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  • 11
    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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  • 12
    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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  • 13
    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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  • 14
    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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  • 15
    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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  • 16
    Electronic Resource
    Electronic Resource
    A stochastic damage model for the rupture prediction of a multi-phase solid (1992)
    Springer
    International journal of fracture 55 (1992), S. 321-340 
    Details
    ISSN: 1573-2673
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract In this paper, a stochastic damage model is proposed for the rupture prediction of a brittle, multi-phase material. The model, based on the macrocrack-microcrack interaction, characterizes damage by microcracking and fracture by macrocracking. The model incorporates uncertainties in locations, orientations and numbers of microcracks. Owing to the high concentration of microcracks within the frontal damage zone near the macro-tip, a higher order analysis based on traction boundary integral equations is formulated for an arbitrary array of cracks. The change of the stress intensity at the macrocrack tip by the configuration of microcracks is investigated through a parametric study. The presence of large fluctuation in the stress intensity at the macro-tip justifies the use of the statistical approach, which will be presented in a companion paper.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00035189
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  • 17
    Electronic Resource
    Electronic Resource
    A stochastic damage model for the rupture prediction of a multi-phase solid (1992)
    Springer
    International journal of fracture 55 (1992), S. 341-361 
    Details
    ISSN: 1573-2673
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract The stochastic damage model, which has been proposed in Part I of this paper, is utilized to analyze quantitatively the effects of uncertainties in locations, orientations and numbers of microcracks at the macro-tip. This is accomplished by introducing a computer simulation model which incorporates a statistical characterization of geometrical parameters of a random microcrack array. The counteracting effects of microcracking on the fracture toughness, namely, toughness enhancement and toughness degradation, are explored statistically through the change of the location and size of the near tip damage zone. The effects of changes in the geometric configuration and density of microcracks at the macro-tip are also examined through the present statistical approach. The validity of the present model is verified by comparing the obtained statistical distribution with the analytic model based on the Neville distribution function. A very good fit achieved by the use of the Neville function demonstrates the potential of the present damage model, in predicting the inherent statistical distribution of the fracture toughness from the intrinsic random microdefects.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00035190
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  • 18
    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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  • 19
    Electronic Resource
    Electronic Resource
    Assumed strain stabilization procedure for the 9-node Lagrange shell element (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 385-414 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An assumed strain (strain interpolation) method is used to construct a stabilization matrix for the 9-node shell element. The stabilization procedure can be justified based on the Hellinger-Reissner variational method. It involves a projection vector which is orthogonal to both linear and quadratic fields in the local co-ordinate system of each quadrature point. All terms in the development involve 2 × 2 quadrature in the 9-node element. Example problems show good accuracy and an almost optimal rate of convergence.
    Additional Material: 14 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280210
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  • 20
    Electronic Resource
    Electronic Resource
    Contact-impact by the pinball algorithm with penalty and Lagrangian methods (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 547-572 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Contact-impact algorithms, which are sometimes called slideline algorithms, are a computationally time-consuming part of many explicit simulations of non-linear problems because they involve many branches, so they are not amenable to vectorization, which is essential for speed on supercomputers. The pinball algorithm is a simplified slideline algorithm which is readily vectorized. Its major idea is to embed pinballs in surface elements and to enforce the impenetrability condition only to pinballs. It can be implemented in either a Lagrange multiplier or penalty method. It is shown that, in any Lagrange multiplier method, no iterations are needed to define the contact surface. Examples of solutions and running times are given.
    Additional Material: 21 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620310309
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