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  • 1
    Electronic Resource
    Electronic Resource
    An Eulerian approach for die compaction processes (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 509-524 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: For the analysis of deformation processes the Eulerian approach is usually formulated in material velocities. To describe the die compaction of compressible media, this paper presents an Eulerian simulation method, basically expressed in displacements. The material behaviour is modelled by the theory of elastoplasticity. Frictional interaction with the surroundings is included. As a spatially fixed finite element mesh is applied, rezoning is governed by the process specification and not, as in the Lagrangian approach, by the mesh distortion. The solution scheme, using a Newton-Raphson algorithm, is considered in detail. A consistent iteration procedure is derived. Examples demonstrate the merits of the method developed.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620310307
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  • 2
    Electronic Resource
    Electronic Resource
    Numerical flow modelling in a locally refined grid (1994)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 37 (1994), S. 497-515 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An algorithm is presented to model two-dimensional, non-isothermal, low Mach number flows with a local steep density gradient. The algorithm uses an adaptive, locally refined, non-staggered grid and has been developed, especially for modelling laminar flames. The governing equations, based on a stream-function-vorticity formulation, are presented and discretized using hybrid finite differences. A (isothermal) test problem is presented to compare the accuracy of the results of the solver presented in this paper, with the results of algorithms found in the literature. However, this test problem proves to be not well suited for the application of a locally refined grid, since it does not contain a local steep gradient. For this reason an additional test problem is constructed that clearly shows the advantages of the locally refined grid as compared to a uniform grid with respect to both the calculation time as well as the number of grid nodes needed. Furthermore, a laminar premixed flame is modelled with simple chemistry to show that the algorithm, presented in this paper, converges to a stabilized flame when an adaptive grid technique is used.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620370308
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  • 3
    Electronic Resource
    Electronic Resource
    Continuity conditions for finite element analysis of solids (1992)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 33 (1992), S. 845-853 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In conventional finite element formulations the concept of node - a point where one of the shape functions is unitary and all others are nil - is used to advantage as it simplifies the definition of interelement continuity conditions.This constraint on the definition of the shape functions hinders the formulation of elements with complex shapes and, in particular, of equilibrium elements.In the approach presented herein linearly independent functions are defined within each element irrespectively of the location of the nodes. Interelement continuity conditions are imposed ‘a posteriori’, as in hybrid elements.The derivation of the element matrices is based upon the equations expressing equilibrium, compatibility and the constitutive relations without explicitly using variational principles.This results in a wider choice of available funciiuns ami in an easier way to formulate equilibrium elements and/or to use conforming or non-conforming elements.As the approach used is independent of the choice of basic functions and of the shape of the elements, it is perfectly general. It allows the parallel analysis of kinematically and statically admissible formulations, as proposed by Fraeijs de Veubeke.1As the interelement continuity conditions are imposed ‘a posteriori’ new variables are used to express this condition.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620330411
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  • 4
    Electronic Resource
    Electronic Resource
    A finite element method of viscoelastic stress analysis with application to rolling contact problems (1969)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 1 (1969), S. 379-394 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A completely numerical method for steady state linear viscoelastic stress analysis is presented by means of the finite element approach. Numerical representations of the measured viscoelastic constitutive relations are used. This method is developed to obtain steady state solutions to mixed boundary value problems in which the character of the boundary conditions at a point changes with time. Such problems cannot be handled by direct application of the correspondence theorem. A numerical example of viscoelastic sheet rolling is presented along with an experimental verification of the solution by photo-viscoelastic observations.
    Additional Material: 11 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620010405
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  • 5
    Electronic Resource
    Electronic Resource
    A numerical study of three-dimensional natural convection during freezing of water (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 899-914 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A numerical study of three-dimensional natural convection with phase change in a rectangular parallelepiped is described. The fluid has temperature-dependent variable properties. The governing equations are approximated by finite differences, second order in space and first order in time. A boundary-fitted co-ordinate system is implemented to predict the shape and the movement of the solid-liquid interface. Preliminary results have been obtained for freezing of water in a cube for Rayleigh numbers in the range of about 105-106.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620300420
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  • 6
    Electronic Resource
    Electronic Resource
    Boundary elements with equilibrium satisfaction - A consistent formulation for potential and elastostatic problems (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 609-621 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A direct boundary element formulation which produces equilibrium satisfaction in the numerical solutions is presented. It consistently originates from the standard boundary integral equation with a simple modification in the fundamental solution and can be applied to general potential and elasticity problems. Since boundary equilibrium is guaranteed for any problem discretization, the procedure is also found useful to generate improved stiffness matrices, which permits combination with finite elements.Some elastostatic examples are included to demonstrate the applicability of the formulation.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620320310
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  • 7
    Electronic Resource
    Electronic Resource
    Computation of heat conduction in materials with random variable thermophysical properties (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 523-536 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A method for the direct computation of mean values and variances of the temperature in conduction-heated objects with random variable thermophysical properties is presented. This method is based on a Taylor expansion of the finite element formulation of the heat conduction equation and offers a powerful alternative to the computationally expensive Monte Carlo method. Both steady-state and transient problems are considered. Some example problems are solved and the results discussed. The simulations indicate that the variability of the thermophysical properties may cause a considerable variability of the temperature within the heated object. This may have important consequences on the design of heating operations in food process engineering.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620360310
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  • 8
    Electronic Resource
    Electronic Resource
    A Petrov-Galerkin formulation for the incompressible Navier-Stokes equations using equal order interpolation for velocity and pressure (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 1135-1149 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new Petrov-Galerkin method for the incompressible Navier-Stokes equations is presented. The use of the so-called ‘optimal upwind’ parameter in multidimensions is justified by a time-scale analysis of the relevant physical processes. The resulting procedure circumvents the Babuška-Brezzi condition and allows equal order interpolation for velocity and pressure to be used.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620310608
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  • 9
    Electronic Resource
    Electronic Resource
    Dynamics of flexible multibody systems using cartesian co-ordinates and large displacement theory (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 1543-1563 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A formulation for the dynamic analysis of flexible systems, composed of slender bodies that can be accurately modelled by beams is presented in this paper. A new set of state variables, composed of Cartesian co-ordinates of points and unit vectors, is introduced to define the beam with respect to an inertial frame. A non-linear Timoshenko beam finite element capable of handling finite displacements with small linear elastic strains is developed. This allows relative displacements between material points of a single beam to be arbitrarily large. Since deformations are not explicit variables, there is no need to define a moving reference frame attached to each flexible body. Instead, deformations are obtained through a displacement-deformation relation based on finite-displacement beam theory. The differential equations of motion are obtained using the Lagrange equations. A symmetric, constant and sparse mass matrix is obtained in the inertial frame. Constraints are introduced with a penalty formulation and the resulting set of ordinary differential equations is integrated with Newmark's family of methods. The whole formulation is extremely simple and the results demonstrate the capabilities and efficiency of the proposed method for dynamic simulation, even when relative displacements are finite in a single beam or coupling effects are significant.
    Additional Material: 14 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620320804
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  • 10
    Electronic Resource
    Electronic Resource
    A quadrilateral hybrid stress element for Mindlin plates based on incompatible displacements (1994)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 37 (1994), S. 279-296 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An hybrid stress element formulation based on internal, incompatible displacements is used to develop efficient Mindlin plate elements. The 4-node quadrilateral Mindlin plate element is derived from a modified energy functional. Both displacements and stresses are defined in the natural co-ordinate interpolation system. The assumed stress field is obtained by tensor transformation and so chosen as to ensure that the element is co-ordinate invariant and stable. Shear locking is avoided through an appropriate identification of the internal, incompatible displacement field. The role played by incompatible displacements in the formulation of hybrid stress elements for thin and moderately thick plates is discussed. Numerical applications are presented to illustrate the accuracy and reliability of the suggested Mindlin plate element.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620370207
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