W. , Wifi A. S.
Published: August 2005

In this paper a discrete element matrix formulation for the analysis of linear and non‐linear bifurcation problems of some elastic structures is introduced. This, combined with a discrete perturbation technique, is implemented into a computer code to solve buckling and initial postbuckling problems of elastic struts.
A new BEM formulation for tow‐ and three‐dimensional elastoplasticity using particular integras
Authors: Henry Donald P. , Banerjee Prasanta K.
Published: August 2005

New two‐ and three‐dimensional boundary element formulations are developed for elastoplastic stress analysis. These new procedures differ from previous work in that volume integration is not required to incorporate the non‐linear effects in the analysis. Instead, initial stess rates are introduced in the boundary element system via particular integrals.

The present formulation is implemented in a general purpose, multi‐region system, and examples are presented to demonstrate the accuracy and versatility of the method.
Non‐smooth multisurface plasticity and viscoplasticity. Loading/unloading conditions and numerical algorithms
Authors: Simo J. C. , Kennedy J. G. , Govindjee S.
Published: August 2005

Rate‐independent plasticity and viscoplasticity in which the boundary of the elastic domain is defined by an arbitrary number of yield surfaces intersecting in a non‐smooth fashion are considered in detail. It is shown that the standard Kuhn‐Tucker optimality conditions lead to the only computationally useful characterization of plastic loading. On the computational side, an unconditionally convergent return mapping algorithm is developed which places no restrictions (aside from convexity) on the functional forms of the yield condition, flow rule and hardening law. The proposed general purpose procedure is amenable to exact linearization leading to a closed‐form expression of the so‐called consistent (algorithmic) tangent moduli. For viscoplasticity, a closed‐form algorithm is developed based on the rate‐independent solution. The methodology is applied to structural elements in which the elastic domain possesses a non‐smooth boundary. Numerical simulations are presented that illustrate the excellent performance of the algorithm.
A finite element model for the analysis of flexibly connected steel frames
Authors: Poggi Carlo
Published: August 2005

A finite element model for the non‐linear analysis of flexibly connected steel frames is proposed. The element is regarded as an assemblage of individual parts whose behaviour is described in terms of generalized stresses and strains. Displacements and plastic strain fields are independently modelled. The former are a function of 13 nodal parameters and constitute a typical application of a hierarchical procedure. The latter are modelled over the cross section, along the element and in the six springs located at the ends of the beam. Examples to show the importance of considering the non‐linear behaviour of the connections in the frame analysis are proposed.
Geometric stiffness of thin‐walled open section beams using a semiloof beam formulation
Authors: Mottershead John E.
Published: August 2005

A geometric stiffness formulation is presented for thin‐walled open section beams using semiloof elements. The validity of the formulation is confirmed by performing torsional and lateral initial stability (buckling) analyses of beams. Results are compared with classical solutions.
Three‐dimensional boundary‐element computation of potential flow in fractured rock
Authors: Medina Daniel E. , Liggett James A.
Published: August 2005

The use of the boundary‐element method (BEM) for three‐dimensional potential flow problems is described herein. The specific application for which the program is designed is the flow in fractured porous media. There are several enhancements to the usual boundary‐element calculations. The method uses linear elements to approximate better the boundary conditions and the solution on the surfaces as compared to constant elements; accurate integration over high‐aspect‐ratio triangles is achieved by computing all the integrals in closed form, as opposed to numerical cubature or mixed exact‐numerical integration schemes; and the zoning for inhomogeneous regions uses an efficient method which reduces the size of the problem and avoids difficulties with singularities.
Geometric and material non‐linear analysis of beam‐columns and frames using the minimum residual displacement method
Authors: Chan Siu Lai
Published: August 2005

A geometric and material non‐linear analysis procedure for framed structures is presented, using a solution algorithm of minimizing the residual displacements. This new non‐linear solution technique is believed to be the optimum in the Newton–Raphson scheme since it follows the shortest path to achieve convergence. The concept of the effective tangent stiffness matrix is introduced and is found to be efficient, simple and logical in handling the non‐linear analysis of frames with braced members and in separating multiple bifurcation points.
A fully implicit splitting method for accurate tidal computations
Authors: Wilders P. , van Stijn Th. L. , Stelling G. S. , Fokkema G. A.
Published: August 2005

Often industrial codes for the numerical integration of the 2D shallow water equations are based on an Alternating Direction Implicit method. However, for large time steps these codes suffer from inaccuracies when dealing with a complex geometry or bathymetry. This reduces the performance considerably. In this paper a new method is presented in which these inaccuracies are absent, even for large time steps. The method is a fully implicit time integration method. In order to obtain linear systems that can be solved efficiently, we introduce a time splitting method. The resulting linear systems are solved iteratively by using the preconditioned Conjugate Gradients Squared method.
A finite element method for elasto‐plastic structures and contact problems by parametric quadratic programming
Authors: Wanxie Zhong , Suming Sun
Published: August 2005

In this paper, the stiffness matrix of a contact element is introduced by means of a penalty function expression of the contact pressure and frictional force. The contact condition and the flow rule are expressed by the same form as in a non‐associated plastic flow problem. A unified PQP (Parametric Quadratic Programming) model related to contact problems as well as to elasto‐plastic structures is constructed. A series of PQP formulae for contact problems and elastic‐plastic structures is derived in the text, and some numerical examples are illustrated as well.