Browsing by Author "Eve, Robin Andrew"

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    Formulation and implementation of conforming finite element approximations to static and eigenvalue problems for thin elastic shells
    (1987) Eve, Robin Andrew; Reddy, B Daya
    In deriving asymptotic error estimates for a conforming finite element analyses of static thin elastic shell problems, the French mathematician Ciarlet (1976) proposed an approach to the formulation of such problems. The formulation he uses is based on classical shell theory making use of Kirchhoff-Koiter assumptions. The shell problem is posed in two-dimensional space to which the real problem, in three-dimensional space, is related by a mapping of the domain of the problem to the shell mid-surface. The finite element approximation is formulated in terms of the covariant components of the shell mid-surface displacement field. In this study, Ciarlet's formulation is extended to include the eigenvalue problem for the shell. In addition to this, the aim of the study is to obtain some indication of how well this approach might be expected to work in practice. The conforming finite element approximation of both the static and eigenvalue problems are implemented. Particular attention is paid to allowing generality of the shell surface geometry through the use of an approximate mapping. The use of different integration rules, in-plane displacement component interpolation schemes and approximate geometry schemes are investigated. Results are presented for shells of different geometries for both static and eigenvalue analyses; these are compared with independently obtained results.
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    Theoretical and numerical aspects of problems in finite-strain plasticity
    (1992) Eve, Robin Andrew; Reddy, B Daya
    A new internal variable theory of plasticity is presented. This theory is developed within a framework of non-smooth convex analysis; a unification of ideas concerning the postulates of plasticity is achieved by using the powerful tools provided by results in this branch of mathematics. A firm mathematical foundation for the study of qualitative aspects of problems involving plastic deformations is provided. Among the features of the theory is the establishment of a clear relationship between conventional formulations, which make use of yield functions, and those formulated in terms of a dissipation function. The role of the principle of maximum plastic work is also made precise. Attention is focussed on application of the theory to finite-strain plasticity. Quasi-static initial-boundary-value problems involving large plastic deformations are considered. An incremental form of such problems arises from a discretisation in time. A variational form of the incremental boundary-value problem is derived using the new theory. This incremental formulation is based on a generalised midpoint rule, evolution equations for plastic variables are defined in terms of a dissipation function, and an assumption of isochoric plastic deformation is imposed explicitly. A spatially discrete form of the incremental problem is obtained by application of the finite element method. An algorithm for solving this discrete problem, based on the Newton-Raphson procedure and having the typical predictor-corrector structure used in computational plasticity, is proposed and investigated. This algorithm is implemented in NOSTRUM, the in-house finite element code of The FRD/UCT Centre for Research in Computational and Applied Mechanics, at the University of Cape Town. A number of standard example problems are analysed using this code and results are compared with those obtained by others. It is shown that a corrector algorithm based on use of a dissipation function is a viable alternative to the conventional return mapping algorithms. While this alternative approach is not necessarily better than the conventional one for simple models of plasticity, it may prove valuable when considering more complex models for materials which exhibit dissipative behaviour. The manner in which an assumption of isochoric plastic deformation is incorporated into the incremental form of the problem is shown to play an important role.