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  • 1
    Electronic Resource
    Electronic Resource
    A linear finite element approach to the solution of the variational inequalities arising in contact problems of structural dynamics (1982)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 18 (1982), S. 1505-1520 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The present paper deals with the theoretical and numerical treatment of dynamic unilateral problems. The governing equations are formulated as an equivalent variational inequality expressing D' Alembert's principle in its inequality form. The discretization with respect to time and space leads to a static nonlinear programming problem which is solved by an appropriate algorithm. Some properties of dynamic unilateral problems are outlined and the influence of several parameters on the solution is investigated by means of numerical examples.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620181006
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  • 2
    Electronic Resource
    Electronic Resource
    Specification of skew conditions in finite element formulation (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 1037-1041 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Fields exhibiting skew symmetry occur frequently in structural problems. There are many situations where non-skew-symmetric functions are conveniently used to analyse these skew fields. Specification of force and displacement conditions on the skew axis reduces the analysis to a half of the domain. The difficulty in using such conditions in an FEM analysis is their non-explicit nature. A method of overcoming this difficulty is developed using concept of generalized forces and displacements.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620120613
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  • 3
    Electronic Resource
    Electronic Resource
    LU decomposition of matrices with augmented dense constraints (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 1451-1459 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Sparse matrices composed of a central band and augmented dense rows and columns are becoming prevalent in the numerical solution of a large class of boundary and initial-value problems. A Fortran Subroutine ARROW is presented for the LU decomposition and solution of linear equation systems with such a structure. The computational speed of the program is compared in MFLOPS (millions of floating point operations per second) to the LINPACK benchmark for the solution of a dense linear system and is found to be of comparable speed on both supercomputers and minicomputers. Use of the Basic Linear Algebra Subroutines (BLAS) available on most machines significantly enhances the speed of ARROW.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620240804
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  • 4
    Electronic Resource
    Electronic Resource
    Neural networks for computing in structural analysis: Methods and prospects of applicationsCertain results of this paper were obtained in the framework of a STRIDE-programme of the EEC concerning the ‘applications of the neural networks in engineering and medicine’, The programme, for which the second author is the scientific co-ordinator, takes place in the Aristotle University of Thessaloniki and the Democritus University of Xanthi in Greece. (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 2305-2318 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A neural network model is proposed and studied for the treatment of structural analysis problems. Both the cases of bilateral and unilateral constraints are considered and Hopfield-like neural models are proposed. Moreover, new results, generalizing the results of Hopfield and Tank,10 are obtained.Numerical applications illustrate the theory and show clearly the advantages of the neural network approach. Finally, the parameter identification problem is formulated and solved as a ‘learning’ problem for a neural network.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620361310
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  • 5
    Electronic Resource
    Electronic Resource
    A remark on pressure correction schemes for transient viscous incompressible flow (1998)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 14 (1998), S. 335-346 
    Details
    ISSN: 1069-8299
    Keywords: pressure-correction scheme ; incompressible flow ; spurious boundary layer ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper presents a discussion of some phenomena related to the pressure-correction scheme implemented in a spectral element or finite element context. Of particular interest are the spurious boundary layers created around prescribed boundaries in which the pressure exhibits spurious behaviour. The flow is very prone to singular behaviour, especially around geometrical singularities. That is why this phenomenon is studied using as an example the flow in a diverging channel with sharp changes in the angle. The reasons for, and a possible remedy to, the singular (and aphysical) behaviour of the numerical solution are discussed. The results of the numerical experiments clearly support the conclusions of this discussion. © 1998 John Wiley & Sons, Ltd.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    Numerical methods for analyzing the effects of uncertainties on the dynamics of periodic structures (1997)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 40 (1997), S. 3749-3765 
    Details
    ISSN: 0029-5981
    Keywords: localization ; disorders ; numerical methods ; periodic structures ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Various approaches are proposed and compared for analysing the effects of structural irregularities and parameter uncertainties on the dynamics of finitely long, one-dimensional, mono-coupled, nearly periodic assemblies with and without structural damping. Computational concerns are raised in regard to the classical method of modal analysis, and alternative methods are formulated which allow for the numerically efficient determination of the exponential decay constant. While modal analysis and Cramer's rule require the solution of an eigenvalue problem, the matrix inversion and matrix partitioning approaches avoid costly eigenvalue computations and require only cost-effective algebraic manipulations. Therefore, implementation of either the direct inversion technique or matrix partitioning both simplifies the analysis and cuts computational costs substantially. © 1997 John Wiley & Sons, Ltd.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    The ‘fractal assumption’ in cracks: Bilateral calculation methods (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 1597-1604 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper considers the fractal nature of cracks by assuming the fractal as the fixed point of a given transformation. This concept enables the study of a sequence of classical-geometry crack problems whose limit gives the solution of the fractal-geometry crack problem. The method is illustrated by a numerical example. It was shown that the fractal nature of the cracks influences the value of the stress intensity factors.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620360911
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  • 8
    Electronic Resource
    Electronic Resource
    On the consideration of unilateral contact and friction in cracks. The boundary integral method (1992)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 35 (1992), S. 1697-1708 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The scope of the present paper is the study of cracks having a given geometry by taking into account unilateral contact and friction phenomena between the two sides of the crack. The arising problem is highly non-classical because of the inequality relations describing the unilateral contact and friction interface conditions. The indirect BIEM is extended appropriately in order to treat this problem. Numerical examples concerning the calculation of stress intensity factors under the unilateral contact and friction interface conditions illustrate the developed method.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620350809
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  • 9
    Electronic Resource
    Electronic Resource
    OPTIMIZATION STRATEGIES IN UNSTRUCTURED MESH GENERATION (1996)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 2055-2071 
    Details
    ISSN: 0029-5981
    Keywords: unstructured mesh generation ; optimization ; smoothing ; finite elements ; finite volume methods ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We propose a new optimization strategy for unstructured meshes that, when coupled with existing automatic generators, produces meshes of high quality for arbitrary domains in 3-D. Our optimizer is based upon a non-differentiable definition of the quality of the mesh which is natural for finite element or finite volume users: the quality of the worst element in the mesh. The dimension of the optimization space is made tractable by restricting, at each iteration, to a suitable neighbourhood of the worst element. Both geometrical (node repositioning) and topological (reconnection) operations are performed. It turns out that the repositioning method is advantageous with respect to both the usual node-by-node techniques and the more recent differentiable optimization methods. Several examples are included that illustrate the efficiency of the optimizer.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
  • 10
    Electronic Resource
    Electronic Resource
    Convex multilevel decomposition algorithms for non-monotone problems (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 1945-1966 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A convex, multilevel decomposition algorithm is proposed in this paper for the solution of static analysis problems involving non-monotone, possibly multivalued laws. The theory is developed here for a model structure with non-monotone interface or boundary conditions. First the non-monotone laws are written in the form of a difference of two monotone functions. Under this decomposition, the non-linear elastostatic analysis problem is equivalent to a system of convex variational inequalities and to non-convex min-min problems for appropriately defined Lagrangian functions. The solution(s) of each one of the aforementioned problems describe the position(s) of static equilibrium of the considered structure. In this paper a multilevel optimization scheme, due to Auchmuty,1 is used for the numerical solution of the problem. The most interesting feature of this method, from the computational mechanics' standpoint, is the fact that each one of the subproblems involved in the multilevel algorithm is a convex optimization problem, or, in terms of mechanics, an appropriately modified monotone ‘unilateral’ problem. Thus, existing algorithms and software can be used for the numerical solution with minor modifications. Numerical results concerning the calculation of elastic and rigid stamp problems and of material inclusion problems with delamination and non-monotone stick-slip frictional effects illustrate the theory.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620361110
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