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  • 1
    Electronic Resource
    Electronic Resource
    From Single-Phase to Compositional Flow: Applicability of Mixed Finite Elements (1997)
    Springer
    Transport in porous media 27 (1997), S. 225-242 
    Details
    ISSN: 1573-1634
    Keywords: fractional flow ; mixed methods ; finite elements ; multiphase flow ; porous media.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract In this paper we discuss the formulation of the governing equations that describe flow of fluids in porous media. Various types of fluid flow, ranging from single-phase flow to compositional flow, are considered. It is shown that all the differential equations governing these types of flow can be effectively rewritten in a fractional flow formulation; i.e., in terms of a global pressure and saturation (or saturations), and that mixed finite element methods can be accurately exploited to solve the pressure equation. Numerical results are presented to see the performance of the mixed methods for the flow equations in three space dimensions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1006507816183
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  • 2
    Electronic Resource
    Electronic Resource
    Slow slumping of a very viscous liquid bridge (1997)
    Springer
    Journal of engineering mathematics 32 (1997), S. 27-40 
    Details
    ISSN: 1573-2703
    Keywords: slumping ; creeping flow ; molten glass ; Stokes flow ; finite elements
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Technology
    Notes: Abstract A layer of very viscous liquid (e.g. tar, molten glass) spans a chasm between two vertical walls. The slow fall or slump of this initially-rectangular liquid bridge is analysed. A semi-analytical solution is obtained for the initial motion, for arbitrary thickness/width ratios. The formal limits of large and small thickness/width ratios are also investigated. For example, the centre section of a thin bridge of liquid of density ρ and viscosity µ, with width 2w and thickness 2h≪2w falls under gravity g at an initial velocity ρgw4/(32μh2). A finite element technique is then employed to determine the slumping motion at later times, confirming in passing the semi-analytical prediction of the initial slumping velocity.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1004200926153
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  • 3
    Electronic Resource
    Electronic Resource
    SUPERCONVERGENT PATCH RECOVERY IN PROBLEMS OF MIXED FORM (1997)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 13 (1997), S. 207-217 
    Details
    ISSN: 1069-8299
    Keywords: plates ; finite elements ; mixed method ; error estimation ; superconvergent patch recovery ; adaptivity ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The superconvergent patch recovery (SPR technique) has been shown to be an effective postprocessing procedure in which an improved solution is obtained based on the original finite element solution. The technique was applied to second order problems with success, but the method has not yet been studied on problems posed in mixed form. This paper demonstrates that the technique can be applied to beam and plate bending problems, characterized by fourth order differential equations. The differential equation is here written as two coupled differential equations of second order leading to a mixed finite element procedure based on approximations of the moment and displacement fields. Two elements of mixed type are handled, namely a triangular plate element with constant moment field and a rectangular element with linearly varying bending moments. Numerical examples are given to show that the postprocessed solution is more accurate and has a higher rate of convergence. © 1997 by John Wiley & Sons, Ltd.
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  • 4
    Electronic Resource
    Electronic Resource
    SIMULATION OF FREE SURFACES IN 3D WITH THE ARBITRARY LAGRANGE EULER METHOD: ERRATUM (1997)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 13 (1997), S. 511-513 
    Details
    ISSN: 1069-8299
    Keywords: finite elements ; arbitrary Lagrange-Euler ; free interfaces ; multiphase flow ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A correction to the free interface condition given in P. Szabo and O. Hassenger (Int. J. Numer. Meth. Engng, 38, 717-734 (1995)) is presented. The corrections to the computations in the paper are found to be within numerical accuracy. © 1997 John Wiley & Sons, Ltd.
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  • 5
    Electronic Resource
    Electronic Resource
    MATRIX EQUATION OF HEAT FLOW IN RANDOM CONDITIONS (1997)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 13 (1997), S. 337-342 
    Details
    ISSN: 1069-8299
    Keywords: heat flow ; finite elements ; probabilistic analysis ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A solution of the thermal problem in random conditions is presented. The heat flow is formulated in terms of finite elements. The theoretical formulation is described which presents probabilistic distributions for temperature, taking into account random initial and boundary conditions as well as thermal properties of material. An example of the thermal analysis is demonstrated.© 1997 John Wiley & Sons, Ltd.
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  • 6
    Electronic Resource
    Electronic Resource
    ERROR ESTIMATES AND ADAPTIVE REMESHING TECHNIQUES IN ELASTO-PLASTICITY (1997)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 13 (1997), S. 285-299 
    Details
    ISSN: 1069-8299
    Keywords: error estimates ; remeshing strategies ; finite elements ; adaptive analysis ; elasto-plastic analysis ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The major difficulty in applying the finite element method to practical problems is the design of a suitable mesh and the assessment of discretization errors. To overcome this difficulty considerable effort has been made in developing adaptive finite element methods, but most of the work has been limited to linear problems. In this paper, fundamental concepts related to error estimates and mesh refinement strategies for non-linear problems are addressed. A simple, but reliable, path-dependent error estimator is proposed. Based on the errors estimated by the present method, a mesh refinement strategy is also suggested. Numerical examples of two ideal plasticity plane stress problems are shown. The non-linear plasticity model is based on an incremental theory using the von Mises yield criterion. © 1997 by John Wiley & Sons, Ltd.
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  • 7
    Electronic Resource
    Electronic Resource
    Simulations of the EW undular bore (1997)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 13 (1997), S. 583-592 
    Details
    ISSN: 1069-8299
    Keywords: RLW equation ; finite elements ; Petrov-Galerkin ; undular bore ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The equal width equation is solved by a Petrov-Galerkin method using quadratic B-spline spatial finite elements. A linear recurrence relationship for the numerical solution of the resulting system of ordinary differential equations is obtained via a Crank-Nicolson approach involving a product approximation. The motion of solitary waves is studied to assess the properties of the algorithm. The development of an EW undular bore is investigated and compared with that of the RLW bore. © 1997 John Wiley & Sons, Ltd.
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  • 8
    Electronic Resource
    Electronic Resource
    A finite element method for evaluating a double integral arising from a Dirichlet problem in fluid mechanics (1997)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 13 (1997), S. 627-634 
    Details
    ISSN: 1069-8299
    Keywords: finite elements ; doubly connected regions ; Poisson's equation ; viscous flow ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper we give a finite element method and its error estimate for evaluating double integrals over a smooth domain. The results are used to compare rates of flow of a viscous incompressible fluid in a pipe-in-pipe system with different doubly connected cross-sections. These numerical results confirm an earlier conjecture regarding the rates of flow. ©1997 John Wiley & Sons, Ltd.
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  • 9
    Electronic Resource
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    A finite element method for plane stress problems with large elastic and plastic deformations (1997)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 13 (1997), S. 963-976 
    Details
    ISSN: 1069-8299
    Keywords: plane stress ; finite elements ; finite strain plasticity ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A two-dimensional finite element method is developed for large deformation plasticity. Principal axes are used for the description of the material behaviour, and the use of principal logarithmic stretches leads to exact formulae for finite deformation problems with large elastic and plastic strains. An efficient return mapping algorithm and the corresponding consistent tangent are derived and applied to plane stress problems. Two examples show the performance of the proposed formulation. © 1997 John Wiley & Sons, Ltd.
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  • 10
    Electronic Resource
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    Imposition of slip boundary conditions without the explicit computation of consistent normals (1997)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 13 (1997), S. 949-961 
    Details
    ISSN: 1069-8299
    Keywords: consistent normal ; discrete normal ; slip boundary conditions ; finite elements ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Computational fluid dynamics simulations often require the imposition of slip boundary conditions: zero-normal velocity. When the geometry is complex, the imposition of this type of boundary condition is not trivial since the current implementations require the computation of consistent normals. The slip boundary condition can be viewed as a constraint to the solution. Hence in the framework of the Lagrange multiplier approach, we present an accurate general implementation of consistent normals. With this new approach, these consistent normals are not computed explicitly at the expense of adding new unknowns - the Lagrange multipliers of the constraint - which can be interpreted as normal forces on the flow. © 1997 John Wiley & Sons, Ltd.
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  • 11
    Electronic Resource
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    Modelling of steam surface condenser using finite element methods (1997)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 13 (1997), S. 909-921 
    Details
    ISSN: 1069-8299
    Keywords: surface condensers ; steam ; finite elements ; modelling ; heat exchangers ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Two numerical procedures are proposed for surface condenser analysis. In the first method a two-noded element is used with a variable heat transfer coefficient for each element. This method is suitable for performance analysis under various operating conditions. A four-noded element is also proposed for studying the axial heat conduction effect in tubes. In the second method, shell side flow and heat transfer are simulated in order to study the flow distribution and pressure drop characteristics. The governing equations are solved in primitive variable form. The finite element method with a Eulerian velocity correction algorithm is used. These two procedures are applied to two different types of surface condensers and the results are found to be in good agreement with experimental data. © 1997 John Wiley & Sons, Ltd.
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  • 12
    Electronic Resource
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    ELASTO-PLASTIC INTERFACE MODEL FOR 3D-FRICTIONAL ORTHOTROPIC CONTACT PROBLEMS (1997)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 40 (1997), S. 599-619 
    Details
    ISSN: 0029-5981
    Keywords: finite elements ; contact compliance ; orthotropic friction law ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The present study deals with the solution of the fully three-dimensional contact/friction problem taking into account microstructural characteristics of the surfaces. An incremental non-associated hardening friction law model analogous to the classical theory of plasticity is used. Two different non-linear friction functions in the orthogonal directions are used to account for the orthotropic properties of the contacting bodies. A frontal solver processing unsymmetric matrices is adopted. Two numerical examples have been selected to show applicability of the method proposed. © 1997 by John Wiley & Sons, Ltd.
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  • 13
    Electronic Resource
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    FORMULATION OF GEOMETRICALLY NON-LINEAR PROBLEMS IN THE SPATIAL REFERENCE FRAME (1997)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 40 (1997), S. 1263-1280 
    Details
    ISSN: 0029-5981
    Keywords: finite elements ; p-version ; geometrically non-linear analysis ; Eulerian reference frame ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents a new formulation for geometrically non-linear problems and their numerical treatment by the p-version of the finite element method. The formulation is characterized by a weak form based on the spatial representation of the equilibrium equations, a deformed geometry mapped by the displacement field, a natural description for non-conservative loads that keeps the symmetry of the equations, and a direct (non-incremental) iterative algorithm to solve the equations. The paper is concerned only with problems for which the solution is unique, i.e. the load-displacement curves are single-valued, and the strains are small. Examples are presented. © 1997 by John Wiley & Sons, Ltd.
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  • 14
    Electronic Resource
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    FINITE ELEMENT SOLUTION OF INCOMPRESSIBLE FLUID-STRUCTURE VIBRATION PROBLEMS (1997)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 40 (1997), S. 1435-1448 
    Details
    ISSN: 0029-5981
    Keywords: fluid-structure ; finite elements ; hydroelasticity ; vibrations ; spectral problems ; spurious modes ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper we solve an eigenvalue problem arising from the computation of the vibrations of a coupled system, incompressible fluid - elastic structure, in absence of external forces. We use displacement variables for both the solid and the fluid but the fluid displacements are written as curls of a stream function. Classical linear triangular finite elements are used for the solid displacements and for the stream function in the fluid. The kinematic transmission conditions at the fluid-solid interface are taken into account in a weak sense by means of a Lagrange multiplier. The method does not present spurious or circulation modes for non-zero frequencies. Numerical results are given for some test cases. © 1997 by John Wiley & Sons, Ltd.
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  • 15
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    ON LARGE DEFORMATIONS OF THIN ELASTO-PLASTIC SHELLS: IMPLEMENTATION OF A FINITE ROTATION MODEL FOR QUADRILATERAL SHELL ELEMENT (1997)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 40 (1997), S. 689-726 
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    ISSN: 0029-5981
    Keywords: shells ; large deformations ; finite rotations ; elasto-plasticity ; finite elements ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A large-deformation model for thin shells composed of elasto-plastic material is presented in this work. Formulation of the shell model, equivalent to the two-dimensional Cosserat continuum, is developed from the three-dimensional continuum by employing standard assumptions on the distribution of the displacement field in the shell body. A model for thin shells is obtained by an approximation of terms describing the shell geometry. Finite rotations of the director field are described by a rotation vector formulation. An elasto-plastic constitutive model is developed based on the von Mises yield criterion and isotropic hardening. In this work, attention is restricted to problems where strains remain small allowing for all aspects of material identification and associated computational treatment, developed for small-strain elasto-plastic models, to be transferred easily to the present elasto-plastic thin-shell model. A finite element formulation is based on the four-noded isoparametric element. A particular attention is devoted to the consistent linearization of the shell kinematics and elasto-plastic material model, in order to achieve quadratic rate of asymptotic convergence typical for the Newton-Raphson-based solution procedures. To illustrate the main objective of the present approach  -  namely the simulation of failures of thin elasto-plastic shells typically associated with buckling-type instabilities and/or bending-dominated shell problems resulting in formation of plastic hinges  -  several numerical examples are presented. Numerical results are compared with the available experimental results and representative numerical simulations. © 1997 by John Wiley & Sons, Ltd.
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  • 16
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    DESIGN OF ENERGY CONSERVING ALGORITHMS FOR FRICTIONLESS DYNAMIC CONTACT PROBLEMS (1997)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 40 (1997), S. 863-886 
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    ISSN: 0029-5981
    Keywords: energy conservation ; dynamics ; contact ; finite elements ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper proposes a formulation of dynamic contact problems which enables exact algorithmic conservation of linear momentum, angular momentum, and energy in finite element simulations. It is seen that a Lagrange multiplier enforcement of an appropriate contact rate constraint produces these conservation properties. A related method is presented in which a penalty regularization of the aforementioned rate constraint is utilized. This penalty method sacrifices the energy conservation property, but is dissipative under all conditions of changing contact so that the global algorithm remains stable. Notably, it is also shown that augmented Lagrangian iteration utilizing this penalty kernel reproduces the energy conserving (i.e. Lagrange multiplier) solution to any desired degree of accuracy. The result is a robust, stable method even in the context of large deformations, as is shown by some representative numerical examples. In particular, the ability of the formulation to produce accurate results where more traditional integration schemes fail is emphasized by the numerical simulations. © 1997 by John Wiley & Sons, Ltd.
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  • 17
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    TREE-COTREE DECOMPOSITIONS FOR FIRST-ORDER COMPLETE TANGENTIAL VECTOR FINITE ELEMENTS (1997)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 40 (1997), S. 1667-1685 
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    ISSN: 0029-5981
    Keywords: finite elements ; vector elements ; magnetostatics ; tree ; cotree ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Edge-based finite elements have important applications in modelling both quasi-static and high-frequency electromagnetic problems. Recent work has demonstrated that formulations that exploit the graph structure of the edge-based finite element mesh may be extended to higher-order elements. This paper presents the details of how such an extension to a first-order complete finite element is accomplished and illustrates its application in two-dimensional magnetostatics. © 1997 by John Wiley & Sons, Ltd.
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  • 18
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    Anisotropic mesh optimization and its application in adaptivity (1997)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 40 (1997), S. 4119-4136 
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    ISSN: 0029-5981
    Keywords: finite elements ; adaptivity ; mesh optimization ; unstructured grids ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The construction of solution-adapted meshes is addressed within an optimization framework. An approximation of the second spatial derivative of the solution is used to get a suitable metric in the computational domain. A mesh quality is proposed and optimized under this metric, accounting for both the shape and the size of the elements. For this purpose, a topological and geometrical mesh improvement method of high generality is introduced. It is shown that the adaptive algorithm that results recovers optimal convergence rates in singular problems, and that it captures boundary and internal layers in convection-dominated problems. Several important implementation issues are discussed. © 1997 John Wiley & Sons, Ltd.
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  • 19
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    A NEW FORMULATION OF ISOPARAMETRIC FINITE ELEMENTS AND THE RELATIONSHIP BETWEEN HYBRID STRESS ELEMENT AND INCOMPATIBLE ELEMENT (1997)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 40 (1997), S. 15-27 
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    ISSN: 0029-5981
    Keywords: formulation ; finite elements ; isoparametric ; hybrid stress ; incompatible ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new method of formulating isoparametric finite element is developed, and the element strains are proposed to be resolved into two parts, constant part and higher-order one. The new method indicates two important properties of isoparametric finite element, and the equivalent relationship between hybrid stress elements and incompatible elements. © 1997 by John Wiley & Sons, Ltd.
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    Finite element analysis of the superplastic forming of thick sheet using the incremental flow formulation (1997)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 40 (1997), S. 3205-3228 
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    ISSN: 0029-5981
    Keywords: finite elements ; superplasticity ; incremental flow formulation ; thick sheet forming ; average deformation gradient element ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper discusses the finite element analysis of the superplastic forming of thick sheet components. The incremental formulation proposed is based on a geometrical approximation of the flow type of constitutive equations that describe the behaviour of the alloy during forming. The spatial discretization is achieved using eight-noded finite elements. An algorithm capable of predicting the correct forming pressure is also presented in a form consistent with the incremental flow formulation. Some experimental validation of these techniques will be shown together with a number of more realistic applications which will illustrate the generality of these techniques and their ability to simulate the forming of complex components. Most of the material in this section is standard but has been included for the purpose of completeness and to introduce the reader to the notation used in the paper. © 1997 John Wiley & Sons, Ltd.
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    C*-convergence in the finite element method (1997)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 40 (1997), S. 4405-4425 
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    ISSN: 0029-5981
    Keywords: convergence ; degrees of freedom ; finite elements ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper a family of higher-order quadrilaterals for the finite element analysis of plane elasticity problems are developed, using the displacement method formulation. The number of nodes and the number of elements are fixed, and refinement is achieved by adding derivatives of the nodal displacements as degrees of freedom at the nodes. It is shown that a higher rate of convergence is achieved compared with existing h- and p-versions of the finite element method. Applications to stress concentration and stress singularity are presented and the condition number is checked. © 1997 John Wiley & Sons, Ltd.
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    FREE VIBRATION ANALYSIS OF KIRCHHOFF PLATES RESTING ON ELASTIC FOUNDATION BY MIXED FINITE ELEMENT FORMULATION BASED ON GÂTEAUX DIFFERENTIAL (1997)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 40 (1997), S. 295-317 
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    ISSN: 0029-5981
    Keywords: finite elements ; plate ; foundation ; dynamic analysis ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The main objective of the present work is to give the systematic way for derivation of Kirchhoff plate-elastic foundation interaction by mixed-type formulation using the Gâteaux differential instead of well-known variational principles of Hellinger-Reissner and Hu-Washizu. Foundation is a Pasternak foundation, and as a special case if shear layer is neglected, it converges to Winkler foundation in the formulation. Uniform variation of the thickness of the plate is also included into the mixed finite element formulation of the plate element PLTVE4 which is an isoparametric C0 class conforming element discretization. In the dynamic analysis, the problem reduces to solution of the standard eigenvalue problem and the mixed element is based upon a consistent mass matrix formulation. The element has four nodes and at each node transverse displacement two bending and one torsional moment is the basic unknowns. Proper geometric and dynamic boundary conditions corresponding to the plate and the foundation is given by the functional. Performance of the element for bending and free vibration analysis is verified with a good accuracy on the numerical examples and analytical solutions present in the literature. © 1997 by John Wiley & Sons, Ltd.
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    AN EFFICIENT STRESS ALGORITHM WITH APPLICATIONS IN VISCOPLASTICITY AND PLASTICITY (1997)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 40 (1997), S. 991-1013 
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    ISSN: 0029-5981
    Keywords: finite elements ; stress algorithm ; viscoplasticity ; plasticity ; kinematic hardening ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper deals with two main topics. The first one concerns the equivalence of stress algorithms, based on a Backward-Euler-step applied on viscoplastic models of Chaboche-type, and their elastoplastic counterpart. Generally, the stress algorithm yields a system of non-linear algebraic equations and the corresponding consistent tangent operator, occurring in the principle of virtual displacements, leads to a system of linear equations. This procedure can be obtained utilizing only numerical methods. The second topic concerns a special constitutive relation based on a kinematic hardening model using a sum of Armstrong/Frederick terms, which is equivalent to a multi-surface plasticity model. Applying this model a so-called problem-adapted stress algorithm is derived, where only one non-linear equation must be solved. This result is independent of the number of terms in the hardening model. Furthermore, only the viscoplastic algorithm must be implemented, since it includes the elastoplastic constitutive model as a special case. © 1997 by John Wiley & Sons, Ltd.
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    ON OPEN BOUNDARIES IN THE FINITE ELEMENT APPROXIMATION OF TWO-DIMENSIONAL ADVECTION-DIFFUSION FLOWS (1997)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 40 (1997), S. 2493-2516 
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    ISSN: 0029-5981
    Keywords: finite elements ; advection-diffusion ; open boundaries ; boundary conditions ; open conditions ; Cauchy conditions ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A steady-state and transient finite element model has been developed to approximate, with simple triangular elements, the two-dimensional advection-diffusion equation for practical river surface flow simulations. Essentially, the space-time Crank-Nicolson-Galerkin formulation scheme was used to solve for a given conservative flow-field. Several kinds of point sources and boundary conditions, namely Cauchy and Open, were theoretically and numerically analysed. Steady-state and transient numerical tests investigated the accuracy of boundary conditions on inflow, noflow and outflow boundaries where diffusion is important (diffusive boundaries). With the proper choice of boundary conditions, the steady-state Galerkin and the transient Crank-Nicolson-Galerkin finite element schemes gave stable and precise results for advection-dominated transport problems. Comparisons indicated that the present approach can give equivalent or more precise results than other streamline upwind and high-order time-stepping schemes. Diffusive boundaries can be treated with Cauchy conditions when the flow enters the domain (inflow), and with Open conditions when the flow leaves the domain (outflow), or when it is parallel to the boundary (noflow). Although systems with mainly diffusive noflow boundaries may still be solved precisely with Open conditions, they are more susceptible to be influenced by other numerical sources of error. Moreover, the treatment of open boundaries greatly increases the possibilities of correctly modelling restricted domains of actual and numerical interest. © 1997 by John Wiley & Sons, Ltd.
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    A finite element formulation of thermomechanical rate-dependent frictional sliding (1997)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 40 (1997), S. 4275-4311 
    Details
    ISSN: 0029-5981
    Keywords: friction ; finite elements ; thermomechanical coupling ; thermal contact ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this work, a combined theoretical and numerical approach is taken to consider the dynamic behaviour and the thermomechanical interactions of systems in which friction has an important role. Emphasis is placed on the proper numerical description of fully coupled thermomechanical response on frictional interfaces. From a theoretical standpoint, the first and second laws of thermodynamics are carefully formulated in the context of large deformations, giving rise to a numerical description of contact interaction that is consistent with these laws. Physical observations encompassed by the proposed interface description include thermal softening of frictional response, rate dependence, pressure dependent heat conduction across the interface, and heat sinks on the interfaces created by trapped wear debris. The finite element implementation of the framework is discussed and demonstrated, with numerical examples successfully describing such phenomena as fading braking torque in automobiles and the observed temperature and friction evolution at the interface between a gun barrel and a projectile passing through it. © 1997 John Wiley & Sons, Ltd.
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    ROBUST PRECONDITIONERS FOR LINEAR ELASTICITY FEM ANALYSES (1997)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 40 (1997), S. 2109-2127 
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    ISSN: 0029-5981
    Keywords: preconditioned conjugate gradients ; incomplete factorization ; unstructured irregular grids ; finite elements ; linear elasticity ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper deals with two forms of preconditioner which can be easily used with a Conjugate Gradient solver to replace a direct solution subroutine in a traditional engineering finite element package; they are tested in such a package (FINAL) over a range of 2-D and 3-D elasticity problems from geotechnical engineering. Quadratic basis functions are used.A number of modifications to the basic Incomplete Choleski [IC(0)] factorization preconditioner are considered. An algorithm to reduce positive off-diagonal entries is shown in numerical experiments to ensure stability, but at the expense of slow convergence. An alternative algorithm of Jennings and Malik is more successful, and a relaxation parameter ο is introduced which can make a further significant improvement in performance while maintaining stability. A heuristic for determining a near-optimal value of ο is proposed. A second form of preconditioning, symmetrically scaled element by element, due to Bartelt, is also shown to perform robustly over a range of problems; it does not require assembly of the global stiffness matrix, and has great potential for parallelization. © 1997 by John Wiley & Sons, Ltd.
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    FINITE ELEMENT MODELLING OF SPATIALLY CHAOTIC STRUCTURES (1997)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 40 (1997), S. 2237-2256 
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    ISSN: 0029-5981
    Keywords: localization ; spatial chaos ; buckling ; discrete system ; mapping ; non-linear ; finite elements ; homoclinic connection ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A simple non-linear mechanical system comprising a pin-jointed string of finite-length links, supported by elastic springs at the pins and compressed by an axial load, is viewed from two perspectives. When seen as an initial-value problem, equilibrium equations provide an iterative non-linear mapping. When seen as a boundary-value problem, it becomes a simple finite element model. At loads less than the critical buckling load, a preferred buckling configuration is found that is localized along the length. In the limit of infinite length this is described as a homoclinic connection in phase space, joining the flat equilibrium state to itself. The infinite sequence of homoclinic points thus defined embeds within the complex topological structure of a homoclinic tangle, within which also appear periodic, quasi-periodic, and chaotic spatial solutions. Implications in the finite element setting are discussed. © 1997 John Wiley & Sons, Ltd.
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    Modelling of progressive short waves using wave envelopes (1997)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 40 (1997), S. 3229-3245 
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    ISSN: 0029-5981
    Keywords: short waves ; diffraction problem ; wave envelope ; phase ; finite elements ; iterative procedure ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We consider progressive waves such that the time independent potential satisfies the Helmholtz equation, for example, the travelling wave diffracted from a body. In order to model the wave potential using finite elements it is usual to discretize the domain such that there are about ten nodal points per wavelength. However, such a procedure is computationally expensive and impractical if the waves are short. The goal is to be able to model accurately with few elements problems such as sonar and radar. Therefore we seek a new method in which the discretization of the domain is more economical. To do so, we express the complex potential φ in terms of the real wave envelope A and the real phase p such that φ=Aeip, and expect that in most regions the functions A and p vary much more gradually over the domain than does the oscillatory potential φ. Therefore instead of modelling the potential we model the wave envelope and the phase.The usual approach then uses the well known geometrical optics approximation (see p. 109 of Reference 1) : if the wave number k is large then the potential can be expanded in decreasing powers of k. The first two terms give the eikonal equation for the phase and the transport equation for the wave envelope respectively (see p. 149 of Reference 2). However, using the geometrical optics approximation (or ray theory) gives no diffraction effects. This approach shall therefore not be considered. (We note though that Keller's theory of geometrical diffraction, an extension to geometrical optics, does allow for diffraction effects and this may be considered at a later date.)We shall consider a new method which shall be described in the present paper and apply it to two-dimensional problems, although the method is equally valid for arbitary three-dimensional problems. (The method has already been validated for the case of one-dimensional problems.) An iterative procedure is described whereby an estimate of the phase is first given and from the resulting finite element calculation for the wave envelope a better estimate for the phase is obtained. The iterated values for the phase and wave envelope converge to the expected values for the test progressive wave examples considered. Even if a very poor estimate for the phase is first given the iterated values converge to the exact values but very slowly. © 1997 John Wiley & Sons, Ltd.
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    BEAM STIFFNESS MATRIX BASED ON THE ELASTICITY EQUATIONS (1997)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 40 (1997), S. 211-232 
    Details
    ISSN: 0029-5981
    Keywords: beam theory ; Timoshenko beam ; finite elements ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new general beam stiffness matrix which accounts for bending, torsion and shear deformation is derived from an elasticity solution of the beam. The influence of shear and torsion is considered using a 3×3 matrix of deformation coefficients. Numerical examples are presented to demonstrate the behaviour of the deformation coefficients and of the beam stiffness matrix. © 1997 by John Wiley & Sons, Ltd.
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