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  • 1
    ISSN: 1432-0924
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract A spatial mesh adaptation procedure in semidiscrete finite element analysis of 2D linear elastodynamic problems is presented. The procedure updates, through an automatic remeshing scheme, the spatial mesh when found necessary in order to gain control of the spatial discretization error from time to time. An a posteriori error estimate developed by Zienkiewicz and Zhu (1987) for elliptic problems is extended to dynamic analysis to estimate the spatial discretization error at a certain time, which is found to be reasonable by analyzing an a priori error estimate. Numerical examples are used to demonstrate the performance of the procedure. It is indicated that the extended error estimation and the procedure are capable of monitoring the moving of steep stress regions by updating the spatial mesh according to a prescribed error tolerance, thus providing a reliable finite element solution in an efficient manner.
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  • 2
    ISSN: 0894-9166
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract The boundary elament method (BEM) for numerical solution to dynamic response of vibration fundation in plane, elastic domains are presented. The dynamic boundary integral equation is derived from the Laplace integral transform of the elestodynamic differential equation. Numerical solution can then be completed by the discrete boundary element in the transform space. Finally, dynamic responsed in time domain will be inverted back from the transform space with the numerical method. Excited harmonic load responses of dynamic rigid foundation are calculated and discussed for different frequencies, Layer depths and foundation embedments. Again, screening of exciting wave is also studied.
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  • 3
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In the paper we present a superconvergent patch recovery technique for obtaining higher-order-accurate finite-element solutions and thus a postprocessed type of L2 norm error estimate. Two modifications make our procedure different from the one proposed by Zienkiewicz and Zhu (1992), in which higher-order-accurate derivatives of the finite-element solution at nodes are determined. Firstly, the recovery process is made for element, not for nodes. An ‘element patch’, which represents the union of an element under consideration and the surrounding elements, is introduced. Secondly, the local error estimate is calculated directly from the improved solution for this element. Numerical tests on both 1D and 2D model problems show that this method can provide an asymptotically exact a posteriori L2 norm error estimate if the used element possesses superconvergent points for the solutions.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
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  • 4
    ISSN: 1069-8299
    Keywords: post processing ; node patch ; element patch ; superconvergence ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Methods to calculate improved postprocessed stresses in elements for the superconvergent patch recovery technique are developed. Based on improved stresses on node patches, the improved element stresses are obtained by using weighting of patch solutions from different patch assembly points. An alternative method is to directly calculate the element stresses for an element patch based on weighted information. Numerical examples show that the performances of the two procedures are of about the same quality.
    Additional Material: 9 Ill.
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  • 5
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    ISSN: 1069-8299
    Keywords: plates ; finite elements ; mixed method ; error estimation ; superconvergent patch recovery ; adaptivity ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The superconvergent patch recovery (SPR technique) has been shown to be an effective postprocessing procedure in which an improved solution is obtained based on the original finite element solution. The technique was applied to second order problems with success, but the method has not yet been studied on problems posed in mixed form. This paper demonstrates that the technique can be applied to beam and plate bending problems, characterized by fourth order differential equations. The differential equation is here written as two coupled differential equations of second order leading to a mixed finite element procedure based on approximations of the moment and displacement fields. Two elements of mixed type are handled, namely a triangular plate element with constant moment field and a rectangular element with linearly varying bending moments. Numerical examples are given to show that the postprocessed solution is more accurate and has a higher rate of convergence. © 1997 by John Wiley & Sons, Ltd.
    Additional Material: 13 Ill.
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  • 6
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A simple a posteriori local error estimator for time discretization in structural dynamic analysis is presented. It is derived from the difference of the solutions between an ordinary integration method (the Newmark scheme) and another higher-order one which assumes that the derivatives of accelerations vary linearly within each time step. It may be obtained directly without resolving new equations, so the additional computational cost is small and the implementation is convenient. Furthermore, it is shown that this error estimator may also be obtained by Taylor expansion or by a post-processing technique. Accordingly, an adaptive time-stepping procedure, which automatically adjusts the time-step size so that the local error at each time step is within a prescribed accuracy, is described. Numerical examples, including two single-DOF problems, a two-DOF problem and a multi-DOF model, are presented. The results show that the presented local error estimator is simple, reliable and accurate.
    Additional Material: 9 Ill.
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  • 7
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper reports some numerical experiments on the effectivity of the Zienkiewicz-Zhu error estimate (1987) and comparisons of two adaptive mesh generators: ADMESH, developed by Jin and Wiberg (1990) and MAD2D by Peraire et al. (1987) and Zhu et al. (1990-91). From the experiments we observe that: (1) without any empirical correction, the effectivity of the error estimate for linear triangular elements is good if post-processed continuous stresses are obtained by adequately using an iterative stress recovery procedure (Zienkiewicz et al., 1985), and is also acceptable by using a simple ‘averaging’ procedure; (2) these two mesh generators are basically comparable.
    Additional Material: 9 Ill.
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  • 8
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: The paper considers the influence of a building wall system on the interaction between the soil and the foundation plate. A simplified semi-analytical finite element method gives an economical solution for large three-dimensional soil-structure interaction problems. The simplified method appears to be sufficiently accurate for engineering purposes.Numerical results presented show significant influence of building walls on the foundation-plate-soil interaction.
    Additional Material: 32 Ill.
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  • 9
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper proposes a generalized least-squares time finite element procedure for analysis of transient field problems. It leads to a very general four parameter and two time level family of schemes. The free parameters are optimized in terms of accuracy, stability and oscillatory behaviour of the computational algorithm. In the case of linear problems an unconditionally stable scheme of fourth-order accuracy is obtained. Special choices of the free parameters also give a number of well-known time-integration schemes, such as the Zienkiewicz-Lewis third-order algorithm, the Goodrich scheme and standard schemes such as the Crank-Nicolson and backward fully implicit schemes. The main disadvantage of the higher order algorithm is a large bandwidth of the system matrix owing to the matrix terms of the form KTK. This drawback is reduced for special choices of the parameters by forming a product formula. Somewhat more computation is required than for popular schemes such as the generalized midpoint rule, depending on the prescribed variables. Numerical comparisons are made between the proposed higher order schemes and standard schemes.
    Additional Material: 9 Ill.
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  • 10
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The efficiency of iterative methods in linear structural mechanics is studied. The efficiency concerns the calculation time, the numerical accuracy and the core storage needed. We state that iterative methods are effective in connection with hierarchical improvement of a primary approximation. Three iterative methods are studied: the conjugate gradient method preconditioned by a modified incomplete factorization matrix, the same method preconditioned by a matrix obtained from natural factors on elemental level, and a Jacobi integration preconditioned by viscous relaxation split in an element-by-element way. We make comparisons with direct methods, Gaussian elimination and factorization by use of natural factors.
    Additional Material: 5 Ill.
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