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  • 11
    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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  • 12
    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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  • 13
    Electronic Resource
    Electronic Resource
    Superconvergent patch recovery with equilibrium and conjoint interpolant enhancements (1994)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 37 (1994), S. 517-536 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The superconvergent patch derivative recovery method of Zienkiewicz and Zhu is enhanced by adding the squares of the residuals of the equilibrium equation and natural boundary conditions. In addition, a new conjoint polynomial for interpolating the local patch stresses over the element which significantly improves the local projection scheme is presented. Results show that in the 4-node quadrilateral, the equilibrium and boundary condition residuals usually improve accuracy but not the rate of convergence, whereas in the 9-node quadrilateral, results are mixed. The conjoint polynomial always improves the accuracy of the derivative field within the element as compared to the standard nodal interpolation, particularly in 4-node quadrilaterals.
    Additional Material: 21 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620370309
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  • 14
    Electronic Resource
    Electronic Resource
    Stabilized rapidly convergent 18-degrees-of-freedom flat shell triangular element (1992)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 33 (1992), S. 149-162 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A rank-sufficient flat triangular shell element with drilling degrees-of-freedom is described. A variational basis for this element has been provided by a three-field variational principle with relaxed interelement compatibility and traction continuity conditions. A generalized spurious mode control procedure has been developed in order to stabilize zero energy kinematical modes. Excellent performance has been found in an obstacle course and buckling problems.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620330111
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  • 15
    Electronic Resource
    Electronic Resource
    A fractal patch test (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 2199-2210 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Element consistency is generally checked using the patch test on an element patch of finite size. This condition may in certain cases be too restrictive, and disqualifies elements that appear to be convergent. A method termed ‘fractal patch test’ is presented, in which the patch size is maintained constant while the distorted mesh is refined. Examples are given for four-node quadrilateral elements used in plane stress and strain analysis, and for plate bending elements.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620261005
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  • 16
    Electronic Resource
    Electronic Resource
    Reproducing kernel particle methods for structural dynamics (1995)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 38 (1995), S. 1655-1679 
    Details
    ISSN: 0029-5981
    Keywords: smooth particle hydrodynamics ; wavelets ; elastic-plastic large deformation ; tensile instability ; correction function ; aliasing control ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper explores a Reproducing Kernel Particle Method (RKPM) which incorporates several attractive features. The emphasis is away from classical mesh generated elements in favour of a mesh free system which only requires a set of nodes or particles in space. Using a Gaussian function or a cubic spline function, flexible window functions are implemented to provide refinement in the solution process. It also creates the ability to analyse a specific frequency range in dynamic problems reducing the computer time required. This advantage is achieved through an increase in the critical time step when the frequency range is low and a large window is used. The stability of the window function as well as the critical time step formula are investigated to provide insight into RKPMs. The predictions of the theories are confirmed through numerical experiments by performing reconstructions of given functions and solving elastic and elastic-plastic one-dimensional (1-D) bar problems for both small and large deformation as well as three 2-D large deformation non-linear elastic problems. Numerical and theoretical results show the proposed reproducing kernel interpolation functions satisfy the consistency conditions and the critical time step prediction; furthermore, the RKPM provides better stability than Smooth Particle Hydrodynamics (SPH) methods. In contrast with what has been reported in SPH literature, we do not find any tensile instability with RKPMs.
    Additional Material: 21 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620381005
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  • 17
    Electronic Resource
    Electronic Resource
    SIMD implementation of a non-linear transient shell program with partially structured meshes (1992)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 33 (1992), S. 997-1026 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The implementation of an explicit transient program for the three-dimensional non-linear finite element analysis of shells on a massively parallel SIMD computer, the CONNECTION Machine, is described. Particular emphasis is placed on interprocessor communication using router and NEWS schemes. A hybrid communication scheme, where NEWS is used within structured subdomains and the router is used to exchange nodal forces between subdomains, is examined. It is shown that the ‘mesh-structure index’ of most large meshes is sufficient to make hybrid schemes effective and this is verified by computer runs. Some benchmark non-linear calculations with 8K to 32K elements are also presented.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620330508
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  • 18
    Electronic Resource
    Electronic Resource
    Implementation of mixed time integration techniques on a vectorized computer with shared memory (1992)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 35 (1992), S. 1803-1828 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The implementation of subcycling in an explicit finite element program executed on a concurrent computer with shared memory is described. The effects of vectorization and parallelization on the speed-up and efficiency achieved with subcycling is discussed. Numerical studies are presented to illustrate the effects of the number of processors, the size of element blocks and problem size. Finally, an efficient allocation algorithm which minimizes the effects of processor idleness is presented.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620350906
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  • 19
    Electronic Resource
    Electronic Resource
    Curvilinear fatigue crack reliability analysis by stochastic boundary element method (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 3841-3858 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper, the stochastic boundary element method, which combines the mixed boundary integral equations method explored in Reference 1 with the first-order reliability method, is developed to study probabilistic fatigue crack growth. Due to the high degree of complexity and non-linearity of the response, direct differentiation coupied with the response-surface method is employed to determine the response gradient. Three random processes, the mode I and mode II. stress intensity factors and the crack direction angle, are included in the expression of the response gradient. The sensitivity of these random processes is determined using a first-order response model. An iteration scheme based on the HL-RF method2 is applied to locate the most probable failure point on the limit-state surface. The accuracy and efficiency of the stochastic boundary element method are evaluated by comparing the cumulative distribution function of the fatigue life obtained with Monte Carlo simulation. The reliability index and the corresponding probability of failure are calculated for a fatigue crack growth problem with randomness in the crack geometry, defect geometry, fatigue parameters and external loads. The response sensitivity of each primary random variable at the design point is determined to show its role in the fatigue failure. The variation of each primary random variable at the design point with the change of probability of failure is also presented in numerical examples.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620362206
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  • 20
    Electronic Resource
    Electronic Resource
    Elastic interactions of a fatigue crack with a micro-defect by the mixed boundary integral equation method (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 2743-2759 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper, the mixed boundary integral equation method is developed to study the elastic interactions of a fatigue crack and a micro-defect such as a void, a rigid inclusion or a transformation inclusion. The method of pseudo-tractions is employed to study the effect of a transformation inclusion. An enriched element which incorporates the mixed-mode stress intensity factors is applied to characterize the singularity at a moving crack tip. In order to evaluate the accuracy of the numerical procedure, the analysis of a crack emanating from a circular hole in a finite plate is performed and the results are compared with the available numerical solution. The effects of various micro-defects on the crack path and fatigue life are investigated. The results agree with the experimental observations.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620361605
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