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  • 1
    Electronic Resource
    Electronic Resource
    A homework exercise in finite elements (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 411-417 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We suggest an exercise which illustrates many of the fundamental ideas of finite elements, and is nevertheless easily programmed and quickly solved. It is governed by a partial differential equation on a circular region, but by maintaining symmetry the stiffness matrix becomes small and tridiagonal. The accuracy of linear elements can be studied in detail, and a straightforward extension leads to the eigenvalue problem, elements of higher degree, numerical integration, isoparametric elements, and a simple example in plasticity.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620110302
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  • 2
    Electronic Resource
    Electronic Resource
    The solution of nonlinear finite element equations (1979)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 14 (1979), S. 1613-1626 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An algorithm is described which appears to give an efficient solution of nonlinear finite element equations. It is a quisi-Nowton method, and we compare it with some of the alternatives. Initial tests of its application to both material and geometric nonlinearities are discussed.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620141104
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  • 3
    Electronic Resource
    Electronic Resource
    Optimal design in elasticity and plasticity (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 22 (1986), S. 183-188 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A direct weight minimization subject to compliance constraints or plastic yielding constraints leads to a non-convex variational problem. Both the theoretical and the numerical analysis are unsatisfactory: the minimum weight is not achieved by any design, and the approximate designs oscillate as the element mesh is refined. We look for equivalent ‘relaxed problems’ with the same minima. They come from allowing composite materials constructed in an optimal way from the original materials. The constructions are different for elasticity and plasticity, but surprisingly the final relaxed problems are in some cases the same.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620220113
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  • 4
    Electronic Resource
    Electronic Resource
    Paradox lost: Natural boundary conditions in the Ritz-Galerkin method (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 2255-2266 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We present a simple calculation which seems at first to yield erroneous results when natural boundary conditions are not enforced. Our example is the static deformation of a cantilever beam under uniform loading. The corresponding variational principle is established and two applications of the Rayleigh-Ritz-Galerkin method are made.(1)The deflection is expanded in a series of cosines. The energy is rendered stationary subject to all boundary conditions, geometric and natural (they are imposed through Lagrange multipliers). The resulting function is exactly the Fourier cosine expansion of the true deflection-which is a fourth-degree polynomial.(2)The deflection is again expanded in a cosine series but now the natural boundary conditions are ignored. The resulting series does not converge to the true solution.Owing to the simplicity of the coefficients, exact summations are possible and the discrepancy is clear. The disagreement is large, and the object of the paper is to decide which method is right.
    Additional Material: 2 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620261009
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