Finite element algorithms for the static and dynamic analysis of time-dependent and time-independent plastic bodies
Doctoral Thesis
1994
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University of Cape Town
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Abstract
Continuum and finite element formulations of the static and dynamic initial-boundary value evolution (elastoplastic) problems are considered in terms of both the classical and internal variable frameworks. The latter framework is employed to develop algorithms in the form of convex mathematical programming and Newton-Raphson schemes. This latter scheme is shown to be linked to the former in the sense that it expresses the conditions under which the convex non-linear function can be minimised. A Taylor series expansion in time and space is extensively employed to derive integration schemes which include the generalised trapezoidal rule and a generalised Newton-Raphson scheme. This approach provides theoretical foundations for the generalised trapezoidal rule and the generalised Newton-Raphson scheme that have some geometrical insights as well as an interpretation in terms of finite differences and calculus. Conventionally, one way of interpreting the generalised trapezoidal rule is that it uses a weighted average of values (such as velocity or acceleration) at the two ends of the time interval. In this dissertation, the generalised trapezoidal scheme is shown to be a special case of the forward-backward difference scheme for solving first order differential equations.
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Includes bibliographical references.
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Kaunda, M. 1994. Finite element algorithms for the static and dynamic analysis of time-dependent and time-independent plastic bodies. University of Cape Town.