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  • Articles  (327)
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  • 1990  (327)
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  • 101
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    Electronic Resource
    Two-level approximation concept in structural synthesis (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 1681-1699 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new concept for complex structural optimization problems is presented. Based on investigation of the mechanical nature of the studied problem, a set of basic mechanical characteristics can be introduced as the generalized variables. A high-quality explicit first-level approximate problem FA is formed by first-order Taylor series expansion of the behaviour constraints in terms of the generalized variables. The FA is explicit but highly non-linear with respect to design variables. Therefore, a second-level approximation is introduced to solve the FA by considering a sequence of second-level approximate problems SA in the design variable space. This approach is a Two-Level Approximation Concept. Its application to space frame synthesis shows its good grasp of the mechanical nature of the problem. The computational results for several examples show that the method presented in this paper is very efficient.
    Additional Material: 5 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620290805
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  • 102
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    Iterated θ-method for hyperbolic equations (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 271-290 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The iterated θ-methods employing residue smoothing for finding both steady state and time-accurate solutions of semidiscrete hyperbolic differential equations are analysed. By the technique of residue smoothing the stability condition is considerably relaxed, so that larger time steps are allowed which improves the efficiency of the method. The additional computational effort involved by the explicit smoothing technique used here is rather low when compared with its stabilizing effect. However, in the case where time-accurate solutions are desired, the overall accuracy may be decreased. This paper investigates the effect of residue smoothing on both the stability and accuracy, and presents a number of explicitly given methods based on the iterated implicit midpoint rule (θ = 1/2). Numerical examples confirm the theoretical results.
    Additional Material: 12 Tab.
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    URL: http://dx.doi.org/10.1002/nme.1620300205
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  • 103
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    Numerical analysis of three-time-level finite difference schemes for unsteady diffusion-convection problems (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 307-330 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: For the linear diffusion-convection model problem, this paper develops the numerical analysis of two classes of three-time-level second order finite difference schemes: weighed schemes similar to two-step schemes for differential equations and LF schemes based on the classical conservative approximation of the wave equation. As in our paper devoted to two-level schemes, Fourier Analysis is an essential tool which yields several key properties (stability, dissipation, numerical diffusion and dispersion). It also permits the analysis of parasitic solutions characteristic of three-level schemes and their control in terms of the starting scheme.The analysis is completed by giving results on the accuracy, positivity and parabolicity of the numerical schemes.The main conclusions are the expected superiority of these schemes over two-level schemes when the diffusion phenomenon is not negligible (cell Reynolds number less than 1) and the very limited possibilities of obtaining satisfactory numerical results (even with upstream differencing) when convection is strongly predominating.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620300207
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  • 104
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    Radiative ignition of fabrics and assemblies: Experiments and modelling (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 859-873 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Radiative ignition studies wre carried out on vertical 2.54 cm circular fabric pairs, and single fabrics of 2.54 cm diameter and 15.2 × 15.2 cm. These fabrics were exposed to a time invariant radiative heat flux using the Large Ignition test Apparatus (LITA) and the Radiative Ignition Time Apparatus (RITA). A model has been developed which uses a quasi-steady-steady-state approximation for the gas pahse. The transient effects and the thermal interaction between the plne-parallel fabrics are accounted for through the variation of the fabric temperature with time. Ignition is considered to occur when the gas phase pyrolysate reaction rate is equal to the rate of pyrolysis. The predicted ignition times are compared with measured values and they show excellent agreement. Ignition times were found to depend strongly on heat flux, fabric size, interface spacing and oxygen concentration. IN the presence of a back fabric, the ignition time of the front fabrics decreases and this reduction is more pronounced at lower radiative heating intensities. Strong thermal interaction between the fabrics was also observed and it is expected that such interactions are responsible for the reduction of ignition time of the front fabric. No evidence of chemical interaciton has been observed.
    Additional Material: 6 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620300418
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  • 105
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    Announcements (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 915-917 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620300421
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  • 106
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    Masthead (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990) 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620300501
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  • 107
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    The dual reciprocity boundary element method for spontaneous ignition (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 953-963 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper studies the non-linear heat conduction problem of spontaneous ignition of a reactive solid by using the dual reciprocity formulation of the boundary element method. First, critical values of the Frank-Kamenetskii parameter δ are computed for some common geometrical shapes. Then, transient analyses are carried out for values of δ below and above δc, producing the expected behaviour, with ignition occurring for δ 〉 δc.
    Additional Material: 6 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620300502
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  • 108
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    Approximate predictions of ice accretion along conductors of finite torsional stiffness and control of rotation using counterweights (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 965-980 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A mathematical/computational model for the approximate prediction of ice accretion on a conductor of finite torsional stiffness is constructed. The model, which is adapted to allow for the attachment of counterweights along the span, is three-dimensional and time-dependent. In the absence of counterweights, axial growth is predicted near the anchors, and cylindrical-sleeve growth at the centre of the conductor span. The latter is caused by eccentric ice loading on the windward side of the conductor which then induces the conductor to rotate.The ‘icing-clock’ model, based on the use of the large relaxation time approximation for particle impaction, yields an upper bound to the mass of ice accreted. At the end of each deposit time the torque density along the conductor span due to ice loading is calculated. On solving the non-linear torsion equation for the conductor the rotation of the conductor and location of the evolving ice surface as a function of the distance from the tower and the accretion time are then deduced.Numerical results are given for conductor with varying mechanical properties, which are represented in terms of a single dimensionless torque parameter, with and without the attachment of counterweights. For a specific case illustrative results are given for the mass of ice accreted and conductor rotation when one, two, three and four counterweights are attached per span.
    Additional Material: 10 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620300503
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  • 109
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    Rates of change of closed-loop eigenvalues and eigenvectors of actively controlled structures (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 1013-1028 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The sensitivity of the closed-loop eigenvalues and eigenvectors of actively controlled flexible structures with distinct eigenvalues is considered. The sensitivity information is essential in the optimization of large space structures with stability/performance robustness, closed-loop eigenvalues or damping ratios treated as objective or constraint functions. The efficiency of the analytical expressions derived for the rates of change of the closed-loop eigenvalues with respect to structural design variables is demonstrated through two numerical examples. The utility of the sensitivity of the closed-loop eigenvalues and eigenvectors in evaluating the derivatives of the stability and performance robustness indices is also indicated and illustrated through numerical examples.
    Additional Material: 10 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620300505
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  • 110
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    Viscous flow and transport with moving free and reactive surfaces (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 1181-1194 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Transport of a chemical species through a viscous fluid with reaction at an interface is modelled by a quasi-static process in which the transient behaviour is dominated by motion of the reactive surface. The reaction is accompanied by a molar volume change which leads to motion of the free surface. A decoupled stream function-vorticity formulation is introduced in conjunction with a moving finite element method. This also permits convenient treatment of the free and reactive surface boundary conditions. The model is applied to the growth of oxide films on silicon surfaces and reveals the effect of surface curvature on film growth.
    Additional Material: 10 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620300607
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  • 111
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    A numerical model for immiscible two-phase fluid flow in a porous medium and its time domain solution (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 1195-1212 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The governing equations for the interaction of two immiscible fluids within a deforming porous medium are formulated on the basis of generalized Biot theory. The displacement of the solid skeleton, the pressure and saturation of wetting fluid are taken as primary unknowns of the model. The finite element method is applied to discretize the governing eqations in space. The time domain numerical solution to the coupled problem is achieved by using an unconditionally stable direct integration procedure. Examples are presented to illustrate the performance and capability of the approach.
    Additional Material: 4 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620300608
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  • 112
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    Conference diary (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 1229-1232 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620300610
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  • 113
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    Masthead (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990) 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620300701
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  • 114
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    Benchmark problems and testing of a finite element code for solidification in investment castings (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 1301-1320 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Owing to an increased interest in numerical (finite element and finite difference) simulation of solidification in commercial investment castings, there is a need for proper evaluation of candidate codes. This paper presents a systematic selection of several benchmark problems designed to test modelling of latent heat release in pure metals and superalloys, thermal resistance at the metal/mould interface, temperature dependent material properties and far field radiation. For purpose of demonstration, these problems were analysed with a 2-dimensional finite element code, TOPAZ, available in the public domain; one problem was analysed with its 3-dimensional counterpart, TOPAZ3D, also. The numerical experimentation in the course of this study resulted in several findings of practical value, which are highlighted in the paper.
    Additional Material: 17 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620300706
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  • 115
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    Finite element simulation of three-dimensional deformation in shape rolling (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 1431-1440 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A method for simulating three-dimensional steady-state deformation in shape rolling with grooved rolls by the rigid-plastic finite element method is proposed. For the three-dimensional element mesh, contact of the nodal points with the roll surface and detachment from the surface are judged in each step of calculation. The boundary conditions of metal flow along the curved roll surface and of friction between the roll and the workpiece are dealt with at each node over the interface. Complex steady-state deformation in shape rolling is simulated by using the non-steady-state scheme and the remeshing technique. As examples of simulation, rolling processes of bars and beams with grooved rolls are chosen. The deforming shape, the rolling torque, the roll separating force and the distributions of stress and strain in the workpiece are computed.
    Additional Material: 11 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620300807
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  • 116
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    A study of heat transfer during flat rolling (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 1459-1469 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Two finite element thermal models of the flat rolling process are presented. The first gives a steady-state convective-diffusion solution in the centre plane and the other a non-steady-state solution in the plane perpendicular to the strip axis. To account for mechanical events the models use a rigid-plastic finite element approach. The predictions of both models are compared with temperature measurements carried out in laboratory conditions during hot rolling of low carbon steel and cold rolling of aluminium. The models are also tested against temperature measurements in the seventh stand of a production type continuous hot strip mill. Conclusions are drawn regarding the adequacy of both two-dimensional models for various kinds of flat rolling processes.
    Additional Material: 8 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620300809
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  • 117
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    Progress in mixed Eulerian-Lagrangian finite element simulation of forming processes (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 1441-1457 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A review is given of a mixed Eulerian-Lagrangian finite element method for simulation of forming processes. This method permits incremental adaptation of nodal point locations independently from the actual material displacements. Hence numerical difficulties due to large element distortions, as may occur when the updated Lagrange method is applied, can be avoided. Movement of (free) surfaces can be taken into account by adapting nodal surface points in a way that they remain on the surface. Hardening and other deformation path dependent properties are determined by incremental treatment of convective terms. A local and a weighed global smoothing procedure is introduced in order to avoid numerical instabilities and numerical diffusion. Prediction of contact phenomena such as gap openning and/or closing and sliding with friction is accomplished by a special contact element. The method is demonstrated by simulations of an upsetting process and a wire drawing process.
    Additional Material: 17 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620300808
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  • 118
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    An automatic remeshing technique for finite element simulation of forming processes (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 1503-1525 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An automatic remeshing scheme has been developed to enable finite element simulation of complicated forming processes. In order to avoid the tedious procedures of interrupting the analysis, performing rediscretization, mapping of current state variables and preparing the new set of boundary conditions, a fully automatic remeshing method is described. The different steps of this method are presented with the help of one industrial example.
    Additional Material: 25 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620300811
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  • 119
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    Computer aided simulation of metal flows in non-axisymmetric extrusions through bridge dies (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 1609-1617 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A computer aided simulation technique based on the upper bound theorem is developed in order to analyse three-dimensional metal flows of workpieces in various extrusion processes. The developed method is applied to simulations of forward extrusions of tubes through bridge dies. The effects of die geometry on extrusion pressure, geometries of dead zone and plastic zone and three-dimensional flow of workpiece are calculated. The results are compared with experimental measurments and fairly good agreement between them is found.
    Additional Material: 10 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620300817
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  • 120
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    Axisymmetric contact of an elastic layer underlain by rigid base (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 57-72 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Axisymmetric contact problems of an elastic layer are studied in this paper. The lower surface of the layer is either bonded to or in smooth contact with a rigid base. The upper surface is in tensionless smooth contact with a rigid flat cylinder, a rigid sphere, an elastic sphere or a circular plate, respectively. A general method is developed so that all these related problems are treated in a straightforward and like manner. In comparison to the other methods used in previous papers, the simplicity and high numerical accuracy are the major advantages of this method. The convergence is proved by comparing the numerical values to some available analytical solutions. Extensive numerical results for contact radii, displacements and contact pressures are provided.
    Additional Material: 8 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620290106
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  • 121
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    Conference diary (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 679-682 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620290314
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  • 122
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    An accurate determination of stresses in thick laminates using a generalized plate theory (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 1-14 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Analytical solutions for displacements and stresses in composite laminates are developed using the laminate plate theory of Reddy. The theory accounts for a desired degree of approximation of the displacements through the laminate thickness, allowing for piecewise approximation of the inplane deformation through individual laminae. The solutions are compared with the 3-D elasticity solutions for the simply supported case and excellent agreement is found. Analytical solutions are also presented for other boundary conditions. The results indicate that the generalized shear deformation plate theory predicts accurate stress distributions in thick composite laminates.
    Additional Material: 12 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620290103
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  • 123
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    Numerical integration strategy for plates and shells (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 105-121 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper compares the overall performance of a wide range of numerical procedures that can be used to integrate through the thickness of plates and shells. Results are presented for the accuracy of the calculations when there are discontinuities in the stress through the depth of the plate, and the available methods are ranked according to their accuracy.
    Additional Material: 5 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620290108
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  • 124
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    Application of the complex variable boundary element method to solving potential problems in doubly connected domains (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 161-179 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The complex variable boundary element method (CVBEM) developed by Hromadka for the solution of potential problems in simply connected domains is extended to the solution of heat conduction problems in doubly connected domains. A cut is made in the doubly connected domain, and it was found that the complex potentials along the cut do not cancel out but result in a complex stream function that plays the role of perturbation in the nodal equations. Cauchy-Riemann conditions are used to derive additional equations which relate the stream functions and the boundary heat fluxes and potentials when Neumann and Robin conditions are imposed on the boundaries. The resulting nodal equations are expressed in matrix form, and coding rules and methods for checking the matrix elements are developed. Three solution methods (implicit, explicit and hybrid) are described, and by means of examples, the efficacy of these methods is discussed and compared.
    Additional Material: 8 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620290111
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  • 125
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    Authors' reply (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 217-218 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 2 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620290115
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  • 126
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    The generalized boundary element approach to Burgers' equation (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 245-261 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The generalized boundary element method is presented for the numerical solution of Burgers' equation. The new method is based on the set of boundary integral equations derived for each subdomain by using the fundamental solution for the linearized differential operator of the equation. The resulting system of quasi-non-linear equations is solved implicitly with use of a simple iterative procedure. The adaptability and the accuracy of the proposed method are demonstrated by three examples and a comparison of the numerical results with the exact solution or other existing solutions is shown for the first example.
    Additional Material: 13 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620290203
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  • 127
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    Adaptivity in hybrid-Trefftz finite element formulation (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 391-405 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: With the advent of computer aided design (CAD), the development of fully or semi-automated procedures by which a solution warranting the specified accuracy can most efficiently be reached has become a necessity. It is now of utmost interest to investigate finite element (FE) formulations offering a simple form of adaptivity, easy to implement.The present study (which is a sequel to an earlier paper1 on error estimation by the authors) identifies as a particularly promising approach of attaining this goal the p-method associated with the so-called hybrid-Trefftz FE model.2 Based on a simple stress error estimator1 and prior knowledge of the convergence rate, the solution warranting specified stress accuracy may be reached in a single trial by suitably respecifying just one parameter in the input data. The reported approach has successfully been implemented into the general purpose FE program SAFE3 and its high efficiency is illustrated in the paper through practical applications involving corner singularities and stress concentrations.
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    URL: http://dx.doi.org/10.1002/nme.1620290212
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    Masthead (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990) 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620290301
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    Automatic step size correction for non-associated plasticity problems (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 579-598 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The finite element method is used in calculating accurate collapse loads. The behaviour of granular materials is described by the non-associated Mohr-Coulomb model. The load-displacement path is traced up to and beyond limit points using an accelerated initial stiffness method. The convergence properties of this method are examined, both for associated and non-associated plasticity.Step sizes in the incremental iterative procedure are adapted during the iteration process, depending on an estimated number of iterations. The automatic step size control thus obtained proves to be robust and particularly appropriate for non-associated plasticity. Some soil collapse calculations are discussed to demonstrate the practical application of the method.
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    URL: http://dx.doi.org/10.1002/nme.1620290308
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    A surface fitting method for three dimensional scattered data (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 633-645 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A method is presented that may be used to empirically establish the type of relationship that is present between a response variable and its influencing factors, by fitting a mathematical model to three dimensional scattered data. The generated response surface is composed of continuous triangular planes that are fitted to the corresponding data in the least squares sense. The method may be easily implemented. It requires some fairly large number of scattered data, two initial boundary conditions and a desired accuracy for the band-wise partitioning of the data. The proposed surface fitting technique has been successfully applied to solar radiation modelling for a number of different data combinations.
    Additional Material: 9 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620290311
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    The multigrid method in solid mechanics: Part II - Practical applications (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 739-753 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The performance of the multigrid algorithm is investigated by solving some large, practical, three dimensional solid mechanics problems. The convergence of the method is sensitive to factors such as the amount of bending present and the degree of mesh non-uniformity, as was also observed in Part I for two dimensional problems. However, in contrast to Part I, no proportionality is observed between the total number of operations to convergence and the problem size. Despite such behaviour, the multigrid algorithm proves to be an effective matrix equation solver for solid mechanics poblems. It is orders of magnitude faster than a direct factorization method, and yields converged solutions several times faster than the Jacobi preconditioned conjugate gradient method.
    Additional Material: 14 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620290405
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    Some observations on time domain and frequency domain boundary elements (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 785-800 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The numerical solution of problems in elastodynamics involving infinite media calls for the use of discrete techniques such as the boundary element method and the finite element method. These techniques can, in turn, be formulated in the time or frequency domains, and have each relative merits and drawbacks. This paper presents a comparative study of the accuracy and limitations of three different implementations of these methods.The problem studied is that of transient loads on the surface of homogeneous elastic halfspaces, and of finite depth strata. In each case, the response is computed first for an uninterrupted (continuous) medium, and then for a medium that includes a trench (or cavity).Three independent computer programs were used that incorporated the following methods: (i) frequency domain boundary element method (FD-BEM), using a discrete fundamental solution; (ii) time domain boundary element method (TD-BEM) using an analytical fundamental solution; and (iii) a coupled time domain boundary element-finite element model (BEM/FEM).It is found that for convex domains (halfspace or stratum without a trench) the three independent implementations are in excellent agreement, while for non-convex domains (trench in the path of the waves), numerical errors associated with non-causal behaviour become evident in some cases.
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    A non-Jacobian numerical quadrature for semi-infinite integrals (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 833-846 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A non-Jacobian numerical quadrature is proposed for evaluating improper integrals over a semi-infinite range. The quadrature first transforms the semi-infinite integration limit into a finite limit between - 1 and 1. Standard numerical integration procedures such as Gauss-Chebyshev or Gauss-Legendre schemes can then be used to obtain the integral value. Unlike traditional methods using Laguerre or Hermite polynomials, numerical results show that no specific weight function is required for the proposed quadrature to converge as long as the integral exists. The transformation also includes a scale parameter which effectively expands the numerical-integration sampling points along its original semi-infinite integration path. Numerical examples shows that selection of the scale parameter is rather flexible and convergence can always be achieved within a wide range of parameter values. Several applied mechanics problems are also illustrated to validate the proposed numerical scheme. The quadrature can be easily incorporated into finite element or boundary element schemes for the evaluation of semi-infinite integrals.
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    Data structures and algorithms for the finite element method on a data parallel supercomputer (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 881-908 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This article describes a formulation of the finite element method and its implementation on a data parallel computing system. The Connection Machine® system, CM-2, has been used as the model architecture. Data structures, storage requirements, communication and parallel arithmetic complexity are analysed in detail for the cases when a processor represents an unassembled finite element and when a processor is assigned to an unassembled nodal point. Data parallel algorithms for the grid generation, the evaluation of the elemental stiffness matrices and for the iterative solution of the linear system are presented. The algorithm for evaluating the elemental stiffness matrices computes the matrix elements concurrently without communication. This concurrency is in addition to the inherent parallelism present among different finite elements. A conjugate gradient solver with diagonal pre-conditioner is used for the solution of the resulting linear system. Results from an implementation of the three-dimensional finite element method based on Lagrange elements are reported. For single-precision floating-point operations, the measured peak performance is approximately 2·4 G flops s-1 for evaluating the elemental stiffness matrices and approximately 850 M flops s-1 for the conjugate gradient solver. On a Connection Machine system with 16K physical processors, the time per conjugate gradient iteration for an application with 400 000 degrees of freedom is approximately 0·13 s for double-precision floating-point operations.
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    URL: http://dx.doi.org/10.1002/nme.1620290414
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    A fixed grid finite element technique for modelling phase change in steady-state conduction-advection problems (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 969-984 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new fixed grid finite element technique for modelling phase-change effects in steady-state conduction-advection problems is described. The method is appropriate for materials that transform at a fixed critical temperature and is based on the assumption that the enthalpy experiences a jump discontinuity at this temperature, yielding a singular specific heat. This singularity is described using a Dirac delta function and the appropriate finite element matrix equations are developed for isoparametric elements. A simple first order upwinding scheme is used to avoid numerical oscillations in advection dominated problems. The utility of the method is illustrated through the solution of a one-dimensional test problem using eight-node hexahedral isoparametric finite elements. The technique may be applied to a wide range of finite element types and offers a number of advantages over other schemes for modelling phase-change effects.
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    URL: http://dx.doi.org/10.1002/nme.1620290505
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    Finite element analysis of multiconductor printed-circuit transmission-line systems (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 1033-1047 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper the finite element method (FEM) is used to analyse general, multiconductor transmission-line systems of arbitrary cross-section. The per-unit-length matrices of capacitance, inductance, conductance and resistance, which characterize a multiconductor transmission line, are obtained from the FEM analysis. Numerical results are presented and compared both with experimental results and other available data.
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    Conference diary (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 1131-1134 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620290515
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    Erratum (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. ii 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620290602
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    Tangent constitutive matrices for inelastic finite element analysis (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 1193-1203 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A general formulation is presented for the tangent constitutive matrices of rate-independent material models which assume that the strain increment consists of two components. One component is related to the stress increment through a known constitutive matrix, while the other component results from deformation mechanisms not reflected in the constitutive matrix. The procedure to modify the known matrix for these additional strains is specified. The formulation is a generalization of the well-known procedure used in plasticity to modify the elastic constitutive matrix for plastic deformation. Application to both the classical and endochronic theories of plasticity and to a smeared crack theory is illustrated.
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    Error indicators for adaptive mesh refinement in the boundary element method - a new approach (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 1247-1269 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper a new approach to the development of a posteriori error indicators for the direct boundary element method (BEM) is presented. It takes advantage of a unique opportunity offered by the collocation BEM, that is the possibility of obtaining more than one numerical solution from a given boundary element mesh. Unlike other approaches, the error indicator introduced in the present paper does not require any explicit evaluation of the residual of the approximate solution. In order to test the capability of the proposed error indicators to actually control a selective mesh refinement process, an h-adaptive refinement strategy is also described, together with the criteria for refinement and for the termination of the adaptive process. Full details on the whole numerical implementation for two-dimensional problems are provided. In particular, there is described a direct method for the numerical evaluation of Cauchy principal value integrals. Numerical examples show that pointwise convergence is always obtained in a few steps and the final meshes look nearly as if they were designed by an expert analyst.
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    URL: http://dx.doi.org/10.1002/nme.1620290610
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    A boundary element algorithm using compatible boundary displacements and tractions (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 1323-1341 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: With the aid of Muskhelishvili's complex plane elasticity solution representation compatible displacement and stress fields are constructed. The complex functions in these formulas are represented by Cauchy integrals, which are discretized along the boundary with the aid of complex shape functions for each boundary element. The constructed displacement and stress functions satisfy the Navier equations and the equilibrium equations, respectively. The use of fifth order complex basis functions with continuous second complex derivatives gives numerical results of high accuracy.
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    Announcement (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. ii 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620290102
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    A full tangent stiffness field-boundary-element formulation for geometric and material non-linear problems of solid mechanics (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 15-35 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The field-boundary-element method naturally admits the solution algorithm in the incompressible regimes of fully developed plastic flow. This is not the case with the generally popular finite-element method, without further modifications to the method such as reduced integration or a mixed method for treating the dilatational deformation. The analyses by the field-boundary-element method for geometric and material non-linear problems are generally carried out by an incremental algorithm, where the velocities (or displacement increments) on the boundary are treated as the primary variables and an initial strain iteration method is commonly used to obtain the state of equilibrium. For problems such as buckling and diffused tensile necking, involving very large strains, such a solution scheme may not be able to capture the bifurcation phenomena, or the convergence will be unacceptably slow when the post-bifurcation behaviour needs to be analysed. To avoid this predicament, a full tangent stiffness field-boundary-element formulation which takes the initial stress-velocity gradient (displacement gradient) coupling terms accurately into account is presented in this paper. Here, the velocity field both inside and on the boundary are treated as primary variables. The large strain plasticity constitutive equation employed is based on an endochronic model of combined isotropic/kinematic hardening plasticity using the concepts of material director triad and the associated plastic spin. A generalized mid-point radial return algorithm is presented for determining the objective increments of stress from the computed velocity gradients. Numerical results are presented for problems of diffuse necking, involving very large strains and plastic instability, in initially perfect elastic-plastic plates under tension. These results demonstrate the clear superiority of the full tangent stiffness algorithm over the initial strain algorithm, in the context of the integral equation formulations for large strain plasticity.
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    Boundary elements in zoned media: Direct and indirect methods (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 1727-1735 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Several formulations of the Boundary Element Method (BEM) are examined herein in the context of heterogeneous media. A strong singularity develops at re-entrant interzonal corners and its effect is made more acute by large differences in the material properties. The effects of this singularity on the performance of the various BEM formulations are illustrated with examples. It is concluded that the direct BEM, either in the collocation or Galerkin formulations, is unable to give good results in zones of low conductivity. On the other hand the indirect BEM does not adequately reproduce the behaviour of the flow field near boundaries. A multi-step version of the direct BEM is formulated to eliminate the difficulties introduced by the interzonal singularities.
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    URL: http://dx.doi.org/10.1002/nme.1620290808
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    Gauss quadrature rules for finite part integrals (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 13-26 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We construct a set of polynomials ϕn(x,ζ) which are orthogonal with respect to w(x)/(x - ζ)2, where w x is a weight function. These polynomials can be used for the definition of a Gauss quadrature formula for the finite part integral The process is exactly the same as the one used for the extraction of the classical Gauss formula for the Riemann integrals. Three different methods are derived.The first and most accurate quadrature formula is successfully tested in some numerical examples. The proposed quadrature formulas have many applications in problems of mathematical physics, mechanics, etc.
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    Dynamics of general flexible multibody systems (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 77-97 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A general treatment is presented for modelling the dynamics of a flexible multibody system, using a lumped mass finite element approach. The system topology considered here is defined as an arbitrary combination of both rigid and flexible bodies, connected together by joints that permit translation and compliance, in a general tree configuration. An extension to handle closed loop kinematic chains is also indicated. Kane's theory of generalized speeds, which is based on the Lagrange-D'Alembert principle, is used to derive the equations of motion, and this results in a very efficient computer oriented methodology for solving the dynamics of such large mechanical systems. To facilitate numerical computations, these dynamical equations are transformed into a system of first-order differential equations for an explicit formulation of the problem. The accuracy of the proposed formulation is assessed via three examples with known solutions. The results obtained indicate the method is accurate, efficient and versatile for the analysis of a general, flexible multibody system.
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    Finite element/Newton method for the analysis of Czochralski crystal growth with diffuse-grey radiative heat transfer (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 133-154 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A quasi-steady-state, integrated system model describing high temperature heat transfer, solidification and the action of capillarity in the Czochralski crystal growth process is solved by a finite element/Newton method. The numerical analysis couples the calculation of the temperature field in all phases and the determination of the melt/crystal and melt/gas interfaces and the crystal radius free boundaries. The analysis includes conductive heat transfer in the melt, crystal, crucible, pedestal, heater and the surrounding insulation and diffuse-grey radiation, which couples the heat transfer between surfaces, the crystal radius and the melt/gas free boundary through the view factors. Finite element approximations are used to reduce the entire problem to a coupled set of non-linear algebraic equations. These are solved simultaneously by Newton's method with the Jacobian matrix computed by a combination of closed form expressions and finite difference approximations. Quadratic convergence of the Newton iteration is demonstrated along with a factor of four increase in computational efficiency over a successive iteration procedure that decouples the calculation of radiation from the rest of the heat transfer model.
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    URL: http://dx.doi.org/10.1002/nme.1620300109
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    Monte Carlo simulation of indoor radiant environment (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 615-627 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper describes a numerical method of radiant environment analysis in a complicated enclosure containing human bodies and furniture. An arbitrary configuration expressed in a three-dimensional co-ordinate system can be treated by this method. A unique space index and another surface index are proposed to specify the geometry of solid body and surface in the enclosure. The Monte Carlo method is used to determine direct interchange areas, which are then transformed into total exchange areas using the zone method. Energy balance equations accounting for thermal radiation, convection, wall conduction and air ventilation are then formulated for each solid surface segment in the enclosure. A human body model with skin temperatures and clothing is also proposed to simulate its heat release and to predict local thermal sensation around the body. As a practical application, this method is applied to the analysis of the radiant environment in a floor-heated meeting room with eight people seated around a table.
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    F.E.M. in steady MHD duct flow problems (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 647-659 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The governing equations and the boundary conditions of steady incompressible magnetohydrodynamic (MHD) problems are adapted to the case of steady MHD flow in simply connected cross sections with arbitrary wall conductance. The problem is then solved numerically by means of the finite element method based on the weighted residual approach, and solutions for industrially relevant Hartmann numbers and non-symmetric kinetic fields are presented.
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    A conservative algorithm for multidimensional conduction phase change (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 697-709 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper, a generally applicable version of an algorithm, for multidimensional phase change conduction, is presented which bridges the gap between ‘full enthalpy’ and ‘equivalent heat capacity’ methods. In the text the problem is formulated first with reference to the three-time-level method for the FE analysis of non-linear heat conduction. Then the suggested algorithm is utilized as a ‘corrector’ which can be activated for the analysis of isothermal phase change problems. In the corrector step the enthalpy balance is recovered from the standard formulation, and temperatures are post-calculated by means of the inverse temperature vs. enthalpy function. The algorithm is verified in one-dimensional situations by comparing the results obtained with available analytical and numerical solutions for boundary conditions of the first kind (temperature) and of the third kind (convection). Finally, as a 2-D test problem, a solution is presented for inward solidification in a cylinder, using Cartesian co-ordinates to demonstrate robustness with respect to space deformation of the mesh.
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    The numerical simulation of heat conduction in irregularly-shaped materials of thermally-dependent properties (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 679-696 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The numerical simulation of conduction heat transfer in arbitrarily-shaped regions is relevant to many engineering applications including the casting of plastics and metals, cold region problems and latent heat storage. This class of problem offers its particular challenges. The accurate computational simulation of conduction with thermally-dependent properties requires a solution technique with good conservation properties. The boundary-fitted co-ordinates of an arbitrary solution domain typically yield grids which are non-orthogonal and which, consequently, make energy conservation difficult to model.In the current article, a technique is described to simulate accurately the conduction heat transfer in materials of thermally-dependent properties in irregular domains. The method combines boundary-fitted co-ordinates with the finite volume method, FVM, to produce a numerical technique which will accurately solve this non-linear conduction problem using a grid which may be highly skewed. This capability is achieved through a unique treatment of the cross-derivative terms that arise when the heat conduction equation is transformed to a non-orthogonal grid. The cross-derivative terms represent the non-normal components of the heat fluxes into the skewed control volume. The tangent components of the heat fluxes are interpreted in a special way to produce finite difference expressions which accurately model the cross-derivative partial.The numerical procedure is validated by comparing it against a purely analytical mathematical method. Although the numerical results have been obtained using a highly skewed grid, they exhibit close agreement with the analytically-derived solution.
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    URL: http://dx.doi.org/10.1002/nme.1620300409
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    A boundary-integral formulation for complex three-dimensional geometries (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 263-273 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new boundary-integral formulation is proposed to analyse the heat transfer in complex three-dimensional geometries. One example of such geometry is the die sets in the injection moulding process. Networks of cooling conduits within the mould and the closely spaced die surfaces require special attention both in formulation and numerical treatment of the integral equations. The proposed formulation couples the boundary formula, the gradient of the boundary formula and the exterior formula. The derivation of the integral equations is presented here along with an efficient method for integration of some of the kernels in these equations and a semi-analytical procedure for the integration of the highly singular integrands which result from differentiating the boundary formula. Although the techniques introduced here are applied to a particular problem in heat transfer, their potential application is much broader.
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    URL: http://dx.doi.org/10.1002/nme.1620290204
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    Free-vibration analysis of three-dimensional solids by BEM (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 1737-1757 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In practical applications, it is often necessary to determine the natural frequencies and mode shapes of a solid, in addition to the static response under a variety of loading conditions. This paper discusses the calculation of natural frequencies and mode shapes of three-dimensional solids using the boundary element method. The method developed is based on the use of particular integrals of the elastic equilibrium equations, and employs only real arithmetic. It represents an extension to three dimensions of work previously carried out for two-dimensional problems in References 1 and 15. The method has been incorporated, for multiregion analysis, in the BEST3D (Boundary Element Solution Technology - Three Dimensional) computer program.Much of the work described in this paper was carried out under the support of National Aeronautics and Space Administration Contract NAS3-23697, ‘3D Inelastic Analysis Methods for Hot Section Components’. The program managers at the NASA-Lewis Research Center are Dr C. C. Chamis and Mr Dale Hopkins. The program manager at Pratt & Whitney is Dr E. S. Todd Results of the boundary element calculations are compared with analytical, finite element and experimental results.
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    Partial hybrid stress element for transient analysis of thick laminated composite plates (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 1787-1796 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The variationally consistent partial hybrid stress element proposed by the authors is extended to transient analysis of thick laminated composite plates in this paper. Through dividing six stress components into flexural (σx, σy, τxy, σz) and transverse shear (τxz, τyz) parts, the corresponding dynamic version of the modified Hellinger-Reissner principle is presented. By assuming stress parameters for transverse shear only, the partial hybrid stress element can be used to solve transient problems without any contradiction. The mass matrix derived is a simply consistent mass regardless of the assumed stress field. Comparisons are made with results available in the literature. Through thickness variations of all the six stress components for a dynamic version of Pagano's example are also presented for the first time. These results can serve as a reference source for future comparisons.
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    Transient finite element computations on 65536 processors: The connection machine (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 27-55 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper reports on our experience in solving large-scale finite element transient problems on the Connection Machine. We begin with an overview of this massively parallel processor and emphasize the features which are most relevant to finite element computations. These include virtual processors, parallel disk I/O and parallel scientific visualization capabilities. We introduce a distributed data structure and discuss a strategy for mapping thousands of processors onto a discretized structure. The combination of the parallel data structure with the virtual processor mapping algorithm is shown to play a pivotal role in efficiently achieving massively parallel explicit computations on irregular and hybrid two- and three-dimensional finite element meshes. The finite element kernels written in C*/Paris have run with success to solve several examples of linear and non-linear dynamic simulations of large problem sizes. From these example runs, we have been able to assess in detail their performance on the Connection Machine. We show that mesh irregularities induce an MIMD (Multiple Instruction Multiple Data) style of programming which impacts negatively the performance of this SIMD (Single Instruction Multiple Data) machine. Finally, we address some important theoretical and implementational issues that will materially advance the application ranges of finite element computations on this highly parallel processor.
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    Generalized axisymmetric elastodynamic analysis by boundary element method (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 115-131 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The boundary element formulation for three-dimensional problems of steady state (periodic) dynamic analysis has been cast into the generalized axisymmetric form by expressing the boundary tractions and displacements in terms of a Fourier series expansion. The resulting formulation has been developed for the dynamic analysis of axisymmetric geometries subjected to non-axisymmetric loading. The analysis has been implemented in a large general purpose analysis capable of analysing both finite as well as semi-infinite domains and a series of examples has been shown to demonstrate the versatility of the implementation.
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    Analysis of locking and stress oscillations in a general curved beam element (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 177-200 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper, we have attempted to provide new insights into the phenomenon of shear and membrane locking in a general quadratic curved beam element. Locking is seen to be accompanied by significant quadratic oscillations in the axial force and cubic oscillations in the shear force. The functional reconstitution technique is applied to derive accurate error estimates for the manner in which locking is relieved and for the magnitude of the stress oscillations. The orthogonally correct field-consistent interpolations are determined for the optimal form of the element using an elegant concept of expanding strain interpolations in terms of Legendre polynomials. The popular two-point Gaussian integrated version of the element is shown to be non-orthogonal, resulting in a cubic oscillation in the shear force that curiously vanishes at the Barlow points.
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    URL: http://dx.doi.org/10.1002/nme.1620300111
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    A triangular element based on Reissner-Mindlin plate theory (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 1029-1049 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new triangular plate bending element based on the Reissner-Mindlin theory is developed through a mixed formulation emanating from the Hu-Washizu variational principle. A main feature of the formulation is the use of a linear transverse shear interpolation scheme with discrete constraint conditions on the edges. The element is shown to avoid shear locking, converge to the Kirchhoff plate theory as the plate thickness approaches zero, and generally exhibit excellent behaviour on a series of standard problems and tests.
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    Conference diary (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 1091-1094 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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    URL: http://dx.doi.org/10.1002/nme.1620300510
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    Hermitian cubic boundary elements for two-dimensional potential problems (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 1051-1062 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A hermite interpolation based formulation is presented for the boundary element analysis of two-dimensional potential problems. Two three-noded Hermitian Cubic Elements (HCE) are introduced for the modelling of corners or points with non-unique tangents on the boundary. These elements, along with the usual two-noded HCE, are used in numerical examples. The results obtained show that faster convergence can be achieved using HCE compared with using Lagrange interpolation type Quadratic Elements (QE), for about the same amount of computing resources.
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    Computational enhancement of an unsymmetric block Lanczos algorithm (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 1083-1089 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An unsymmetric block Lanczos algorithm has been employed for the dynamic analysis of a large system which has arbitrary damping and/or repeated (or closely spaced) eigenvalues. In the algorithm development, the right and left Lanczos vectors are all theoretically biorthogonal to each other. However, these vectors may lose the biorthogonality owing to cancellation and roundoff errors. For the unsymmetric case there can be a breakdown, even without numerical errors. This paper describes computational techniques which have led to a robust unsymmetric block Lanczos algorithm.
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    A mixed-penalty finite element formulation of the linear biphasic theory for soft tissues (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 1063-1082 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Hydrated soft tissues of the human musculoskeletal system can be represented by a continuum theory of mixtures involving intrinsically incompressible solid and incompressible inviscid fluid phases. This paper describes the development of a mixed-penalty formulation for this biphasic system and the application of the formulation to the development of an axisymmetric, six-node, triangular finite element. In this formulation, the continuity equation of the mixture is replaced by a penalty form of this equation which is introduced along with the momentum equation and mechanical boundary condition for each phase into a weighted residual form. The resulting weak form is expressed in terms of the solid phase displacements (and velocities), fluid phase velocities and pressure. After interpolation, the pressure unknowns can be eliminated at the element level, and a first order coupled system of equations is obtained for the motion of the solid and fluid phases. The formulation is applied to a six-node isoparametric element with a linear pressure field. The element performance is compared with that of the direct penalty form of the six-node biphasic element in which the pressure is eliminated in the governing equations prior to construction of the weak form, and selective reduced integration is used on the penalty term. The mixed-penalty formulation is found to be superior in terms of tendency to lock and sensitivity to mesh distortion. A number of example problems for which analytic solutions exist are used to validate the performance of the element.
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    Announcements (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 1095-1098 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620300511
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    Minimax multiobjective optimization in structural design (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 1213-1228 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The use of multiobjective optimization techniques, which may be regarded as a systematic sensitivity analysis, for the selection and modification of system parameters is presented. A minimax multiobjective optimization model for structural optimization is proposed. Three typical multiobjective optimization techniques - goal programming, compromise programming and the surrogate worth trade-off method - are used to solve such a problem. The application of multiobjective optimization techniques to the selection of system parameters and large scale structural design optimization problems is the main purpose of this paper.
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    An adaptive remeshing technique for non-Newtonian fluid flow (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 1555-1567 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An unstructured mesh generator is integrated in a finite element solver for the adaptive solution of non-Newtonian fluid flows. An a posteriori error estimate for the equations of motion is presented and is shown to behave according to theoretical convergence rates. The estimate is used to drive the refinement process, and the resulting iterative remeshing algorithm leads to reduction of the error level in the case of an axisymmetric contraction. Original data structures used to speed-up remeshing and interpolation between unstructured grids are also presented.
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    Finite element analysis of sheet metal forming problems using a selective viscous bending/membrane formulation (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 1577-1593 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper the possibilities of the viscous voided shell approach for deriving bending/membrane finite elements for sheet metal forming problems are presented. These elements can be selectively used for membrane or full bending analysis of some parts of the sheet according to the nature of the deformation. Numerical aspects of this approach are discussed and some examples of application are also given.
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    A numerical analysis of wrinkle formation tendencies in sheet metals (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 1595-1608 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A numerical analysis for the assessment of wrinkle formation tendencies in sheet metals is presented. A doubly-curved thin shell element under biaxial plane stress states is considered, and the critical stress values for wrinkling are determined. The analysis is based on plastic bifurcation theory for the buckling of thin shells in short-wavelength shallow modes. The effects of the various material and geometric parameters on wrinkling are investigated.
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    Simulation of the processing of thermoset polymers (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 1633-1647 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 11 Ill.
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    Finite element simulation of metal powder forming (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 1649-1674 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 11 Ill.
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    Elastic-viscoplastic implicit formulation for finite element simulation of complex sheet forming processes (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 1675-1697 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A formulation for numerical simulation of complex forming processes with generally shaped tools is developed. Special attention is drawn to the accuracy, efficiency and robustness. An incremental displacement approach based on Lagrangian formulation as well as an elastic-viscoplastic material model with Hill's cross-anisotropy, power law hardening and strain rate sensitivity are assumed. An implicit integration of the constitutive equations is derived. Frictional contact conditions yield additional constraint relations which, together with equilibrium equations, form the basis for derivation of the consistent tangent matrix. To further increase efficiency and accuracy, application of the adaptive remeshing procedures for sheet forming is investigated. The performance of the proposed algorithm is shown by comparison of the numerical results with the analytical solution for an in-plane stretching test and with the experimental measurements from 3-D sheet forming pressings where materials, radius and wall dimensions used are similar to those from industrial applications.
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    Numerical simulation of the superplastic forming of thin sheet components using the finite element method (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 1719-1737 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Superplastic forming is a manufacturing process whereby titanium or aluminium sheet is blow formed into a die to produce very light and strong aerospace components. Of crucial importance is the prediction of the final thickness distribution and the pressure cycle necessary to maintain superplasticity. This paper discusses a finite element based solution to these problems and presents examples for typical components including diffusion bonding effects.
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    On numerical modelling of hot rolling of metals (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 1699-1718 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A transient, thermomechanical model, METFORM, based on viscoplasticity and heat and mass transport theories has been developed specifically for the prediction of the flow behaviour of metals during hot rolling. The coupling of metal flow, heat transport and microstructural changes is discussed and a framework to account for the coupling behaviour is formulated. The model is partially verified by experiments and is applied to the hot strip mill roughing process, with the focus of interest on skid mark effects and related difficulties frequently observed in hot rolling. Methods for overcoming these difficulties are proposed based on the results obtained from the model. The coupling between microstructure development and the variations of local strain, strain gradient and temperature is confirmed by the predicted strain/strain gradients and micrographs obtained from a hot rolling experiment.
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    Finite element analysis of sheet forming processes (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 1739-1758 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper discusses several aspects of the simulation of sheet forming processes using finite elements. We begin with a brief description of the class of problems treated, emphasizing the main deformation modes present. The choice of finite element type for modelling the sheet - continuum, shell, membrane, or special purpose - is discussed in realation to the geometrical simplifications made with respect to deformation. We pay particular attention to the kinematic implementation of membrane (plane stress) deformation. Modelling problems associated with the interaction between the sheet and dies are then discussed: in particular, problems related to rigid surface representation and friction. A simplified model of drawbeads is described, which allows for macro-representation of this die detail. Some practical application examples are included to illustrate these points. The paper concludes with a general discussion of developments which we believe to be desirable for this type of simulation.
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    Hybrid method for transient response of circular pins (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 303-314 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The combined application of the Laplace transform and the finite element method is used to analyse the transient response of circular pins. The present method removes the time-dependence terms from the governing differential equations and boundary conditions using the Laplace transform and then the eigenfunction expansion method is applied to reduce the two-dimensional boundary value problem to that of one dimension. Accordingly, the final transformed equation can easily be solved by the finite element method. The transformed temperature is inverted to the physical quantity numerically. The present results agree well with analytical solutions. In addition, it is seen that the results of axisymmetric transient heat conduction problems with the central node at r = 0 can accurately be obtained using the present method.
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    Free vibration of axisymmetric solids by BEM using particular integrals (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 985-1001 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The free vibration of solids of revolution had never been solved by the Boundary Element Method (BEM) until a previous paper10 by the authors, in which the BEM was combined with the method of particular integrals to solve axisymmetric free vibration problems. In this paper the previously developed analysis is extended to study the non-axisymmetric free vibration of axisymmetric solids. The developed analysis has been implemented in a general purpose BEM system. Free vibrations of solid and hollow cylinders, a hyperbolic cooling tower and a gas turbine shell are used as examples, and their results are compared with those given by other methods. Except for low modes of very thin shells, good agreement can be seen.
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    URL: http://dx.doi.org/10.1002/nme.1620290506
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    Dynamic modelling of skeletal systems with arbitrary mass distributions (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 1219-1228 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This study develops and illustrates a dynamic model for vibration analysis of rod and beam elements with arbitrary mass distributions. This arbitrary mass model represents the element shape function using a frequency dependent series that becomes exact as the number of terms in the series approaches infinity. The arbitrary mass model yields the natural frequencies and modes of elements with mass distributions which vary as continuous functions of the spanwise co-ordinate.The arbitrary mass model, implemented using the unsymmetric formulation for vibration analysis, is illustrated in examples and compared with other dynamic models which use stepped mass representations to model the arbitrary mass distributions. Studies show that the arbitrary mass model is more computationally efficient than the stepped mass representation models, particularly when accuracy requirements are high.
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    URL: http://dx.doi.org/10.1002/nme.1620290608
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    An efficient L2 Galerkin finite element method for multi-dimensional non-linear hyperbolic systems (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 1229-1245 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An L2 Galerkin approximation is obtained by the use of specially chosen spaces of trial and test functions. The method combines the features of the orthogonal collocation and Galerkin finite element methods. This new algorithm can be more efficient by orders of magnitude than conventional discontinuous Galerkin finite element procedures in solving non-linear problems which require frequent reformulation of the coefficient matrices and right-hand-side vectors.
    Additional Material: 8 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620290609
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    Masthead (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990) 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620290701
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    Curved shell elements based on hierarchical p-approximation in the thickness direction for linear static analysis of laminated composites (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 1393-1420 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents a new curved shell finite element formulation for linear static analysis of laminated composite plates and shells, where the displacement approximation in the direction of the shell thickness can be of an arbitrary polynomial order p, thereby permitting strains of at least (p - 1) order. This is accomplished by introducing additional nodal variables in the element displacement approximation corresponding to the Lagrange interpolating polynomials in the element thickness direction. The resulting element displacement approximation has an important hierarchical property i.e. the approximation functions and the generalized nodal variables corresponding to an approximation order p are a subset of those corresponding to an approximation order (p + 1). The element formulation ensures C0 continuity or smoothness of displacements across the interelement boundaries.The element properties (stiffness matrix and equivalent load vectors) are derived using the principle of virtual work and the hierarchical element approximation. The formulation is extended for generally orthotropic material behaviour where the material directions are not necessarily parallel to the global axes. Further extension of this formulation for laminated composites is accomplished by incorporating the material properties of each lamina by numerically integrating the element stiffness matrix for each lamina. The formulation has no restriction on either the number of laminas or the layup pattern of the laminas. Each lamina can be generally orthotropic, and the material directions and the lamina thicknesses may vary from point to point within each lamina. The geometry of the laminated shell element is described by the co-ordinates of the nodes lying on the middle surface of the element and the lamina thicknesses at each node. The formulation permits any desired order displacement or strain approximation in the shell thickness direction without remodelling.Numerical examples are presented to demonstrate the accuracy, efficiency, and overall superiority of the present formulation. The results obtained from the present formulation are compared with those available in the literature as well as the analytical solutions.
    Additional Material: 16 Ill.
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    On the use of one point and two points singularity elements in the analysis of kinked cracks (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 1487-1499 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A 3-noded triangular two singular points finite element is proposed to model two variable order singularities lying at close proximities as in the case of a kinked crack. The element meets the rigid body mode and the interelement compatibility of the convergence criteria. A degenerate form of the element is a one point variable order singularity element, which meets all the convergence requirements. A number of kinked crack problems have been analysed using the new element and its degenerate form. The computed results are compared with analytical solutions. The accuracy of the results is found to be good.
    Additional Material: 9 Ill.
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    Conference diary (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 1589-1593 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620290714
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    Effect of integration methods on the solution of an adiabatic shear banding problem (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 1639-1652 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Equations governing the thermomechanical deformations of a block made of a viscoplastic material, and undergoing overall simple shearing deformations, are stiff in the sense that time scales associated with the heat conduction, viscous effects, strain hardening and strain-rate hardening may differ by several orders of magnitude as localization of the deformation initiates and proceeds. Because of the presence of high spatial gradients within the region of localization of the deformation, we also consider a viscoplasticity theory in which the strain gradient is taken as a kinematic variable. The Galerkin approximation of the pertinent initial-boundary-value problem yields an initial-value problem involving a set of coupled non-linear ordinary differential equations. The solution of these equations by the Crank-Nicolson, Adams-Moulton and the Gear methods reveals that the three methods give qualitatively similar results. However, quantitatively the results by the three methods differ somewhat, the difference being more for the dipolar theory.
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    On the superconvergence of the Satisfying-Babuska-Brezzi method (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 1715-1726 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A simple two-point boundary value problem, written in a mixed form, is shown to have superconvergence characteristics using the Satisfying-Babuska-Brezzi (SBB) method. Convergence and accuracy analyses reveal superior performance of the method compared to the usual Galerkin method.
    Additional Material: 4 Ill.
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    A numerical technique for the solution of two dimensional elasticity problems (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 1759-1785 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A numerical technique for the solution of two dimensional elasticity problems, referred to as The Method of Complex Finite Domains, is presented. The technique is based on assumed piecewise continuous fields of the Kolosov-Muskhelishvile complex potentials φ(z), Ψ(z). External loads and boundary conditions are modelled as continuous functions in terms of the functions' values at suitable quadrature points on the boundary. The method has a wide scope of applications because the structure of the complex potentials is known for many important regions and because of its flexiblity in modelling complex loads and boundary conditions. A numerical example that demonstrates the convergence and applicability of the method as well as the efficiency of the boundary load model is presented.
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    Conference diary (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 1799-1803 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Masthead (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990) 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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    URL: http://dx.doi.org/10.1002/nme.1620300101
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    Finite element solution of two-dimensional inverse elastic problems using spatial smoothing (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 57-75 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A finite element method (FEM) is presented for calculating the surface tractions on a body from internal measurements of displacement at discrete sensor locations. The solution algorithm employs a sensitivity analysis which minimizes the difference between the calculated and measured displacements at each sensor location. Spatial regularization is one technique employed to stabilize the minimization process by imposing various degrees of smoothness on the solution. It also allows the problem to be solved with fewer sensors than traction boundary nodes. As an alternative to spatial regularization, a method based on ‘keynodes’ is introduced which assumes that each component of the boundary traction distribution can be described by a polynomial of specified order. The methods are applied to several two-dimensional examples including a rolling contact problem. The effects of parameters such as the number of sensors, the location of the sensors and the error in the sensor displacements are discussed.
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    A general procedure for the direct computation of turning and bifurcation points (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 155-176 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 10 Ill.
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    Masthead (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990) 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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    URL: http://dx.doi.org/10.1002/nme.1620300201
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    A hybrid strain finite element for plates and shells (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 233-257 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper describes a new hybrid strain finite element for geometrically linear analysis of plates and shells. The formulation for materially linear problems is based on a mixed variational principle having strain and displacement rates as independently varied fields. To facilitate extension to materially non-linear analysis, the variational principle is used in rate form and the plane stress assumption is not imposed a priori in the formulation. When desired, the plane stress assumption is imposed in a manner similar to imposition of fixed boundary conditions. The element geometry is based on a nine-noded quadrilateral with biquadratic interpolation of the displacement field. The strain field is based on a bilinear interpolation with additional non-linear terms, chosen on the basis of eigenvalue analysis. The element passes the required patch tests, does not display either membrane or shear locking effects, and is free of communicable spurious modes. Numerical results are presented for elastic analyses of several standard plate and shell test problems.
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    URL: http://dx.doi.org/10.1002/nme.1620300203
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    Power series expansions of dynamic stiffness matrices for tapered bars and shafts (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 259-270 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Stiffness and consistent mass matrices for tapered bars and shafts are derived with the aid of static displacement functions. Moreover, the corresponding dynamic stiffness matrices are developed in the Laplace transform domain from the exact solutions of axial/torsional governing equations. Power series expansions of the Bessel functions comprising the dynamic stiffness influence coefficients show that the stiffness and consistent mass matrices can be mathematically derived from the dynamic stiffness matrices. A discussion on the convergence of the power series expansions is also presented. The developments provide further insight into the approximations present in conventional consistent mass formulations of frameworks with tapered members.
    Additional Material: 1 Ill.
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    A Petrov-Galerkin/modified operator formulation for convection-diffusion problems (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 331-347 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new Petrov-Galerkin method to deal with convection-diffusion problems is presented. The formulation is derived from the concept of using a modifying function to make the differential operator self-adjoint. The so-called ‘optimal upwind’ parameter (α) arises naturally from the process of approximating the modifying function. Transient and steady-state examples on uniform and non-uniform meshes are shown.
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    Books received (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 389-390 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    URL: http://dx.doi.org/10.1002/nme.1620300212
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    Masthead (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990) 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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    URL: http://dx.doi.org/10.1002/nme.1620300301
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    Non-diffusive N + 2 degree Petrov-Galerkin methods for two-dimensional transient transport computations (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 397-418 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new non-diffusive Petrov-Galerkin type finite element method which uses test functions two polynomial degrees higher than the trial functions is developed for the transient convection dominated transport equation in two dimensions. The scheme uses bilinear quadrilateral finite elements for the spatial discretization and Crank-Nicolson finite differencing for the time integration. The standard product extension of very successful one-dimensional N + 2 degree upwinding functions to two dimensions is ineffective for general 2-D flow problems, especially at higher Courant numbers where cross-derivative truncation terms become important. Therefore effective N + 2 degree test functions are developed through an analysis by which the truncation error terms in the discrete nodal equation are eliminated up to fifth order. The new scheme is very effective for general 2-D flows over a wide Courant number range and eliminates the troublesome cross-derivative truncation terms. The scheme is simple and robust in that the upwinding coefficients are readily defined and only dependent on Courant number. Numerical examples illustrate the excellent behaviour of the new scheme.
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    An implementation of the hp-version of the finite element method for Reissner-Mindlin plate problems (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 459-471 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Reissner-Mindlin plate theory is still a topic of research in finite element analysis. One reason for the continuous development of new plate elements is that it is still difficult to construct elements which are accurate and stable against the well-known shear locking effect. In this paper we suggest an approach which allows high order polynomial degrees of the shape functions for deflection and rotations. A balanced adaptive mesh-refinement and increase of the polynomial degree in an hp-version finite element program is presented and it is shown in numerical examples that the results are highly accurate and that high order elements show virtually no shear locking even for very small plate thickness.
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    A unified numerical integration formula for the perfectly plastic von Mises model (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 491-504 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The accuracy of numerical integration of the perfectly plastic constitutive equation of von Mises is examined. Based on the analysis of the three existing numerical integration schemes a unified numerical integration formula (UNIF) is derived, which encompasses the three existing schemes as special cases and allows one to integrate the constitutive equation more accurately. According to the UNIF there are, in fact, many integration schemes depending on the direction of the trial stress. The validity of the UNIF is verified by presenting ten contours of constant angular error calculated with the UNIF. We then come to the conclusion that the three widely used schemes are by no means the most accurate ones. Some other schemes with better accuracy are thereby suggested. The determination of the number of substeps is also discussed in conjunction with the UNIF, when a multi-step method is used.
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    The finite element method Vol. 1: Basic formulation and linear problems, Fourth Edition by O. C. Zienkiewicz and R. L. Taylor, McGraw-Hill, Maidenhead, England, 1989. No. of pages: 648. Price (cloth): £25.00 ISBN: 0-07-084174-8 (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 565-567 
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    Keywords: Engineering ; Engineering General
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    URL: http://dx.doi.org/10.1002/nme.1620300312
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    Recent advances, trends and new perspectives via enthalpy-based finite element formulations for applications to solidification problems (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 803-820 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The present paper describes recent advances and trends in finite element developments and applications for solidification problems. In particular, in comparison to traditional methods of approach, new enthalpy-based architectures based on a generalized trapezoidal family of representations are presented which provide different perspectives, physical interpretation and solution architectures for effective numerical simulation of phase change processes encountered in solidification problems. Various numerical test models are presented and the results support the proposition for employing such formulations for general phase change applications.
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    Computer simulation of salami drying (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 767-777 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Salami sorts are made of special meat pastes filled in hygroscopic casing and preserved by drying.The characteristic features and the time of drying are greatly affected by the operational conditions. Factories are interested in reducing the time of the drying treatment. To determine a reliable and economic drying schedule a physical-mathematical model has been elaborated and used. The system of equations has been solved numerically by using the FDM technique for the determination of the temperature, concentration and stress fields as a function of the time. Computed results have been verified by experiments.By the numerical analysis it has been proved that the maximum rate of drying to be permitted is limited by the danger of possible deformations and inner fissures caused by tensile stresses occurring if shrinkage is prevented.On the basis of the proper drying schedule an algorithm and a strategy of the microprocessing operational control has been elaborated.
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