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  • 1
    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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  • 2
    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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  • 3
    Electronic Resource
    Electronic Resource
    On using different recovery procedures for the construction of smoothed stress in finite element method (1998)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 43 (1998), S. 1223-1252 
    Details
    ISSN: 0029-5981
    Keywords: stress recovery ; superconvergent patch recovery technique ; recovery by equilibrium in patches ; equilibrium and boundary constraints ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The performance of three different stress recovery procedures, namely, the superconvergent patch recovery technique (SPR), the recovery by equilibrium in patches (REP) and a combined method known as the LP procedure is reviewed. Different order of polynomials and various patch formation strategies have been employed in the numerical studies for the construction of smoothed stress fields. Two 2-D elastostatic problems of different characteristics are used to assess the behaviour of the stress recovery procedures. The numerical results obtained indicate that when the order of polynomial used in the recovery procedure is equal to that of the finite element analysis, the behaviours of all three recovery procedures are very similar and all of them are adequate to provide a reliable recovered stress field for error estimation. In case that the order of polynomial of the recovered stress is increased, the LP procedure seems to give a more stable recovery matrix and a more reliable recovered stress field than the REP procedure. © 1998 John Wiley & Sons, Ltd.
    Additional Material: 8 Ill.
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  • 4
    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.
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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
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  • 6
    Electronic Resource
    Electronic Resource
    AUTOMATIC ADAPTIVE 3-D FINITE ELEMENT REFINEMENT USING DIFFERENT-ORDER TETRAHEDRAL ELEMENTS (1997)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 40 (1997), S. 2195-2226 
    Details
    ISSN: 0029-5981
    Keywords: automatic refinement ; 3-D tetrahedral elements ; preconditioned conjugate gradient method ; efficiency of elements ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Automatic refinement finite element analyses were carried out employing three different-order tetrahedral solid elements for the solution of 3-D stress analysis problems. Numerical results indicated that the adaptive refinement procedure could eliminate effectively the effect of singularities and the optimal convergence rate was achieved in all the examples tested. The preconditioned conjugate gradient technique was used for the solution of the large system of simultaneous equations. By interpolating the initial guess of the iteration solver from the previous converged solution, the number of iterations needed for the solution is lower than expected. Furthermore, when the mesh density distribution pattern has converged, it became even more efficient and independent of the number of degrees of freedom in the finite element mesh. The relative efficiency of the three different-order tetrahedral elements has also been compared in terms of storage and computational cost needed for achieving a certain accuracy. It is found that although the cubic T20 element can achieve the highest convergence rate, the T10 element is the most competitive and effective element in terms of storage and computational cost needed. © 1997 John Wiley & Sons, Ltd.
    Additional Material: 24 Ill.
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  • 7
    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.
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  • 8
    Electronic Resource
    Electronic Resource
    Finite element solution for the continuum traffic equilibrium problems (1998)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 43 (1998), S. 1253-1273 
    Details
    ISSN: 0029-5981
    Keywords: finite element method ; continuum modelling ; traffic equilibrium ; user-optimal pattern ; fixed demand ; variable demand ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper, we consider a city with a highly compact Central Business District (CBD), and the commuters’ destinations from the CBD are dispersed over the whole city. The street network is approximated as a continuum and commuters’ movements in the city are measured by the flow intensity, and the local travel cost depends on the location and the traffic flow intensity. We extend the continuum user equilibrium problem to deal with the case of variable demand, in which the traffic demand from any destination in the city to the CBD is assumed to be a function of both the destination location and the total travel cost to the CBD. An equivalent mathematical model is formulated and proved to satisfy the user equilibrium conditions, which is then solved by a finite element solution algorithm. Numerical examples are given to illustrate the effectiveness of the proposed method. © 1998 John Wiley & Sons, Ltd.
    Additional Material: 11 Ill.
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