bluuebunny/crossref_metadata_2025 huggingface dataset:
Numerical solutions to contact, friction and crack problems with applications
Authors: Fredriksson Billy , Torstenfelt Bo , Endahl Nils
Published: February 2008

The importance of contact and friction problems in different application areas is discussed. Methods and algorithms for numerical solutions using the finite element method are presented. Both elastic and elastic plastic materials are included as well as combination of contact and crack problems. The methods are applied to practical applications such as bolted joints, lugs and roller bearings.
Formulation of quasi‐axisymmetric boundary value problems for finite element analysis
Authors: Gens A. , Potts D.M.
Published: February 2008

In the finite element method two options are currently available for dealing with problems involving an axisymmetric geometry but in which loads, displacements or other boundary conditions do not have rotational symmetry. The first involves a full three‐dimensional solution whereas the second is to use a two‐dimensional (2D) axisymmetric formulation and to express the non‐symmetric loads/displacements as Fourier series in the circumferential direction. There are some cases, however, that, in spite of not being truly axisymmetric, it can be shown that the non‐zero components of the full strain tensor number four or less. In this paper it is shown that such problems may be solved using simple 2D finite element formulations and two alternative solution methods are presented. One of these involves a modification to the matrix relating strains to displacements and the second employs conventional 2D formulations with tied degrees of freedom. The solution procedures are applied to three examples which have some geotechnical interest, namely the behaviour of a long rigid pile under either torsional or vertical loading and the behaviour of a hollow cylinder sample subjected to torsion. In all three cases the soil is modelled by means of an elastoplastic constitutive law of the Cam‐clay type.
Eigenvalue analysis and transient response of fluid—structure interaction problems
Authors: Geradin M. , Robert G. , Huck A.
Published: February 2008

The computer implementation of a method for calculating coupled vibration eigenmodes and eigenfrequencies and the transient response of an elastic enclosure filled with a compressible fluid is described. The formalism is based on a simultaneous discretization of the fluid pressure and the fluid displacement potential. Attention is focused on the resulting form of the dynamic equilibrium equations and on their solution both in free vibration and transient analyses. In the eigenvalue analysis, an adapted Lanczos iteration scheme is proposed which takes account of the specific form of the equations. Applications are presented which demonstrate the effectiveness of the method.
Thermomechanical stress on a high‐temperature‐heat‐exchanger unit under solar‐specific operating conditions
Authors: Agatonovic Petar , Dogigli Michael
Published: February 2008

Gas‐cooled solar heat exchanger units (panels) are envisaged for installation in solar tower power plants. The thermal stresses arising in the panel in solar operation are high and are in part unique, so that design and development of this hot component has to rely on experimental studies. The present paper describes experimental studies done on a panel. For the tests a 3 MW hot‐gas test facility built primarily for the testing of hot components is used. Solar operating conditions are simulated on a panel prototype and the resulting thermal loads measured on critical panel components. Planning and optimizing of the test program as well as the evaluation of test results have been supported with finite element computing. The test results presented here show what stresses are exerted on the components by the solar‐specific operating conditions. Moreover, it is shown how rapidly changing unsteady thermal loads at high temperatures can be precisely detected and evaluated. In combination with efficient modern methods of calculation (e.g. finite element analysis) these results can be also be used to solve similar problems on other hot components.
Numerical solution of non‐premixed reactive flows in a swirl combustor model
Authors: Ramos J.I.
Published: February 2008

A mathematical model has been developed to study turbulent, confined, swirling flows under reacting non‐premixed conditions. The model solves the conservation equations of mass, momentum, energy, species, and two additional equations for the turbulent kinetic energy and the turbulent length scale. Combustion has been modelled by means of a one‐step overall chemical reaction. The numerical predictions based on the eddy‐break‐up model of turbulent combustion show a recirculation zone in the form of a one‐celled toroidal vortex at the combustor centreline. High levels of turbulence characterize the recirculation zone, whose diameter and velocity first decrease and then increase as the magnitude of the outer swirl number is first decreased from counter‐swirl to zero and then increased to co‐swirl flow conditions. Counter‐swirl produces steeper velocity gradients at the inter‐jet shear layer, promotes faster mixing and yields better combustion efficiency than co‐swirl. The numerical results are compared with those obtained under non‐reacting conditions in order to assess the influence of the heat release on the size of the recirculation zone.
A shape function routine for the constant moment triangular plate bending element
Authors: Wood R.D.
Published: February 2008

A Fortane shape function routine is presented for the constant moment triangular plate bending element. The routine also contains the shape functions for the constant inplane stress triangular element enabling it to be used for facet shell analysis. Details are included on calculation of the element stiffness matrix and equivalent nodal forces.
Pseudo 3‐D projections from isoparametric surfaces
Authors: Byrne D.J.
Published: February 2008

Graphical representations play an integral part in the interpretation of the numerical data, resulting from finite element analysis techniques. An algorithm is presented for the efficient mapping of nodal variables derived from isoparametric element formulations, onto a regular Cartesian grid. In addition, a simple and economical technique is described, for the subsequent graphical presentation of the grid values, as a pseudo 3‐dimensional projection, with hidden line removal.
Sensitivity studies in reliability‐based plastic design
Authors: Frangopol Dan M.
Published: February 2008

The paper attempts to establish the connection between structural reliability and structural optimization for the particular case of plastic structures. Along this line, the paper outlines a reliability‐based optimization approach to design plastic structures with uncertain interdependent strengths and acted on by random interdependent loads. The importance of such interdependencies, and of some of the other statistical parameters used as input data in probabilistic computations, is demonstrated by several examples of sensitivity studies on both the probability of collapse failure as well as the reliability‐based optimum solution.
An algorithm for assembly of stiffness matrices into a compacted data structure
Authors: Nour‐Omid Bahram , Taylor Robert L.
Published: February 2008

A data structure is described that stores only the non‐zero terms of the assembled stiffness matrix. This storage scheme results in considerable reduction in memory demand during the assembly phase of a finite element program. Therefore, larger matrices can be formed in the main memory of the computer. When secondary store must be used this approach reduces the I/O cost during the assembly stage. An algorithm is derived that starts with the element connectivity information and generates the compacted data structure. The element matrices are then assembled to form the stiffness matrix with this storage scheme. The assembly algorithm is described and a FORTRAN listing of the routines is presented. The reduction in storage is demonstrated with the aid of numerical examples.
Computerized generalized displacement method for finite element analysis of incompressible material
Authors: Xi‐Kui Li
Published: February 2008

A new approach to deal with the finite element analysis of incompressible material is presented. The constrained variational problem relating to the analysis of incompressible material is transformed into two unconstrained variational problems in two corresponding displacement subspaces, which are called the incompressible‐deviatoric (Sd) and the compressible‐undeviatoric (Sc) displacement subspaces respectively. The displacement and deviatoric stress, and the pressure fields, are determined by means of variations in the two subspaces respectively. As compared with some current methods, it is found that the present method is capable of solving the problem of incompressible material with v = 0.5, and that there is no problem about the existence of solution. Further, the ill‐conditioning of the global matrix can be entirely eliminated and the computational effort can be considerably reduced as well. The formulation for the finite element analysis of incompressible material with material or geometrical non‐linearity based on the subspace Sd are given in the paper. The numerical results for some examples show the advantages of the approach presented in the paper.
Analysis of steel orthotropic deck plates in the non‐elastic state under variable loads
Authors: Mańko Zbigniew
Published: February 2008

Steel orthotropic bridge deck plates have a remarkable reserve of carrying capacity which should usefully be studied further in practice. This paper shows the application of the finite strip method to the non‐elastic analysis of such plates with arbitrary cross‐sections of the longitudinal ribs (open and closed). It should be underlined that the application of this method is partly limited and approximate; however, some known advantages of this method in some cases are particularly beneficial. The constitutive equations are deduced on the basis of the Prandtl—Reuss theory of plastic flow and the von Mises criterion of flow for the elastic‐ideal plastic material. The methods of variable stiffness of initial distortion, which requires only once stating the stiffness matrix, were used. The calculations were made for two models of such plates for two different load schemes. The results obtained in this way were verified by the experimental investigations of four models of such plates on the big scale (the investigations were made in 1973) and quite good convergency of results in the studied range were obtained.
Use of inhomogeneous finite elements for the prediction of stress in rope terminations
Authors: Zhang S. , Leech C.M.
Published: February 2008

An inhomogeneous element method of solving the strain and stress distribution of a cone‐like synthetic rope termination, which is designed and manufactured to enhance the strength of end connection of the rope, is described. The 8‐node quadrilateral isoparametric axisymmetric element was used. Different material constants were specified at different Gauss sampling points, so as to simulate the non‐homogeneity of the termination. The results indicate that maximum axial stress value in strand is much larger than the element average stress value. This element proved to be useful in calculating stresses and strains in reinforcing fibre strand embedded in resin matrix. The results obtained give some insight into the non‐uniformity of the stress distribution and will be meaningful to the designer of the rope end termination.
Large CYBER 205 model of the Euler equations for vortex‐stretched turbulent flow around delta wings
Authors: Rizzi Arthur , Purcell Charles J.
Published: February 2008

The large‐scale numerical simulation of fluid flow is described as a discipline within the field of software engineering. As an example of such work, a vortex flowfield is analysed for its essential physical flow features, an appropriate mathematical description is presented (the Euler equations with an artificial viscosity model), a numerical algorithm to solve the mathematical equations is described, and the programming methodology which allows us to attain a very high degree of vectorization on the CYBER 205 is discussed. Four simulated flowfields with vorticity shed from wing edges are computed with up to as many as one million grid points and verify the realism of the simulation model. The computed solutions show all the qualitative features that are expected in these flows. The twisted cranked‐and‐cropped delta case is one where the leading‐edge vortex is highly stretched and unstable, displaying ultimately inviscid large‐scale turbulent‐like phenomena.
A new treatment of the recombination term in the current continuity equations of semi‐conductor device models
Authors: Miller John J.H.
Published: February 2008

An integral identity is derived by the method of Marchuk for the continuity equation of a carrier current in a semi‐conductor device. The coefficients of this identity are then approximated systematically. The terms involving the discretization of the carrier current turn out to be the same as those in the well known finite difference scheme of Scharfetter and Gummel, while those involving the recombination term are different. It is suggested that this new finite difference scheme will perform significantly better than the Scharfetter‐Gummel scheme especially in regions of the device where the net recombination is sharply peaked.
Finite Element Education Survey
Authors: Mair W.M. , Hodge M.H. , Creechan A.
Published: February 2008

In view of the importance of finite element (FE) techniques in the design, analysis and validation of many engineering products, the National Agency for Finite Element Methods and Standards (NAFEMS) was established in 1983 to take an overview of the FE scene in the United Kingdom. NAFEMS is currently funded by the Department of Trade and Industry, but it is expected that it will eventually be self‐funding. Its headquarters is located at the National Engineering Laboratory, East Kilbride, Glasgow.
Elasto‐viscoplastic analysis of anisotropic laminated plates and shells
Authors: Owen D.R.J. , Qiang Liu Guo
Published: February 2008

An elasto‐viscoplastic analysis of anisotropic plates and shells is undertaken by means of the finite element displacement method. A thick shell formulation accounting for shear deformation is considered and a layered approach is adopted in order to model property changes through the shell thickness. In order to avoid ‘locking’ behaviour as the shell thickness is reduced, the nine‐node Lagrangian and heterosis elements are introduced into the present model. Viscoplastic yielding is based on the Huber—Mises criterion extended by Hill for anisotropic materials. Time integration of the strain rate equations is accomplished by both explicit and implicit algorithms and special consideration is given to the evaluation of the viscoplastic strain increment for anisotropic situations. The computer code developed is demonstrated by application to a range of numerical examples.
Application of variable metric methods to structural synthesis
Authors: Vanderplaats Garret N. , Sugimoto Hiroyuki
Published: February 2008

Much recent work in numerical optimization has emphasized the use of variable metric methods which use the Lagrangian. The principal concept is to use a variable metric algorithm to create an approximation to the Lagrangian function. This is used in a quadratic programming sub‐problem to find a search direction in design space which will drive the design to the satisfaction of the Kuhn—Tucker necessary conditions for optimality. A one‐dimensional search is then performed to achieve the design improvements. Experience with this algorithm applied to structural optimization has shown it to be a powerful design tool. The implementation of this general method will be described, including several modifications for its successful application to practical design. The methods has been implemented in the new general‐purpose optimization program, ADS. It is concluded that the algorithm is both a powerful tool for structural optimization, and a good general‐purpose algorithm for other design applications.
Calibration and application of an elastic viscoplastic constitutive equation for steels in hot‐rolling conditions
Authors: Cescotto S. , Grober H.
Published: February 2008

An elastic viscoplastic constitutive equation for steels at high temperature is calibrated on a set of torsion tests performed by IRSID for different temperatures, strain rates and steel qualities. The integration of this equation in a computer code is examined and results for strip hot‐rolling are given.
Application of the FEM to elastoplastic wave propagation in metals
Authors: El‐Magd E. , Abdel‐Ghany W. , Homayun M.
Published: February 2008

Under dynamic loading shock waves propagate in metallic materials and may be concentrated after reflection from fixed boundaries. In these cases high strain rate gradients are initiated in the material, which are accompanied by a change in temperature due to the adiabatic character of high rate deformation processes. In order to estimate the mechanical behaviour of the material under multiaxial dynamic loading constitutive equations must be worked out, which have to be valid over wide ranges of strain rate and temperature. Often a viscoplastic behaviour is assumed using the equation of Perzyna:
Numerical solution to pneumatic forming problems of axisymmetric superplastic thin shells
Authors: Gavriushin S.S. , Gavriushina N.T.
Published: February 2008

A numerical method is presented for analysis of the pneumatic forming process of axisymmetric superplastic thin shells. The governing non‐linear partial differential equations are derived from membrane shell theory, using total Lagrangian description and considering a hardening creep material model. The method of lines used in the computational algorithm, involves two steps: first the Cauchy problem in time is considered, then the boundary problem is solved by finite differences. The effectiveness of the proposed algorithm is illustrated by several examples.
A 4‐node thin hybrid plate finite element
Authors: Loikkanen Matti J.
Published: February 2008

A 4‐node, 12‐d.o.f. plate bending element based on the assumed‐stress hybrid formulation is described. The nine stress fields are derived from the 12‐term, Adini—Clough polynomial and the cubic ‘beam shape functions’ are used for the boundary displacements. The element passes the patch test and is invariant to the coordinate system and the node numbering.
Structural analysis of large scale problems using a microcomputer
Authors: Brown Steven A. , Kamat Manohar P.
Published: February 2008

A successful implementation of user‐friendly large scale finite element (SNAP/FE) and boundary element (SNAP/BE) structural numerical analysis programs on an IBM PC with 256 kbyte of internal memory and two 360 kbyte disk drives is reported. The key to this adaptation was the use of split BASIC—FORTRAN operation, highly efficient compacted matrix storage schemes and equally efficient element‐by‐element (EBE) in‐core and out‐of‐core solution schemes. The effectiveness of the in‐core SNAP/FE program is demonstrated for the stress analysis of a 288 degrees of freedom space truss model and a 179 degrees of freedom plane elasticity model of a gear tooth. In principle, however, SNAP/FE has the capability to solve virtually any size problems currently employing 3‐D truss, beam, membrane or thick shell elements.
Uplifting and stability of wind‐loaded vertical cylindrical shells
Authors: Rammerstorfer F.G. , Auli W. , Fischer F.D.
Published: February 2008

The present paper deals with the numerical calculation of the behaviour of vertical wind‐loaded cylindrical shells (large liquid storage tanks) with a very flexible bottom plate resting on an elastic foundation. The base of the tank, i.e. the lower boundary of the shell and the bottom plate, may partially uplift due to the shell deformations under the dead load, a hydrostatic pressure and due to wind forces. This behaviour represents non‐linear boundary conditions of the tank wall. Hence, the stability of the wind‐loaded tank is extremely influenced by the uplift conditions. This non‐linear problem (large deformations and variable contact) is solved by the FE method.
More efficient implicit box‐lambda scheme for non‐isentropic flows
Authors: Magi Vinicio
Published: February 2008

A new implementation of the implicit lambda scheme recently proposed by other authors is provided. One‐dimensional compressible non‐isentropic flows inside four different nozzles and Fanno and Rayleigh's subsonic/ supersonic flows are computed, which demonstrate the superior efficiency and accuracy of the present formulation.
Shear‐constraints and folded‐plated structures
Authors: Crisfield M.A.
Published: February 2008

‘Shear‐constraints’ can be used to produce efficient Mindlin/Reissner or ‘discrete Kirchhoff’ bending elements. The paper shows that ‘selective shear‐constraints’ can be used to produce an effective formulation for folded‐plated structures.
Kinematics of small and large deformations of continua
Authors: Annigeri Balkrishna S. , Cassenti Brice N. , Dennis Anthony J.
Published: February 2008

The kinematics of small and large deformations (displacements, rotations and strains) is described by use of the engineering strain, the logarithmic strain, the Seth‐Hill class of strains and the rate‐type strains derived using the Lagrangian and the ‘Relative’ descriptions. The displacement gradient is computed for two and three dimensions and the error associated with use of the small rotation approximation is plotted. The components of the rotation tensor are derived for a four‐noded isoparametric quadrilateral finite element for determining the error due to small displacement and rotation approximations. Finally, the various strain measures are computed and plotted for representative problems.
Simulating curved beams via offset straight elements
Authors: Hawla D.L. , Neishlos H.
Published: February 2008

The behaviour of curved beams may be simulated via the use of straight elements with constant offset. The theoretical basis for this approach is developed and numerical examples demonstrating the effectiveness of the offset elements are presented.
Model‐size reduction technique for the analysis of symmetric anisotropic structures
Authors: Noor Ahmed K. , Peters Jeanne M.
Published: February 2008

A two‐step computational procedure is presented for reducing the size of the analysis model for an anisotropic symmetric structure to that of the corresponding orthotropic structure. The key elements of the procedure are: (a) decomposition of the stiffness matrix into the sum of an orthotropic and non‐orthotropic (anisotropic) parts; and (b) successive application of the finite element method and the classical Rayleigh—Ritz technique. The finite element method is first used to generate few global approximation vectors (or modes). Then the amplitudes of these modes are computed by using the Rayleigh—Ritz technique. The global approximation vectors are selected to be the solution corresponding to zero non‐orthotropic matrix and its various‐order derivatives with respect to an anisotropic tracing parameter (identifying the non‐orthotropic material coefficients). The size of the analysis model used in generating the global approximation vectors is identical to that of the corresponding orthotropic structure. The effectiveness of the proposed technique is demonstrated by means of numerical examples and its potential for solving other quasi‐symmetric problems is discussed.
A solution of structural random response applied to cylindrical shell in a turbulent flow
Authors: Kuželka V.
Published: February 2008

The paper deals with the basis of a method for numerical solution of structural vibration response to the effect of random fluid flow forces and describes its application to a cylindrical shell in a turbulent flow. The physical model of a cylindrical shell with supported ends is used to demonstrate the influence of modal matrix, damping and flow parameters.
An analysis of the Semiloof shell element stiffness and mass matrices
Authors: Oliveira C.A.M. , Martins R.A.F.
Published: February 2008

The Semiloof shell element stiffness and mass matrices are analysed. Various integration rules for the stiffness matrix are used, and the influence of these rules on the existence of mechanisms and on the element spectra is studied. Some methods for lumping the mass matrix are attempted with special reference to a method imposing a given behaviour of the spectra of eigenvalues.
A numerical method for the determination of the transient response of semiconductor devices
Authors: Griffin P.D. , Marques J.
Published: February 2008

In recent years, substantial research effort has been expended on the simulation of the behaviour of semiconductor devices. Since the internal behaviour of even the simplest device is highly complex, few analytical solutions of practical value exist. Consequently, particular emphasis has been placed on numerical approaches as a means to simulate, first, terminal characteristics of interest to the circuit designer, and secondly, internal device mechanisms, the primary concern of device designers and physicists.
Solution of linear equations by a profile solver
Authors: Taylor R.L.
Published: February 2008

The solution of linear algebraic equations using a profile solver is discussed and a set of subprograms written in FORTRAN 77 are presented which can be used to solve symmetric and non‐symmetric problems.
Software virtual machines for development of finite element systems
Authors: Dodds Robert H. , Lopez Leonard A.
Published: February 2008

The software virtual machine (SVM) concept is described as a methodology to reduce the manpower required to implement and maintain finite element software. A SVM provides the engineering programmer with high‐level languages to facilitate the structuring and management of data, to define and interface process modules, and to manage computer resources. A prototype finite element system has been successfully implemented using the SVM approach. Development effort is significantly reduced compared to a conventional all‐FORTRAN approach. The impact on execution efficiency of the SVM is described along with special procedures developed to minimize overhead in compute‐bound modules. Planned extensions of capabilities in the SVM used by the authors are outlined.
Data structures for finite element modelling
Authors: Servranckx D. , Mufti A.A.
Published: February 2008

The graphical representation of a finite element model (undirected graphs) imposes some constraints on the choice of storage techniques and data structures; first, the storage structure must deal efficiently with sparse matrices; second, the retrieval method of an edge, of a finite element model, around selected nodes must minimize the multiple occurrences of the same edge if plotting efficiency is to be achieved; and third, the insertion and extraction of edges in a data structure must be independent of the selected nodes identification scheme. This paper evaluates the relative merit of elementary storage methods and data structures in terms of the time and space costs required to satisfy the above constraints. The theoretical costs are derived and the experimental costs are evaluated and compared. Depending on the homogeneity of the degree of the nodes, a static data structure or a linked list data structure using listed or sectioned hashing techniques are shown to yield the minimum time and space costs.
Non‐linear vibration analysis of multilayer sandwich plates by incremental finite elements: 2. Solution techniques and examples
Authors: Iu V.P. , Cheung Y.K.
Published: February 2008

The theoretical development of the incremental finite element for non‐linear vibration of multilayer sandwich plates was presented in Part 1 and the equation of motion was established. In the second part of the paper, the solution techniques are described and a number of examples are given.
Incompressible swirling flows
Authors: Ramos J.I.
Published: February 2008

A mathematical model has been developed to study incompressible, isothermal, turbulent, confined, swirling flows. The model solves the conservation equations of mass, momentum, and two additional equations for the turbulent kinetic energy and the rate of dissipation of turbulent kinetic energy. The numerical predictions show a recirculation zone in the form of a one‐celled toroidal vortex at the combustor centreline. High levels of turbulence characterize the recirculation zone. The length, diameter and maximum velocity of the recirculation zone first decrease and then increase as the magnitude of the outer swirl number is first decreased from counter‐swirl to zero and then increased to co‐swirl flow conditions. Counter‐swirl produces steeper velocity gradients at the inter‐jet shear layer and promotes faster mixing than co‐swirl. The numerical results also indicate that the mass of the recirculation zone first decreases and then increases as the outer swirl number is first decreased from counter‐swirl to zero and then increased to co‐swirl conditions. The diameter, maximum velocity and mass of the recirculation zone are monotonically increasing functions of the inner jet swirl number. The recirculation zone length, diameter and mass are almost independent of the Reynolds number and outer‐to‐inner jet axial velocity ratio.
Improvement of stress accuracy in the hybrid finite element method
Authors: Cheng Huang Hou , Yu Zhang Jing
Published: February 2008

We describe how to improve the accuracy of stress in the application of the hybrid finite element method. The idea is based on the fact that the assumed stress hybrid method is equivalent to both the principle of minimum complementary energy within the interior of each element and the principle of the minimum potential energy in the entire domain. It is known that when a good hybrid model is used for the displacement solution, the stress model must satisfy equilibrium within individual elements and be comparable with the boundary displacements. However, the compatibility in the elements is usually ignored and through variational operation it may be only approximately satisfied. So the stress model cannot approach a corresponding analytical stress field. In the present study, after nodal displacements are solved, we propose that a different stress model could be used to find the stress coefficients according to the principle of minimum complementary energy in each element in order to get an improved stress field.
Towards effective interactive three‐dimensional colour postprocessing
Authors: Bailey Bruce C. , Hajjar Jerome F. , Abel John F.
Published: February 2008

Recommendations for the development of effective three‐dimensional, graphical colour postprocessing are made. First, the evaluation of large, complex numerical models demands that a postprocessor be highly interactive. A menu of available functions should be provided and these operations should be performed quickly so that a sense of continuity and spontaneity exists during the post‐processing session. Second, an agenda for three‐dimensional colour postprocessing is proposed. A postprocessor must be versatile with respect to application and basic algorithms must be designed so that they are flexible. A complete selection of tools is necessary to allow arbitrary specification of views, extraction of qualitative information, and access to detailed quantitative and problem information. Finally, full use of advanced display hardware is necessary if interactivity is to be maximized and effective postprocessing of today's numerical simulations is to be achieved.
Perturbation technique with characteristics in convection‐dominated flows with small diffusion and dispersion
Authors: Cekirge H.M. , Fraga R.J.
Published: February 2008

The proposed method utilizes characteristics to model convection and perturbation technique for diffusion and dispersion. Thus, each physical process is treated by a numerical scheme well suited to it. The theory is treated in three dimensions and applied to a one‐dimensional problem. The objective of the paper is the improvement of numerical techniques used in enhanced oil recovery problems which involve convection‐dominated flows with small diffusion and dispersion.
Pseudo‐corner theory: a simple enhancement of J2‐flow theory for applications involving non‐proportional loading
Authors: Hughes Thomas J.R. , Shakib Farzin
Published: February 2008

A simple modification of J2‐flow theory is made which enables it to approximately represent the reduced stiffness and increased plastic flow of corner‐theory response to non‐proportional loading. The key idea involves making the plastic modulus a function of the loading direction. A concise radial‐return type numerical algorithm is presented for the constitutive integration.
Efficient non‐linear finite element shell formulation involving large strains
Authors: Parisch Horst
Published: February 2008

A previously presented finite element shell formulation is extended to the application of large strains. The finite elements are those based on the concept of ‘the degenerated solids’, which are widely used in non‐linear finite element programs. The constitutive equation of hyperelastic incompressible material is adopted and specialized to the Mooney‐Rivlin law. The additional state variable, the hydrostatic pressure, which occurs for incompressible materials, is eliminated on element level using the plane stress condition. Attention is drawn to the efficient calculation of the element matrices by applying a layer concept. The effectiveness of the proposed total Lagrangian formulation is demonstrated in a number of example problems.
CALFEM — a program for computer‐aided learning of the finite element method
Authors: Dahlblom Ola , Peterson Anders , Petersson Hans
Published: February 2008

A computer program, CALFEM, is presented. This interactive computer program is designed as a tool for teaching of the finite element method. No programming knowledge is needed. The program is well suited to solve problems in structural mechanics and for solution of field problems. A variety of finite elements is available. One objective when designing CALFEM was that the user shall understand every part of the computational procedure. The program is based on a command language. All information is stored in user‐defined matrices created by usage of commands. Required input to matrices are given on request from the program. The contents of the matrices can be looked upon at any time and new decisions can be made in the course of the run. The user of the program determines in which way he wants to proceed with the calculation process by choosing proper commands. This means that everything in the computational procedure is under the direct control of the user. This is in contrast to many conventional ‘black box’ finite element programs. Commands can be stored on user‐defined secondary storage files. The files can be edited in CALFEM and be used further on in the calculation procedure. The program is written in FORTRAN 77 and all calculations are performed in double precision.
A microcomputer solution of Biot's two‐dimensional consolidation theory
Authors: Thomas H.R. , Liu C.H.
Published: February 2008

The implementation of the finite element solution of Biot's consolidation theory on a low‐cost microcomputer is described. A two‐dimensional linear elastic model is solved using bilinear rectangular elements and a fully implicit timestepping algorithm. The machine used is the Acorn Computers model B, BBC microcomputer, a popular low‐cost engineering applications machine. The program is written in Basic but to increase speed of computation certain sections of the solution procedure involving matrix manipulation are written in Assembly language. The results obtained are encouraging from the point of view of accuracy, problem size and computational time. It is concluded that there is scope for the use of the present generation of low‐cost microcomputer, as typified by this machine, in the numerical solution of the more straightforward, but still realistic, consolidation problems.
Design of small and effective finite element systems
Authors: Lindgren Lars‐Erik
Published: February 2008

A system consisting of a preprocessor, a finite element program and a postprocessor has been developed. Some features which make preprocessors and postprocessors user‐friendly are described. Although microcomputers become more advanced it is still important that the finite element programs are fast and that they need small central memory. Programming details which accomplish this are also described. A Fortran program is appended which can assist the programmer who wants to implement the described routines for fast calculating of the shape functions and their derivatives.
Finite element analyses of secondary flow problems
Authors: Medwell J.O. , Gethin T.D. , Taylor C. , Rance J.
Published: February 2008

A method is presented for the determination of secondary flow fields in three practical examples. In one, the flow is laminar and the other two turbulent. The latter were analysed using a one‐equation or two‐equation model of turbulence in conjunction with the equations of motion. Methods of improving the boundary condition for secondary flow prediction by introducing a ‘slip’ condition at near wall locations are referred to, and its effect demonstrated. Finally, a fluid film of extremely high aspect ratio and in laminar motion was investigated and the existence of recirculatory flow pockets predicted.
Computing angular velocity in multibody systems
Authors: Huston Ronald L.
Published: February 2008

This paper presents algorithms for computing the angular velocities of the bodies of a multibody system. A multibody system is any collection of connected bodies. The focus is upon multibody systems consisting of spherically pinned rigid bodies which do not form closed loops. Simple formulae are presented for computing the angular velocities. It is shown that once the angular velocities are known the entire kinematical description and hence, the dynamics of the system, may be developed routinely and in automated fashion. Extension to more general multibody systems follows without conceptual change in the procedures.
Numerical experiment with inviscid vortex‐stretched flow around a cranked Delta wing: supersonic speed
Authors: Rizzi Arthur , Purcell Charles J.
Published: February 2008

A numerical method that solves the Euler equations for compressible flow is used to study vortex stretching. The particular case simulated is supersonic flow M∞=1.2 α=10 degrees around the twisted and cambered cranked‐and‐cropped TKF delta wing of MBB. This geometry induces multiple leading‐edge vortices in a straining velocity field that brings about flow instabilities but the result is a state of statistical equilibrium. The discretization contains over 600,000 cells and offers sufficient degrees of freedom in the solution to resolve the small‐scale unstable modes that lead to disordered vortex flow.
Preconditioned conjugate gradient method for the non‐linear finite element analysis with particular reference to 3D reinforced concrete structures
Authors: Cervera M. , Liu Y.C. , Hinton E.
Published: February 2008

A hierarchically preconditioned conjugate gradient (PCG) method for finite element analysis is presented. Its use is demonstrated for the difficult problem of the non‐linear analysis of 3D reinforced concrete structures. Examples highlight the dramatic savings in computer storage and more modest savings in solution times obtained using PCG especially for large problems.
Non‐linear finite element modelling of concrete structures: basic analysis, phenomenological insight, and design implications
Authors: Kotsovos Michael D. , Pavlović Milija N.
Published: February 2008

A non‐linear finite element program for concrete structures is outlined, with emphasis on the material modelling. It is shown that the package can be used with confidence in the analysis of practical structural forms. In addition, there is considerable potential for the application of the program to research and design.
Numerical modelling of glass forming processes
Authors: Cesar de Sa J.M.A.
Published: February 2008

Application of the finite element method to the simulation of glass forming processes is described. The forming process results in a coupled thermal/mechanical problem with interaction between the heat transfer analysis of the temperature distribution in the glass and the viscous flow formulation describing the deformation of molten glass being a dominant factor. Particular attention must be given to derivation of the appropriate non‐linear thermal boundary conditions and also to monitoring of the mechanical contact between the glass and mould. The technique described provides both the glass and temperature distribution at each instant of the forming process and thus can provide invaluable information for mould and plunger design, optimum operation times, etc. Numerical examples are provided for both wide neck and narrow neck press and blow forming processes and the results obtained compare well with commercial observations.
A four node Marguerre element for non‐linear shell analysis
Authors: Jetteur Philippe , Frey François
Published: February 2008

A non‐linear shallow thin shell element is described. The element is a curved quadrilateral one with corner nodes only. At each node, six degrees of freedom (i.e. three translations and three rotations) make the element easy to connect to space beams, stiffeners or intersecting shells. The curvature is dealt with by Marguerre's theory. Membrane bending coupling is present at the element level and improves the element behaviour, especially in non‐linear analysis. The element converges to the deep shell solution. The sixth degree of freedom is a true one, which can be assimilated to the in‐plane rotation. The present paper describes how overstiffness due to membrane locking on the one hand and to the sixth degree of freedom on the other hand can be corrected without making use of numerical adjusted factors. The behaviour of this new element is analysed in linear and non‐linear static and dynamic tests.
A simple efficient algorithm for elasto‐plastic plate bending
Authors: Kwon Y.W. , Akin J.E.
Published: February 2008

A simple efficient algorithm is presented for an elasto‐plastic analysis of plate bending problems. The element is a mixed isoparametric plate element which includes three moment components as unknown variables at each node. This element is very simple to use and gives quite accurate solutions. Moreover, the presented algorithm makes a great contribution to reduction of the computing time.
Colour graphics with three‐dimensional finite element meshes
Authors: Stelzer J.F.
Published: February 2008

The application of colour for an improved presentation of 3‐D structures with finite elements is reported. Also shown is how the hidden‐surface technique can be used for: (1) generating pictures in the hidden line alike mode, (2) generating photo‐alike pictures by shading the surfaces according to Lambert's cosine law, (3) showing the regions of different materials or properties by distinct colouring, (4) the presentation of temperature and stress fields by colouring. This colouring is done with smooth colour transitions and delivers pictures similar to those gained by thermography or stress optics. Furthermore, (5) it is possible to generate contour lines on the remaining visible surfaces. The problems arising with the attachment of a colour hardcopier are also considered.
Modal superposition dynamic analysis on concurrent multiprocessors
Authors: Farhat Charbel , Wilson Edward
Published: February 2008

Computational algorithms for finite element dynamic analysis of large‐scale structural problems that exploit both concurrent and parallel features of multiple instruction multiple data streams computers are presented. A new computer program architecture is used in which large finite element domains are automatically divided into subdomains. The number of subdomains generated is equal to the number of available processors. The spatial solution is obtained using a basis of orthogonal vectors. The temporal solution is computed exactly. Discussion is focused on the concurrent generation of global Ritz vectors. Examples run on a hypercube multiprocessor confirm the potential of the proposed scheme.
A class of flux‐splitting explicit second‐order finite difference schemes and application to inviscid gas dynamic equations
Authors: Billet G.
Published: February 2008

A class of flux‐splitting explicit second‐order finite difference schemes is set up. An ‘optimal’ scheme is defined for 1‐D flows and applied to 2‐D flows with CFL being able to reach 2. The results obtained show that this ‘optimal’ scheme is well adapted to the unsteady flows.
Materially non‐linear analysis of body contact using a finite element method
Authors: Kwon Y.W. , Akin J.E.
Published: February 2008

A new algorithm to solve contact body problems is presented. The contact boundaries are divided into finite elements, and contact element matrices and vectors are computed using a modified variational principle. The contact conditions are incorporated into the total functional using the Lagrange multiplier method. This algorithm considers surface contacts rather than point contacts, and computes contact tractions directly. The Coulomb friction law is used as the friction condition. A transformation matrix based on static equilibrium is developed to solve extensive sliding problems. This algorithm is extended to the elasto‐plastic analysis and several example problems are presented to demonstrate the algorithm.
Structural analysis in quasi‐static elasto‐viscoplasticity
Authors: Benallal A.
Published: February 2008

Complex constitutive equations including non‐linear kinematic as well as isotropic hardening rules are introduced in the framework of the finite element method to analyse the behaviour of structures in quasi‐static elasto‐viscoplasticity under cyclic loadings. An implicit time marching process is developed together with a substructuring technique and the corresponding numerical details are underlined. Practical examples are treated to demonstrate the capabilities of the proposed finite element code.
Prediction of the flow, reaction and heat transfer in an oxy‐fuel glass furnace
Authors: Carvalho M.G.M.S. , Durão D.F.G. , Pereira J.C.F.
Published: February 2008

A three‐dimensional computer simulation of a combustion chamber used in the glass production industry is presented. A numerical solution technique is used to solve the governing time‐averaged partial differential equation and the physical modelling for turbulence, combustion and thermal radiation. A two‐equation turbulence model is employed along with a combustion model based on a fast kinetics statistical approach. A radiation model is used along with the Hottel mixed grey gas model. To solve the governing differential equations an implicit technique of finite‐difference kind is applied. The economy of the computations is very considerably enhanced by the separate calculation of the burner and bulk glass combustion chamber regions, in a manner which takes account of the differing physical nature of their flows. The burner outlet region is calculated with an axisymmetric model. Such two‐dimensional calculations allowed a good resolution of the burner outlet, and provide the inlet conditions for the three‐dimensional calculations of the glass furnace. The prediction procedure is applied to an industrial glass furnace, which operates with oxy‐fuel conditions. Measurements of mean gas temperature and concentrations were performed at different locations in the furnace. The calculated flame length, temperature field and concentrations are with satisfactory agreement with the measured ones.
Numerical analysis of dynamic quasi‐bifurcation
Authors: Kleiber M. , Kotula W. , Saran M.
Published: February 2008

A simple finite element approach to problems of dynamic structural instability under step loading is discussed. The method proposed is believed to yield important information about the structural behaviour in the non‐linear range. Incorporation of the method into existing finite element codes is straightforward.