Browsing by Author "Weber, Marc Anton"

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    Stochastic structural analysis of engineering components using the finite element method
    (1993) Weber, Marc Anton; Penny, R K
    This thesis investigates probabilistic and stochastic methods for structural analysis which can be integrated into existing, commercially available finite element programs. It develops general probabilistic finite element routines which can be implemented within deterministic finite element programs without requiring major code development. These routines are implemented in the general purpose finite element program ABAQUS through its user element subroutine facility and two probabilistic finite elements are developed: a three-dimensional beam element limited to linear material behaviour and a two-dimensional plane element involving elastic-plastic material behaviour. The plane element incorporates plane strain, plane stress and axisymmetric formulations. The numerical accuracy and robustness of the routines are verified and application of the probabilistic finite element method is illustrated in two case studies, one involving a four-story, two-bay frame structure, the other a reactor pressure vessel nozzle. The probabilistic finite element routines developed in this thesis integrate point estimate methods and mean value first order methods within the same program. Both methods require a systematic sequence involving the perturbation of the random parameters to be evaluated, although the perturbation sequence of the methods differ. It is shown that computer-time saving techniques such as Taylor series and iterative perturbation schemes, developed for mean value based methods, can also be used to solve point estimate method problems. These efficient techniques are limited to linear problems; nonlinear problems must use full perturbation schemes. Finally, it is shown that all these probabilistic methods and perturbation schemes can be integrated within one program and can follow many of the existing deterministic program structures and subroutines. An overall strategy for converting deterministic finite element programs to probabilistic finite element programs is outlined.
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    The study of creep in machine elements using finite element methods
    (1990) Weber, Marc Anton; Penny, R K
    In this thesis a simplified analysis procedure is developed, in which creep laws are decoupled from damage laws, for the purposb of constructing methods of use in the early stages of high temperature design. The procedure is based on the creep and damage laws proposed by Kachanov and Rabotnov. The creep laws are normalised. with respect to a convenient normalising stress. As a consequence of this normalisation, the dependence of the creep law on the stress constant, the time and temperature functions, and the actual load level is removed. In addition, if the reference stress of the component is chosen as the normalising stress, the creep law becomes insensitive to the stress exponent. The non-dimensional creep laws are then implemented in a standard finite element scheme, from which the results of a stationary state creep analysis are then in non-dimensional form. In order to estimate rupture times, the maximum stationary stresses in a component are used together with the damage laws. Conservative failure criteria are derived from the creep and damage laws to extend the method to residual life assessment and damage monitoring. The procedure is illustrated and tested against simple examples and case studies.