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  • Articles  (12)
  • Finite elements  (12)
  • 2015-2019
  • 1990-1994  (12)
  • 1945-1949
  • 1992  (12)
  • 1947
  • Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics  (12)
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  • Articles  (12)
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  • 2015-2019
  • 1990-1994  (12)
  • 1945-1949
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  • Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics  (12)
  • Physics  (2)
  • Computer Science  (1)
  • 1
    Electronic Resource
    Electronic Resource
    Basic features of the time finite element approach for dynamics (1992)
    Springer
    Meccanica 27 (1992), S. 119-130 
    Details
    ISSN: 1572-9648
    Keywords: Finite elements ; Time integration ; Dynamics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Description / Table of Contents: Sommario Due differenti formulazioni agli elementi finiti nel tempo sono presentate in questo lavoro quali casi particolari di una formulazione generale a tre campi: la prima è una formulazione agli spostamenti, mentre la seconda è una formulazione mista dove i campi indipendenti sono costituiti da spostamenti e momenti cinetici. Dopo aver sviluppato la linearizzazione e l'approssimazione agli elementi finiti delle forme, viene discussa una tecnica per il trattamento di vincoli di olonomia ed anolonomia. Le principali caratteristiche numeriche dei due metodi vengono infine evidenziate facendo anche ricorso ad esempli semplici ma significativi.
    Notes: Abstract Very general weak forms may be developed for dynamic systems, the most general being analogous to a Hu-Washizu three-field formulation, thus paralleling well-established weak methods of solid mechanics. In this work two different formulations are developed: a pure displacement formulation and a two-field mixed formulation. With the objective of developing a thorough understanding of the peculiar features of finite elements in time, the relevant methodologies associated with this approach for dynamics are extensively discussed. After having laid the theoretical bases, the finite element approximation and the linearization of the resulting forms are developed, together with a method for the treatment of holonomic and nonholonomic constraints, thus widening the horizons of applicability over the vast world of multibody system dynamics. With the purpose of enlightening on the peculiar numerical behavior of the different approaches, simple but meaningful examples are illustrated. To this aim, significant parallels with elastostatics are emphasized.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00420590
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  • 2
    Electronic Resource
    Electronic Resource
    A new viewpoint on mixed elements (1992)
    Springer
    Meccanica 27 (1992), S. 3-11 
    Details
    ISSN: 1572-9648
    Keywords: Elliptic PDEs ; Finite elements ; Mixed elements ; Differential geometry ; Whitney forms ; Tonti diagrams ; Complementarity ; Duality
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Description / Table of Contents: Sommario Gli elementi misti sono elementi finiti speciali per campi vettoriali le cui funzioni di interpolazione non sono necessariamente continue in tutte le componenti; tali elementi vengono usati nell'ambito delle formulazioni ‘a due campi’, per esempio quando si calcolano simultaneamente spostamento e tensione in elasticità. In questo articolo viene presentata una famiglia di elementi finiti che traggono origine da un costrutto di geometria differenziale che in apparenza non ha alcun nesso con l'analisi numerica (le forme di Whitney): vengono illustrate le proprietà strutturali complessive di tale famiglia. Questa presentazione getta una nuova luce sugli elementi misti, sotto la quale essi acquistano un carattere più naturale.
    Notes: Abstract Mixed elements are special finite elements for vector fields, whose shape functions are not necessarily continuous in all their components. They are used in connection with ‘two-field’ formulations, for instance when one tries simultaneously to compute displacement and stress in elasticity. We present here a family of finite elements which originate from a chapter of differential geometry apparently unconnected with numerical analysis (Whitney forms) and insist on the structural properties of this family considered as a whole. This sheds a new light on mixed elements, under which they acquire a more natural character than in previous presentations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00452998
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  • 3
    Electronic Resource
    Electronic Resource
    A one-dimensional moving grid solution for the coupled non-linear equations governing multiphase flow in porous media. 2: Example simulations and sensitivity analysis (1992)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 14 (1992), S. 47-69 
    Details
    ISSN: 0271-2091
    Keywords: Partial differential equations ; Non-linear equations ; Coupled system ; Numerical methods ; Finite elements ; Adaptive grid ; Flow in porous media ; Groundwater contamination ; Multiphase flow ; Immiscible flow ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: This paper presents numerical examples for the moving grid finite element algorithm derived in Part Ito solve the non-linear coupled set of PDEs governing immiscible multiphase flow in porous media in one dimension. Examples include single- and double-front simulations for two- and three-phase flow regimes and incorporating a mass sink. The modelling approach is shown to achieve significant savings in computation time and memory allocation when compared with fixed grid solutions of equivalent accuracy. This work includes sensitivity analyses for the parameters which are incorporated in the grid adaptation method, including the curvature weights, artificial viscosity and artificial repulsive force. It is found that the curvature weights are exponential functions of the negative ratio of the square root of the domain length to the number of discrete nodes. These weighting parameters are also shown to depend upon the shape of the front. On the basis of the examined simulations, it is recommended that artificial viscosity be neglected in the solution of the coupled non-linear set of PDEs governing multiphase flow in porous media. Similarly, use of a repulsive force is found to be unnecessary in simulations involving the migration of two liquid phases. For multiphase flows incorporating a gas phase it is recommended to use a non-zero value for the repulslive force to avoid development of an ill-conditioned nodal distribution matrix. An equation to evaluate the repulsive force under these circumstances is suggested.
    Additional Material: 13 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650140105
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  • 4
    Electronic Resource
    Electronic Resource
    Prediction of three-dimensional general shape extrudates by an implicit iterative scheme (1992)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 14 (1992), S. 609-625 
    Details
    ISSN: 0271-2091
    Keywords: 3D extrusion ; Moving boundaries ; Kinematic condition ; Remeshing ; Finite elements ; Free surfaces ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: This paper presents a numerical technique for solving three-dimensional free surface problems in extrusion applications. The method is fully implicit in the sense that a Newton-Raphson scheme is applied on all variables, and geometrically general. In particular, the die section shape may be complex and contains multiple corners: very few restrictions apply on the mesh generation because the method does not require the nodes to be located on straight lines (spines). A clear distinction is introduced between the directions associated with the kinematic condition and the remeshing rules. As a difference with respect to earlier publications, these concepts are handled separately. Only Stokes problems are solved in this paper and we have not introduced surface tension. Therefore corners in the die section propagate discontinuities in the extrudate shape, an a method for relocating corners without losing the quadratic convergence of the scheme is presented. Data structures used for the implementation are briefly discussed.We present results on the extrusion of various profiles, including a rectangular die (a benchmark problem) and various complex sections containing multiple corners.
    Additional Material: 15 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650140507
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  • 5
    Electronic Resource
    Electronic Resource
    A finite element study of incompressible flows past oscillating cylinders and aerofoils (1992)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 15 (1992), S. 1073-1118 
    Details
    ISSN: 0271-2091
    Keywords: Space-time ; Finite elements ; Incompressible flows ; Galerkin/least-squares ; Deforming spatial domain ; Oscillating cylinder ; Pitching aerofoil ; Clustered element-by-element ; GMRES ; Vortex shedding ; Vortex-induced oscillations ; Lock-in ; Hysteresis ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: We present our numerical results for certain unsteady flows past oscillating cylinders and aerofoils. The computations are based on the stabilized space-time finite element formulation. The implicit equation systems resulting from the space-time finite element discretizations are solved using iterative solution techniques.One of the problems studied is flow past a cylinder which is forced to oscillate in the horizontal direction. In this case we observe a change from an unsymmetric mode of vortex shedding to a symmetric one. An extensive study was carried out for the case in which a cylinder is mounted on lightly damped springs and allowed to oscillate in the vertical direction. In this case the motion of the cylinder needs to be determined as part of the solution, and under certain conditions this motion changes the vortex-shedding pattern of the flow field significantly. This non-linear fluid-structure interaction exhibits certain interesting behaviour such as ‘lock-in’ and ‘hysteresis’, which are in good agreement with the laboratory experiments carried out by other researchers in the past. Preliminary results for flow past a pitching aerofoil are also presented.
    Additional Material: 39 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650150911
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  • 6
    Electronic Resource
    Electronic Resource
    Time-dependent solution of the incompressible Navier-Stokes equations to simulate air-conditioning (1992)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 15 (1992), S. 967-974 
    Details
    ISSN: 0271-2091
    Keywords: Permeable walls ; Bulk friction ; Time-dependent ; Incompressible Navier-Stokes ; Pressure correction ; Projection ; Semi-implicit ; Finite elements ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Computer simulations may contribute significantly to the optimal design of air-conditioning systems. To capture the effects of partially permeable walls such as bookshelves on the movement of air and heat, it is necessary to extend the density-dependent Navier-Stokes equations by an additional friction term. The finite element technique is convenient to approximate the extended equations in spatial co-ordinates. For the time co-ordinate a recently proposed semi-implicit finite difference method is very efficient in terms of accuracy and computational complexity. A pressure correction approach is most appropriate to decouple the primitive variables in the extended Navier-Stokes equations. The resulting algorithm has the interesting feature that small symmetric positive definite systems of equations can be solved sequentially for each of the primitive variables. Iterative solution of the systems of equations with preconditioned conjugate gradients combined with a compressed storage scheme allows fine grid computations at affordable costs. As an example a two-dimensional version of the code was applied to an enclosure which was heated from the side and contained a porous wall. The time-dependent computational results are compared with measurement data.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650150903
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  • 7
    Electronic Resource
    Electronic Resource
    A one-dimensional moving grid solution for the coupled non-linear equations governing multiphase flow in porous media. 1: Model development (1992)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 14 (1992), S. 25-45 
    Details
    ISSN: 0271-2091
    Keywords: Partial differential equations ; Non-linear equations ; Coupled system ; Numerical methods ; Finite elements ; Adaptive grid ; Flow in porous media ; Groundwater contamination ; Multiphase flow ; Immiscible flow ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A straightforward moving grid finite element method is developed to solve the one-dimensional coupled system of non-linear partial differential equations (PDEs) governing two- and three-phase flow in porous media. The method combines features from a number of self-adaptive grid techniques. These techniques are the equidistribution, the moving grid finite element and the local grid refinement/coarsening methods. Two equidistribution criteria, based on solution gradient and curvature, are employed and nodal distributions are computed iterativcly. Using the developed approach, an intermingle-free nodal distribution is guaranteed. The method involves examination of a single representative gradient to facilitate the application of moving grid algorithms to solve a non-linear coupled set of PDEs and includes a feature to limit mass balance error during nodal redistribution. The finite element part of the developed algorithm is verified against an existing finite difference model. A numerical simulation example involving a single-front two-phase flow problem is presented to illustrate model performance. Additional simulation examples are given in Part 2 of this paper. These examples include single and double moving fronts in two- and three-phase flow systems incorporating source/sink terms. Simulation sensitivity to the moving grid parameters is also explored in Part 2.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650140104
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  • 8
    Electronic Resource
    Electronic Resource
    A finite element solutionof three-dimensional mixed convection gas flows in horizontal chnnels using preconditioned iterative metrix methods (1992)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 14 (1992), S. 817-841 
    Details
    ISSN: 0271-2091
    Keywords: Mixed convection ; Finite elements ; CVD ; Iterative methods ; Preconditioning ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: An algorithm is presented for the finite element solution of three-dimensional mixed convection gas flows in channels heated from below. The algorithm uses Newton's method and iterative matrix methods. Two iterative solution algorithms, conjugate gradient squared (CGS) and generalized minimal residual (GMERS), are used in conjunction with a preconditioning technique that is simple to implement. The preconditioner is a subset of the full Jacobian matrix centered around the main diagonal but retaining the most fundamental axial coupling of the residual equations. A domain-renumbering scheme that enhances the overall algorithm performance is proposed on the basis of and analysis of the preconditioner. Comparison with the frontal elimination method demonstrates that the iterative method will be faster when the front width exceeds approximately 500. Techniques for the direct assembly f the problem into a compressed sparse row storage format are demonstrated. Elimination of fixed boundary conditions is shown to decrease the size of the matrix problem by up to 30%. Finally, fluid flow solutions obtained with the numerical technique are presented. These solutions reveal complex three-dimensional mixed convection fluid flow phenomena at low Reynolds numbers, including the reversal of the direction of longitudinal rolls in the presence of a strong recirculation in the entrance region of the channel.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650140705
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  • 9
    Electronic Resource
    Electronic Resource
    A new decoupled finite element algorithm for viscoelastic flow. Part 1: Numerical algorithm and sample results (1992)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 14 (1992), S. 1367-1376 
    Details
    ISSN: 0271-2091
    Keywords: Finite elements ; Viscoelastic flow ; Convergence failure ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: This paper presents an algorithm for two-dimensional Steady viscoelastic flow Simulation in which the Solution of the momentum and continuity equations is decoupled from that of the constitutive equations. The governing equations are discretized by the finite element method, with 3 × 3 element subdivision for the stress field approximation. Non-consistent Streamline upwinding is also used. Results are given for flow through a converging channel and through an abrupt planar 4:1 contraction.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650141107
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  • 10
    Electronic Resource
    Electronic Resource
    A new decoupled finite element algorithm for viscoelastic flow. Part 2: Convergence properties of the algorithm (1992)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 14 (1992), S. 1377-1382 
    Details
    ISSN: 0271-2091
    Keywords: Finite elements ; Viscoelastic flow ; Convergence failure ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: We present the results of some numerical experiments which were carried out in order to investigate the general characteristics of the algorithm described in Part I of this paper.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650141108
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  • 11
    Electronic Resource
    Electronic Resource
    Adaptive h-refinement on 3D unstructured grids for transient problems (1992)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 14 (1992), S. 1407-1419 
    Details
    ISSN: 0271-2091
    Keywords: Adaptive mesh refinement ; Finite elements ; Compressible flow ; Transient problems ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: An adaptive finite element scheme for transient problems is presented. The classic h-enrichment/coarsening is employed in conjunction with a tetrahedral finite element discretization in three dimensions. A mesh change is performed every n time steps, depending on the Courant number employed and the number of ‘protective layers’ added ahead of the refined region. In order to simplify the refinement/coarsening logic and to be as fast as possible, only one level of refinement/coarsening is allowed per mesh change. A high degree of vectorizability has been achieved by pre-sorting the elements and then performing the refinement/coarsening groupwise according to the case at hand. Further reductions in CPU requirements arc realized by optimizing the identification and sorting of elements for refinement and deletion. The developed technology has been used extensively for shock-shock and shock-object interaction runs in a production mode. A typical example of this class of problems is given.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650141204
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  • 12
    Electronic Resource
    Electronic Resource
    Transient finite element method for calculating steady state three-dimensional free surfaces (1992)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 14 (1992), S. 343-360 
    Details
    ISSN: 0271-2091
    Keywords: Free surfaces ; Extrusion ; Conjugate gradients ; Finite elements ; Three-dimensional free surfaces ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: In order to reduce the cost of large three-dimensional calculations of steady state free surfaces, we have combined a time-dependent approach, a decoupling algorithm and a conjugate gradient solver along the lines introduced earlier by Gresho and Chan. The free surface is calculated separately by applying the kinematic condition to a number of faces defined on the undeformed surface. For the pseudo-time-marching technique we show that it is economical to adopt different time steps for the free surface calculation and the other fields. The accuracy of the method is tested on the well-known circular die problem; the method is then used to reveal the effects of inertia and shear thinning on square and rectangular dies.
    Additional Material: 15 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650140307
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