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  • 1
    Electronic Resource
    Electronic Resource
    Dispersion analysis of finite element semidiscretizations of the two-dimensional wave equation (1982)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 18 (1982), S. 11-29 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The dispersive properties of finite element semidiscretizations of the two-dimensional wave equation are examined. Both bilinear quadrilateral elements and linear triangular elements are considered with diagonal and nondiagonal mass matrices in uniform meshes. It is shown that mass diagonalization and underintegration of the stiffness matrix of the quadrilateral element markedly increases dispersive errors. The dispersive properties of triangular meshes depends on the mesh layout; certain layouts introduce optical modes which amplify numerically induced oscillations and dispersive errors. Compared to the five-point Laplacian finite difference operator, rectangular finite element semidiscretizations with consistent mass matrices provide superior fidelity regardless of the wave direction.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620180103
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  • 2
    Electronic Resource
    Electronic Resource
    A stabilization procedure for the quadrilateral plate element with one-point quadrature (1983)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 19 (1983), S. 405-419 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A stabilization procedure is developed for controlling the kinematic modes of the four-node, bilinear quadrilateral element when single-point quadrature is used. These kinematic modes manifest themselves by spatial oscillations or singularity of the total stiffness. In this stabilization procedure, additional generalized strains are defined which are activated by the kinematic modes; these generalized modes are furthermore not activated by rigid body motions regardless of the shape of the quadrilateral. By using a scaling law developed in an earlier paper, the stabilization parameters are defined so they do not adversely affect the element's performance. Several problems which are subject to kinematic modes are presented to illustrate the performance of this stabilization procedure for linear problems.
    Additional Material: 11 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620190308
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Efficient linear and nonlinear heat conduction with a quadrilateral element (1984)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 931-948 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A method is presented for performing efficient and stable finite element calculations of heat conduction with quadrilaterals using one-point quadrature. The stability in space is obtained by using a stabilization matrix which is orthogonal to all linear fields and its magnitude is determined by a stabilization parameter. It is shown that the accuracy is almost independent of the value of the stabilization parameter over a wide range of values; in fact, the values 3, 2 and 1 for the normalized stabilization parameter lead to the 5-point finite difference, 9-point finite difference and fully integrated finite element operators, respectively, for rectangular meshes; numerical experiments reported here show that the three have identical rates of convergence in the L2 norm. Eigenvalues of the element matrices, which are needed for stability limits, are also given. Numerical applications are used to show that the method yields accurate solutions with large increases in efficiency, particularly in nonlinear problems.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620200510
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  • 4
    Electronic Resource
    Electronic Resource
    Partitioned rational Runge Kutta for parabolic systems (1984)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 1581-1597 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new family of coupled time integration operators of different orders is developed. It permits different time integration operators to be used simultaneously in various regions of the model. This approach has the advantage of applying a very accurate time integrator, such as Runge Kutta method of order two to four, to the local nonlinear region of interest and a simple time integrator, such as the implicit-explicit or mixed time implicit-explicit method of order one, for the remaining region. The computer implementation aspects, stability analysis as well as the numerical evaluations of these new methods are presented. This is another attractive addition to the repertoire of time integration methods.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620200904
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    Paper (German National Licenses)
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  • 5
    Electronic Resource
    Electronic Resource
    Stability of explicit-implicit mesh partitions in time integration (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 1575-1586 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The stability of time integration for a semidiscretization of structures and continua where the mesh is partitioned into subdomains integrated simultaneously by explicit and implicit methods is considered. Stability in energy is proven for linear systems subject to the Courant condition in the explicit subdomain for a central difference explicit and trapezoidal implicit integrator. Numerical examples are presented to demonstrate the procedure.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620121008
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  • 6
    Electronic Resource
    Electronic Resource
    On reduced matrix inversion for operator splitting methods (1984)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 385-386 
    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.1620200215
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    Paper (German National Licenses)
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  • 7
    Electronic Resource
    Electronic Resource
    Eigenvalues and stable time steps for the bilinear Mindlin plate element (1985)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 21 (1985), S. 1729-1745 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Eigenvalues are obtained for the 4-node Mindlin plate element with one-point quadrature. Both isotropic and some anisotropic matenals are considered, but for the latter only bounds are obtained on the eigenvalues. These eigenvalues provide stable time steps for explicit time integration algorithms.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620210913
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  • 8
    Electronic Resource
    Electronic Resource
    Improvements in 3-node triangular shell elements (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986), S. 1643-1667 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Low-order triangular finite shell elements are computationally economical and easy to implement, but often exhibit very slow convergence. Two new membrane formulations for triangular shell elements are examined which rectify these drawbacks. The first element is based on the Marguerre shallow shell theory and a strain projection method that eliminates spurious membrane strain energy. Resulting expressions are provided in an explicit form for easy implementation of the element. The second element is based on a linear membrane field governed by normal rotations and reduced quadrature.The difficulties with shell-normal rotations are analysed and a method for omitting these rotations while preserving rigid body motion is presented and tested. Finally, a set of test problems are examined which show the importance of mesh patterns and degrees-of-freedom per node on triangular element performance.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620230906
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  • 9
    Electronic Resource
    Electronic Resource
    Random field finite elements (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986), S. 1831-1845 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The probabilistic finite element method (PFEM) is formulated for linear and non-linear continua with inhomogeneous random fields. Analogous to the discretization of the displacement field in finite element methods, the random field is also discretized. The formulation is simplified by transforming the correlated variables to a set of uncorrelated variables through an eigenvalue orthogonalization. Furthermore, it is shown that a reduced set of the uncorrelated variables is sufficient for the second-moment analysis. Based on the linear formulation of the PFEM, the method is then extended to transient analysis in non-linear continua.The accuracy and efficiency of the method is demonstrated by application to a one-dimensional, elastic/plastic wave propagation problem and a two-dimensional plane-stress beam bending problem. The moments calculated compare favourably with those obtained by Monte Carlo simulation. Also, the procedure is amenable to implementation in deterministic FEM based computer programs.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620231004
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  • 10
    Electronic Resource
    Electronic Resource
    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 
    Details
    ISSN: 0029-5981
    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.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620281003
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