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  • 1
    Electronic Resource
    Electronic Resource
    Uniform rational approximation on large data sets (1982)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 18 (1982), S. 1569-1575 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We report on a very effective program for uniform approximation of functions (or discrete data) by generalized rational functions of any number of variables over point sets so large that conventional methods are inapplicable. The points need not be arranged in a regular pattern, but if they are, the number of points is normally limited only by the computer time available. The program extends the differential correction algorithm discussed in an earlier article in this journal by combining it with a first Remes-type exchange procedure, while retaining the flexibility and robustness of differential correction. Furthermore, this algorithm is guaranteed to converge in theory. Testing has shown that, even when the point set is small enough for differential correction to be applied directly, this algorithm is usually faster. We discuss the algorithm and program along with several numerical examples, one of which involves more than three million data points. A FORTRAN listing with illustrative output can be obtained from the first author.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620181011
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  • 2
    Electronic Resource
    Electronic Resource
    Local linearization of the finite element method and its applications to compressible flows (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 565-577 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In applications of the finite element method to complicated nonlinear problems, it is proposed to simplify the operator in each element, typically by a linerization process. Local approximations can then be more easily constructed in the usual manner, and a proper assembly can be made. Such an approach would lead to an approximate global variational statement; or if the variational principle exists but is hard to handle, it should suggest an iterative scheme with a built-in physical basis, hence a better chance to converge. The case of high subsonic flow over a circular cylinder is studied in detail by this method. With linear triangular elements, numerical results are obtained for 100 nodal unknowns in each quadrant. The convergence is extremely rapid up to a free stream Mach number of 0.42, slightly above critical. The accuracy is excellent as compared against Imai's analytical results.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620100307
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  • 3
    Electronic Resource
    Electronic Resource
    Application of a Cam-Clay model to overconsolidated clay (1983)
    New York, NY [u.a.] : Wiley-Blackwell
    International Journal for Numerical and Analytical Methods in Geomechanics 7 (1983), S. 173-186 
    Details
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: The yield locus governing the stress-strain response of a soil may degrade during rebound at high overconsolidation ratios. The cause can be attributed to a breakdown in bonding. A Cam-Clay model is applied to account for the degrading yield locus, and the influence of this degradation is assessed using a theoretical approach for friction pile capacity. Stress changes in the soil continuum due to pile installation and setup are simulated by cylindrical cavity expansion and radial consolidation, anda segment loading model is used to determine the effective stress change in the soil at peak load transfer under undrained conditions. The results indicate that plastic rebound affects peak load transfer to at least the same extent as shear strength.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nag.1610070204
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  • 4
    Electronic Resource
    Electronic Resource
    Two canonical wedge problems for the Helmholtz equation (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 877-899 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Boundary-transmission problems for two-dimensional Helmholtz equations in a quadrant and its complement, respectively, are considered in a Sobolev space setting. The first problem of a quadrant with Dirichlet condition on one face and transmission condition on the other is solved in closed form for the case where all the quadrants are occupied by the same medium. Unique solvability can also be shown in the case of two different media up to exceptional cases of wave numbers, while the Fredholm property holds in general. In the second problem, transmission conditions are prescribed on both faces. Similar results are obtained in the one-medium case, but the two-media case turns out to be more complicated and the equivalent system of boundary pseudodifferential equations cannot be completely analysed by this reasoning.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670171104
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  • 5
    Electronic Resource
    Electronic Resource
    Variational principles and hybrid approach for finite deformation analysis of shells (1991)
    New York, NY [u.a.] : Wiley-Blackwell
    Communications in Applied Numerical Methods 7 (1991), S. 429-434 
    Details
    ISSN: 0748-8025
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A complementary Hu-Washizu functional Γ3, based on formulae presented by Atluri (1984), is given in dyadic notation. By introducing Legendre transformation, the Heillinger-Reissner functional Π2, Γ2 and the classic potential energy functional Π1 are obtained. An incremental modelling of functional Γ3 for the analysis of finite deformation and finite rotations of arbitrarily shaped shells is presented. The numerical results are shown to be in good agreement with those found in published literature.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1630070603
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