bluuebunny/crossref_metadata_2025 huggingface dataset:
Non‐orthogonal cracks in a smeared finite element model
Authors: de Borst R. , Nauta P.
Published: February 2008

A new model for handling non‐orthogonal cracks within the smeared crack concept is described. It is based on a decomposition of the total strain increment into a concrete and into a crack strain increment. This decomposition also permits a proper combination of crack formation with other non‐linear phenomena such as plasticity and creep and with thermal effects and shrinkage. Relations are elaborated with some other crack models that are currently used for the analysis of concrete structures. The model is applied to some problems involving shear failures of reinforced concrete structures such as a moderately deep beam and an axisymmetric slab. The latter example is also of interest in that it confirms statements that ‘reduced integration’ is not reliable for problems involving crack formation and in that it supports the assertion that identifying numerical divergence with structural failure may be highly misleading.
‘Extended’ variational formulations and finite element models for the elastohydrodynamic lubrication problem
Authors: Alliney S. , Strozzi A. , Tralli A.
Published: February 2008

A finite element model for the elastohydrodynamic lubrication problem is presented. A coupling between the hydrodynamic equation and the foundation compliance equation is performed, then the resulting functional problem is given an ‘extended’ variational formulation. Some preliminary numerical results are also presented.
A command reader for interactive programming
Authors: Felippa Carlos A.
Published: February 2008

A simplified command line reader suitable for building interactive programs based on Fortran 77 is presented. The reader is a 20:1 condensation of the comprehensive command language interpreter CLIP that supports the NICE integrated software system. The present reader, called TinyCLIP. has been prepared to illustrate basic elements of command‐driven programming for beginners interested in writing Fortran‐based interactive applications software. The reader is table driven. Data lines given to the reader are parsed into items which are stored in a table. The table can be subsequently accessed by the program that processes the commands. Tools for extending the basic language are briefly discussed and specific extensions suggested.
Interpolation method for preparation of input data of water depth in finite element analysis of shallow water flow
Authors: Kashiyama Kazuo , Kawahara Mutsuto
Published: February 2008

An interpolation is presented for preparation of input data of water depth in finite element analysis for shallow water problems. The algorithm, computer program for interpolation of water depth and example are shown.
An infinite element for analysis of transient fluid—structure interactions
Authors: Olson Lorraine G. , Bathe Klaus‐Jürgen
Published: February 2008

An infinite element based on the doubly asymptotic approximation (DAA) for use in finite element analysis of fluid—structure interactions is presented. Fluid finite elements model the region near the solid. Infinite elements account for the effects of the outer fluid on the inner region. The DAA‐based infinite elements involve an approximate calculation of the added mass using static mapped infinite elements, plus a consistent damping term. Simple test analyses for a range of fluid properties demonstrate the performance of the solution technique. The analyses of a Helmholtz resonator (open pipe) and a circular plate in water indicate the practical use of the solution approach.
Stress analysis of pressure vessels and piping using the boundary integral equation method
Authors: Abdul‐Mihsein M.J. , Bakr A.A. , Fenner R.T.
Published: February 2008

The boundary integral equation (BIE) numerical technique is applied to several practical pressure vessels and piping problems. Axisymmetric and three‐dimensional formulations of the BIE method for linear elastic stress analysis are reviewed. Isoparametric quadratic elements which exhibit excellent modelling capabilities are used to discretize the surfaces. Several three‐dimensional and axisymmetric structures are analysed.
Local equivalent constant representation of non‐linear damping mechanisms
Authors: Rakheja S. , Sankar S.
Published: February 2008

The non‐linear damping mechanisms are expressed in two general forms: velocity dependent and displacement dependent. The non‐linear damping phenomena are expressed by an array of ‘local constants’, whose value depends upon excitation frequency, excitation amplitude, and type of non‐linearity. Thus, the non‐linear system is replaced by several localized linear systems corresponding to every discrete frequency and amplitude of excitation. Each of the localized linear systems, thus formulated, characterizes the response behaviour of the original non‐linear system, quite accurately in the vicinity of the specific frequency and amplitude of excitation. An algorithm is developed, which expresses the non‐linear damping by an array of ‘local constants’. The algorithm then employs the usual linear design tools to generate the response characteristics almost identical to the response behaviour of the non‐linear system.
Non‐linear vibration analysis of multilayer sandwich plates by incremental finite elements: 1. Theoretical development
Authors: Iu V.P. , Cheung Y.K.
Published: February 2008

The first part of this paper presents an incremental variational principle and an incremental finite element in time‐space domain for the analysis of large amplitude, periodic vibration of multilayer sandwich plates. A reduced basis composed of eigenvectors corresponding to linear free vibration is introduced to reduce the order of the resulting linearized equations governing the non‐linear motion which are solved incrementally in association with Newton‐Raphson iterative method and an extrapolating technique. In the second part the solution techniques are described in detail and a number of examples on various non‐linear responses of rectangular multilayer sandwich plates, including superharmonic, subharmonic and internal resonance, are included in the study. Viscous modal damping is also considered when the structure is under forced excitation.
Numerical techniques for cyclic plasticity at variable temperature
Authors: Burlet H. , Cailletaud G.
Published: February 2008

A formulation of non‐linear kinematic hardening in plasticity is given, with a short description of the model properties under cyclic loading. A resolution algorithm based on the initial stress method is implemented in a two‐dimensional finite element code (ZEBULON). The procedure is tested on examples including mechanical and thermal loading. Some remarks are made on the maximum increment size, the relative efficiency of ‘radial return’ and ‘secant stiffness method’ is discussed. Finally, the possibilities of the model concerning ratchetting, cyclic hardening and softening are shown.
A profile matrix solver with built‐in constraint facility
Authors: Bettess Peter , Bettess Jacqueline A.
Published: February 2008

A profile solver which factorizes the profile matrix K into the form LDLT, is described. D is a diagonal matrix and L is a lower triangular matrix. LT is stored by columns, using a steering vector, to locate the elements. In addition a fixity vector is used. This indicates which degrees of freedom are free and which are fixed. A main program uses a random number generator to set up test data. Full listings are given, together with information on how to get a copy of the program.
Optimal pressure vessel shape design to maximize limit load
Authors: Middleton J. , Petruska J.
Published: February 2008

The problem of optimal design of pressure vessel heads to maximize limit load behaviour is presented. Incremental elasto‐plastic analysis is used and a formulation based on the finite element method is presented whereby an approximate design model is generated which can be optimized via sequential programming. Results are presented for torispherical head shapes and tables are provided in order to evaluate the influence of different geometrical forms on limiting pressure loads. The method is generally applicable and can be applied to the design of components which are required to exhibit limited plastification under increasing load.
A method for the simulation of plane or axisymmetric flows of incompressible fluids based on the concept of the stream function
Authors: Clermont J.R. , de la Lande M.E.
Published: February 2008

A new numerical method is presented for the simulation of flows of incompressible fluids in plane or axisymmetric flows. Under certain assumptions, the physical domain can be transformed into a rectangular domain. This method can involve free surface flow problems. In Newtonian and non‐Newtonian cases, the relevant equations are non‐linear and the solution is carried out in the transformed domain where the stream lines are parallel straight lines.
Non‐linear fracture mechanics and finite elements
Authors: Hellen T.K. , Blackburn W.S.
Published: February 2008

A review is made of methods for calculating parameters characterizing crack tip behaviour in non‐linear materials. Convenient methods of calculating J‐integral type quantities are reviewed, classified broadly into two groups, as domain integrals and virtual crack extension techniques. In addition to considerations of how such quantities may be calculated by finite elements, assessment methods of conducting the actual incremental analyses are described.
Three discrete Kirchhoff elements for shell analysis with large geometrical non‐linearities and bifurcations
Authors: Talbot M. , Dhatt G.
Published: February 2008

The comparative efficiency of three flat triangular shell elements is being assessed for analysing non‐linear behaviour of general shell structures. The bending formulation of the three elements is based on a discrete Kirchhoff model (namely the well‐known 3‐node DKT element and a new 6‐node DKTP element). The in‐plane behaviour is defined by constant (CST), linear (LST)and quadratic (QST) strain approximations. The super‐position of bending and membrane elements leads to the 3‐node DCT element (DKT plus CST), the 3‐node DQT element (DKT plus QST) and the 6‐node DLT element (DKTP plus LST). The geometrically non‐linear formulation is based on an approximate updated Lagrangian formulation (AULF) and the solution is obtained by using the Newton‐Raphson method with an automatic arc‐length control method. Illustrative examples include pre‐ and post‐buckling of different shell structures showing, in particular, some bifurcation points, large rotations and displacements and very important membrane‐bending coupling.
A hierarchical structure for automatic meshing and adaptive FEM analysis
Authors: Kela Ajay , Saxena Mukul , Perucchio Renato
Published: February 2008

This paper deals initially with a new algorithm for generating automatically, from solid models of mechanical parts, finite element meshes that are organized as spatially addressable quaternary trees (for 2D work) or octal trees (for 3D work). Because such meshes are inherently hierarchical as well as spatially addressable, they permit efficient substructuring techniques to be used for both global analysis and incremental re‐meshing and re‐analysis. The paper summarizes the global and incremental techniques, and presents some results from an experimental closed loop 2D system in which meshing, analysis, error evaluation, and re‐meshing and re‐analysis are done automatically and adaptively. The paper concludes with a progress report on a 3D implementation.
Automatic finite element modelling: geometry control for direct models
Authors: Shephard M.S. , Baehmann P.L. , Grice K.R.
Published: February 2008

The general structure of geometrically‐based automatic finite element modelling systems is discussed. The development of a specific system employing the modified‐quadtree and modified‐octree mesh generators is presented. The application of this approach to metal forming analysis is then given.
An improved 9 DOF Hybrid—Trefftz triangular element for plate bending
Authors: Venkatesh A. , Jirousek J.
Published: February 2008

This paper presents a new 9 DOF triangular element for plate bending. It is an analytically integrated improved version of the simplest member in the hierarchy of numerically integrated elements. These elements have been based on the so‐called Hybrid—Trefftz model (HT), a recently developed hybrid model associated with enforcing interelement continuity on locally based displacement fields chosen such that they a priori verify the Lagrange plate equation over the element. In the process of development of the element stiffness matrix in a standard HT model, one has to invert the so‐called natural stiffness matrix, a 7 × 7 matrix associated with the expression of the strain energy in terms of the Trefftz's functions of the element. The inversion of this fully populated matrix represents the most expensive part of the calculation of the element. The basic improvement of the standard Hybrid—Trefftz 9 DOF triangle consists in replacing the original Trefftz's functions by new ones which are energy orthogonal and consequently, result in a diagonal natural stiffness matrix. This not only alleviates considerably the computer cost, but also significantly simplifies the algebra making analytical integrations possible. The practical efficiency of the new element which passes the patch test is demonstrated through numerical examples including the difficult simply supported skew plate problem with a strong singularity at its 150° obtuse corner.
Some developments in the numerical simulation of metal forming processes
Authors: St. Doltsinis J. , Luginsland J. , Nölting S.
Published: February 2008

The paper describes developments in the numerical analysis of metal forming processes mainly motivated by industrial applications. It deals with a complete consideration of the unsteady contact developing between the material and the die, the regeneration of the finite element mesh during the course of the calculation, and with the simulation of superplastic forming processes. In particular, an approach relating both the contact pressure and the friction force to the motion of the material relative to the die surface leads to a convenient computational procedure and to a smooth numerical behaviour under friction. The topological part of the contact algorithm appears well‐suited also for the redefinition of the discretization mesh. As a selected application, superplastic forming is considered in conclusion. Industrial practice requires the adjustment of the forming pressure to a prescribed value of the maximum rate of deformation in the material.
Plasticity computations using the Mohr—Coulomb yield criterion
Authors: Crisfield M.A.
Published: February 2008

The paper describes the derivation and application of a range of numerical algorithms for implementing the Mohr—Coulomb yield criterion in a non‐linear finite element computer program. Emphasis is placed on the difficulties associated with the corners of the yield surface. In contrast to the more conventional forward‐Euler procedures, a backward‐Euler integration technique is adopted. A range of methods, including a ‘consistent approach’ are used to derive the tangent modular matrix. Numerical experiments are presented which involve solution algorithms including the modified and full Newton—Raphson procedures, ‘line‐searches’ and the arc‐length method. It is shown that the introduction of efficient integration and tangency algorithms can lead to very substantial improvements in the convergence characteristics.
Finite element analysis of reinforced rubber shells
Authors: Cesar de Sa J.M.A. , Owen D.R.J.
Published: February 2008

The application of numerical techniques to the solution of practical problems which exist in rubber technology is described. Structures and components in the form of reinforced rubber shells are widely used in industry and prediction of their performance is complicated by both the anisotropic nature of composite construction and the incompressible behaviour of the basic material. A layered shell element is developed for the solution of such problems with general anisotropic behaviour independently permitted in each layer. The approach adopted permits the easy location of reinforcement patterns. Numerical solution is based on a single field formulation by eliminating at integrating point level the Lagrange multiplier imposing the incompressible constraint. Large deformation, including large rotation, behaviour is accommodated and a total Lagrangian solution process is adopted. The code developed permits the simulation of non‐conservative loading and its versatility is demonstrated by the solution of some practical examples.
Dynamic analysis and modelling of heavy machinery foundations
Authors: Medina Francisco , Estay J. , Moroni M.O.
Published: February 2008

The modelling of soil‐foundation systems and the evaluation of the foundation compliance functions through a finite/infinite element technique is presented. By means of in situ measurements performed upon heavy machinery foundations, the actual dynamic foundation loading condition is computed. The results obtained are used for redesigning the foundations according to maximum allowable vibration patterns. The procedure clearly shows the advantages of the technique, which leads to efficient designs for all types of foundations.
Error indicators and accuracy improvement of finite element solutions
Authors: Noor Ahmed K. , Peters Jeanne M.
Published: February 2008

Error indicators are introduced as part of a simple computational procedure for improving the accuracy of the finite element solutions for plate and shell problems. The procedure is based on using an initial (coarse) grid and a refined (enriched) grid, and approximating the solution for the refined grid by a linear combination of a few global approximation vectors (or modes) which are generated by solving two uncoupled sets of equations in the coarse grid unknowns and the additional degrees of freedom of the refined grid. The global approximation vectors serve as error indicators since they provide quantitative pointwise information about the sensitivity of the different response quantities to the approximation used. The three key elements of the computational procedure are: (a) use of mixed finite element models with discontinuous stress resultants at the element interfaces; (b) operator splitting, or additive decomposition of the finite element arrays for the refined grid into the sum of the coarse grid arrays and correction terms (representing the refined grid contributions); and (c) application of a reduction method through successive use of the finite element method and the classical Bubnov—Galerkin technique. The finite element method is first used to generate a few global approximation vectors (or modes). Then the amplitudes of these modes are computed by using the Bubnov—Galerkin technique. The similarities between the proposed computational procedure and a preconditioned conjugate gradient (PCG) technique are identified and are exploited to generate from the PCG technique pointwise error indicators. The effectiveness of the proposed procedure is demonstrated by means of two numerical examples of an isotropic toroidal shell and a laminated anisotropic cylindrical panel.
Numerical analysis of fire effects on beam structures
Authors: Contro R. , Poggi C. , Cazzani A.
Published: February 2008

A known finite element model is significantly enriched in order to take into consideration the variations of material parameters that are provoked by elevated temperatures due to fire environment. On the basis of this ‘heterogeneity acquired model’ a numerical iterative procedure is implemented that permits to describe the performances of beam structures exposed to fire. Efficiency of the proposed model and relevant procedure are shown by some numerical results which are partly and successfully compared with experimental ones obtained by other researchers.
Axisymmetric thermoelasticity by combined boundary and finite elements
Authors: Rudolphi Thomas J.
Published: February 2008

The boundary element and finite element methods have been combined so as to allow for arbitrary intermixing of element types in modelling problems of axisymmetric thermoelasticity, including body forces due to rotational inertia. The formulation for combining the methods is given, and a general purpose, finite element program has been generalized to accommodate both types of elements and to determine stresses within and on the boundary of boundary‐type elements after the primary solution for the displacements. Example problems demonstrate the validity and accuracy of the technique.
Partitioned analysis for coupled mechanical systems
Authors: Felippa Carlos A. , Geers Thomas L.
Published: February 2008

Partitioned analysis is a method by which sets of time‐dependent ordinary differential equations for coupled systems may be numerically integrated in tandem, thereby avoiding brute‐force simultaneous solution. The coupled systems addressed pertain to fluid—structure, fluid—soil, soil—structure, or even structure—structure interaction. The paper describes the partitioning process for certain discrete‐element equations of motion, as well as the associated computer implementation. It then delineates the procedure for designing a partitioned analysis method in a given application. Finally, examples are presented to illustrate the concepts. It is seen that a key element in the implementation of partitioned analysis is the use of integrated, as opposed to monolithic software.
Comparison of various models for strain‐softening
Authors: Pijaudier‐Cabot Gilles , Bažant Zdeněk P. , Tabbara Mazen
Published: February 2008

This paper presents a comparison of various models for strain‐softening due to damage such as cracking or void growth, as proposed recently in the literature. Continuum‐based models expressed in terms of softening stress—strain relations, and fracture‐type models expressed in terms of softening stress—displacement relations are distinguished. From one‐dimensional wave propagation calculations, it is shown that strain‐localization into regions of finite size cannot be achieved. The previously well‐documented spurious convergence is obtained with continuum models, while stress—displacement relations cannot model well smeared‐crack situations. Continuum models may, however, be used in general if a localization limiter is implemented. Gradient‐type localization limiters appear to be rather complicated; they require solving higher‐order differential equations of equilibrium with additional bourdary conditions. Non‐local localization limiters, especially the non‐local continuum with local strain, in which only the energy dissipating variables are non‐local, is found to be very effective, and also seems to be physically realistic. This formulation can correctly model the transition between homogeneous damage states and situations in which damage localizes into small regions that can be viewed as cracks. The size effect observed in the experimental and numerical response of specimens in tension or compression is shown to be a consequence of this progressive transition from continuum‐type to fracture‐type formulations.
Simulation of hot flat rolling of steel by the finite element method
Authors: Kapaj N. , Amici E. , Ghini S. , Pietrosanti C.
Published: February 2008

This paper presents a finite element simulation of the hot fiat rolling of steel. An elastoplastic behaviour of steel and plane strain are assumed. The results presented here were calculated with the finite element program MARC and they have shown good agreement with experimental data.
Solution of incompressible steady flow problems in closed conduits using finite elements and a structural analogy
Authors: Cifuentes Arturo O.
Published: February 2008

A problem that arises very frequently in many industrial applications is the study of steady incompressible flows in a network of pipes. This paper introduces a structural analogy that allows the problem to be treated with a certain class of non‐linear finite elements. The advantage of this formulation is that it falls within the range of capabilities offered by most structural analysis codes available in the market.
A material law for coupled local yielding and geometric instability
Authors: Kröplin B. , Dinkler D.
Published: February 2008

The load carrying capacity of steel structures, built of slender members like bridge cross‐sections, depends on coupled yielding and buckling of the stringers and the plate strips as well as on the global buckling. Therefore, the common techniques of modelling the limit load by an elasto‐plastic layer model fail. In order to overcome the difficulty a material law is developed, in which local buckling failure and yielding is considered. This is based on an energy function, which describes the elasto‐plastic intermediate and ultimate state of plates and webs dependent on only a few parameters. The application is shown on large scale examples of stiffened steel bridge decks.
Integration along the path of loading in elastic‐plastic problems
Authors: Martin J.B. , Bird W.W.
Published: February 2008

This paper considers the classical problem of the deformation of an elastic‐plastic body subjected to a prescribed history of loading. Attention is focused on the basis for the time discretization of the problem for numerical solution. It is suggested that this discretization can be achieved consistently by conceiving of the problem as a sequence of holonomic, or non‐linear elastic, problems. Complementary work bounds can be given, in special circumstances, for increasing numbers of time steps. The holonomic problem for a single time step is a non‐linear mathematical programming problem: it is shown that the conventional Newton‐Raphson algorithm used in elastic‐plastic finite element analysis can be interpreted as an iterative procedure for finding the least value of the holonomic potential work functional.
Effects of non‐proportional loadings in cyclic elasto‐viscoplasticity: experimental, theoretical and numerical aspects
Authors: Benallal A. , Marquis D.
Published: February 2008

An elasto‐viscoplastic constitutive model valid under general complex cyclic loadings is proposed to describe the multiaxial behaviour of engineering metallic materials. Its numerical implementation in the framework of the finite element method is underlined. Its application to the prediction of some various tests is compared to the experimental responses.
Viscoelastic finite element analysis in design of potash mines
Authors: Yu Y.S. , Ong C.G. , Mottahed P.
Published: February 2008

Computer simulation is playing an increasingly important role in evaluating the short and long term structural stability of underground mine openings, and in ground control studies related to mine design and layout. Such simulations are increasingly being used in the design of underground salt and potash mines. Because of the viscoelastic nature of salt rock, simulation models used in these deposits must take into consideration their time dependent properties if they are to correctly predict opening closures, ground stresses, and ground stability based on prescribed failure criteria. A number of computer codes have been developed in Canada in recent years meeting these requirements. This paper describes the use of one of these codes to predict the ground behaviour of a typical room and pillar mining section of a Western Canadian potash mine. Predicted ground behaviour, based on use of the code, was compared with actual behaviour through field measurements. The study provided good correlation between predicted and measured ground behaviour, and is an encouragement to greater use of numerical modelling in mine stability studies related to mine design.
Numerical solutions for elastic‐plastic problems
Authors: Mitchell G.P. , Owen D.R.J.
Published: February 2008

Recent publications have highlighted the effectiveness of using a consistent tangent modulus when solving elastic‐plastic problems. The formulation of a consistent tangent modulus is closely related to the scheme used to integrate the constitutive equations. Recent work has shown how many of these schemes currently in use can be derived from certain broad classes of algorithms. In this paper these procedures are examined for a number of commonly used yield/failure criteria. For certain cases a remarkably simple formulation results which can lead to considerable savings in computational time.
An unsymmetric FRC laminate C° finite element model with 12 degrees of freedom per node
Authors: Kant Tarun , Manjunatha B.S.
Published: February 2008

A C° finite element formulation for flexure‐membrane coupling behaviour of an unsymmetrically laminated plate based on a higher‐order displacement model and three‐dimensional state of stress and strain is presented. This theory incorporates the more realistic non‐linear variation of displacements through the plate thickness, thus eliminating the use of a shear correction coefficient. The discrete element chosen is a nine‐noded quadrilateral with 12 degrees of freedom per node. The computer program developed incorporates the realistic prediction of interlaminar stresses from equilibrium equations. The present solution for deflection and stresses is compared with those obtained using three‐dimensional elasticity theory, another higher‐order shear deformation theory and Mindlin theory. In addition, numerical results for unsymmetric sandwich plates are presented for future reference.
Using Lanczos vectors and Ritz vectors for computing dynamic responses
Authors: Chen Harn C. , Taylor Robert L.
Published: February 2008

The Lanczos vectors and the Ritz vectors have been used for computing the dynamic response of linear structures. Although the procedures of using these two sets of vectors appear similar to the procedure of using the eigenvectors to find an approximate solution, the fundamental mechanisms of the three are different. We compare the three sets of vectors in detail to show some of the important differences in the hope that this comparison will be helpful to the use of the Lanczos vectors or the Ritz vectors for computing dynamic responses.
Implicit integration of composite yield surfaces with corners
Authors: Pramono Eddy , Willam Kaspar
Published: February 2008

Numerical solutions in computational plasticity are severely challenged when concrete and geomaterials are considered with non‐regular yield surfaces, strain‐softening and non‐associated flow. There are two aspects that are of immediate concern within load steps which are truly finite: first, the iterative corrector must assure that the equilibrium stress state and the plastic process variables do satisfy multiple yield conditions with corners, Fi(σ, q) = 0, at discrete stages of the solution process. To this end, a reliable return mapping algorithm is required which minimizes the error of the plastic return step. Second, the solution of non‐linear equations of motion on the global structural level must account for limit points and premature bifurcation of the equilibrium path. The current paper is mainly concerned with the implicit integration of elasto‐plastic hardening/softening relations considering non‐associated flow and the presence of composite yield conditions with corners.
A direct formulation of finite element models in mechanics
Authors: Maunder E.A.W.
Published: February 2008

This paper offers a simple valid alternative approach to the formulation of finite element models. Using two‐dimensional steady state heat conduction as a representative problem, the paper formalizes and extends a direct approach, normally restricted to constant strain triangular (CST) elements, to the construction of general finite element models. The approach is illustrated with the conventional 4, 8, and 9 noded quadrilateral elements. The sufficient conditions for convergence are explained in straightforward physical terms. The direct approach is based on the dual roles of shape functions, and does not require the use of variational methods or functional analysis. The formulation is shown to be equivalent to a weak form of Galerkin which makes explicit use of three forms of residual. This approach is intended to enable engineering students to gain a sound understanding of basic finite element methods with a minimum of mathematics.
A 4‐node quadrilateral membrane element with in‐plane vertex rotations and modified reduced quadrature
Authors: Stander Nielen , Wilson Edward L.
Published: February 2008

An assessment is made of a 4‐node quadrilateral membrane element with one rotational and two translational degrees of freedom per node, as formulated by Taylor and Simo. The element, QC9, is formed by degeneration of the 9‐node Lagrange element and condensation of the centre degrees of freedom. An 8‐point, modified reduced integration scheme is implemented in this element, QC9(8), to improve on the 3 × 3 quadrature performance, yet avoid the additional rank deficiency due to reduced integration (2 × 2). QC9(8) performs as good or better than all elements surveyed. It is shown that a similar degeneration of the 16‐node Lagrangian element can be carried out, but that the resulting element fails the patch test.
A concrete material model based on non‐associated plasticity and fracture
Authors: Dvorkin Eduardo N. , Cuitiño Alberto M. , Gioia Gustavo
Published: February 2008

A concrete material model is presented. The model is based on non‐associated plasticity for the pre‐failure and ductile post‐failure regimes and fracture (smeared crack approach) for the brittle post‐failure regime. The implementation of the constitutive model in the 2‐D elements of a general purpose non‐linear incremental finite element code is discussed. Some important numerical features of the implementation are the implicit integration of the stress/strain relation and the use of an efficient symmetric stiffness formulation for the equilibrium iterations.
Finite strip method for groundwater modelling in a parallel computing environment
Authors: Puckett J.A. , Schmidt R.J.
Published: February 2008

The finite strip method has been shown to apply to many problems in continuum mechanics. Within the constraints of the method, it has been shown to be superior to the finite element method in terms of data preparation, program complexity and execution time. The finite strip method has been recently extended to groundwater flow problems. The orthogonality of appropriately selected shape functions gives the finite strip method its computational efficiency. The uncoupling achieved from this orthogonality also produces a numerical method which is intrinsically parallel. Consequently, additional efficiencies can be obtained in a parallel environment. Numerical studies of the finite strip method to model a two‐dimensional groundwater flow problem demonstrate the accuracy of the solution and the superior performance of the numerical procedure in a parallel environment.
Numerical prediction of an oil‐fired water tube boiler
Authors: da Graça Carvalho Maria , Jorge Coelho Pedro
Published: February 2008

A fully three‐dimensional model has been applied to an oil‐fired water tube boiler in order to predict the flow, temperature, mixture fraction, species concentrations and the heat flux distributions to the furnace walls. The partial differential equations governing conservation of mass, momentum and energy as well as those describing the combustion phenomena are discretized by a finite volume method and solved numerically. Radiative heat transfer is handled by the discrete transfer method. Predicted results are presented and compared with experimental data for the heat fluxes. The results have suggested that 3‐D models of the present kind can be used with some confidence for design calculations.
An expert system for forming quadrilateral finite elements
Authors: Liu Y.C. , ElMaraghy H.A. , Zhang K.F.
Published: February 2008

A knowledge‐based system for forming quadrilateral finite elements, XFORMQ, was developed at the Centre of Flexible Manufacturing Research and Development of McMaster University, Canada. It automatically forms quadrilateral elements of good quality in conjunction with existing triangular mesh generators. XFORMQ can model geometries as complicated as those handled by triangular mesh generators. It allows for pre‐specified element sizes and rapid transition of element density. The concepts of ‘layer’ and ‘polygon patterns’, which considerably simplify the mesh generation rules and ensure the quality of formed elements, are introduced. Several test cases with different degrees of difficulties were used to evaluate XFORMQ's capabilities with satisfactory results. XFORMQ has the potential of generating meshes arising from the adaptive finite element analysis with quadrilateral elements.
A fully non‐linear axisymmetrical membrane element for rubber‐like materials
Authors: Wriggers P. , Taylor R.L.
Published: February 2008

An axisymmetrical membrane element for large deformations is developed which is based on Ogden's non‐linear elastic material law. Special attention is given to the linearization procedure to obtain a quadratically convergence behaviour within Newton's method. Several examples show the applicability and performance of the proposed formulation.
Automatic generation of shape functions for finite element analysis using REDUCE
Authors: Barbier Christine , Clark Philip J. , Bettess Peter , Bettess Jacqueline A.
Published: February 2008

The use of algebraic languages such as REDUCE makes possible the automatic generation, from fairly concise data, of the main families of two and three dimensional C0 continuous finite element shape functions, with a high confidence in their correctness. This paper gives a tutorial introduction to the REDUCE language and describes how it was used to generate shape function routines.
INFINITE ELEMENTS FOR DYNAMIC PROBLEMS: PART 1
Authors: BETTESS PETER , BETTESS JACQUELINE A.
Published: February 2008

This paper is concerned with infinite elements for dynamic problems, that is, those which change in time. It is a sequel to our earlier paper on static problems. The paper is in a number of sections. The first is an introduction. In the second the state‐of‐the‐art review of infinite elements is updated. In the third, ‘added mass’ type effects are considered. In the fourth, time dependent problems of the diffusion type, which only involve the first time derivative are considered. Wave problems are considered in the fifth and the necessary radiation conditions for such problems are summarized. Section six deals with dynamic problems of a repetitive nature, that is periodic or harmonic problems. In section seven completely transient problems are dealt with and some fundamental difficulties are noted. Conclusions are drawn in section eight.
ANALYTICAL AND COMPUTATIONAL STUDIES ON THE CONSOLIDATION OF MULTILAYERED SOILS
Authors: SADIKU S.
Published: February 2008

Using the Heaviside operator, a single partial differential equation is obtained for the space‐time variation of the pore pressure in two adjacent soil layers undergoing simultaneous consolidation. A closed form expression for the solution to the problem is given as a generalized Fourier series. The coordinate functions of the series are the eigenfunctions of the composite medium obtained computationally through the application of the extended Galerkin method.
ONE‐DIMENSIONAL NON‐LINEAR TRANSIENT HEAT CONDUCTION IN NUCLEAR WASTE REPOSITORIES
Authors: ESTRADA‐GASCA C.A. , COBBLE M.H. , ALVAREZ GARCIA G.
Published: February 2008

Two analytical solutions of thermal problems connected with the disposal of nuclear waste are presented. Non‐linear diffusion problems are analysed. The use of the Kirchhoff transformation and the transformation of coordinates are made along with a numerical solution. Also comparison is made for the exact and numerical solutions for temperature histories at a nuclear waste site. A time dependent heat source is considered.
FINITE ELEMENT MODELLING OF THICK ISOTROPIC PLATES
Authors: GOMAA SAID T. , BALUCH MOHAMMED H. , ABDEL‐RAHMAN HAMDY H. , MOHAMMED AMMAR K.
Published: February 2008

A finite element formulation for flexure of isotropic plates based on a recent refined theory is developed. The refined theory incorporates effects of transverse shear, transverse normal stress and transverse normal strain. The Galerkin finite element method was used to develop the finite element equations for both plate bending and inplane problems. The performance of the proposed finite element model was evaluated by solving problems of uniformly loaded thick plates with different support conditions. The results of the present formulation are compared with Mindlin/Reissner and elasticity solutions.
STATIC CONTACT PROBLEMS—A REVIEW
Authors: ZHONG ZHI‐HUA , MACKERLE JAROSLAV
Published: February 2008

Contact problems are among the most difficult ones in mechanics. Due to its practical importance, the problem has been receiving extensive research work over the years. The finite element method has been widely used to solve contact problems with various grades of complexity. Great progress has been made on both theoretical studies and engineering applications. This paper reviews some of the main developments in contact theories and finite element solution techniques for static contact problems. Classical and variational formulations of the problem are first given and then finite element solution techniques are reviewed. Available constraint methods, friction laws and contact searching algorithms are also briefly described. At the end of the paper, a bibliography is included, listing about seven hundred papers which are related to static contact problems and have been published in various journals and conference proceedings from 1976.
SUPERQUADRICS AND MODAL DYNAMICS FOR DISCRETE ELEMENTS IN INTERACTIVE DESIGN
Authors: WILLIAMS JOHN R. , PENTLAND ALEX P.
Published: February 2008

This paper discusses advances in interactive discrete element simulation for use in computer‐aided concurrent design. We highlight the computational problems of creating a ‘virtual world’ populated by objects which behave much as real world objects and propose a system based on a new class of volumetric models, called superquadrics. These functions have significant advantages for calculating multibody interactions, and by coupling volumetric representation to a modal decomposition method for the physical dynamics we have been able to gain up to two orders of magnitude in efficiency. The modal method allows us to trade off high order modes for improved stability, time step magnitude, temporal aliasing and speed of response, and so provide almost real time feedback to the designer. We believe that virtual manufacturing systems will be especially useful in conceptual design, in design for manufacture and in the new thrust in concurrent design.
DISCONTINUOUS DEFORMATION ANALYSIS: A NEW NUMERICAL MODEL FOR THE STATICS AND DYNAMICS OF DEFORMABLE BLOCK STRUCTURES
Authors: SHI GEN‐HUA
Published: February 2008

A numerical model of deformable block systems that gives a unique solution for large displacement, large deformation and failure computations is presented. The forces acting on each block, from external loading or contact with other blocks, satisfy the equilibrium equations. Equilibrium is also achieved between external forces and the block stresses. Furthermore, the analysis fulfills constraints of no tension between blocks and no penetration of one block into another. Also, Coloumb's law is fulfilled at all contact positions for both static and dynamic computations. The program ready algorithms with brief derivations are stated in this paper.
A NOVEL AUTOMATIC IDENTIFICATION SYSTEM FOR THREE‐DIMENSIONAL MULTI‐BLOCK SYSTEMS
Authors: IKEGAWA Y. , HUDSON J.A.
Published: February 2008

Until now, identification of three‐dimensional non‐convex (concave) blocks has not been accomplished. However, a direct body concept, which is introduced here, can deal with both convex and concave blocks in the same process in connection with detection of individual blocks and computation of physical quantities. Thus, the dilemma in the generalization of identifying three‐dimensional multi‐block systems has been eliminated. The directed body concept used in geometrical identification problems makes it possible to build a novel automatic identification system for three‐dimensional multi‐block systems. This new system eliminates the time‐consuming work on geometrical identification, and copes with a variety of applications in multi‐body systems, such as rock masses.
A GENERALIZED FORMULATION OF THE DISCRETE ELEMENT METHOD
Authors: MUSTOE GRAHAM G.W.
Published: February 2008

A generalized weighted residual method is used to formulate the discrete element method (DEM) for rigid or deformable bodies. It is shown that this approach provides a unified methodology for deriving many of the different discrete element techniques in current use today. This procedure is used to develop a number of different element formulations for use in problems in which the distinct bodies exhibit complex deformation behaviour such as beam or plate flexure, membrane action, and additional reinforcement of a jointed discontinuum. A covergence proof for the two‐dimensional beam element is given for mathematical validation. A number of examples are also presented which illustrate the usefulness of different discrete element types in engineering analyses of discontinuum problems.
A NUMERICAL LABORATORY FOR GRANULAR SOLIDS
Authors: TRENT B.C. , MARGOLIN L.G.
Published: February 2008

The distinct element method has been used to perform a number of numerical experiments, analogous to physical tests routinely carried out for real geologic materials. The ability to prescribe exactly the material properties and the boundary conditions allows us to study in detail the influence of microscopic structure on macroscopic response. These macroscopic quantities are usually the only data obtained in physical experiments. We are now in a position to formulate a general constitutive model, based on physical mechanisms and appropriate for use in a continuum code.
INVESTIGATION OF MICROMECHANICAL FEATURES OF IDEALIZED GRANULAR ASSEMBLIES USING DEM
Authors: BATHURST RICHARD J. , ROTHENBURG LEO
Published: February 2008

The development of physically‐correct models of granular behaviour under shear deformations must recognize the discrete nature of the medium and the mechanical properties of the constituent grains at the particle level. Numerical simulation of idealized granular materials offers the researcher the possibility of recovering complete information on these systems that can then guide the development of micromechanical‐based models of granular systems. A numerical technique that has proved useful in meeting this goal is the discrete element method (DEM). The computer implementation of this method to observe microfeatures of idealized granular assemblies was first reported in the published literature by Cundall and Strack. Since that time a number of researchers have used the technique to explore the behaviour of idealized granular systems comprising cohesionless assemblies of discs and assemblies of discs comprising indestructible (bonded) contacts. The paper reviews some of the numerical simulation work that has been carried out by the authors to verify stress‐force‐fabric relationships first proposed by Rothenburg and constitutive stress‐strain laws for dense isotropic assemblies of bonded discs. The numerical technique in each case is the same and involves the solution of the equations of motion of each particle using an explicit time/finite difference algorithm which is the essential feature of the DEM.