- Title
- Finite element algorithms for elastoplasticy and consolidation
- Creator
- Abbo, Andrew
- Relation
- University of Newcastle Research Higher Degree Thesis
- Resource Type
- thesis
- Date
- 1997
- Description
- Research Doctorate - Doctor of Philosophy (PhD)
- Description
- Finite element analysis of nonlinear problems invariably uses piecewise linearisation to generate approximate solutions. In geomechanics, this linearisation may appear as: •Discrete strain increments for the integration of nonlinear constitutive laws. •Discrete load increments in nonlinear analyses. •Discrete time steps in the analysis of consolidation. The size and distribution of these increments (or steps) has a direct bearing on the accuracy of the resulting solution. This Thesis describes several new algorithms for controlling the error caused by the use of discrete increments in nonlinear finite element analysis. The new schemes are unified by the fact that they all treat the governing relations as a system of ordinary differential equations. These equations are solved by adaptive integration with respect to real or pseudo time, and automatically adjust the size of each step by computing a local error measure. By holding this local error below a specified threshold, the schemes aim to constrain the global linearisation error to lie near a known tolerance. Adaptive substepping schemes for controlling the linearisation error in the solution of elastoplastic constitutive laws were first formulated by Sloan (1987). These methods are explicit and automatically subincrement the imposed strain increment at each stress point. Several important improvements to these methods are developed in this Thesis. The performance of the enhanced explicit schemes is compared to several implicit schemes for a variety of boundary value problems. These examples illustrate that adaptive explicit methods are very competitive with implicit methods, and have the advantage of being simpler to implement for complex constitutive laws. The remainder of the Thesis is concerned with the development of new adaptive integration schemes for the solution of elastoplastic and coupled consolidation problems. These methods are applied at the global level and, for a given mesh, govern the overall accuracy of the solution. While the elastoplastic and consolidation schemes both have essentially the same structure, they differ in the method used to estimate the local error. The algorithm for integrating the global elastoplastic equations uses an explicit forward Euler/modified Euler pair to provide the error estimate and incorporates a correction to reduce drift from equilibrium. In contrast, the consolidation algorithm uses an implicit pair of equations to ensure unconditional stability. Numerical examples are presented which demonstrate the performance of both types of schemes. The results suggest that the algorithms are not only efficient, but also very robust. The latter attribute is very important in geomechanics computations which often employ complex constitutive relations. While this Thesis is concerned primarily with the behaviour of nonlinear solids, the methods developed are quite general and can be extended to deal with many types of nonlinear problems in structural mechanics.
- Subject
- finite element methods; elastoplasticity; geotechnical engineering; consolidation
- Identifier
- http://hdl.handle.net/1959.13/1060166
- Identifier
- uon:16748
- Rights
- Copyright 1997 Andrew Abbo
- Language
- eng
- Full Text
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| View Details Download | ATTACHMENT02 | Thesis | 2 MB | Adobe Acrobat PDF | View Details Download |