- Title
- Three-dimensional lower bound limit analysis using nonlinear programming
- Creator
- Lyamin, Andrei Vadimovich
- Relation
- University of Newcastle Research Higher Degree Thesis
- Resource Type
- thesis
- Date
- 1999
- Description
- Research Doctorate - Doctor of Philosophy (PhD)
- Description
- Lower bound limit analysis of large scale two-dimensional problems in continuum mechanics is usually performed using linear programming (LP) techniques. In this approach, a linear stress finite field is assumed for a finite element discretisation of the continuum and a linearised yield surface is employed to generate a LP optimisation problem. Although useful for two-dimensional geometries, this approach is unsuitable for the solution of three-dimensional problems. This is because in many cases of practical interest, it is both difficult and cumbersome to linearise three-dimensional yield criteria to an acceptable degree of accuracy. Moreover, even if the yield surface linearisation is done dynamically (in a local manner) to allow the LP technique to be employed, the computational effort is unacceptable because of the large number of iterations involved. The major part of this Thesis describes a new lower bound formulation which can be used to solve two- and three-dimensional limit analysis problems. The formulation uses linear stress finite elements in conjunction with any convex nonlinear yield criterion and results in a convex optimisation problem. This problem, in turn, gives rise to a set of Kuhn-Tucker optimality conditions which can be solved very efficiently using an interior point, two-stage, quasi-Newton algorithm. The quasi-Newton algorithm, originally presented by Zouain et al. (1993) for solving limit analysis problems arising from a mixed formulation, has been modified substantially to allow for the nature of the optimisation problem that is generated by the lower bound formulation. The proposed scheme can deal with any type of yield criterion and permits optimisation with respect to surface or body forces. The performance of the newly developed formulation is verified for a broad range of two- and three-dimensional problems. The comparisons presented in the Thesis show that the new technique is vastly superior to the most effective linear programming formulation, especially for large scale problems. A secondary part of the Thesis is concerned with the development of an efficient mesh generation scheme which is suitable for lower bound limit analysis. A special feature of the lower bound discretisation is the need to incorporate statically admissible discontinuities along the edges of all elements in the finite element mesh. The presence of these discontinuities can greatly affect the accuracy of a computed lower bound and they are essential for the generation of useful solutions. Because it is most convenient to use linear stress finite elements in order to guarantee a mathematically rigorous lower bound on the actual collapse load, attention is focused on the generation of meshes of triangular or tetrahedral elements with discontinuities at all shared edges or faces. The presence of these discontinuities makes the lower bound mesh generators quite different from those for conventional displacement finite element analysis, and new techniques needed to be developed. Although not fully automatic, the new mesh generation schemes presented in this Thesis have proved very convenient in the analysis of a variety of practical problems. They are based on a parametric mapping technique, in conjunction with middle point splitting algorithm, and can be used for both two-dimensional and three-dimensional limit analysis.
- Subject
- linear programming techniques; lower bound formulation; mesh generation scheme; parametric mapping techniques
- Identifier
- http://hdl.handle.net/1959.13/1418090
- Identifier
- uon:37296
- Rights
- Copyright 1999 Andrei Vadimovich Lyamin
- Language
- eng
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| Thumbnail | File | Description | Size | Format | |||
|---|---|---|---|---|---|---|---|
| View Details Download | ATTACHMENT01 | Thesis | 148 MB | Adobe Acrobat PDF | View Details Download | ||
| View Details Download | ATTACHMENT02 | Abstract | 6 MB | Adobe Acrobat PDF | View Details Download |