bluuebunny/crossref_metadata_2025 huggingface dataset:
A generalized mixed time integration program for structural dynamics
Authors: Coyette J.P.
Published: February 2008

The numerical treatment of coupled field interaction problems frequently uses mixed time integration methods. These methods permit different time integration methods (implicit, explicit) and/or different timesteps to be used simultaneously in different parts of the mesh. This paper summarizes the various mixed time integration methods and provides a unified presentation. Computer implementation of the generalized scheme is provided through a 1D linear structural dynamics program (GEMIX). Two common examples illustrate the use of GEMIX program.
Influence of shear deformation in a composite equilibrium element for the analysis of thin plates
Authors: Maunder E.A.W.
Published: February 2008

A composite triangular equilibrium element for modelling thin plate behaviour is investigated when shear deformation, according to Reissner's theory, is included in addition to bending deformation. The element flexibility matrix is formed as the sum of two component matrices containing the contributions from piecewise linear moment fields and piecewise constant shear fields separately. Properties of the shear component matrix, including its rank, are determined, and the influence of load basis on the pattern of this matrix is studied. The way these properties affect the condition of a flexibility matrix is investigated when the element size/thickness ratio varies, and particularly when this ratio tends towards zero. Load bases are suggested which could avoid certain problems of ill‐conditioning. Condition parameters are evaluated for an equilateral element. Finally, the application of kinematic boundary conditions to the equilibrium is considered.
CRE method of element testing and the Jacobian shape parameters
Authors: Robinson John
Published: February 2008

A general method of element testing is presented. The method applies to any shape of element with any number of nodes. The shape parameters for a quadrilateral are shown to be contained within the Jacobian matrix and it is also shown that the determinant of this matrix can be expressed in terms of the shape parameters.
Static analysis of contained fluids with potential‐based and displacement‐based fluid finite elements
Authors: Olson Lorraine
Published: February 2008

We compare potential‐based (ø‐U‐P0) and displacement‐based finite element methods for static analysis of contained fluids. A general transient formulation may be specialized to static analysis in both cases. In the potential‐based method velocity potentials (ø) and a single pressure (P0) variable are the unknowns in the fluid region. Displacements are the unknowns in the fluid for displacement‐based methods. Higher‐order displace‐ment‐based elements may produce singular matrices for some static analyses, restricting us to four‐node elements for reliability. While both methods can yield excellent results when compared with experimental data, potential‐based methods appear to have computational advantages over displacement‐based methods.
New triangular finite element for plates and shells
Authors: Abu‐Farsakh Ghazi
Published: February 2008

A new triangular shell finite element ‘TNTE.1’ (Ten Node Triangular Element, Model 1) is presented. The formulation is based on Sanders' theory which involves the inclusion of the normal rotation Φn in the bending‐strain relations only. The element displacement functions are complete cubic polynomials for inplane displacements u and v. For out‐of‐plane displacement w, three new singular rational shape functions were added at the element corners. Thus a conforming triangular element with twenty seven degrees‐of‐freedom is obtained after eliminating the internal displacements by static condensation. The formulation of this element is new in that an integration technique is developed and applied to the element stiffness matrix and load vector. This technique is based on performing all the necessary integrations externally (i.e. outside the main computer program) and then modifying the formulation of the element matrices to account for this change. Hence, such a method allows the inclusion of higher‐order integration rules without any loss of economy, due to computer time, in the main program. Results using this element showed good agreement with other finite element and closed form solutions.
Non‐linear analysis of symmetric structures with unsymmetric boundary conditions
Authors: Noor Ahmed K. , Whitworth Sandra L.
Published: February 2008

Two efficient computational procedures are presented for generating the global approximation vectors used in conjunction with the reduction methods for the large‐deflection non‐linear analysis of symmetric structures with unsymmetric boundary conditions. Both procedures are based on restructuring the governing equations for each of the unsymmetric global approximation vectors to delineate the different contributions to the symmetric and antisymmetric components of this vector. In the first procedure the unsymmetric global approximation vectors are approximated by linear combinations of symmetric and antisymmetric modes, which are generated by using the finite element method. The amplitudes of these modes are computed by using the classical Rayleigh‐Ritz technique. The second procedure is based on using a preconditioned conjugate gradient (PCG) technique for generating the global approximation vectors, and selecting the preconditioning matrix to be the matrix associated with the symmetric response. In both procedures the size of the analysis model used in generating the global approximation vectors is identical to that of the corresponding structure with symmetric boundary conditions. The similarities between the two procedures are identified, and their effectiveness is demonstrated by means of two numerical examples of large‐deflection, non‐linear static problems of shells.
Model‐size reduction for the non‐linear dynamic analysis of quasi‐symmetric structures
Authors: Noor Ahmed K. , Peters Jeanne M.
Published: February 2008

A computational procedure is presented for the efficient non‐linear dynamic analysis of quasi‐symmetric structures. The procedure is based on approximating the unsymmetric response vectors, at each time step, by a linear combination of symmetric and antisymmetric vectors, each obtained using approximately half the degrees of freedom of the original model. A mixed formulation is used with the fundamental unknowns consisting of the internal forces (stress resultants), generalized displacements and velocity components. The spatial discretization is done by using the finite element method, and the governing semi‐discrete finite element equations are cast in the form of first‐order non‐linear ordinary differential equations. The temporal integration is performed by using implicit multistep integration operators. The resulting non‐linear algebraic equations, at each time step, are solved by using iterative techniques. The three key elements of the proposed procedure are: (a) use of mixed finite element models with independent shape functions for the stress resultants, generalized displacements, and velocity components and with the stress resultants allowed to be discontinuous at interelement boundaries; (b) operator splitting, or restructuring of the governing discrete equations of the structure to delineate the contributions to the symmetric and antisymmetric vectors constituting the response; and (c) use of a two‐level iterative process (with nested iteration loops) to generate the symmetric and antisymmetric components of the response vectors at each time step. The top‐ and bottom‐level iterations (outer and inner iterative loops) are performed by using the Newton—Raphson and the preconditioned conjugate gradient (PCG) techniques, respectively. The effectiveness of the proposed strategy is demonstrated by means of a numerical example and the potential of the strategy for solving more complex non‐linear problems is discussed.
Numerical solution of the elastohydrodynamic problem in soft reciprocating seals
Authors: Strozzi Antonio
Published: February 2008

A class of exact solutions to the elastohydrodynamic problem to be used as test cases is presented. A numerical solution to the elastohydrodynamic problem according to the Petrov—Galerkin method is developed. The appearance of spurious numerical undulations in the film profile is examined. A comparison between analytical and numerical results is employed to determine which numerical schemes limit the outcome of numerical oscillations without compromising the solution accuracy.
A solution algorithm for the finite element analysis of creep problems
Authors: Marais N.J. , Martin J.B.
Published: February 2008

A solution algorithm for the transient analysis of bodies undergoing creep under constant or time varying loads is presented. The constitutive equation adopted is of the form: έc=γσm. The finite element formulation is carried out in terms of displacements and creep strains as internal variables. The time discretization is achieved with a trapezoidal time integration scheme. The creep strains are condensed out to give an equation for displacement increments involving a modified stiffness matrix and force vector. A Newton—Raphson iterative scheme is used for the non‐linear creep strain rate‐stress relation, and creep strains are updated at the end of the time step. The algorithm has been implemented in NOSTRUM for two‐dimensional structural and plane continuum problems, with a von Mises type potential function governing the multiaxial creep constitutive relationship. Numerical results are presented.
An improved subroutine for the estimation of torsional properties of thin walled open cross‐sections
Authors: Coyette J.P.
Published: February 2008

This paper suggests some improvements to the computer‐aided estimation of the torsional properties of open cross‐sections as presented in a previous paper. The complete listing is given herein.
Application of computational plasticity to the analysis of vehicle cab frames
Authors: Kearns Christopher F.
Published: February 2008

The application of computational plasticity to the very practical engineering problem of crash‐worthiness of vehicle safety cab frames during impact and rollover incidents is described. The resulting behaviour of these structures cannot be determined solely by strict elastic analyses as plastic behaviour is intrinsic to the problem. The importance of predicting the deformations of the cab structure under extreme loadings lies in a consideration for the safety of its occupants. Physical testing is extremely valuable here but is costly and time‐consuming. The role of the computer is thus evident in producing rapid estimates of cab collapse modes, loadings and deformations. Three main causes of non‐linearity are identified in the behaviour of ductile framed structures under static loading, i.e. the effects of plasticity in the structural material, the effects of axial forces and the effects of large displacements of the structure under load. The paper describes and compares two computer programs which have been used to model the behaviour of vehicle cab frames when subjected to roof crush loading in a static test. Both programs employ non‐linear beam finite elements to model the behaviour of a framed structure. One program runs in an iterative fashion while the other runs in an incremental fashion.
Re‐analysis procedure based on the mixed formulation
Authors: Noor Ahmed K. , Peters Jeanne M.
Published: February 2008

A simple and efficient re‐analysis procedure is presented for large‐scale structural systems. The procedure is based on using a mixed formulation with the fundamental unknowns consisting of both stress and displacement parameters. The other key elements of the procedure are: (a) lumping of the large number of design variables into a single tracing parameter; (b) operator splitting or additive decomposition of the different arrays in the finite element equations of the modified structure into the corresponding arrays of the original structure plus correction terms; and (c) application of a reduction method through the successive use of the finite element method and the classical Bubnov‐Galerkin technique. The finite element method is first used to generate a few approximation vectors (or modes). Then the amplitudes of these modes are computed by using the Bubnov—Galerkin technique. The re‐analysis procedure is applied to the linear static and free vibration problems of plate and shell structures. Changes in both the sizing and shape (configuration) design variables are considered. The high accuracy of the proposed technique, for sizable changes in the design variables, is demonstrated by means of numerical examples of composite plates and shells.
Rate form of the equation of state for thermalhydraulic systems: numerical considerations
Authors: Garland W.J. , Sollychin R.
Published: February 2008

In conjunction with the usual rate forms of the conservation equations, the time derivative form of the equation of state is investigated from a numerical consideration point of view. First, the derivation of the rate form of the equation of state is presented. Systematic comparison between the new method and the traditional iterative method is made by applying the method to a simple flow problem. The comparison is then extended to a practical engineering problem requiring accurate prediction of pressure. The rate method is found to be more advantageous in many aspects. It is more intuitive for system analysis, more appropriate for eigenvalue extraction, as well as easier to program and to implement. Numerically, the rate method is found to be more efficient and accurate than the traditional method.
A velocity approach to finite element calculation of elastoplastic and viscoplastic deformation processes
Authors: Chenot J.L.
Published: February 2008

The constitutive equations for the deformation of elastoplastic, viscoplastic or compressible materials are presented for the small strain approximation and for the large strain theory of Hill. A velocity approach is proposed for time discretization, which leads to a second order approximation for small strain, and an incrementally objective second order approximation for large deformation processes. Two other quasi second order formulations are discussed. The finite element space discretization is outlined and the solution procedure is described.
Semi‐loof shell, plate and beam elements—new computer versions: Part 1. Elements formulation
Authors: Martins R.A.F. , Oliveira C.A.M.
Published: February 2008

The semi‐loof element is probably one of the most efficient for the solution of thin shells of arbitrary geometry. It was originally published by Irons and since then it has been the object of much research with respect to its philosophy and performance in various structural situations.
A viscoplastic model for soft rock
Authors: Reed M.B.
Published: February 2008

The aim of the model is to represent the main features of soft or brittle rock strata, using a small number of physically‐meaningful material parameters. The yield surface is based on either the Mohr—Coulomb or Hoek—Brown criterion, and a simple small‐dilation flow rule allows the implicit algorithm of elasto‐viscoplasticity to be used. Elastic—brittle plastic behaviour is modelled, resulting in stress discontinuities across the interface between intact and failed rock. The effects of lamination and jointing are taken into account. Results are presented for a tunnelling problem with axial symmetry.
Comparison of four finite element solutions of self‐adjoint and non‐self‐adjoint problems governed by differential equations with predominant lower order derivatives
Authors: Kanarachos A.E. , Spentzas C.N.
Published: February 2008

Considering typical self‐adjoint and non‐self‐adjoint problems that are governed by differential equations with predominant lower order derivatives, a comparison is presented of their finite element solutions by Ritz, Galerkin, least square (LSQ) and discrete least square (DLSQ) methods.
Multi‐variable finite element algorithm based on the generalized Galerkin method
Authors: Zhang J.Y. , Hsu T.R.
Published: February 2008

A multi‐variable finite element algorithm based on the generalized Galerkin method is presented. This algorithm takes advantages from the hybrid finite element method and the quasi‐conforming element method. Therefore, it has more flexibility and makes the hybrid and quasi‐conforming concepts easily applied to various physical problems. The formulation of a hybrid quadrilateral finite element with a unified singularity for both thermal and stress analyses has been derived using this algorithm. Some numerical examples are included to illustrate advantages of the hybrid algorithm in both stress and thermal analyses. It is also convenient to employ the algorithm in finite displacement problems.
A simple method for the calculation of postcritical branches
Authors: Wagner W. , Wriggers P.
Published: February 2008

The practical behaviour of problems exhibiting bifurcation with secondary branches cannot be studied in general by using standard path‐following methods such as arc‐length schemes. Special algorithms have to be employed for the detection of bifurcation and limit points and furthermore for branch‐switching. Simple methods for this purpose are given by inspection of the determinant of the tangent stiffness matrix or the calculation of the current stiffness parameter. Near stability points, the associated eigenvalue problem has to be solved in order to calculate the number of existing branches. The associated eigenvectors are used for a perturbation of the solution at bifurcation points. This perturbation is performed by adding the scaled eigenvector to the deformed configuration in an appropriate way. Several examples of beam and shell problems show the performance of the method.
An isoparametric eccentrically stiffened plate bending element
Authors: Thompson P.A. , Bettess P. , Caldwell J.B.
Published: February 2008

An 8 noded, eccentrically stiffened, plate bending element is introduced. The formulation allows for any number of stiffeners arbitrarily orientated within a plate element without disturbing their individual properties and positions. This is a distinct improvement over conventional lumped stiffener modelling and equivalent orthotropic plate theory and considerably simplifies the modelling of stiffened structures. A technique is also presented which transforms stiffener positions defined in the global cartesian system to the local, isoparametric coordinates of the plate element which contains the given stiffener. Several examples are given which demonstrate the usefulness of the element.
Hybrid transfinite element modelling/analysis of non‐linear heat conduction problems involving phase change
Authors: Tamma Kumar K. , Railkar Sudhir B.
Published: February 2008

The present paper describes the applicability of hybrid transfinite element modelling/analysis formulations for non‐linear heat conduction problems involving phase change. The methodology is based on application of transform approaches and classical Galerkin schemes with finite element formulations to maintain the modelling versatility and numerical features for computational analysis. In addition, in conjunction with the above, the effects due to latent heat are modelled using enthalpy formulations to enable a physically realistic approximation to be effectively dealt computationally for materials exhibiting phase change within a narrow band of temperatures. Pertinent details of the approach and computational scheme adapted are described in technical detail. Numerical test cases of comparative nature are presented to demonstrate the applicability of the proposed formulations for numerical modelling/analysis of non‐linear heat conduction problems involving phase change.
Free vibration analysis of plates, bridges and axisymmetric shells using a thick finite strip method
Authors: Suárez B. , Miquel Canet J. , Oñate E.
Published: February 2008

A unified approach for the vibration analysis of curved or straight prismatic plates and bridges and axisymmetric shells using a finite strip method based in Reissner—Mindlin shell theory is presented. Details of obtaining all relevant strip matrices and vectors are given. It is also shown how the use of the simple linear two node strip with reduced integration leads to direct explicit forms of all relevant matrices. Examples of application which show the accuracy of the linear strip for free vibration analysis of structures are presented.
Contact analysis of large numbers of interacting bodies using discrete modal methods for simulating material failure on the microscopic scale
Authors: Williams John R.
Published: February 2008

There has been interest recently in analysing soil, ceramic powders and other materials on the microscopic level so that macroscopic phenomena, such as failure, can be related to microscopic properties. The discrete element method provides a numerical tool for conducting such analyses. Here the basic theory behind the method is reviewed and various formulations derived from a finite element basis. The automatic detection of contact surfaces between bodies is a major problem in analysing the interaction of numerous bodies, common to both finite elements and discrete elements. Various approaches to geometric contact detection and the need for efficient algorithms and data structures utilizing recent developments in the field of computer graphics and solid modelling are discussed. Examples are given of the collapse of a soil embankment, penetration of a projectile into a soil and the large deformation of a space structure.
Dynamic elastic‐plastic behaviour of a frame
Authors: Messmer Stefan , Sayir Mahir
Published: February 2008

The full time response of a space frame under impact loading perpendicular to the frame plane is discussed. Theoretical solutions and experimental results are presented and compared. A space frame clamped at its two ends is loaded by a 0.22 lead bullet that hits a mass in the middle of the transversal beam of the frame. The loading time is about 40 to 60 ?sec and the impact impulses in experiment from 0.5 to 1 Ns. The time response of this frame can be divided into four phases where different physical effects are dominant: (a) the ‘loading’ phase where elastic wave motion dominates the time response. Because of the high impact impulses, plastic deformation occurs in the vicinity of the mass and must be included in a theoretical model. The influence of reflections at the corners on the time response is shown; (b) the ‘evolution’ phase. Within this phase, a plastic collapse mechanism develops. Most of this phase is dominated by elastic deformation but local plastic deformations beside the mass are also present. Because many reflections at the corners and the clampings occur within this phase, a modal analysis method is used to predict time histories; (c) the ‘plastic’ phase with plastic zones at the clampings. This phase sets in after the bending wave reaches the clampings. It is characterized by plastic deformation near the clampings and elastic deformation of the other parts of the frame. We used a modal analysis including plastic ‘modes’ to get accurate results; (d) the ‘elastic vibration’ phase.
Exact closed‐form solution of the return mapping algorithm in plane stress elasto‐viscoplasticity
Authors: Simo J.C. , Govindjee S.
Published: February 2008

In Simo and Taylor, the classical radial return algorithm of Wilkins and Krieg and Key for plane strain and three‐dimensional J2‐flow theory, is extended to the case of plane stress. In three dimensions (or plane strain), enforcement of the discrete consistency condition reduces to a simple radial scaling of the trial stress onto the yield surface; i.e., the return map is radial. In plane stress, on the other hand, the return map, that restores the trial stress back to the yield surface, is constrained to remain in the plane stress subspace, and thus no longer reduces to a simple radial scaling. The determination of the final stress point from the trial stress now involves the solution by Newton's method of a non‐linear scalar equation, referred to as the discrete consistency equation in what follows, that yields the discrete consistency parameter λn+>0. The requirement that λn+>1 be positive is a direct consequence of the discrete Kuhn‐Tucker optimality conditions.
Microcomputer prediction of temperatures in the cooling of chipped hot rolled asphalt wearing course during laying
Authors: Hunter Robert N. , McGuire George R.
Published: February 2008

Bituminous pavement materials have low viscosity at elevated temperatures. This allows effective compaction during the laying process. In laying unchipped materials compaction is necessary to densify the mix whereas in laying chipped materials compaction is necessary to embed the chippings and also densify the matrix. Since wearing courses are normally 40 mm thick the time available for these aims to be met is limited. This time period is a function of the hot‐mix and underlying material properties and ambient parameters prevailing when it is laid.
An approach to sheet metal forming using discretization techniques
Authors: Belingardi G. , Calderale P.M. , Cozzari G. , Zingariello F.
Published: February 2008

The automotive industry is very interested in sheet metal forming simulation using numerical techniques such as the finite element method. A cooperative research program between the Stamping Division of FIAT Auto and the Mechanics Department of the Politecnico di Torino was established with the aim of exploring the present possibilities of these techniques. This paper deals with the simulation of the deep forming of an axisymmetrical component, the axisymmetry being characterized by a double curvature profile, and is considered to be the first feasibility study. A sheet was modelled by fournode axisymmetric elements; the punch, the die and the blankholder were modelled by gap elements. The metal sheet was free to move along the punch and the die edges, with a continuous variation of the boundary conditions. The highly non‐linear problem requires an adequate description through the carefully considered use of the appropriate options of the MARC package (release K2). Moreover, some subroutines were written ad hoc to complete the discretization. Results are presented as strain and stress histories during the stamping process and as total forming force exerted by the punch to deform the sheet. In addition the spring‐back phase was considered in order to calculate the back deformation and the residual stress. Lastly, a comparison of the behaviour obtained with two different kinds of steel are reported.
TRIXEL: a simple, efficient algorithm for colour‐fill contouring
Authors: Campbell John S. , Robinson James
Published: February 2008

The TRIXEL algorithm and theory are presented for colour‐fill contouring. The algorithm is simple, efficient, easily implemented and it readily adapts to parallel processing. Examples are given and a Fortran 77 source listing is included.
A review of expert systems development tools
Authors: Mackerle J.
Published: February 2008

Expert systems are being effectively applied to a variety of engineering problems. A growing number of languages and development tools are available for their building. Expert systems building tools (shells) are not so flexible as the high‐level languages, but they are easier to use. The problem is that there are too many development tools on the market today, no standards for their evaluation are available, so it is quite difficult to choose the ‘best’ tool for the developer's/user's needs. This paper is an attempt to review the situation on the confused market. Eighty‐six development tools are described in a table form for easy comparisons. Tools implemented on the AI machines only are not included in this survey.
Graphical postprocessing for 3‐D mesh quality evaluation
Authors: Panthaki M.J. , Abel J.F. , Wawrzynek P.A.
Published: February 2008

An important objective of 3‐D graphical finite element postprocessing is the facility to indicate to the engineer the accuracy of analysis results. The inclusion of mesh quality sensors permits a subjective evaluation of the adequacy of a single analysis being interpreted. For graphical approaches, both strain energy density gradients and discontinuities of unsmoothed responses and their gradients have proved to be effective sensors. Interactive graphical tools which can display discontinuity information effectively are described; these are essentially different from the ordinary methods used for the viewing of smoothed results.
Post‐processing techniques for assessing element distortion errors
Authors: Ulbin M. , Hellen T.K.
Published: February 2008

Finite element meshes can today be used to represent very complex structures because of high performance hardware and software. Although a very successful contributor to modern engineering analysis, such techniques are prone to certain classes of numerical analysis errors which have been long recognized and widely investigated. A more recently recognized source of error has, however, received the attention of analysts, being due to the shape distortion effects of popular types of element, such as isoparametric elements. A mesh scanning program, BERQUAL, part of the BERSAFE system, highlights such potential sources of error, but a more precise assessment is only possible from the final results since element performance depends on the stress gradients in each element. Hence additional error checking using certain stress error measures has been devised and implemented in the post‐processing program PLOTTER, part of the BERSAFE system, to enable rapid, interactive, screen diagnosis. The error measures and implementation details are described and illustrated with suitable examples of progressive shape distortion effects.
An assessment of assumed strain methods in finite rotation shell analysis
Authors: Stander Nielen , Matzenmiller Anton , Ramm Ekkehard
Published: February 2008

A critical assessment of the 4‐node assumed strain element as proposed by Dvorkin and Bathe is made. The element performed excellently in all investigated shell problems which sometimes caused difficulties for other assumed strain techniques. For efficient computation in the non‐linear range, linearization of the virtual work equation is done to yield the consistent tangent stiffness. The shell formulation is done for stress and strain tensors based on local element coordinates. To demonstrate the effectiveness and rapid convergence of the non‐linear formulation, three examples are tested for large displacements.
Exact evaluation of contact stress state in computational elasto‐plasticity
Authors: Pankaj Bicanic Nenad
Published: February 2008

Various stress return algorithms in elastoplastic analyses using the finite element method require the evaluation of the contact (or penetration) stress state (Figure 1), defining the transition from elastic to elastoplastic behaviour. Various iterative schemes are commonly used to evaluate contact stress state with a great degree of precision, as subsequent analysis process (forward Euler, mid‐point rule stress return scheme) is greatly affected by the evaluation of the contact stress state, as has been stressed by several authors.
Intelligent real‐time system management: towards an operator companion for nuclear power plants
Authors: Garland W.J. , Poehlman W.F.S. , Solntseff N. , Hoskins J. , Williams L.
Published: February 2008

This paper reports on an investigation of the integration of symbolic computation and reasoning into highly computerized numerically‐based realtime control systems for complex plant process management. This is the natural next step in an evolving maturation of the use of computers for automated monitoring and control of continuous processes. A particular implementation involving nuclear power plant intelligent monitoring is being developed from which overall principles and specifications can be distilled, ultimately leading to a general methodology that can be applied to other continuous plant processes.
Finite element modelling of the near wall zone of confined turbulent flows
Authors: Xia J.Y. , Taylor C. , Medwell J.O.
Published: February 2008

An inherent problem when analysing confined turbulent flows, using a numerical approach, is mapping within the conventionally termed ‘near wall zone’. In order to accommodate the rapid variations in both velocities and turbulent kinetic energies the region would, if conventional techniques are employed, require an extremely fine spatial subdivision.
The discrete vortex method and parallel processing using transputers
Authors: Downie Martin J. , Bettess Peter
Published: February 2008

A simple discrete vortex program written in the Occam language for implementation on transputers is presented. The programming methodology and logic are described, with an emphasis on the use of parallel features. Listings of procedures discussed in the text are given.
A virtual work derivation of the Biot consolidation finite element formulation
Authors: Ding D. , Naylor D.J.
Published: February 2008

A derivation for the finite element equations of consolidation by the principle of virtual work and virtual complementary work is presented. This provides a simple alternative to derivation by variational principles or the Laplace transform. In the final part of the paper the equations are rearranged into a form suitable for time stepping for non‐linear applications.
Linearization of elasto‐plastic consolidation equations
Authors: Borja Ronaldo I.
Published: February 2008

In the framework of the finite element method, the problem of elasto‐plastic consolidation gives rise to a system of non‐linear, coupled residual equations which satisfy the conditions of balance of momentum and balance of mass. In determining the roots of these equations it is necessary that the coupled equations be linearized. To this end, the concept of ‘consistent linearization’ proposed by Simo and Taylor for a single‐phase system is applied to the two‐phase soil‐water system. The roots of the coupled residual equations are solved iteratively by employing Newton's method. It is shown that in non‐linear consolidation analyses, the use of a tangent coefficient matrix derived consistently from the integrated constitutive equation defining the characteristics of the solid skeletal phase results in an iterative solution scheme which preserves the asymptotic rate of quadratic convergence of Newton's method. Numerical examples involving combined radial and vertical flows through an elasto‐plastic soil medium are presented to demonstrate the computational superiority of the above technique over the method based on standard ‘elasto‐plastic continuum formulations’ adopted in most finite element codes.
An iterative solution to non‐symmetric diagonal dominant simultaneous equations
Authors: Chan A.H.C.
Published: February 2008

The Lanczos method with the Golub and Kahan bidiagonalization algorithm is used to solve non‐symmetric diagonal dominant simultaneous equations. The method is very suitable for sparse matrix and vector computer. The problem with loss of orthogonal property is dealt with by restating the iteration. Numerical examples together with FORTRAN 77 routine are given to illustrate the algorithm. Both scalar and vector CPU times are given for comparison.
MAKEBASE, an information retrieval system in structural mechanics for main‐frames and personal computers
Authors: Mackerle J.
Published: February 2008

Information is the most valuable but least valued tool the scientist/engineer has. The computer program developments based on the finite element and boundary element techniques is now receiving considerable attention of the engineering community. The same is valid for their satellite programs such as pre‐ and post‐processors. Recently also expert systems are being developed in the field of structural mechanics. There are thousands of different programs in use and new ones are continuously being developed. Output of related literature on the finite element (FE) and boundary element (BE) technology has grown at a prodigious rate in the last two decades. An effective retrieval of information is necessary, but this is impossible without computer assistance. MAKEBASE is a special purpose, menu‐driven database which stores all types of information listed above. The development of this database was started five years ago. Today, MAKEBASE contains information about 1600 different FE/BE programs and more than 30,000 literature references. It is updated on a daily basis. MAKEBASE is implemented on VAX 11/780 (VMS), Apollo workstations, and different subjects of literature references have also been transferred into the microcomputer environment for individual PC databases. This paper describes the latest version of MAKEBASE and outlines the philosophy for the use of individual, special‐tailored micro‐databases for PCs.
Finite element formulation of a higher‐order theory for dynamic response of laminated composite plates
Authors: Mallikarjuna  , Kant Tarun
Published: February 2008

A C° continuous finite element higher‐order displacement model is developed for the dynamic analysis of laminated composite plates. The displacement model accounts for non‐linear distribution of inplane displacement components through the plate thickness and the theory requires no shear correction coefficients. Explicit time marching schemes are adopted for integration of the dynamic equilibrium equation and a diagonal ‘lumped’ mass matrix is employed with a special procedure applicable to Lagrangian parabolic isoparametric elements. The parametric effects of the time step, finite element mesh, lamination scheme and orthotropy on the transient response are investigated. The effect of the coupling on the transient response is also investigated. Numerical results for deflections and stresses are presented for rectangular plates under various boundary conditions and loadings and compared with results from other sources.
Graphical representation of anisotropic failure envelopes
Authors: Zhang Wenchao , Evans K.E.
Published: February 2008

In the design of anisotropic materials, such as advanced fibre‐reinforced composites, the failure envelope has a crucial role. A geometrical representation of the envelope is of particular value to investigate the highly anisotropic nature of the strength of the material. This provides the design engineer with a visualization of the failure envelope by graphically representing it using a CAD package. Use is made of both stress‐based and strain‐based polynomial failure criteria and examples are given of changes in the failure envelope due to changes in fibre orientation for a high strength graphite/epoxy composite lamina.
Finite element implementation of Robinson's unified viscoplastic model and its application to some uniaxial and multiaxial problems
Authors: Arya V.K. , Kaufman A.
Published: February 2008

A description of the finite element implementation of Robinson's unified viscoplastic model into the general purpose finite element program, MARC, is presented. To demonstrate its application, the implementation is applied to some uniaxial and multiaxial problems. A comparison of the results for the multiaxial problem of a thick internally pressurized cylinder, obtained using the finite element implementation and an analytical solution, is also presented. Excellent agreement obtained confirms the correct finite element implementation of Robinson's model.
Occurrence of spurious mechanisms in computations of strain‐softening solids
Authors: de Borst René , Rots Jan G.
Published: February 2008

The behaviour of cracked finite elements is investigated. It is shown that spurious kinematic modes may emerge when softening type constitutive laws are employed. These modes are not always suppressed by surrounding elements. This is exemplified for a double‐notched concrete beam and for a Crack‐Line‐Wedge‐Loaded Double‐Cantilever‐Beam (CLWL—DCB). The latter example has been analysed for a large variety of finite elements and integration schemes. To investigate the phenomenon in greater depth an eigenvalue analysis has been carried out for some commonly used finite elements.
Finite element solution of turbulent pipe flows
Authors: Wang Mo‐Hwa , Bathe Klaus‐Jürgen
Published: February 2008

The primitive variable finite element formulation is used in a straightforward manner to solve for two turbulent pipe flows. The solution is based on the use of the Nikuradse—van Driest mixing‐length formula but no special wall element is employed. The finite element solutions are compared with experimental results.
A mixed finite element for laminated composite plates based on the use of bubble functions
Authors: Pinsky Peter M. , Jasti Raja V.
Published: February 2008

A new laminated composite plate finite element is proposed that is numerically stable and accurate in displacements and stresses, including transverse shear stress. The formulation is based on the Hellinger—Reissner principle with Mindlin kinematics. All stress components are given independent approximations and do not satisfy equilibrium conditions a priori. A novel feature of the formulation is the additive decomposition of the displacement field into two parts corresponding to nodal interpolations and independent local basis functions. The additional basis functions and their associated parameters play an important role in characterizing the accuracy of the element. These functions eliminate shear locking in the lower order elements and provide additional variational constraints on the stresses, leading to very accurate results. A 4‐node and a 9‐node version are developed and it is shown that both elements pass the patch test suggested by Zienkiewicz et al. and are stable in the sense of the Babuška—Brezzi condition. The special structure of the element flexibility matrix provides computational efficiency approaching that of displacement based formulations.
Numerical solutions of one‐dimensional rheological models of combined consolidation and creep
Authors: Thomas H.R. , Bendani K.
Published: February 2008

A solution algorithm which enables various rheological models of combined one‐dimensional consolidation and creep to be accommodated in a unified approach, is used to solve three models which have appeared in the literature. The theories are those of Tan, Gibson and Lo, and Schiffman, Ladd and Chen. Comparisons between these hereditary rheological models are performed and assessments of the various features of the models presented.
Numerical simulation of thin sheet forming processes by the finite element method
Authors: Bellet M. , Massoni E. , Chenot J.L.
Published: February 2008

A numerical model for solving either elastic‐plastic, elastic‐viscoplastic or purely viscoplastic deformation of thin sheets is presented, using a membrane mechanical approach. The finite element method is used associated with an incremental procedure. The mechanical equations are the principle of virtual work written in terms of plane stress, which is solved at the end of each increment, and an incremental semi‐implicit flow rule obtained by the time integration of the constitutive equations over the increment. These equations are written using curvilinear coordinates, and membrane elements are used to discretize them. The resolution method is the Newton‐Raphson algorithm. The contact algorithm is presented and allows for applications to cold stretching and deep‐drawing problems and to the superplastic forming of thin sheets.
Automatic non‐linear solution with arc length and Newton‐Lanczos methods
Authors: Papadrakakis M. , Nomikos N.
Published: February 2008

The application of the preconditioned Lanczos method is proposed for the solution of the linearized equations resulting from a non‐linear solution routine based on Newton methods. A path‐following solution algorithm with an arc length method is employed for tracing all types of post‐critical branches of a load‐displacement curve. The proposed methodology retains all characteristics of an iterative method by avoiding the complete factorization of the current stiffness matrix. The necessary eigenvalue information is retained in the tridiagonal matrix of the Lanczos approach.
Mixed Eulerian‐Lagrangian finite element analysis of transient flow with a moving boundary
Authors: Tou S.K.W.
Published: February 2008

This paper presents a mixed Eulerian and Lagrangian finite element method for solving 2‐D transient flows involving a moving/free boundary. The method combines the simplicity of a solution with a fixed computational grid associated with the Eulerian concept and the computational power of Lagrangian approach which is especially effective for a moving grid defined in the physical domain. The method employs a time‐dependent boundary‐fitted coordinate transformation to allow the physical grid to follow the moving boundary which remains always an element boundary while the computational grid is held fixed. The method is demonstrated by an example in which transient wave propagation in an open channel is simulated. The method is efficient and requires no iterative procedures and no mesh re‐zoning.
Decomposition of the initial stability problem for a cylindrical shell under non‐symmetric loads
Authors: Wiśniewski Krzysztof , Taylor Robert L.
Published: February 2008

Numerical aspects of initial stability analysis of a cylindrical shell of non‐constant parameters along the generator and under non‐symmetrical loads are considered. A variational approach based on Sanders' and Donnell's non‐linear equations of thin, elastic shells is applied. The problem is decomposed to determine: the stability vectors in the axial direction in the first step, and the critical load and the stability vector in the circumferential direction in the second step. The discretization is based on finite Fourier representations and the finite difference method. To find the approximate stability vector in the axial direction an auxiliary problem for axisymmetric loads is solved. The error of the method is defined and the effectiveness of the method is estimated. The decomposition leads to small and fast algorithms suitable for personal computers. Shells with constant and stepped thicknesses under wind loads are calculated as examples. Tested algorithms show considerable effectiveness and good accuracy of results.
Efficient partitioning schemes for fluid‐structure interaction problems
Authors: Singh R.K. , Kant T. , Kakodkar A.
Published: February 2008

This paper demonstrates the capability of staggered solution procedure for coupled fluid‐structure interaction problems. Three possible computational paths for coupled problems are described. These are critically examined for a variety of coupled problems with different types of mesh partitioning schemes. The results are compared with the reported results by continuum mechanics priority approach—a method which has been very popular until recently. Optimum computational paths and mesh partitionings for two field problems are indicated. Staggered solution procedure is shown to be quite effective when optimum path and partitionings are selected.
Automatic crack propagation studies in T‐junctions and cross bars
Authors: Remzi E.M. , Blackburn W.S.
Published: February 2008

Theoretical investigations have been performed on slowly propagating cracks in T‐junctions and cross bars using computer procedures developed to analyse the amount and direction of crack growth using automatic mesh modification and the finite element stress analysis program, BERSAFE. The procedures may be used in a linear or non‐linear material. The crack growth for the linear elastic case is calculated to be in the direction of the maximum energy release rate. For the non‐linear case, the direction is taken to be that of Jwi. These procedures have been applied to fatigue crack growth calculations in this paper.