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  • Engineering General  (1,261)
  • 1990-1994  (725)
  • 1985-1989  (536)
  • 1980-1984
  • 1935-1939
  • 1992  (725)
  • 1989  (536)
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  • 1990-1994  (725)
  • 1985-1989  (536)
  • 1980-1984
  • 1935-1939
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  • 1
    Electronic Resource
    Electronic Resource
    Non-linear stochastic response of marine vehicles (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 27 (1989), S. 169-183 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The dynamic behaviour of marine vehicles in extreme sea states is a matter of great concern following some recent and dramatic mishaps. The complex problem of its prediction can be approached from the study, yet of broader scope, of non-linear dynamic systems subjected to stochastic excitations. However, a general non-linear stochastic dynamic theory is not yet available.A new technique, the so-called linearize-and-match method, for predicting the response statistics of non-linear systems, is presented. Essentially, the technique involves the construction of an infinite series of linear systems aimed at the prediction of the response statistical moments of a given order.The linear systems are successively defined by linearizing the original, non-linear system and matching the Volterra functional model response statistics to the desired order. The linear system for predicting second order statistics is shown to coincide with the one obtained using the method of equivalent linearization.Response probability distributions can be constructed from the knowledge of such statistics. Particular attention is devoted to the distribution of maximum entropy and its justification in such underdetermined moment problems.Finally, applications to the roll motion of ships serve to exemplify as well as to assess the accuracy and the versatility of the overall method. Response distributions of maxima so predicted compare very well with digital simulation estimates.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620270114
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  • 2
    Electronic Resource
    Electronic Resource
    F.E. solution of a vertically averaged model for regional land subsidence (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 27 (1989), S. 215-230 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper a mathematical model is presented, based on the application of an averaging technique, in which the equations governing the behaviour of saturated porous media are integrated (averaged) over the smallest dimension of the domain of the problem (thickness). This results in a two dimensional model, in which the three dimensional nature of the problem is accounted for. In fact, the solution is sought in terms of the mean values over the thickness of the field variables and of the transverse displacement components. For the solution of the resulting governing equations a partitioned procedure is employed, which improves the efficiency of the method. The proposed model is very useful in solving problems in which the spatial nature prevents the applications of two dimensional models.Examples are presented, which illustrate the validity of this approach.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620270117
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  • 3
    Electronic Resource
    Electronic Resource
    Some recent developments in numerical modelling of fracture toughness in brittle matrix composites (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 27 (1989), S. 233-255 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Finite element analysis was used to study the fracture toughening of a ceramic by a stress induced dilatant transformation of second phase particles. The finite element method was based on a continuum theory which modelled the composite as subcritical material. Transient crack growth was simulated in the finite element mesh by a nodal release technique. The crack's remote tensile opening load was adjusted to maintain the near-tip energy release rate at the level necessary for crack advance. The transformation zone surrounding the crack developed as the crack propagated through the composite. Resistance curves were computed from the analysis; and the results show that during crack advance maximum toughness is achieved before a steady state is reached.The toughening effect of a crack-bridging ductile phase in a brittle material may be predicted if ligament deformation is characterized. A plastically deforming ligament constrained by surrounding elastic matrix material is modelled using finite elements and the relevant toughness enhancement information extracted. Comparison is made to model experiments as well as to toughness measured for technologically important materials. The results suggest that debonding along the interface between the ligament and the matrix may enhance the toughening effect of a ductile phase.
    Additional Material: 21 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620270203
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  • 4
    Electronic Resource
    Electronic Resource
    Fatigue life estimation of graphite/epoxy laminates under consideration of delamination growth (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 27 (1989), S. 323-341 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A closed form approach to the assessment of the fatigue life of graphite/epoxy laminates under cyclic tension-compression loading has been developed. The model is mechanistic and uses cyclic energy release rates for prediction of delamination growth and of critical delamination sizes which induce buckling and the final failure of the laminates. Tests performed with graphite/epoxy specimens of stacking order [0n, φm]s with severed central plies [φ], and of stacking order [02, +45, 02, -45, 0, 90]s with a central unloaded hole, indicate good correlation between estimated values and observed delamination growth, critical buckling strength of separated plies and load cycles to failure.
    Additional Material: 16 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620270208
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  • 5
    Electronic Resource
    Electronic Resource
    Analysis of viscoelastic structural elements in the frequency domain (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 27 (1989), S. 429-436 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper presents a formulation in the frequency domain for the viscoelastic material behaviour of structural elements. This approach is equally valid for deterministic forces, but also in the case of probabilistic descriptions of those forces. The method takes advantage of readily available experimental data and shows how to introduce them in e.g. finite element formulations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620270213
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  • 6
    Electronic Resource
    Electronic Resource
    Conference diary (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 27 (1989), S. 449-452 
    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.1620270215
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  • 7
    Electronic Resource
    Electronic Resource
    A dual adaptive procedure for the automatic determination of iteration parameters for Chebyshev acceleration (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 27 (1989), S. 483-499 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Chebyshev acceleration for a symmetrizable basic iterative method u(n+1) = Gu(n) + k; requires estimates of the extreme eigenvalues m(G) and M(G) of the iteration matrix G. Adaptive procedures are often used in order to obtain good estimates for m(G) and M(G). Some existing adaptive procedures are able to give an estimate of either m(G) or M(G) but not both on any given iteration. In this paper we present an adaptive procedure which can estimate both m(G) and M(G) at the same time and which has other useful properties. Numerical results are given which show the new procedure usually requires fewer iterations than previous procedures.
    Additional Material: 3 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620270305
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  • 8
    Electronic Resource
    Electronic Resource
    Experience with the conjugate gradient method for stress analysis on a data parallel supercomputer (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 27 (1989), S. 523-546 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The storage requirements and performance consequences of a few different data parallel implementations of the finite element method for domains discretized by three-dimensional brick elements are reviewed. Letting a processor represent a nodal point per unassembled finite element yields a concurrency that may be one to two orders of magnitude higher for common elements than if a processor represents an unassembled finite element. The former representation also allows for higher order elements with a limited amount of storage per processor. A totally parallel stiffness matrix generation algorithm is presented. The equilibrium equations are solved by a conjugate gradient method with diagonal scaling. The results from several simulations designed to show the dependence of the number of iterations to convergence upon the Poisson ratio, the finite element discretization and the element order are reported. The domain was discretized by three-dimensional Lagrange elements in all cases. The number of iterations to convergence increases with the Poisson ratio. Increasing the number of elements in one special dimension increases the number of iterations to convergence, linearly. Increasing the element order p in one spatial dimension increases the number of iterations to convergence as pα, where α is 1·4-1·5 for the model problems.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620270307
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  • 9
    Electronic Resource
    Electronic Resource
    On an SSOR matrix relationship and its consequences (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 27 (1989), S. 559-570 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A matrix relationship connecting the Jacobi and the Symmetric Successive Overrelaxation (SSOR) matrices associated with a k-cyclic consistently ordered matrix A is presented. Next the equivalence of the SSOR method and a certain monoparametric k-step one for the solution of the linear algebraic system Ax = b is established. The aforementioned equivalence can be exploited to derive regions of convergence, optimum parameters involved, etc. of the two iterative methods above. This is done by studying the simplest of the two methods that is the monoparametric k-step one. To show how the idea works the case k = 2 is very briefly discussed.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620270309
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  • 10
    Electronic Resource
    Electronic Resource
    On a class of preconditioned iterative methods on parallel computers (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 27 (1989), S. 637-654 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The standard implementations of iterative solvers for finite element and finite difference methods frequently use a diagonal (Jacobi) preconditioner, particularly for element-by-element schemes. However, for such methods the actual order of the condition number with respect to mesh size is not reduced by the preconditioner. In the present paper we describe an iterative method where, in addition, the condition number is reduced by an order of magnitude. Moreover, the scheme may also be implemented as an element-by-element method. The method uses a generalized SSOR preconditioner and a wave front or multi-frontal ordering of the mesh nodes. For a general irregular finite element mesh a striped irregular wave front ordering may be used. The performance of the method as well as various iterative acceleration techniques for a parallel computer are examined in the numerical studies.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620270314
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  • 11
    Electronic Resource
    Electronic Resource
    Correction (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. ii 
    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.1620280102
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  • 12
    Electronic Resource
    Electronic Resource
    Geometrically non-linear formulation for three dimensional curved beam elements with large rotations (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 43-73 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents a geometrically non-linear formulation (GNL) for the three dimensional curved beam elements using the total Lagrangian approach. The element geometry is constructed using co-ordinates of the nodes on the centroidal or reference axis and the orthogonal nodal vectors representing the principal bending directions. The element displacement field is described using three translations at the element nodes and three rotations about the local axesThe element displacement field has also been described in the literature using Euler parameters, Milenkovic parameters, or Rodriges parameters representing the effects of large rotations.. The GNL three dimensional beam element formulations based on these element approximations are restricted to small nodal rotations between two successive load increments. The element formulation presented here removes such restrictions. This is accomplished by retaining non-linear nodal terms in the definition of the element displacement field, and the consistent derivation of the element properties. The formulation presented here is very general and yet can be made specific by selecting proper non-linear functions representing the effects of nodal rotations. The details of the element properties are presented and discussed. Numerical examples are also presented to demonstrate the behaviour and the accuracy of the elements. A comparison of the results obtained from the present formulation with those available in the literature using a linearized element approximation clearly demonstrate the superiority of the formulation in terms of large load steps, large rotations between two load steps and extremely good convergence characteristics during equilibrium iterations. The displacement approximation of these elements is fully compatible with the isoparametric curved shell elements (with large rotations), and since the elements possess offset capability, these elements can also serve as stiffeners for the curved shells.
    Additional Material: 16 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280106
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  • 13
    Electronic Resource
    Electronic Resource
    Evaluation of boundary integrals for plate bending (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 75-93 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The alternative to quadrature, as a procedure for dealing with the integrations required in the direct boundary element method (DBEM), is to carry out the integration analytically and code the results directly. The potential benefits are efficient computer programs; the avoidance of numerical instability; and generally, better accuracy. The technique is developed in this paper.Serious problems arise when Gauss quadrature is employed for the integration of functions which contain, or are close to singularities. A numerical integration approach may fail at the first stage of the analysis, that is, during the assembly of the discrete equations; or it may fail at the subsequent stage of computing domain points near the boundary. The severity of the problem is dependent both on the strength of the singularity, and on geometry. These points are illustrated with examples.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280107
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  • 14
    Electronic Resource
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    Frictionless geometrically non-linear contact using quadratic programming (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 127-144 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The successive quadratic programming (SQP) method is used with the finite element method (FEM) to solve frictionless geometrically non-linear contact problems involving large deformations of the elastica in the presence of flat rigid walls. To formulate the SQP problems, the potential energy (PE) is expanded in a Taylor series of second order in displacement increments about a configuration near a contact solution. The SQP problems consist of minimizing the Taylor expansion of the PE subject to the inequality constraints which represent contact. The quadratic programming (QP) method is made part of a Newton-Raphson (NR) search in which the QP corrections are made when a NR step does not satisfy the constraints. A revised simplex method developed by Rusin is used to solve the QP problems. The elastica is modelled with a total Lagrangian FEM developed by Fried. Solutions are obtained for the end loaded buckled elastica in point contact with a rigid wall and for a uniformly loaded elastica in regional contact with a rigid wall. The problems are also solved using a penalty method. The results obtained for the point contact problem are compared to an analytical solution. Calculations were made to obtain numerical information on maximum load step size and the number of inverse operations required for each load step. Cases in which the elastica stiffened substantially as a result of the initiation of contact are also discussed.
    Additional Material: 11 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280110
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  • 15
    Electronic Resource
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    The FDM in arbitrary curvilinear co-ordinates - formulation, numerical approach and applications (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 261-277 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The basic concept, formulation and numerical application of a fully automatic version of the finite difference method (FDM) on a two-dimensional manifold embedded in three-dimensional Euclidean space are presented. This version of the FDM was developed in order to enable automatic solution of problems formulated in arbitrary curvilinear co-ordinate systems in terms of covariant derivatives (e.g. shell equations).In the classical version of the FDM all operations in the curvilinear co-ordinates (the derivation of base vectors, curvature tensors and so on) have to be performed manually. The goal of the present work was to transfer this job to a computer, in order to minimize the user's effort during the numerical formulation of the physical problem. The relevant version of the fully automatized program FIDAMF, based on the FDM on arbitrary irregular grids,1,2 has been worked out. This code performs automatically all stages of the numerical analysis, starting from the mesh generation and approximation of the shape of the manifold, through computation of necessary objects on this manifold, to the solution of linear or non-linear problems formulated in terms of covariant derivatives.The method has been extended to the analysis of problems in which the co-ordinate system changes during the computation (e.g. the analysis of large deformations in the convectional description). This version of the curvilinear FDM was applied to the analysis of large deformations of hyperelastic membrane shells.The approach and the numerical routines, although used here with the FDM, can be combined with any other approximation method, in particular the finite element method.
    Additional Material: 16 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280203
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  • 16
    Electronic Resource
    Electronic Resource
    Approximate direct-search minimax circuit optimization (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 359-368 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A direct-search optimization strategy, involving pattern-searches, pattern-moves and a simplex algorithm, has been applied to a number of frequency-domain circuit problems. We show that an approximate minimax result can be obtained with our simple approach, which includes using a modified minimax error function. In the examples attempted, the method comes quite close to the accuracy, if not the efficiency, of true minimax optimizers, and yields an accuracy as good as or better than a least-pth (p = 10) gradient optimizer. The method is broadly appropriate wherever it is difficult or inconvenient to calculate the gradients required for conventional minimax optimization.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280208
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  • 17
    Electronic Resource
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    Implementation of curvilinear geometry into p-version HT plate elements (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 431-443 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The formulation of the recently presented hybrid-Trefftz (HT) p-version elements1 has thus far been restricted to straight-sided polygonal elements. The present paper removes this limitation. Two alternative formulations are studied. In the first one any curvilinear geometry is represented accurately but the rigid body modes are recovered only in the limit as the p-refinement level is increased. In contrast, the second formulation represents the rigid modes exactly while the actual curvilinear geometry is approached with increasing accuracy as the p-refinement level is increased. The practical efficiency of the two alternative approaches is studied and assessed on pertinent examples of thin plates in bending.
    Additional Material: 9 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620280212
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  • 18
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    Books received (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 477-478 
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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.1620280217
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  • 19
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    Conference diary (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 483-487 
    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.1620280220
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  • 20
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    A discrete shear triangular nine D.O.F. element for the analysis of thick to very thin plates (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 533-560 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper deals with the formulation and the evaluation of a new three node, nine d.o.f. triangular plate bending element valid for the analysis of thick to thin plates. The formulation is based on a generalization of the discrete Kirchhoff technique to include the transverse shear effects. The element, called DST (Discrete Shear Triangle), has a proper rank and is free of shear locking. It coincides with the DKT (Discrete Kirchhoff Triangle) element if the transverse shear effects are not significant. However, an incompatibility of the rotation of the normal appears due to shear effects. A detailed numerical evaluation of the characteristics and of the behaviour of the element has been performed including patch tests for thin and thick plates, convergence tests for clamped and simply supported plates under uniform loading and evaluation of stress resultants. The overall performance of the DST element is found to be very satisfactory.
    Additional Material: 19 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620280305
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  • 21
    Electronic Resource
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    Efficient optimization of integrated aerodynamic-structural design (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 593-607 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The introduction of composite materials is having a profound effect on the design process. Because these materials permit the designer to tailor material properties to improve structural, aerodynamic and acoustic performance, they require a more integrated multidisciplinary design process. Because of the complexity of the design process numerical optimization methods are required.The present paper is focused on a major difficulty associated with the multidisciplinary design optimization process - its enormous computational cost. We consider two approaches for reducing this computational burden: (i)development of efficient methods for cross-sensitivity calculation using perturbation methods; and (ii) the use of approximate numerical optimization procedures. Our efforts are concentrated upon combined aerodynamic-structural optimization. Results are presented for the integrated design of a sailplane wing. The impact of our computational procedures on the computational costs of integrated designs is discussed.
    Additional Material: 5 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620280308
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  • 22
    Electronic Resource
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    Structural modifications simulated by virtual distortions (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 645-666 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A numerical strategy for the simulation of structural modifications by virtual distortions is proposed. Two cases of structural modification are considered: the first concerns modifications of material distribution, and the second modifications of local constitutive relations (e.g. unilateral constraints for stresses or deformations). A formaulation of the fundamental equations of the simulation method is presented. These equations are applicable to the general structural modification problem of a truss-like structure. Then numerical algorithms which refer to particular applications, such as progressive collapse analysis or the analysis of structures with gaps, are discussed.The versatility of the method is illustrated with a number of examples, and the computational advantages of structural modification by the virtual distortion method are discussed.
    Additional Material: 16 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620280312
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  • 23
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    Computational plasticity, Edited by D. R. J. Owen, E. Hinton and E. Oñate, Pineridge Press, Swansea, U.K., 1987. No. of pages: 1865. ISBN 0-906674-61-1 (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 725-726 
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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.1620280317
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  • 24
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    First-order design sensitivities for transient conduction problems by an adjoint method (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 733-752 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An adjoint approach is presented for the design sensitivity analysis of transient conduction problems. Variations of a general design functional are expressed in explicit form with respect to all design quantities, i.e. material properties, shape, applied thermal loads including convection, and initial conditions. The methodology incorporates the mutual energy between the real and adjoint thermal problems and a geometric mapping to describe shape variations. Finite element implementation of the method is discussed and an example is provided. Some potential difficulties that might be encountered when using the adjoint method with the finite element method are addressed. These involve the application of impulse loadings and Dirac temperature fields in the adjoint loadings.
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    A comparison of direct and preconditioned iterative techniques for sparse, unsymmetric systems of linear equations (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 801-815 
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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 compare direct and preconditioned iterative methods for the solution of nonsymmetric, sparse systems of linear algebraic equations. These problems occur in finite difference and finite element simulations of semiconductor devices, and fluid flow problems.We consider five iterative methods that appear to be the most promising for this class of problems: the biconjugate gradient method, the conjugate gradient squared method, the generalized minimal residual method, the generalized conjugate residual method and the method of orthogonal minimization. Each of these methods was tested using similar preconditioning (incomplete LU factorization) on a set of large, sparse matrices arising from finite element simulation of semiconductor devices. Results are shown where we compare the computation time and memory requirements for each of these methods against one another, as well as against a direct method that uses LU factorization to solve these problems.The results of our numerical experiments show that preconditioned iterative methods are a practical alternative to direct methods in the solution of large, sparse systems of equations, and can offer significant savings in storage and CPU time.
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    URL: http://dx.doi.org/10.1002/nme.1620280406
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    On the modelling of scalar and mass transport in combustor flows (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 861-877 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The results of a numerical study of swirling and non-swirling combustor flows with and without density variations are presented. Constant-density arguments are used to justify closure assumptions invoked for the transport equations for turbulent momentum and scalar fluxes, which are written in terms of density-weighted variables. Comparisons are carried out with measurements obtained from three different axisymmetric model combustors. The three experiments cover recirculating flow, swirling flow and variable-density, swirling flow inside model combustors. Together, they offer wide ranging flow conditions to test the validity of the models. Results show that the Reynolds stress/flux models do a credible job of predicting constant-density, swirling and non-swirling combustor flows with passive scalar transport. However, their improvements over algebraic stress/flux models are marginal. The extension of the constant-density models to variable-density flow calculations shows that the models are equally valid for such flows. Therefore, the present results argue well for the adoption of constant-density models for variable-density flows until a successfully validated variable-density model is available.
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    Numerical modelling of wave propagation using parabolic approximation with a boundary-fitted co-ordinate system (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 27 (1989), S. 37-55 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: With a boundary-fitted curvilinear co-ordinate system, the parabolic approximation is applied to the mildslope equation to describe the wave propagation. Both refraction and diffraction are included in the numerical model. Because the shoreline coincides with one of the curvilinear co-ordinates, the numerical model can be used to compute wave propagations near an irregular shoreline.
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    Study of the behaviour of oscillatory waves in a lagoon (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 27 (1989), S. 103-112 
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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.1620270109
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    A three dimensional global weather prediction model using a finite element scheme for vertical discretization (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 27 (1989), S. 129-144 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A global three dimensional model for numerical weather prediction is described. It uses spheric harmonic basis functions with triangular truncation in the horizontal and a finite element discretization for the vertical. Model experiments are used to compare this model with another version, which uses a finite difference scheme for vertical discretization.
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    The influence of the form of the log-conductivity covariance on non-Fickian dispersion in random permeability fields (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 27 (1989), S. 185-193 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper deals with non-Fickian dispersion of inert solutes in random permeability fields. Attention is focused critically on the statistical characterization of the porous medium which affects pollutant dispersion in groundwater. After a brief account of recent results of stochastic theories of transport in porous media and of the fundamental indications of large-scale field experiments, it is inferred from numerical studies that the particular choice of an analytical form of covariance of log-conductivity has a poor influence on the overall dispersion process. In fact, different covariance structures with the same macroscale (a measure of the distance between two points beyond which the permeability ceases to be correlated) yield very similar dispersion processes. The result has a noteworthy bearing on field studies of pollutant dispersion in groundwater because it underlines the reliability of exponential correlation structures yielding analytical expression for time-varying macrodispersion coefficients.
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    Preface (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 27 (1989), S. 231-231 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    URL: http://dx.doi.org/10.1002/nme.1620270202
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    A consistent tangent stiffness matrix for three-dimensional non-linear contact analysis (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 1803-1812 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A consistent tangent stiffness matrix for the analysis of non-linear contact problems is presented. The associated element has three or four nodes and establishes contact between three-dimensional structures like solids and shells. It accounts for the non-linear kinematics of large deformation analysis and guarantees a quadratic convergence rate. Two formulations, the penalty method and the Lagrange multiplier method, are investigated.
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    On the accuracy of some domain-by-domain algorithms for parallel processing of transient structural dynamics (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 1855-1874 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Two domain-by-domain algorithms, suitable for coarse-grained parallel processing analysis of the transient structural dynamics equation, are investigated for accuracy. The application under specific consideration is the analysis of three-dimensional framed structures subjected to time-varying loading. The domain-by-domain approaches attempt to include the advantageous aspects of both conditionally stable explicit algorithms, which require no simultaneous solution of equations and employ simple communication, and unconditionally stable implicit algorithms, which permit large time steps. The alternating group explicit algorithm is developed for finite element analysis, and its accuracy is investigated for a linear formulation. The group implicit algorithm is extended to non-linear finite element analysis, and its accuracy is investigated for the frame dynamics application. Both algorithms are shown to provide inadequate accuracy for practical time step sizes.
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    Accuracy in finite element computation for eigenfrequencies (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 1929-1949 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper we propose an original numerical method to get upper and lower bounds for the eigenfrequencies of an elastic structure.This method is based on a ‘static’ formulation for eigenvalue problems built up from a new quotient Rs which is defined on a load space. From Rs properties, upper and lower bounds for the exact eigenfrequencies are proved. The application of the method requires the solution of an eigenvalue problem of finite dimension and the computation of a constant which is characteristic of the discretization subspace. Results of numerical tests are given for the vibration problem of an elastic clamped membrane.
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    A new BEM formulation for acoustic eigenfrequency analysis (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 1965-1967 
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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.1620280817
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    Conference diary (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 1971-1975 
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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.1620280819
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    Efficient approximation concepts using second order information (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 2041-2058 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The primary goal of this paper is to show how second derivative information can be used in an effective way in structural optimization problems. The basic idea is to generate such an information at the expense of only one more ‘virtual load case’ in the sensitivity analysis part of the finite element code. To achieve this goal a primal-dual approach is employed, that can also be interpreted as a sequential quadratic programming method.Another objective is to relate the proposed method to the well known family of approximation concepts techniques, where the primary optimization problem is transformed into a sequence of non-linear explicit subproblems. When restricted to diagonal second derivatives, the new approach can be viewed as a recursive convex programming method, similar to the ‘Convex Linearization’ method (CONLIN), and to its recent generalization, the ‘Method of Moving Asymptotes’ (MMA).This new method has been successfully tested on simple problems that can be solved in closed form, as well as on sizing optimization of trusses. In all cases the method converges faster than CONLIN, MMA or other approximation techniques based on reciprocal variables.
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    Numerical study of incompressible fluids in unbounded domains (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 2203-2218 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The aim is to build up and test a numerical method to calculate the velocity of stationary two-dimensional flows. Both inviscid and viscous fluids are considered. They act in the unbounded domain surrounding a given profile and a stream function is introduced. A variational procedure, adapted to unbounded domains, reduces the problem to solving a finite sequence of hormonic equations, posed in bounded domains. Some profiles are tested using a finite element method.
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    A study of stabilization and projection in the 4-node Mindlin plate element (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 2223-2238 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper, a Mindlin plate element is formulated based on the Hellinger-Reissner principle and the γ-technique. The stiffness consists of a constant stress (one-point quadrature) matrix and a stabilization matrix. The stabilization matrix is compared with those previously proposed. In addition, the element uses a projection to modify the nodal displacements so that the patch test is satisfied. The projection matrix is based on a mode decomposition. Several numerical cases are presented, and it is shown that the mode decomposition projection is necessary both for satisfaction of the patch test and convergence.
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    Modal parameter identification using Z-transforms (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 2307-2321 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A method for the time domain identification of modal parameters of a vibrating structure using Z-transformation sequences is presented in this paper.This identification proceeds using the Z-transfer function of a vibrating structure from which an auto-regressive and moving-average (ARMA) model of the vibrating structure is derived. From this ARMA model and time domain data, the modal parameters can be identified. The time domain data can be obtained from single point or multiple shaker excitation modal testing. To demonstrate the application and efficiency of the method, a test on a simulated cantilever beam is presented.
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    The dynamic analysis of a suspended cable due to a moving load (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 2361-2381 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The dynamic behaviour of a saggy suspension cable under a moving load was investigated. First of all, the updated Lagrangian formulation and the finite element method were used to derive the property matrices of a saggy suspension cable in order to define the discretized equations of motion. Then, the Jacobi method was applied to the determination of the natural frequencies and the mode shapes of the suspended cable. The moving-load-induced dynamic responses of the saggy suspended cable were obtained by using the Newmark direct integration method incorporated with the Newton-Raphson iteration technique. The influence of some pertinent factors, such as speed of moving load, ratio of axial rigidity to total cable weight (AE/0m̄g0L) and ratio of moving load mass to total cable mass, is the key point of the dynamic analysis.
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    A simple stress error estimator for Hybrid-Trefftz p-version elementsA preliminary version1 of this paper has been presented at NUMETA 87 Conference, The University of Swansea, 6-10 July 1987 (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 211-236 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An a posteriori error estimator is presented which allows a good pointwise evaluation of the error in predicted stresses and can easily be implemented in existing FE codes. Although this estimator has especially been developed for and tested on p-version Hybrid-Trefftz (HT) elements, it is anticipated that it can also be applied to conventional conforming p-version elements. The practical efficiency of the estimator is illustrated through the solution of various plate bending problems by using the HT p-version Kirchhoff plate elements.2
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    A moving boundary circulation model for regions with large tidal flats (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 245-260 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A numerical model is developed for computing two-dimensional circulation in coastal regions dominated by large tidal flat motion. This model is based on the shallow water momentum and continuity equations being operated upon by the Galerkin finite element method. The particular advantage of the model lies in its ability to accommodate a changing domain boundary. This is accomplished by adopting finite elements that change shape so as to consistently move with the water's edge. Application of the model to the Kuwait Bay is described, and the associated results on circulation are given.
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    A boundary element method analysis of electrostatics in a tank during filling operations (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 315-329 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Electrostatic charging inside a tank is analysed numerically using the boundary integral method. The electrostatic charge is transmitted to the tank through a charged liquid. Profiles for the charge density and potential are obtained in the tank during the filling operation. The analysis is based on the equation governing the transport of charge and Poisson's equation. The results are characterized by two dimensionless parameters, the dimensionless Debye length given by the Debye length divided by the height of the tank, and the number Pe defined as a Peclet number. The results show where the maximum charge density and potential occur and give a prediction of when during the filling operation a hazardous situation may occur.
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    Assumed strain stabilization procedure for the 9-node Lagrange shell element (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 385-414 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: An assumed strain (strain interpolation) method is used to construct a stabilization matrix for the 9-node shell element. The stabilization procedure can be justified based on the Hellinger-Reissner variational method. It involves a projection vector which is orthogonal to both linear and quadratic fields in the local co-ordinate system of each quadrature point. All terms in the development involve 2 × 2 quadrature in the 9-node element. Example problems show good accuracy and an almost optimal rate of convergence.
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    Delaunay triangulation of non-convex planar domains (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 2695-2707 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper investigates the possibility of integrating the two currently most popular mesh generation techniques, namely the method of advancing front and the Delaunay triangulation algorithm. The merits of the resulting scheme are its simplicity, efficiency and versatility. With the introduction of ‘non-Delaunay’ line segments, the concept of using Delaunay triangulation as a means of mesh generation is clarified.An efficient algorithm is proposed for the construction of Delaunay triangulations over non-convex planar domains. Interior nodes are first generated within the planar domain. These interior nodes and the boundary nodes are then linked up together to produce a valid triangulation. In the mesh generation process, the Delaunay property of each triangle is ensured by selecting a node having the smallest associated circumcircle. In contrast to convex domains, intersection between the proposed triangle and the domain boundary has to be checked; this can be simply done by considering only the ‘non-Delaunay’ segments on the generation front.Through the study of numerous examples of various characteristics, it is found that high-quality triangular element meshes are obtained by the proposed algorithm, and the mesh generation time bears a linear relationship with the number of elements/nodes of the triangulation.
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    Conference diary (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 2713-2714 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    A mixed-variable continuously deforming finite element method for parabolic evolution problems. Part III: Numerical implementation and computational results (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 2715-2760 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: In Part I of this paper,1 the conceptual framework of a rate variational least squares formulation of a continuously deforming mixed-variable finite element method was presented for solving a single evolution equation. In Part II2 a system of ordinary differential equations with respect to time was derived for solving a system of three coupled evolution equations by the deforming grid mixed-variable least squares rate variational finite element method. The system of evolution equations describes the coupled heat flow, fluid flow and trace species transport in porous media under conditions when the flow velocities and constituent phase transitions induce sharp fronts in the solution domain. In this paper, we present the method we have adopted to integrate with respect to time the resulting spatially discretized system of non-linear ordinary differential equations. Next, we present computational results obtained using the code in which this deforming mixed finite element method was implemented. Because several features of the formulation are novel and have not been previously attempted, the problems were selected to exercise these features with the objective of demonstrating that the formulation is correct and that the numerical procedures adopted converge to the correct solutions.
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    Error estimates and adaptive refinement for plate bending problems (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 2839-2853 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The Zienkiewicz-Zhu error estimator is shown to be effective in problems of plate flexure. When used in conjunction with triangular elements and an adaptive mesh generator allowing a prescribed size of elements to be developed, very fast adaptive convergence for results of specified accuracy is achieved.
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    Selective refinement/derefinement algorithms for sequences of nested triangulations (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 2889-2906 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The construction of changing sequences of irregular and nested triangulations, based on the use of conforming refinement/derefinement algorithms for triangulations, is presented and discussed. This strategy is particularly appropriate to combine adaptivity and full multigrid algorithms for dealing with moving fronts or fluid dynamics problems. It is shown that the quality of all the triangulations iteratively generated depends only on the geometric characteristics of the initial grid. A data structure suitable to create, manage and modify series of nested triangulations as well as the main features of the DEREF prototype package are described, and numerical examples are given.
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    URL: http://dx.doi.org/10.1002/nme.1620281212
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    Tracing the equilibrium path beyond simple critical points (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 2923-2941 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A unified presentation of some popular continuation procedures used in the non-linear finite element analysis of structural mechanics is introduced. An extension of the elliptical constraint equation proposed by Crisfield is given. It is shown that in the proposed procedure real roots can always be obtained in solving the iterative change of the load parameter. Updated weighting factors are introduced in the constraint equation in order to get better convergence characteristics in the case when localized deformations occur. For bifurcation points a modification of Rheinboldt's branching procedure is presented. Post critical response after limit and bifurcation points is determined in some numerical examples.
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    URL: http://dx.doi.org/10.1002/nme.1620281214
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    Error estimates and convergence rates for various incompressible elements (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 2191-2202 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This note reports numerical experiments on the efficiency of simple error estimates derived earlier1 applied to incompressible mixed or related penalty type formulations. The rate of convergence and performance of various mixed elements is compared. Numerical results from a driven cavity and an incompressible elastic problem demonstrate that the T6B1/3D and T6/3C elements give a faster rate of convergence than the T6/1D element. However, in the case of a plane extrusion analysis (stronger singularity), the rate of convergence for the T6B1/3D element drops and is inferior to that of the T6/1D, while the T6/3C element still proves superior to the other two elements.
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    A C0 finite element formulation for thin-walled beams (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 2239-2255 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Timoshenko's and Vlasov's beam theories are combined to produce a C0 finite element formulation for arbitrary cross section thin-walled beams. Section properties are generated using a curvilinear co-ordinate system to describe the cross section dimensions. The element includes both shear and warping deformations caused by the bending moments and the bimoment. A Gauss quadrature order is employed which exactly integrates the bending and warping stiffness matrices and provides a reduced integration order for the shear stiffness matrices. Numerical results are presented for a channel section cantilever beam. The influence of shear deformation is investigated and the calculated results are shown to be in excellent agreement with the classical solutions.
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    Virtual crack extension methods for non-linear materials (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 929-942 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The virtual crack extension technique is a very efficient and accurate approach to fracture mechanics calculations in the numerical analysis of bodies containing cracks using the finite element method. A few variations of the technique have been described in the literature, and have been extensively used in linear elastic fracture mechanics, where good validation has frequently been available with accepted alternative solutions for standard tests. However, for non-linear materials extra complications arise in the technique, particularly in describing material response in a compatible manner. It is shown that, using few assumptions, a very competitive virtual crack extension technique based, on a direct minimization of potential energy is available for elastic non-linear elastic materials. Such materials can be closely approximated to elastic-plastic behaviour for monotonically increasing loads including mechanical, thermal and body force forms. The technique is described and demonstrated via examples to be in good agreement with alternative fracture parameter evaluations when evaluated in the same computer system, BERSAFE.
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    Numerical methods in transient and coupled problems, R. W. Lewis, E. Hinton, P. Bettess and B. A. Schrefler, Wiley (Chichester) 1987. No. of pages: 350. ISBN: 0 471 91200X (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 979-979 
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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.1620280419
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    Wave plan computation method in study of the Calvi Bay erosion in Corsica, France (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 27 (1989), S. 71-85 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A study of linear monochromatic wave propagation is presented, based on a theory of potentials. The usual Berkhoff equation has been extended by the addition of partially pervious solid boundary effects and the bed friction.The problem has been solved by a hybrid finite element method including the effect of singular local elements such as the end of breakwaters or wharfs. This numerical method confirms the interest in quadratic Lagrangian finite elements.The comparisons with analytical solutions and existing numerical results show the validity of the method. Some original examples also prove the good performance of the proposed computation method.As an example, the study of the erosion of the beach of Calvi Bay in Corsica, France is presented. The phenomenon had started already in 1960, but the problem began to be very severe four years ago, after the implementation of a new harbour in 1982 and buildings, hotels, restaurants, and a main sewer on the beach. To consider the impact of these constructions and other factors like waves, currents and geomorphological aspects, the studies were divided into four parts: sedimentological, currents, wave propagation and geomorphological.This paper will describe the results of a complete two years study on the site, from February 1986 to December 1987.Findings show that the erosion process is due to the rise of the relative sea level with, as a catalyst, tourist behaviour and the implementation of the new constructions.
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    Calculation of the force coefficients of a tubular jacket structural member with an appurtenance by the discrete vortex method (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 27 (1989), S. 153-167 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Jacket structures have many sub-sea appurtenances attached to them. For example, a typical jacket structure has hundreds of sacrificial anodes attached to its members. The fluid loading of these structures is calculated using Morison's formula. The force coefficients used in the equation are based on experiments carried out, for the most part, on single cylinders in laboratories in ideal flow. There are very few experimental data available for the fluid loading of cylinders with appurtenances. Moreover, it is not possible to calculate theoretically the loading on such configurations in flows of practical interest using approaches such as the finite element method. However, appurtenances can contribute significantly to the overall loading on a structure. This paper presents the preliminary theoretical work that has been carried out as part of a programme to establish a rational method for estimating the fluid loading on tubular members with appurtenances.
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    Masthead (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 27 (1989) 
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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.1620270201
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    Conference diary (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 2943-2946 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620281215
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    Large deflection elastic-plastic analysis of plate structures by the finite strip method (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 331-358 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The finite strip method is applied to the non-linear analysis of plate structures. Large deflection effects are included via first order non-linearities in the strain-displacement relations, and material non-linearities are included via the von Mises yield criterion and associated flow rule. The virtual work equations are integrated numerically using Gauss quadrature, and the resulting non-linear equations are solved by Newton-Raphson iteration. Numerical results are presented for many applications including uniformly loaded rectangular and I beams, and square plates with either simply supported or clamped ends (or edges). The results are compared with known results from analytical and/or finite element analyses. Finally, a uniformly loaded stiffened panel is analysed and the results are compared with finite element results. In all cases, the results indicate that a single bending mode in the strip direction is sufficient to yield engineering accuracy for design purposes.
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    Correction (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. ii 
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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.1620281002
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    Three-dimensional crack analysis using singular boundary elements (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 2257-2273 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A multi-domain method of solving three-dimensional elastic crack problems in an infinite elastic body using the boundary element method is proposed. The \documentclass{article}\pagestyle{empty}\begin{document}$ \sqrt r $\end{document} displacement and \documentclass{article}\pagestyle{empty}\begin{document}$ 1/\sqrt r $\end{document} traction behaviours near a crack front are incorporated in special crack elements. The elimination of singularities arising from the \documentclass{article}\pagestyle{empty}\begin{document}$ 1/\sqrt r $\end{document} term combined with Kelvin's kernel for displacement in the integrals is discussed in detail. Stress intensity factors of modes I, II and III are obtained directly from crack-front nodal values, without any extrapolation as in some other methods. No differentiation of conventional boundary integral equations (with Kelvin's tensor kernels) is necessary in the current approach. This method is applicable to cracks of arbitrary shape. Infinite bodies are modelled precisely as such, not approximated as large finite bodies. Numerical solutions of stress intensity factors are given for several problems involving a penny-shaped crack.
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    On updating the structure of sparse matrix factors (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 2339-2360 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Structural analysis often involves the solution of a sparse system of linear equations using matrix factorization. For structural reanalysis problems, the system of equations is progressively changing and matrix factorization is required at each iteration step. In this paper, we study the problem of updating the structure of sparse matrix factors using an ordered-tree model. The ordered-tree model provides the information needed to symbolically compute the non-zero structure of the matrix factor of a sparse matrix. Furthermore, for matrix factor modification problems, this tree model can be used to determine the numerically modified entries in the matrix factor. Examples for modification of a structure and h-adaptive refinement of a finite element model are given to illustrate the potential application of the procedures developed in this study.
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    A time domain boundary element method for poroelasticity (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 2423-2449 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The development of a general boundary element method (BEM) for two- and three-dimensional quasistatic poroelasticity is discussed in detail. The new formulation, for the complete Biot consolidation theory, operates directly in the time domain and requires only boundary discretization. As a result, the dimensionality of the problem is reduced by one and the method becomes quite attractive for geotechnical analyses, particularly those which involve extensive or infinite domains.The presentation includes the definition of the two key ingredients for the BEM, namely, the fundamental solutions and a reciprocal theorem. Then, once the boundary integral equations are derived, the focus shifts to an overview of the general purpose numerical implementation. This implementation includes higher-order conforming elements, self-adaptive integration and multi-region capability. Finally, several detailed examples are presented to illustrate the accuracy and suitability of this boundary element approach for consolidation analysis.
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    On the problem of modelling for parameter identification in distributed structures (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 2451-2463 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Structures are often characterized by parameters, such as mass and stiffness, that are spatially distributed. Parameter identification of distributed structures is subject to many of the difficulties involved in the modelling problem, and the choice of the model can greatly affect the results of the parameter identification process. Analogously to control spillover in the control of distributed-parameter systems, identification spillover is shown to exist as well and its effect is to degrade the parameter estimates. Moreover, as in modelling by the Rayleigh-Ritz method, it is shown that, for a Rayleigh-Ritz type identification algorithm, an inclusion principle exists in the identification of distributed-parameter systems as well, so that the identified natural frequencies approach the actual natural frequencies monotonically from above.
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    Treatment of corners in BIE analysis of potential problems (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 2569-2581 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: At corners or edges in the boundary of the domain of a potential problem the local normal gradient of potential is double-valued. When Dirichlet boundary conditions are specified there are thus two unknowns at a single nodal point, and the sets of equations resulting from the usual BIE discretization are rendered indeterminate. We discuss here earlier approaches to the resolving of this problem, and describe a further approach which appears to offer some advantages. Both normal gradients can be approximated directly from local potential boundary conditions, showing the problem indeed to be formally overdetermined. This ability is discarded, in favour of yielding a robust and well-conditioned relationship between the two gradients. This, in conjunction with the BIE analysis, permits solutions of considerable accuracy to be found, including the gradients at such corner nodes. Illustrative calculations are presented for rectilinear and curvilinear domains. These show that, even with as few elements as there are corners, and thus one and a half times as many unknowns as there are nodal points, good approximations to the gradients can be obtained. The need for progressively finer discretization as a corner is approached is thus much reduced.
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    Process modelling of metal forming and thermomechanical treatment, C. R. Boer, N. Rebelo, H. Rydstad and G. Schroder, Springer-Verlag, Berlin, 1986. No. of. pages: 410. ISBN 3-540-16401-4 (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 2710-2711 
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    Keywords: Engineering ; Engineering General
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    URL: http://dx.doi.org/10.1002/nme.1620281116
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    Computational structural mechanics and fluid dynamics CASV 30/1-2H, edited by A. K. Noor, ISBN 008 0371973, Pergamon Press, Oxford OX3 OBW, U.K., 1988. Price: £70.00 $125.00 (hardback). No. of pages: 465 (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 2711-2711 
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    Keywords: Engineering ; Engineering General
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    An efficient through-thickness integration scheme in an unlimited layer doubly curved isoparametric composite shell element (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 2777-2793 
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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 an efficient numerical integration scheme for evaluating the matrices (stiffness, mass, stress-stiffness and thermal load) for a doubly curved, multilayered, composite, quadrilateral shell finite element. The element formulation is based on three-dimensional continuum mechanics theory and it is applicable to the analysis of thin and moderately thick composite shells.The conventional formulation requires a 2 × 2 × 2 or 2 × 2 × 1 Gauss integration per layer for the calculation of element matrices. This method becomes uneconomical when a large number of layers is used owing to an excessive amount of computations. The present formulation is based on explicit separation of the thickness variable from the shell surface parallel variables. With the through-thickness variables separated, they are combined with the thickness dependent material properties and integrated separately. The element matrices are computed using the integrated material matrices and only a 2 × 2 spatial Gauss integration scheme. The response results using the present formulation are identical to those obtained using the conventional formulation. For a small number of layers, the present method requires slightly more CPU time. However, for a larger number of layers, numerical data are presented to demonstrate that the present formulation is an order-of-magnitude economical compared to the conventional scheme.
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    On the rotation of conductors of finite torsional stiffness by eccentric snow loading and control of rotation using counterweights (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 2829-2838 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper is concerned with the prevention of snow loading on an overhead conductor caused by the mechanism of cylindrical-sleeve growth. The eccentric snow loading on the windward side of the conductor, having finite torsional stiffness, causes the conductor to rotate and a theoretical study of how this rotation can be controlled on attaching counterweights along the span of the conductor is presented. In the absence of counterweights, the non-linear rotation equation is solved analytically in terms of elliptic functions, simulating ice loading by a uniform torque density; for large torque density an asymptotic solution is obtained using matched asymptotic expansions. In the rotation equation the counterweights producing torque at discrete points are incorporated as delta functions which enable the discontinuity in the twisting couple at such locations to be accounted for by means of an integral moment balance. A simple algorithm is then presented for integrating the equation of rotation as an initial value problem which can deal with any distribution of counterweights along the span of the conductor. Illustrative numerical results are presented for zero, one, two, three and four counterweights per span; in the absence of counterweights analytical and numerical solutions are in exact agreement.
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    Fast algorithm for assembling blocks of global equations in FE programs (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 2907-2922 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new method for assembling blocks of global equations in FE programs is presented. The method has been implemented in SAP IV, the well-known FE program.The new assembling process consists of two phases. First, for each pair of blocks, the numbers of active elements are determined in ascending order. Then, from the sequential file containing element matrices, active records only are read and processed, the non-active ones being skipped.The most important features of the new method as compared to the method previously used are the following: (i) it saves up to 2/3 of the CPU-time for assembling, (ii) the amount of data on an auxiliary file is negligible, (iii) it does not require any additional high speed storage, (iv) it can be directly applied in any FE program with blocks using the constant bandwidth row storage scheme, (v) after some modifications it can be applied also in FE programs with blocks using the skyline column storage scheme.The full source code in FORTRAN IV is given in Appendix II.
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    Preconditioned conjugate- and secant-Newton methods for non-linear problems (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 1299-1316 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The preconditioned conjugate gradient (CG) method is becoming accepted as a powerful tool for solving the linear systems of equations resulting from the application of the finite element method. Applications of the non-linear algorithm are mainly confined to the diagonally scaled CG. In this study the coupling of preconditioning techniques with non-linear versions of the conjugate gradient and quasi-Newton methods creates a set of conjugate- and secant-Newton methods for the solution of non-linear problems. The preconditioning matrices used to improve the ellipticity of the problem and to reduce the computer storage requirements are obtained by the application of the partial preconditioning and the partial elimination techniques. Both techniques use a drop-off parameter ψ to control the computer storage demands of the method, making it more versatile for any computer hardware environment. Consideration is given to the development of a highly effective stability test for the line search minimization routine, which computes accurate values without much effort. This results in a beneficiary effect not only on the convergence properties of the methods but on their efficiency as well.
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    An efficient 3-D infinite element for water wave diffraction problems (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 1371-1387 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An efficient and simple infinite element for modelling the far field potential of water wave diffraction problems is presented. The shape functions in the radial direction comprise the first two terms of the asymptotic expansions of Hankel functions. The integrals with infinite limit for calculating the coefficient matrix have been worked out. Numerical tests on the diffraction by a surface-piercing circular cylinder give surprisingly accurate resultant forces even if the infinite elements are placed very near to the cylinder. Other typical three dimensional examples also show that satisfactory results can be obtained by the use of this simple infinite element. A computer program, WALOAD, has been developed for computing the wave forces on fixed two and three dimensional bodies.
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    Softening and snap-back instability in cohesive solids (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 1521-1537 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The nature of the crack and the structure behaviour can range from ductile to brittle, depending on material properties, structure geometry, loading condition and external constraints. The influence of variation in fracture toughness, tensile strength and geometrical size scale is investigated on the basis of the π-theorem of dimensional analysis. Strength and toughness present in fact different physical dimensions and any consistent fracture criterion must describe energy dissipation per unit of volume and per unit of crack area respectively. A cohesive crack model is proposed aiming at describing the size effects of fracture mechanics, i.e. the transition from ductile to brittle structure behaviour by increasing the size scale and keeping the geometrical shape unchanged.For extremely brittle cases (e.g. initially uncracked specimens, large and/or slender structures, low fracture toughness, high tensile strength, etc.) a snap-back instability in the equilibrium path occurs and the load-deflection softening branch assumes a positive slope. Both load and deflection must decrease to obtain a slow and controlled crack propagation (whereas in normal softening only the load must decrease). If the loading process is deflection-controlled, the loading capacity presents a discontinuity with a negative jump. It is proved that such a catastrophic event tends to reproduce the classical LEFM-instability (KI = KIC) for small fracture toughnesses and/or for large structure sizes. In these cases, neither the plastic zone develops nor slow crack growth occurs before unstable crack propagation.
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    URL: http://dx.doi.org/10.1002/nme.1620280705
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    Non-linear steady state vibration of frames by finite element method (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 1599-1618 
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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 based on the virtual work principle to determine the steady state response of frams in free or forced periodic vibration is introduced. The axial and flexural deformations are coupled by mean of the induced axial force along the element. The spatial discretization of the deformations is achieved by the usual finite element method and the time discretization by Fourier coefficients of the nodal displacements. No unconventional element matrices are needed. After applying the harmonic balance method, a set of non-linear algebraic equations of the Fourier coefficients is obtained. These equations are solved by the Newtonian iteration method in terms of the Fourier coefficient increments. Nodal damping can easily be included by a diagonal damping matrix. The direct numerical determination of the Fourier coefficient increments is difficult owing to the presence of peaks, loops and discontinuities of slope along the amplitude-frequency response curves. Parametric construction of the response curves using the phase difference between the response and excitation is recommended to provide more points during the rapid change of the phase (i.e. at resonance). For undamped natural vibration, the method of selective coefficients adopted.Numerical examples on the Duffing equation, a hinged-hinged beam, a clamped-hinged beam, a ring and a frame are given. For reasonably accurate results, it is shown that the number of finite elements must be sufficient to predict at least the linear mode at the frequency of interest and the number of harmones considered must satisfy the conditions of completeness and balanceability, which are discussed in detail.
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    3-D boundary element method for cracks in a plate (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 1703-1713 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: New fundamental solutions which automatically satisfy boundary conditions at the interfaces of an elastic plate perfectly bonded to two elastic halfspaces are implemented in a 3-D boundary element method (BEM) for crack problems. The BEM features a new integration scheme for highly singular kernels. The capability is achieved through a part analytic and part numerical integration procedure, such that the analytic part of the integration is similar for all slip/opening variations, ‘Part-through’ elliptic cracks in an elastic plate with traction-free surfaces are analysed and the stress intensity factor (SIF) values along the crack front are found to compare favourably with widely accepted numerically obtained SIF results by Raju and Newman.1
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    URL: http://dx.doi.org/10.1002/nme.1620280716
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    Projection methods in flexible multibody dynamics. Part II: Dynamics and recursive projection methods (1992)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 35 (1992), S. 1941-1966 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In Part I of this paper the kinematic relationships between the absolute, elastic and joint accelerations are developed. In this paper, these kinematic equations are used with the generalized Newton-Euler equations and the relationship between the actual and generalized reaction forces to develop a recursive projection algorithm for the dynamic analysis of open-loop mechanical systems consisting of a set of interconnected rigid and deformable bodies. Optimal matrix permutation, partitioning and projection methods are used to eliminate the elastic accelerations while maintaining the inertia coupling between the rigid body motion and the elastic deformation. Recursive projection methods are then applied in order to project the inertia of the leaf bodies onto their parent bodies. This leads to an optimal symbolic factorization which recursively yields the absolute and joint accelerations, and the joint reaction forces. The method presented in this paper avoids the use of Newton-Raphson algorithms in the numerical solution of the constrained dynamic equations of open-loop kinematic chains since the joint accelerations are readily available from the solution of the resulting reduced system of equations. Furthermore, the method requires only the inversion or decomposition of relatively small matrices and the numerical integration of a minimum number of co-ordinates. Open-loop multibody robotic manipulator systems are used to compare the results and efficiency of the recursive methods with that of the augmented formulations that employ Newton-Raphson algorithms.
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    URL: http://dx.doi.org/10.1002/nme.1620351003
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    Coupling finite elements and magnetic networks in magnetostatics (1992)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 35 (1992), S. 1991-2002 
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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 method for computing non-linear magnetostatic fields is introduced, which allows the simultaneous coupling of a finite element structure with a magnetic network. Combining the advantages of both methods while avoiding their drawbacks, this coupling yields both an accurate and time-efficient computation.The traditional method of the unknown mesh fluxes is applied for the solution of the magnetic network. The finite element solution, on the other hand, is based on a classical first-order interpolation of the unknown vector potential. The coupling is established by a proper organization of the unknowns on the boundary common to the finite element and network regions. In this way, a single system of non-linear equations is obtained.Moreover, it is shown that the coupled system of equations is equivalent to a single finite element system if generalized base functions are allowed. Consequently, various results from finite element theory may be applied. For instance, the matrix governing the iteratively linearized system of equations can directly be shown symmetrical and positive definite.Finally, the field inside a permanent magnet motor is calculated with the coupled method. Although the number of unknowns is dramatically reduced compared to a full FE calculation, the same level of accuracy is achieved. Hereby, the benefit of the coupled method is clearly proved.
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    A consistent model for first-order moderate rotation plate theory (1992)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 35 (1992), S. 2049-2066 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The first-order shear deformation plate theory can be used in the small strain and moderate rotation non-linear elasticity by defining correctly the displacement vector form. In this paper, the problem of the consistency between the displacement vector form and the finite strain tensor approximation is analysed. Then, a new moderate rotation theory is proposed. The variational form of the governing equations is derived for the beam and the plate problems in a consistent way. Then, an iterative numerical procedure based on the finite element method and the secant striffness matrix is developed in order to solve the non-linear differential equation problem. Computations are made for one- and two-dimensional structures, in order to assess the performance of the von Kármán, finite elasticity, classical and the proposed moderate rotation theories.
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    Conference diary (1992)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 35 (1992), S. 2103-2104 
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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.1620351012
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    Direct evaluation of singular boundary integrals in two-dimensional biharmonic analysis (1992)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 35 (1992), S. 2067-2078 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Development of techniques to provide rapid and accurate evaluation of the integrations required in boundary element method (BEM) formulations are receiving more attention in the literature. In this work, a series of direct expressions for surface integrals, required for a boundary element solution of the non-homogeneous biharmonic over a general two-dimensional curvilinear surface, are presented. The concept of an isoparametric representation, usually applied to the variation of the field variables and the geometry, is extended to the parametric mapping of the curvilinear geometry. The result renders the typically complicated Jacobian function into a series of polynomial expressions based on the shape function set and several discrete Jacobian values. An application of the isoparametric approximation of the Jacobian for a quadratic element representation is developed. Implementation of this approximation significantly improves the accuracy of the boundary integral solution by eliminating error associated with numerical quadrature. Overall computational efficiency is improved by reducing the time necessary to calculate individual surface integrals and evaluate field variables at internal points. A numerical solution of the boundary integral equations of phenomena governed by the biharmonic equation is presented and compared with an exact analysis.
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    An infinite boundary element formulation for three-dimensional potential problems (1992)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 35 (1992), S. 2079-2100 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An infinite boundary element (IBE) is presented for the analysis of three-dimensional potential problems in an unbounded medium. The IBE formulations are done to allow their coupling with the finite element (FE) matrices for finite domains and to obtain the overall matrices without destroying the banded structure of the FE matrices. The infinite body is divided into a number of zones whose contributions are expressed in terms of the nodal quantities at FE nodes by employing suitable decay functions and performing mainly analytical integrations of the boundary element kernels. The continuity and compatibility conditions for the potential and the flux at the FE-IBE interface are developed. The relationships for the contributions of the IBE flux vectors to the FE load vectors are given. The final equations for the IBE are obtained in the usual FE stiffness-load vector form and are easily assembled with the FE matrices for the finite object. A series of numerical examples in heat transfer and electromagnetics were solved and compared with alternative solutions to demonstrate the validity of the present formulations.
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    Creep deformation structural analysis using an efficient numerical algorithm (1992)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 35 (1992), S. 1427-1442 
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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 fast numerical algorithm for the implementation of material models for creep into finite element codes. First, an overview of existing algorithms for transient and steady-state creep is given. Next, a new formulation is presented which reduces the constitutive integration to the solution of a scalar non-linear algebraic equation. A solution is shown to exist without the need for subincrementation. Details of the numerical algorithm are then discussed. The paper closes with several numerical examples which illustrate the speed, robustness and accuracy of the proposed procedure as implemented in the Lawrence Livermore National Laboratory finite element codes NIKE2D and NIKE3D.
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    How to recognize the order of infinitesimal mechanisms: A numerical approach (1992)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 35 (1992), S. 1351-1395 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Structures presenting kinematical inderterminacy are usually called mechanisms. This paper is entirely concerned with assemblies which reveal themselves to be mechanisms at a null value of the load. Among them a first distinction is made between infinitesimal and finite ones, the former being characterized by one or several directions of lower (but not zero) stiffness, whereas the latter show at least one finite admissible displacement for which none of the bars undergoes any elongation. Moreover, there exists the possibility to make a further distinction among the infinitesimal mechanisms, according to which is the order of the stiffness along the direction considered above. The way of evaluating this order is to perform a local analysis of the strain energy of the assembly, once the displacement field is parametrized in terms of a suitable parameter. By means of a finite element technique, this analysis can be easily performed through the numerical approach presented in this report.
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    Solutions to shape and topology eigenvalue optimization problems using a homogenization method (1992)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 35 (1992), S. 1487-1502 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A solution strategy to find the shape and topology of structures that maximize a natural frequency is presented. The methodology is based on a homogenization method and the representation of the shape of the structure as a material property. The problem is formulated as a reinforcement problem in which a given structure is reinforced using a prescribed amount of material. Two dimensional, plane elasticity problems are considered. Examples are presented for illustration.
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    Announcements (1992)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 35 (1992), S. 1541-1542 
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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.1620350710
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    Masthead (1992)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 35 (1992) 
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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.1620350901
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    Masthead (1992)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 33 (1992) 
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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.1620330101
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    Numerical solution of integral equations with a logarithmic kernel by the method of arbitrary collocation points (1992)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 33 (1992), S. 143-148 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An integral equation whose kernel presents logarithmic singularity is numerically solved by the method of arbitrary collocation points (ACP). As a first step a Gaussian quadrature of order n (hence of polynomial accuracy 2n- 1) is employed for the numerical approximation of the integral. Until now the collocation, which follows, was performed on special points x̄k, determined as roots of appropriate transcedental functions, in order to retain the 2n - 1 degree of polynomial accuracy of the Gaussian quadrature. In this paper an appropriate interpolatory technique is proposed, so that xk may be arbitrary and yet the high (2n - 1) accuracy of the Gaussian quadrature is retained.
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    Stabilized rapidly convergent 18-degrees-of-freedom flat shell triangular element (1992)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 33 (1992), S. 149-162 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A rank-sufficient flat triangular shell element with drilling degrees-of-freedom is described. A variational basis for this element has been provided by a three-field variational principle with relaxed interelement compatibility and traction continuity conditions. A generalized spurious mode control procedure has been developed in order to stabilize zero energy kinematical modes. Excellent performance has been found in an obstacle course and buckling problems.
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    Some comments on: Benchmark problems and testing of a finite element code for solidification in investment castings (1992)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 33 (1992), S. 213-215 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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    Computational structural mechanics and optimal control - the simulation of substructural chain theory to linear quadratic optimal control problemsJoint project of the Natural Science Foundation of China and the Royal society. (1992)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 33 (1992), S. 197-211 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The theory of optimal control and the theory of a substructural chain in static structural analysis are mutually simulated issues. From the minimum potential energy variational principle of the substructural chain, the generalized variational principle with two kinds of variables is derived first. By comparing that generalized variational principle with the variational principle in LQ control theory, the simulation relation is established. Based on that relation, the potential energy and mixed energy formulation of the algebraic Riccati equations are derived, then iterative algorithms are proposed which give the upper and lower bounds to the solution matrix. By using the solutions of the positive and negative co-ordinate algebraic Riccati equations, the canonical transformation matrices for the eigenproblems of the substructural chain and LQ control are constructed respectively, which reduce the eigenproblem to half-size. The properties of the solutions are analysed, which establishes the basis for expansion solutions.
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    Computer-aided analysis and design of electromagnetic devices, by S. Rantajeevan H. Hoole, Elsevier Science Publishing company, New York. 1989. ISBN 0-444-01327-x (1992)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 33 (1992), S. 217-219 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Reliability in computational mechanics, edited by J. T. Oden, Elsevier Science Publications, NY, 1990. No. of pages: 388. Price: $192.25. ISBN 0-444-88560-9 (1992)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 33 (1992), S. 220-220 
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    Keywords: Engineering ; Engineering General
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    Conference diary (1992)
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    International Journal for Numerical Methods in Engineering 33 (1992), S. 221-222 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Masthead (1992)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 33 (1992) 
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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.1620330201
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    Free vibration of axisymmetric and beam-like cylindrical shells, partially filled with liquid (1992)
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    International Journal for Numerical Methods in Engineering 33 (1992), S. 235-268 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A theory is presented for the determination of the free vibration characteristics of anisotropic thin cylindrical shells, partially or completely filled with liquid, for two circumferential wave numbers, n = 0, axisymmetric and n = 1, beam-like. The method used was a combination of finite element analysis and classical shell theory. The shell was subdivided into cylindrical finite elements and the displacement functions were obtained using the shell equations. Expressions for the mass and stiffness matrices for a finite element and for the whole structure were obtained. A finite element was developed for the liquid in cases of potential flow. The natural frequencies of the shell, both empty and partially filled, were obtained and compared with existing experiments and other theories.
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    Effective modelling of spatial buckling of beam assemblages, accounting for warping constraints and rotation-dependency of moments (1992)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 33 (1992), S. 469-502 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A simple, two-noded, finite element model for the three-dimensional buckling analysis of beam assemblages is developed. The underlying generalized-beam theory employed accounts for all coupled significant modes of deformations, including stretching, bending, shear and torsion, as well as warping. Its mixed formulation is of the two-field type, utilizing linear and constant interpolants for displacements and strain fields. Due considerations are given to the effect off inite rotations in space on the non-linear kinematic descriptions as well as the configuration-dependent behaviour of externally applied moment vectors of the conservative and non-conservative types. The performance of the model, and particularly the accuracy of its geometric and load-correction stiffnesses, is assessed in a fairly complete set of numerical simulations.
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    Finite element calculation of energy release rate for 2-D rubbery material problems with non-conservative crack surface tractions (1992)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 33 (1992), S. 907-927 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The energy release rate G for 2-D rubbery material problems with non-conservative crack surface tractions is calculated by a modified version of virtual crack extension method with finite element solutions. The formulation is demonstrated to be ‘patch-independent’ and therefore a complicated finite element model around the crack tip is not required.
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    A numerical technique for the analysis of cracks subjected to normal compressive stresses (1992)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 33 (1992), S. 929-942 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The purpose of the present paper is the development of a numerical method for the evaluation of the Stress Intensity Factor in mode II at the tips of closed cracks subjected to compressive normal stresses and monotonically increasing shear stresses. A hybrid Boundary Element Technique, originally developed for the analysis of open cracks, has been suitably modified. The Stress Intensity Factor is evaluated directly on the basis of the displacement discontinuities computed at the crack tip element, by taking into account the development of frictional resistance on the crack surfaces. A limited number (10-15) of displacement discontinuity elements is found to be sufficient for an accurate evaluation of the Stress Intensity Factor. Some basic aspects of the mechanical behaviour of closed cracks are also investigated on the basis of the proposed method.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620330504
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