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  • 1
    Electronic Resource
    Electronic Resource
    Computer algorithms for calculating efficient initial vectors for subspace iteration method (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 1841-1848 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper, the effects of selecting initial vectors on computation efficiency for a subspace iteration method are investigated. Four algorithms are used for selecting the initial vectors. First, arbitrary starting iteration vectors are chosen according to Bathe and Wilson's algorithm.1 In the other algorithms, the initial vectors are the retrieved eigenvectors from the Guyan and quadratic reduction methods. Improvement of the eigenvalue approximations of the subspace iteration method over reduction methods is presented. The computation effort is examined for the various algorithms used for initial iteration vectors.
    Additional Material: 8 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620241003
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  • 2
    Electronic Resource
    Electronic Resource
    Three-dimensional computer code for dynamic response of solids to intense impulsive loads (1979)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 14 (1979), S. 1865-1871 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Earlier publications demonstrated the capability of the EPIC-3 code to perform high velocity impact computations in three dimensions.1,2 These capabilities were demonstrated with simplified material and sliding surface models in a core-contained computer program. This paper presents recent developments which include more comprehensive material and sliding surface formulations, and an expanded computer program which can handle problems of unlimited size by beffering data between disc files and core. The EPIC-3 code is based on an explicit, finite element, Lagrangian formulation which uses constant strain tetrahedral elements.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620141208
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  • 3
    Electronic Resource
    Electronic Resource
    Who was ‘-Raphson’? (1979)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 14 (1979), S. 148-152 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620140112
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Dynamic Lagrangian computations for solids, with variable nodal connectivity for severe distortions (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986), S. 509-522 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents an algorithm for dynamic Lagrangian computations for solids, in plane strain geometry, with variable nodal connectivity to allow for severe distortions. The nodes are somewhat analogous to flexible circular disks. When they move closer together than their equilibrium distance they generate compressive, repulsive forces. Conversely, when they move apart, they generate tensile, attractive forces. Material strength effects are also included. Because a node can only be affected by its ‘neighbour’ nodes, the approach has been designated the ‘NABOR’ approach. The key to this approach is that it is possible to have variable nodal connectivity - a node can acquire new neighbours, thus allowing all forms of distortion. The NABOR algorithm has been incorporated as an option into the explicit finite element code, EPIC-2. By using both the NABOR grid and the EPIC-2 finite element grid together, it is possible to perform Lagrangian computations for a wide range of problems.
    Additional Material: 11 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620230313
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  • 5
    Electronic Resource
    Electronic Resource
    On the accuracy of polynomial finite elements for crack problems (1981)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 17 (1981), S. 1835-1842 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A square tensile sheet with symmetric edge cracks is analysed by the finite element method to demonstrate the accuracy obtained with polynomial elements when the mesh patterns are chosen on the basis of the element's interpolation functions. Numerical results are provided for the accuracy of the total strain energy, the stress intensity factor, and the numerical condition of the global stiffness matrix. The stress intensity factor is determined to within 1.0 per cent accuracy using quadratic (linear strain) triangular elements with only 138 degrees-of-freedom.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620171208
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  • 6
    Electronic Resource
    Electronic Resource
    Evaluation of some numerical schemes for consolidation (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 7 (1973), S. 243-254 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Five finite difference and two finite element schemes for solution of the one-dimensional consolidation problem are compared and evaluated from the viewpoints of convergence, accuracy, stability and computational efforts. An example problem involving laboratory experiments is also solved by using various schemes. Conclusions are drawn regarding relative suitability of these schemes for practical applications.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620070303
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  • 7
    Electronic Resource
    Electronic Resource
    Quadratic reduction for the eigenproblem (1980)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 15 (1980), S. 911-923 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A quadratic method is presented for solving the eigenvalue problem of a structural system having a large number of degrees-of-freedom. The eigenproblem is reduced to a smaller problem by condensing the system stiffness and mass using Guyan reduction. Application of a set of corrective displacements to the reduced system subsequently leads to an eigenproblem of quadratic form involving an additional mass term. To obtain the solution to the reduced problem, inverse iteration with spectrum shifts based on the eigenvalues of the Guyan problem is used. The resulting eigenvalues and mode shapes represent a corrected Guyan approximation to the solution of the unreduced system. In addition, it is shown that the amount of improvement over the Guyan solution can be approximated by employing a first-order error analysis procedure. Numerical examples of vibrations of a bar, a beam and a plate demonstrate that the solutions obtained from the quadratic reduction procedure are very accurate and require relatively little additional computational effort in comparison with the solutions of the corresponding linear eigen-problem. The relationship of the present method to that proposed by Przemieniecki is illustrated by an example.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620150609
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  • 8
    Electronic Resource
    Electronic Resource
    An automatic sliding interface algorithm for intense impulsive loading computations (1996)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 885-896 
    Details
    ISSN: 1069-8299
    Keywords: interfaces ; sliding ; contact ; impact ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents an automatic sliding interface algorithm for intense impulsive loading computations due to high velocity impact and explosive detonation. This algorithm allows the user to perform computations involving complex sliding interfaces without having to predetermine the sliding interfaces; everything is automated. The interface determination algorithm, the searching algorithm and the contact algorithm are included.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
  • 9
    Electronic Resource
    Electronic Resource
    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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  • 10
    Electronic Resource
    Electronic Resource
    Dispersion properties of simple 3D finite elements (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 97-103 
    Details
    ISSN: 1069-8299
    Keywords: dispersion relation ; isotropy ; numerical dispersion ; stiffness integration ; zero wave speed ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The dispersion properties of plane waves, propagating in an infinite uniform mesh with linear cubic 3D finite elements, are investigated. Time discretization is performed with the central-difference time-stepping scheme in combination with lumped mass matrices. The stiffness matrices are integrated analytically with different integration schemes, and dispersion relations are derived. The results show that the stiffness integration scheme can be chosen to reduce dispersion and improve the isotropy of wave propagation. It is also observed that the numerical wave speed becomes zero along certain wave propagation directions for specific wave numbers.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640110203
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