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  • 1
    Electronic Resource
    Electronic Resource
    On using different finite elements with an automatic adaptive refinement procedure for the solution of 2-D stress analysis problems (1997)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 40 (1997), S. 4547-4576 
    Details
    ISSN: 0029-5981
    Keywords: adaptive refinement procedure ; error estimation ; 2-D stress analysis ; performance of different 2-D elements ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A series of numerical tests is carried out employing some commonly used finite elements for the solution of 2-D elastostatic stress analysis problems with an automatic adaptive refinement procedure. Different kinds of elements including Lagrangian quadrilateral and triangular elements, serendipity quadrilaterals, incompatible elements and hybrid elements have been tested. It is found that for a general problem involving compressible material and when a moderate accuracy of the final solution is sought, the nine-node Lagrangian (L9) element will be the most effective element, while when an extremely accurate solution is needed, higher order Lagrangian quadrilaterals or triangles will be a suitable choice. However, if only linear elements are available, the well known 5βI linear hybrid element is the best choice. © 1997 John Wiley & Sons, Ltd.
    Additional Material: 25 Ill.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Automatic adaptive refinement for plate bending problems using Reissner-Mindlin plate bending elements (1998)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 41 (1998), S. 1-63 
    Details
    ISSN: 0029-5981
    Keywords: automatic adaptive refinement ; Reissner-Mindlin plate bending model ; assumed strain elements ; boundary layer effects ; singular point effects ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The influence of the presence of singular points and boundary layers associated with the edge effects in a Reissner-Mindlin (RM) plate in the design of an optimal mesh for a finite element solution is studied, and methods for controlling the discretization error of the solution are suggested. An effective adaptive refinement strategy for the solution of plate bending problems based on the RM plate bending model is developed. This two-stage adaptive strategy is designed to control both the total and the shear error norms of a plate in which both singular points and boundary layers are present. A series of three different order assumed strain RM plate bending elements has been used in the adaptive refinement procedure. The locations of optimal sampling points and the effect of element shape distortions on the theoretical convergence rate of these elements are given and discussed. Numerical experiments show that the suggested refinement procedure is effective and that optimally refined meshes can be generated. It is also found that all the plate bending elements used can attain their full convergence rates regardless of the presence of singular points and boundary layers inside the problem domain. Boundary layer effects are well captured in all the examples tested and the use of a second stage of refinement to control the shear error is justified. In addition, tests on the Zienkiewicz-Zhu error estimator show that their performances are satisfactory. Finally, tests of the relative effectiveness of the plate bending elements used have also been made and it is found that while the higher order cubic element is the most accurate element tested, the quadratic element tested is the most efficient one in terms of CPU time used. © 1998 John Wiley & Sons, Ltd.
    Additional Material: 43 Ill.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    On solving nearly incompressible 2D problems using an adaptive refinement procedure (1998)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 14 (1998), S. 409-418 
    Details
    ISSN: 1069-8299
    Keywords: adaptive refinement procedure ; nearly incompressible problems ; error estimation ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A numerical study is carried out employing some selected 2D elements and an automatic adaptive refinement procedure for the solution of a problem involving a nearly incompressible material. For a material with Poisson's ratio close to 0·5, it is found that both hybrid elements and high-order Lagrangian triangles can be used to provide a reliable solution. Furthermore, the rate of convergence of the elements is not affected by the high value of Poisson's ratio, and a near-optimal convergence rate is achieved in all the numerical tests run. © 1998 John Wiley & Sons, Ltd.
    Additional Material: 9 Ill.
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  • 4
    Electronic Resource
    Electronic Resource
    Numerical stability of dynamic relaxation analysis of non-linear structures (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 1407-1410 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The estimation of the parameters (‘fictitious densities’) which control the convergence and numerical stability of a non-linear Dynamic Relaxation solution is described. The optimal values of these parameters vary during the iterative solution and they are predicted from the Gerschgörin bounds, that is rowsums of the stiffness matrix, which are divided into constant and variable parts for computational convenience. The procedure is illustrated by reference to the analysis of an axially loaded beam on a non-uniform elastic foundation.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620100620
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  • 5
    Electronic Resource
    Electronic Resource
    Corrigendum: Automatic adaptive refinement for shell analysis using nine-node assumed strain element (1998)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 41 (1998), S. 777-777 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: No Abstract
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    Automatic adaptive refinement for shell analysis using nine-node assumed strain element (1997)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 40 (1997), S. 3601-3638 
    Details
    ISSN: 0029-5981
    Keywords: automatic adaptive refinement ; shell analysis ; assumed strain element ; error estimations ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An automatic adaptive refinement procedure for the analysis of shell structures using the nine-node degenerated solid shell element is suggested. The basic adaptive refinement principle and the effects of singularities and boundary layers on the convergence rate of the nine-node element used are discussed. A new stress recovery procedure based on the patch convective co-ordinate system concept is developed for the construction of a continuous smoothed stress field over the shell domains. The stress recovery procedure is easy to implement, requires a modest computational effort and needs only local patch information. It can be applied to shells with non-uniform thickness as well as to multi-layered shell structures. The smoothed recovered stress obtained is then used with the Zienkiewicz and Zhu error estimator for a posteriori error estimation during the adaptive refinement analysis. Numerical results which are in good agreement with theoretical predictions are obtained and they indicate that the current adaptive refinement procedure can eliminate the effect of singularities inside the problem domains so that a near-optimal convergence rate is achieved in all the numerical examples. This also indicates that the stress recovery procedure can produce an accurate stress field and as a result the error estimator can reflect the error distribution of the finite element solution. Even though in the current study only one type of element is used in the analysis, the whole adaptive refinement scheme can be readily applied to any other types of degenerated solid element. © 1997 John Wiley & Sons, Ltd.
    Additional Material: 24 Ill.
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  • 7
    Electronic Resource
    Electronic Resource
    Comment on ‘consolidation analysis of layered anisotropic foundations’ (1977)
    New York, NY [u.a.] : Wiley-Blackwell
    International Journal for Numerical and Analytical Methods in Geomechanics 1 (1977), S. 407-407 
    Details
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nag.1610010407
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